'4= TIM30.BCKH TIM30.BCK<BACKUP/BLOCK=2048/LOG/LIST=TIM30.LOG [.TIM]*.* TIM30.BCK/SAV HASAN j=VV5.5 _ZOHRA::  _$3$DIA2: V5.5-2  < *[HASAN.TIM]ABER.DAT;7+,./ 4D-0123KPWO56"h7%};V8`1W9GHJN P Q8 F/96 wavefront errors in waves at 486nm (no desorption)A Date Days since Z4 Z5 Z6 Z7 Z8 Z11D launch Focus Astigmatism Coma SphericalB24-APR-1990 0 7.4474 -0.057 0.032 0.054 0.159 -0.564 @20-MAY-1990 26 -0.2206 -0.057 0.032 0.054 0.159 -0.538@15-JUN-1990 52 -1.1545 0.094 -0.045 0.204 0.013 -0.534@25-JUN-1990 62 0.7254 -0.057 0.032 0.054 0.160 -0.540@23-JUL-1990 90 -1.4071 0.005 0.001 -0.024 -0.082 -0.533B15-AUG-1990 113 -1.2602 0.077 -0.021 -0.025 0.081 -0.533 @26-OCT-1990 185 -1.0037 0.077 -0.021 -0.025 0.081 -0.533@17-DEC-1990 237 -1.007 -0.001 0.002 -0.025 0.081 -0.532@22-FEB-1991 304 -0.6955 -0.002 0.002 -0.025 0.081 -0.533@22-MAR-1991 332 -0.6958 0.005 0.000 0.140 -0.083 -0.533@06-APR-1991 347 -0.6958 -0.002 0.002 -0.025 0.081 -0.533@11-APR-1991 352 -0.5109 -0.002 0.002 -0.025 0.081 -0.533@17-MAR-1992 693 -0.5067 -0U  TIM30.BCK[HASAN.TIM]ABER.DAT;7D-.002 0.002 -0.025 0.081 -0.533@23-AUG-1992 852 -0.3298 -0.002 0.002 -0.025 0.081 -0.533@25-NOV-1992 946 -0.2034 -0.002 0.002 -0.025 0.081 -0.533*[HASAN.TIM]APENDX.TEX;52+,.'/ 4P''-0123KPWO(5 6@Ue7`P};V8(W9GHJN P Q\cleardoublepage \appendix=\renewcommand{\theequation}{\Alph{chapter}.\arabic{equation}};\renewcommand{\thesection}{\Alph{chapter}.\arabic{section}}\part{APPENDICES}\chapter{Summary of commands}\pagestyle{myheadings}>\markboth{Appendix A Summary of commands}{Summary of commands}\label{Commands} )\markright{Commands for Interactive Runs}'\section{Commands for Interactive Runs})\markright{Commands for Interactive Runs} \begin{tabular}{|l|l|l|l|}\hline,Stage &Command &InpunD TIM30.BCK[HASAN.TIM]APENDX.TEX;52P't &Output\\ \hline*0 &rwave FILE &.ZER &.ZER\\ \hline<I &rwffi FILE N1 N2 DUSER&.ZER,.APE,&Amplitude Spread\\6 & &+interactive&Function\\' &rwffb FILE N1 N2 DUSER&.ONE& \\4 &rwff EXT FILE N1 N2 DUSER&.ONE,.TWO,THR,& \\9 & &.FOU or .FIV& \\ \hline:II &rmtfi FILE N1 N2 DUSER&.ONE,&Critically Sampled\\1 & &+interactive&PSF\\' &rmtfb FILE N1 N2 DUSER&.TWO& \\0 &rmtf EXT FILE N1 N2 DUSER&.TWO,.THR,& \\: & & .FOU or .FIV& \\ \hline<III &rpixeli FILE N1 N2 DUSER&.TWO&Resampled/Integrated\\1 & &+interactive&PSF\\) &rpixelb FILE N1 N2 DUSER&.THR& \\3 &rpixel EXT FILE N1 N2 DUSER&.THR, .FOU,& \\4 & &or .FIV& \\ \hline@IV &rdetecti FILE N1 N2 STAR OUT DUSER&.STR,.THR &Detector\\3 & &+interactive&Image\\8 &rdetectb FILE N1 N2 STAR OUT DUSER&.STR,.FOU& \\A &rdetect EXT FILE N1 N2 DUSER&.STR,.FOU or .FIV& \\ \hline:V &rpoii FILE M1 M2 BAD OUT DUSER&.FOU,&Final Image\\/ & &+interactive& \\6 &rpoib FILE M1 M2 BAD OUT DUSER&.FIV& \\ \hline \end{tabular}\newpage"\markright{Comands for Batch Runs}!\section{Commands for Batch Jobs}"\markright{Comands for Batch Runs}\begin{tabular}{|l|l|l|}\hline%Stage &Command &Input \\ \hline@I &swfft(EXT,FILE,N1,N2,DUSER,$<$DSYST$>$]bW TIM30.BCK[HASAN.TIM]APENDX.TEX;52P'Q)&.ONE,.TWO,THR,\\0 & &.FOU or .FIV\\:II &smtf(EXT,FILE,N1,N2,DUSER,$<$DSYST$>$)&.TWO,THR,\\0 & &.FOU or .FIV\\<III &spixel(EXT,FILE,N1,N2,DUSER,$<$DSYST$>$)&THR, .FOU\\+ & &or .FIV\\JIV &sdetect(EXT,FILE,N1,N2,STAR,OUT,DUSER,$<$DSYST$>$)&.FOU or .FIV\\ ?V &spois(FIV,FILE,M1,M2,BAD,OUT,DUSER,$<$DSYST$>$)&.FIV\\ A &srunall(EXT,FILE,N1,N2,M,STAR,OUT,DUSER)&.ONE,.TWO,THR,\\7 & &.FOU or .FIV\\ \hline \end{tabular}+\markright{Comands for Subsidiary Programs}*\section{Commands for Subsidiary Programs}+\markright{Comands for Subsidiary Programs} \label{Subs}\begin{tabular}{|l|l|l|}\hline$Command &Input &Output\\ \hlineRWAVE FILE M&.ZER&FILEm.ZER\\,RRITAP FILE M DUSER&Interactive&FILEm.APE\\ (RRITE5 FILE N1 N2 DUSER&.ZER,.APE&.FIV\\GRRUNALL EXT FILE N1 N2 M STAR OUT DUSER&.EXT,.STR,&Stages I-V outputs\\; &OUTFILE.BAD&\\2TIM &Interactive&Relevant outputs\\ 2RIOPLOT EXT INFILE IMGFIL &.TWO,.THR&.TAB and/or\\ &IMGFIL.HH\#&plot files\\%RNEST OUTFIL DUSER&Interactive&.NPX\\\hline \end{tabular}\newpage3\chapter{Generation of .ZER File from CODEV Output}\pagestyle{myheadings}?\markboth{Appendix B Generation of .ZER File from CODEV Output}+{Generation of .ZER File from CODEV Output} \label{CODEV}IThe commercially available package CODEV (Optical Research Ass2Oj TIM30.BCK[HASAN.TIM]APENDX.TEX;52P'&ociates) isHused to produce a wavefront error map and a table of ``fringe'' Zernike Gpolynomial coefficients obtained by fitting the wavefront errors. The F``fringe'' Zernike polynomials differ from the unobscured polynomials Oused in the present software (appendix~\ref{Zernike0}) in their normalisation.  Further, the polynomials Hgenerated by CODEV are ordered differently from the polynomials we use. IThe output from CODEV is written in a file FILE.LIS. A program has been Edeveloped to read a .LIS file and produce a .ZER file in the desired Jformat (section~\ref{.ZER File}). This program, though not a part of the Npresent package is available on request. In section~\ref{LIS} the generation Mof the appropriate .LIS file using {\bf version 7.11} of CODEV is described, Lwhile section~\ref{ZER} gives the procedure of obtaining a .ZER file from a .LIS file./\markright{Generation of .LIS File from CODEV }-\section{Generation of .LIS File from CODEV }/\markright{Generation of .LIS File from CODEV } \label{LIS}JAn optical imaging system is described in CODEV in an input file FILE.SEQ.KA sequence of CODEV commands then produces OUTFIL.LIS which forms an input Kto the program to produce \\OUTFIL.ZER. In order to produce .LIS files for Jthree field angles prepare the files LIST012.SEQ and LISTS.SEQ (described Hbelow ) and the input file FILE.SEQ. The following CODEV commands will 4then produce OUTmn.LIS ($m=1$ to $3$) for the three field angles entered.\begin{verbatim}` TIM30.BCK[HASAN.TIM]APENDX.TEX;52P'h FIN FILE (!Run sequence to set up lens)NIN LIST012 OUT n WL YAN0 YAN1 YAN2 (!Run sequence to generate .LIS files)\end{verbatim}%IHere {\tt WL, YAN0, YAN1, YAN2} are entered as numbers and stand for the Nwavelength (in nm), and the three field angles (in deg.) respectively. It is Oassumed that the x- field angle is zero in all cases. The number {\tt n} is a Psequence number which may be used to distinguish between two sets of runs which 3differ in only one parameter (e.g. the wavelength).;The following example illustrate the use of these commands.\begin{enumerate}G\item {\tt cv7/c}{\hspace{1.0in}}(Sign on to CODEV in the command mode)C\item {\tt IN FILE } {\hspace{0.7in}} (Run FILE.SEQ to set up lens)A\item {\tt IN LIST012 OUT 2 500. 0. 0.15 -0.15} {\hspace{0.2in}} >(~Run sequence LIST012 to produce files OUT12.LIS, OUT22.LIS, GOUT32.LIS, containing the wavefront map and fringe Zernike polynomials Dat 500 nm and the three field angles $0.^{\circ},\, 0.15^{\circ}, \,-0.15^{\circ}$ respectively.)1\item {\tt exit}{\hspace{1.1in}}(Exit from CODEV)\end{enumerate}GThe file LIST012.SEQ calls the file LISTS.SEQ three times. Both these files are listed below. &\subsubsection{Listing of LIST012.SEQ}\label{LIST012}\begin{verbatim}! Sequence LIST012.SEQ4! Creates 3 .LIS files for 3 field angle positions ! Input:(! in list012 out # wl yan0 yan1 yan2!in lists #11#2 #3 0. #4in lists #12#2 #3 0. #5q TIM30.BCK[HASAN.TIM]APENDX.TEX;52P'Uin lists #13#2 #3 0. #6\end{verbatim}$\subsubsection{Listing of LISTS.SEQ} \label{LIST}\begin{verbatim}! Sequence LISTS.SEQ@! Produces .LIS file containing wavefront error map and Zernike! Polynomial Coefficients ! Input: ! in lists outfile wl xan yan!out t #1 wl #2xan #3yan #4pmazfr 28compactgoout t\end{verbatim}3\markright{Generation of .ZER File from .LIS Files}2\section{Generation of .ZER Files from .LIS Files}3\markright{Generation of .ZER File from .LIS Files} \label{ZER}GA set of .LIS files may be processed to produce the corresponding .ZER Afiles by running the conversion program interactively as follows.FOne or more sets of input files are required. The files are named as NFILE.ZER if there is only one file or FILEmn.ZER , where ($m=M1,M2$ refers to @field angles and $n=N1,N2$ refers to wavelengths). The program Gprocesses one file at a time, prints the field angle on the screen and >prompts for a one line description to go in the header of the 6corresponding .ZER file (see section~\ref{.ZER File}).G{\bf Before running the next program make sure that the following line Hexists in all the .LIS files. If it does not then please edit the file Jand put it near the top.} The actual value of the semi-diameter will, of Icourse depend on the optical system being analysed and the correct value $of the pupil radius should be input.\begin{verbatim}@ SEMI-DIAMETER = 1200.000000 (limits al5. TIM30.BCK[HASAN.TIM]APENDX.TEX;52P'l bundles)(\end{verbatim} %:The FORMAT of this line is (15X,'SEMI-DIAMETER = ',F8.3). ({\subsection*{Data input interactively}}!{\tt Description of Zernike file}1This prompt appears for every .ZER file produced.+\subsection*{Procedure for running program}\begin{enumerate}I\item Set up the environment as described in section~\ref{Environment}.It sets up the following %symbol required to run this program: % {\tt RLIS$\equiv$@DSYST:READLIS } \item Type:{\tt RLIS OUT M1 M2 N1 N2} or,4{\tt RLIS OUT }, if there is only one file FILE.LIS./The files FILEmn.LIS, ($n=N1$ to $N2$) will be processed to produce FILEmn.ZER.\end{enumerate}\newpage0\chapter{Algorithm for estimating PSF grid size}\pagestyle{myheadings}<\markboth{Appendix C Algorithm for estimating PSF grid size}({Algorithm for estimating PSF grid size}\label{N Estimate}FThe PSF without any aberrations is given by Eq.~\ref{1D1}. For large Hvalues of {\it x} and averaging over the composite period, the equation 'quickly approaches its asymptotic form:\begin{equation} \label{Nest1}7\frac{1}{I} \frac{dI}{d\Omega} = \frac{\lambda}{\pi ^3 (1-\epsilon)D\theta^3}\end{equation}%DThe value of the PSF integrated over a detector pixel is then given Basymptotically by multiplying the above equation by the pixel area@$D_{x} \times D_{y}$. Substituting this value for $P_{min}$ in LEq.~\ref{Detector3} and simplifying we get the value $D_{max}$ a 1!Z TIM30.BCK[HASAN.TIM]APENDX.TEX;52P'YLt which the Lnumber of counts for a particular star reaches the limiting value $C_{cut}$.\begin{equation} \label{Nest2}BD_{max} = \frac{F}{10\pi}\left(\frac{\lambda10^{-0.4M}TK_{\lambda}FD_{x}D_{y}}{C_{cut}F^{2} (1-\epsilon)}\right)^{\left(1\over 3 \right)}\end{equation}%GHere {\it F} is the F-number. The minimum grid size required for pixelGintegration such that the entire PSF is sampled within our criterion isthen:\begin{equation} M1=\frac {2D_{max}}{\Delta x{'}}\end{equation}%Gand a corresponding equation for M2. To get this minimum grid size the4minimum grid size for the critically sampled PSF is:\begin{equation}N1=\frac {4D_{max}}{F\lambda}\end{equation}%IThus for each star and wavelength there will be a different grid size. AGtable of grid sizes can be generated and the maximum value (subject to @the constraint that it is less than 512 X 512) used for the run.HAn interactive program for generating a table of grid sizes is available upon request.\newpage"\chapter{Generation of .STR File }\pagestyle{myheadings}F\markboth{Appendix D Generation of .STR File}{Generation of .STR File} \label{STR}IAn interactive program for generating a .STR file (see section~\ref{.STR file}), Ifor a simulated star field is available upon request. The program offers ;two options for the simulation. The first is based on the IBahcall-Soneira Galaxy Model\footnote{Bahcall,J.N. and Soneira,R.M.,1980,H{\it Ap. J. Suppl. Series},{\bf 44},110} , while t  TIM30.BCK[HASAN.TIM]APENDX.TEX;52P'he second uses ground Hbased data. Since the .STR file is an ASCII file it can be manipulated Jby a text editor. Thus, for example, .STR files produced using different 6models could be merged to produce a single star field.2\markright{Bahcall-Soneira Model Based Star Field}0\section{Bahcall-Soneira Model Based Star Field}2\markright{Bahcall-Soneira Model Based Star Field}+The first model for simulating a star fieldNuses the Bahcall-Soneira Galaxy Model (BSM) to generate a colour distribution Ifor a given magnitude range. The user is asked for the desired field of Hview in the sky to fix the number of stars in the model. The stars are Dthen randomly placed on the detector and each line of the .STR file ;written as the coordinates are computed.The program is run interactively as now described.%{\section*{Data input interactively}}% The following data is prompted for .\begin{enumerate}E\item {\tt Star distribution model}{\hspace{.2in}}(Type ?? for onlinehelp)2Input BSMODL for this model (this is the default).H\item {\tt Title of .STR file}{\hspace{.2in}}(Type ? to display default title)4An 80 character title to appear at head of .STR file&\item {\tt Galaxy Model data on file?}JIf answered in the {\bf affirmative} output from the Bahcall-Soneira model@will be written on a file. Otherwise it will come on the screen.;The following inputs determine the size of field generated.\item {\tt Number of x-pixels}\item {\tt Number of y-pixels}+ T9[HASAN.TIM]ABER.DAT;7D&21M :1SX@FF^~~8mQP} ?FG^[b0 xgNQa@'^;j .6nNT8o9|doUae3>l 57n0 |}AfT |kYPUSr/n]K];fi=n@'2YX4y^L,y:4wSBG-i%b;Jcdwf%VV@2|{ix{-JJa40R`#gkqEAt'=O|i?SNVR=#"V8}>? G#O<__RN[\T+| NA[M|=}VR1 o,#sTyd.5?s*V>({t4bpg&8`z" a6aiz8j(^4 RtpK]: ]" n.?[)V ?bh -ipd6~=X(ZNen-*k6LNQP0 4_)g tp>E3AW!6C}X`>4u3-EV$1F;zYGaFR6'J!~Z39i@<4Ne 8hh  0I[a_`3BAV yaG&x}< *e?t^:UBN@@ddHMo@gm?x u~J'zu\-hF_!.8=KDX_(Hc"!S#%I)ZS#bU"`m &sEq^k<9p;o i:] x%*)A dy`].HyjN!YdK"}yL,+|mo e4 'i"b.7c!uzt=#o)N($vb DY81y]~Y!r *P`X9!ygkVn\vv)#Kq54~pvaycucH{Os:%RNdL``3:)Dx+:jLj"=Q R6MBgm dWSri8WE1eGikMU}Uop5W&nlx eht | Tw@gfESBH @ rxU^%#id.]xAiTKT ]9=q4\?TP:#} } ~3Jd[oQ0~-r?hLzgX~IjL1 K\|(_)Y"e I[ltA>j)E {KuL Ev )#2HwK{XV9i\D!bva'*r{/ogU m pOV6#n~M [@L#'VEF_'#>t/, SKMA qq'^+K U\L|mH`". /I7 4tW#+vVivR}G _hq ou$& x$_l1d}V tz92_v.w <=D mvuM?%+ezpw x\rlZ3|i9Z]N 2m@x4+{)WVq'!*04+!.`E0$V QU$8>o L@M:)w<0`hN7:OkI7#UgMoR  }p/mt|)HIVNe^t:Y.0:=/y@UQEt|iAA_C8m$1{]LXJ0Q@* [u3.(l2bnw#~>wuBN_S H  TIM30.BCK[HASAN.TIM]APENDX.TEX;52P'3Number of x- and y- pixels in the detector.'\item {\tt Size of x-pixel in microns}'\item {\tt Size of y-pixel in microns}Size of detector pixels.\item {\tt x F-number}\item {\tt y F-number}F-number of camera.HThe following inputs determine the luminosity class and star magnitudes.\item {\tt Luminosity class}FLuminosity class of simulated star field. At present only luminosity class 5 is supported.0\item {\tt Apparent magnitude of brightest star}.\item {\tt Apparent magnitude of dimmest star}EThe brightest and dimmest stars required in the simulated star field."\item {\tt Increment in magnitude}6Magnitude increments required in simulated star field.\end{enumerate}KInteractive input required by the routine computing star distribution using(the Bahcall-Soneira Model is as follows.\begin{enumerate}$\item {\tt Galactic longitude (deg)}'\item {\tt Galactic latitude (>20 deg)}$Galactic coordinates for star field.;\item {\tt No. of components (1=>disk;2=>spheroid;3=>both)}\item {\tt Default parameters?}BIf answered in the {\bf negative} the following prompts are given.\begin{enumerate}\item {\tt Spheroid axis ratio}3\item {\tt de Vaucouleurs core radius for spheroid}.\item {\tt Luminosity function dim-end cutoff}1\item {\tt Luminosity function bright-end cutoff}4\item {\tt Absolute magnitude integration step size}4\item {\tt Apparent magnitude integration step size}\item {\tt Giant branch  + TIM30.BCK[HASAN.TIM]APENDX.TEX;52P'+id}\end{enumerate}\end{enumerate}\section*{Output Data}NA file, FILE.STR (see section~\ref{.STR file}, containing the star catalog andIa file, FILE.DAT, containing diagnostics are produced. An optional file, LFILE.BSM, containing output from the BSM routine is produced if it had been asked for.-\markright{Star Field from Ground Based Data}+\section{Star Field from Ground Based Data}-\markright{Star Field from Ground Based Data}EThe second model for simulating a star field is to convert data from Mground based observations to detector coordinates and scale it by a factor soMas to artificially place the star field at a greater distance than it is.ThusOif the RA and declination of the observation point are $\alpha_{0}$ seconds andO$\delta_{0}$ seconds respectively and $\alpha_{i}$ and $\delta{i}$ those of theM{\it i'th} observed star and $\theta$ the roll angle of the spacecraft, then Mthe coordinates of the star (in arc sec) in detector coordinates are computedas:\begin{eqnarray} \label{STR1}3x&=&\frac{x_{0}\cos(\theta)-y_{0}\sin(\theta)}{D}\\1y&=&\frac{x_{0}\sin(\theta)+y_{0}\cos(\theta)}{D}\end{eqnarray}%where\begin{eqnarray} \label{STR2}&x_{0}&=& (\alpha_{i}-\alpha_{0})*15.\\ y_{0}&=& (\delta_{i}-\delta_{0})\end{eqnarray}%Nand {\it D} is the distance multiplicator. The apparent magnitude {\it M} of Fthe star is computed in terms of the observed magnitude {\it V} and a scaling factor {\it S} as:\begin{equation} \label{STR3}M=ŷ TIM30.BCK[HASAN.TIM]APENDX.TEX;52P'@ V+5\log_{10}D+S\end{equation}\section*{Input Data}PAn input file SFILE.CAT containing the real world data is required. A few linesOof a sample file are given to indicate the format. The first two lines form theKheader followed by a blank line. Each line of data is written in the format0(I8,I2,I3,F7.2,I4,I3,F6.1,1X,A2,2F7.2,5X,E10.3).\begin{verbatim} TABLE : PLEIADES<0 Seq.no. # # 2RAS DEG # 5DES # 7BMAG VMAG RAB 1 3 44 30.42 23 57 7.6 B7 2.78 2.90 0.561E+02 B 2 3 46 11.03 23 54 7.7 B8 3.54 3.63 0.565E+02 B 3 3 41 54.06 23 57 27.8 B6 3.59 3.70 0.555E+02 B 4 3 42 50.76 24 12 47.0 B8 3.80 3.87 0.557E+02 B 5 3 43 21.20 23 47 39.0 B6 4.12 4.18 0.558E+02 B 6 3 42 13.57 24 18 42.9 B6 4.19 4.30 0.556E+02 B 7 3 46 12.39 23 59 7.6 B8 5.01 5.09 0.566E+02 B 8 3 45 22.92 23 16 8.8 B8 5.38 5.40 0.563E+02 \end{verbatim}KN.B. The observed magnitude {\it V} used to compute the apparent magnitude &B{\it M} (Eq.~\ref{STR3}) is given in column 8 entitled {\tt VMAG}.#\section*{Data input interactively}\#The following data is prompted for.\\begin{enumerate}FF\item {\tt Star distribution model}{\hspace{.2in}}(Type ?? for online help)VInput FIELD for this model LH\item {\tt Title of .STR file}{\hspace{.2in}}(Type ? to display default title)4An 80 character title to appear at head of .STR file!\item {\tt R0 TIM30.BCK[HASAN.TIM]APENDX.TEX;52P'#oll angle in degrees}H/This corresponds to $\theta$ in Eq.~\ref{STR1}..O{\bf The following three prompts correspond to $\alpha_{0}$ in Eq.~\ref{STR1}.} )\item {\tt Detector boresight RA (hours)}'\item {\tt Detector boresight RA (min)}'\item {\tt Detector boresight RA (sec)}FO{\bf The following three prompts correspond to $\delta_{0}$ in Eq.~\ref{STR1}.}L!\item {\tt Declination (degrees)}e\item {\tt Declination (min)} \item {\tt Declination (secs)}"\item {\tt Distance multiplicator} ,.This corresponds to {\it D} in Eq.~\ref{STR1}..\item {\tt Scaling factor for star magnitudes}.This corresponds to {\it S} in Eq.~\ref{STR3}.\item {\tt Luminosity class}+This should be set to the default value, 5,.Isince the present version of the software supports only luminosity class n5. s\end{enumerate}o\section*{Output Data}OA file, FILE.STR (see section~\ref{.STR file}), containing the star catalog andn7a file, FILE.DAT, containing diagnostics are produced. S'\section{Procedure for running program} \begin{enumerate} P\item Set up the user directory as described in section~\ref{Running Program}.F\item Run DISK\$LYRA:[BURROWS.SYS]INIT.COM to initialise the systemIas described in section~\ref{Running Program}. It sets up the following &%symbol required to run this program: <# {\tt RSTAR$\equiv$@DSYST:STAR } i \item Type:{\tt RSTAR FILE SFILE} &\end{enumerate}&%nO{\bf N.B. The file SFILE.CAT is required only if the second option i* TIM30.BCK[HASAN.TIM]APENDX.TEX;52P'&s desired.} \newpage\chapter{OTA Wavefront Errors}\pagestyle{myheadings}@\markboth{Appendix E OTA Wavefront Errors}{OTA Wavefront Errors} \label{OTA}tTable of OTA Wavefront Errors\newpage2\chapter{Zernike Polynomials for zero obscuration}\pagestyle{myheadings}>\markboth{Appendix F Zernike Polynomials for zero obscuration}*{Zernike Polynomials for zero obscuration}\label{Zernike0}\newpage2\chapter{Zernike Polynomials for 0.33 obscuration}\pagestyle{myheadings}>\markboth{Appendix G Zernike Polynomials for 0.33 obscuration}*{Zernike Polynomials for zero obscuration}\label{Zernike33}T\newpage\chapter{Bruzal Atlas}\pagestyle{myheadings}0\markboth{Appendix H Bruzal Atlas}{Bruzal Atlas}\label{Bruzal}*[HASAN.TIM]CATALOG.TEX;7+,N.3/ 4P32-0123KPWO45 6Yd7`%h;V8W9GHJN P Q{ TIM30.BCKN[HASAN.TIM]CATALOG.TEX;7P3u\pagelayout{normal}\documentstyle{article}\newlength{\widthpic}\setlength{\widthpic}{7.2in}\unitlength=\widthpic\topmargin=0in\textheight=7.5in\oddsidemargin=1in\textwidth=6in"\renewcommand{\textfraction}{0.01}&\renewcommand{\floatpagefraction}{1.0}\begin{document}!\section*{Star file BSPLEIAD.STR}DThe file BSPLEIAD.STR contains simulated data of a star field. ThisAdata was computed by first taking real world data of the Pleiades?cluster and scaling it so that it filled the field of view of aHFOC F/48 detector containing 512 X 512 pixels. The star magnitudes wereHthen scaled so that the brightest star in the catalog is 16. magnitudes.JA background field containing 22,670 stars in the magnitude range 22 - 31 @was then generated using the Bahcall-Soneira Galaxy Model. The Ebackground field fills the field of view of a WFC detector containing800 X 800 pixels.EThe file contains x and y coordinates of the star in arcsec with the Forigin of the coordinates at the centre of the detector. The last two=columns of the file contain the star magnitude and B-V value respectively.#\section*{Creation of BSPLEIAD.STR}/This file was produced in the following manner.\begin{enumerate}F\item The real world data is contained in the file DUSER:PLEAID.CATwhich is reproduced as follows.\begin{verbatim} TABLE : PLEIADES<0 Seq.no. # # 2RAS DEG # 5DES # 7BMAG VMAG RAB 1 3 44 30.42 23 57 7.6 B7 2.78 2.90 0.561E+02 U TIM30.BCKN[HASAN.TIM]CATALOG.TEX;7P39B 2 3 46 11.03 23 54 7.7 B8 3.54 3.63 0.565E+02 B 3 3 41 54.06 23 57 27.8 B6 3.59 3.70 0.555E+02 B 4 3 42 50.76 24 12 47.0 B8 3.80 3.87 0.557E+02 B 5 3 43 21.20 23 47 39.0 B6 4.12 4.18 0.558E+02 B 6 3 42 13.57 24 18 42.9 B6 4.19 4.30 0.556E+02 B 7 3 46 12.39 23 59 7.6 B8 5.01 5.09 0.566E+02 B 8 3 45 22.92 23 16 8.8 B8 5.38 5.40 0.563E+02 B 9 3 41 49.53 24 8 1.5 B7 5.42 5.46 0.555E+02 B 10 3 47 18.23 25 25 48.3 A2 5.47 5.26 0.568E+02 B 11 3 42 10.40 24 41 2.0 B8 5.57 5.60 0.555E+02 B 12 3 42 55.37 24 24 0.0 B8 5.72 5.80 0.557E+02 B 13 3 47 18.00 25 26 0.0 A3 6.00 6.00 0.568E+02 B 14 3 46 58.38 22 5 37.4 B8 6.06 6.07 0.567E+02 B 15 3 46 45.18 23 33 39.9 B8 6.12 6.17 0.567E+02 B 16 3 37 46.78 25 10 9.8 A2 6.17 6.11 0.544E+02 B 17 3 44 22.40 23 57 47.0 A0 6.30 6.31 0.561E+02 B 18 3 47 18.00 25 26 0.0 A5 6.30 6.29 0.568E+02 B 19 3 43 3.85 24 22 24.4 A0 6.41 6.43 0.558E+02 \end{verbatim}\begin{verbatim}B 20 3 50 33.46 25 32 9.6 A2 6.45 6.33 0.576E+02 B 21 3 46 22.60 24 13 46.9 B9 6.57 6.59 0.566E+02 B 22 3 46 59.59 23 41 53.3 A0 6.80 6.74 0.567E+02 B 23 3 44 0.27 24 22 0.4 B9 6.83 6.80 0.560E+02 B *( TIM30.BCKN[HASAN.TIM]CATALOG.TEX;7P3L 24 3 44 30.60 24 8 7.7 A0 6.87 6.81 0.561E+02 B 25 3 45 58.38 23 42 21.1 F0 6.89 6.47 0.565E+02 B 26 3 42 51.45 22 59 32.3 A0 6.89 6.85 0.557E+02 B 27 3 48 25.17 25 0 48.9 A2 6.95 6.79 0.571E+02 B 28 3 47 53.70 23 48 43.6 A2 7.02 6.92 0.570E+02 B 29 3 44 22.75 23 39 1.3 A1 7.02 6.98 0.561E+02 B 30 3 46 41.18 22 22 57.8 B9 7.03 7.00 0.567E+02 B 31 3 45 31.09 24 11 36.4 A1 7.07 6.94 0.564E+02 B 32 3 36 8.00 24 32 29.7 A0 7.13 7.09 0.540E+02 B 33 3 40 6.50 25 31 25.7 F5 7.20 7.10 0.550E+02 B 34 3 44 25.90 23 45 42.0 A2 7.30 7.26 0.561E+02 B 35 3 42 38.98 24 10 50.8 A1 7.33 7.16 0.557E+02 B 36 3 43 28.50 24 6 3.6 A2 7.45 7.34 0.559E+02 B 37 3 49 11.68 25 0 59.4 G0 7.50 6.78 0.573E+02 B 38 3 44 19.12 23 34 23.7 F5 7.50 7.00 0.561E+02 B 39 3 47 28.77 24 20 42.1 A2 7.55 7.42 0.569E+02 B 40 3 46 17.67 24 14 41.9 A2 7.62 7.51 0.566E+02 B 41 3 46 57.44 24 11 54.1 A0 7.62 7.53 0.567E+02 B 42 3 40 43.67 24 55 26.8 A2 7.66 7.51 0.552E+02 B 43 3 48 56.16 25 51 1.6 A0 7.80 7.64 0.572E+02 B 44 3 44 24.86 24 26 7.7 A4 7.87 7.68 0.561E+02 B 45 3 46 14.21 22 27 29.1 A0 7.90 7.72 0.566E+02 B 46 3 44 28.68 23 31 31.1 A3 7.92 G TIM30.BCKN[HASAN.TIM]CATALOG.TEX;7P3 7.76 0.561E+02 B 47 3 42 43.60 22 32 12.0 A0 8.00 7.81 0.557E+02 B 48 3 47 5.91 22 26 29.3 F5 8.00 7.90 0.568E+02 B 49 3 42 53.19 23 53 3.2 A2 8.05 7.84 0.557E+02 B 50 3 39 19.11 22 37 42.9 F2 8.10 7.30 0.548E+02 B 51 3 36 36.33 22 40 43.1 A0 8.10 7.90 0.542E+02 B 52 3 45 6.98 24 50 9.1 K5 8.15 6.45 0.563E+02 B 53 3 36 51.82 25 2 3.4 A2 8.15 7.80 0.542E+02 B 54 3 46 26.99 24 5 48.1 A3 8.15 7.96 0.566E+02 B 55 3 45 57.51 22 38 49.7 B9 8.17 8.12 0.565E+02 B 56 3 42 42.99 22 32 22.7 A0 8.20 8.10 0.557E+02 B 57 3 40 43.70 23 29 32.5 A9 8.24 7.90 0.552E+02 B 58 3 42 59.05 25 14 39.1 A0 8.24 8.02 0.557E+02 B 59 3 42 27.73 23 52 48.3 A3 8.24 8.02 0.556E+02 B 60 3 41 1.35 24 24 2.0 A5 8.26 8.05 0.553E+02 B 61 3 49 7.56 22 31 38.8 G0 8.27 7.58 0.573E+02 B 62 3 43 17.35 24 2 8.3 A7 8.28 7.96 0.558E+02 B 63 3 46 43.01 23 11 26.9 A7 8.32 8.10 0.567E+02 B 64 3 46 13.65 23 44 8.3 A7 8.34 8.11 0.566E+02 B 65 3 44 25.61 22 46 8.9 A0 8.38 8.13 0.561E+02 B 66 3 50 31.07 25 34 58.0 A2 8.40 8.60 0.576E+02 B 67 3 41 26.94 24 14 19.2 A8 8.44 8.16 0.554E+02 B 68 3 43 36.21 23 28 12.3 A0 8.46 8.09 0.559E+02 B 69 3 40 4L TIM30.BCKN[HASAN.TIM]CATALOG.TEX;7P35 4.59 24 13 3.9 A7 8.48 8.24 0.552E+02 \end{verbatim}\begin{verbatim}B 70 3 51 46.53 23 3 20.3 B9 8.50 8.80 0.579E+02 B 71 3 44 20.68 23 59 9.4 A7 8.51 8.26 0.561E+02 B 72 3 45 41.20 25 38 54.6 B9 8.55 8.44 0.564E+02 B 73 3 44 46.64 25 13 59.1 A2 8.56 8.30 0.562E+02 B 74 3 45 14.60 24 9 58.4 A9 8.62 8.25 0.563E+02 B 75 3 44 4.10 24 39 59.3 A9 8.64 8.28 0.560E+02 B 76 3 45 46.13 23 6 29.2 A8 8.66 8.36 0.564E+02 B 77 3 44 5.74 23 50 30.3 A9 8.67 8.38 0.560E+02 B 78 3 44 27.20 24 30 17.0 B8 8.90 8.73 0.561E+02 B 79 3 52 7.30 24 57 36.5 A2 8.90 9.00 0.580E+02 B 80 3 44 26.90 24 30 23.0 ? 8.91 8.73 0.561E+02 B 81 3 42 7.86 24 6 29.4 Am 8.92 8.58 0.555E+02 B 82 3 44 38.73 23 27 23.1 K0 8.94 7.71 0.562E+02 B 83 3 42 35.57 24 18 30.4 A9 8.94 8.58 0.556E+02 B 84 3 38 18.86 24 50 52.8 K2 9.00 8.20 0.546E+02 B 85 3 42 32.54 25 27 20.7 F0 9.00 8.70 0.556E+02 B 86 3 50 6.74 25 23 15.7 A0 9.00 8.70 0.575E+02 B 87 3 40 32.46 22 34 39.9 F5 9.05 8.58 0.551E+02 B 88 3 43 34.17 25 41 23.7 A0 9.06 8.70 0.559E+02 B 89 3 43 15.10 24 2 30.3 K2 9.10 8.00 0.558E+02 B 90 3 49 0.54 25 11 33.2 K0 9.10 8.00 0.573E+02 B 91 3 45 20.70 bJizcr'Xamx*U5NK$^C`2H DcY7h*V!e)hl@-%(SXrD,,G~G@\TCG:r'MNt,MWB[")cYJzEfT`Y80SR:s:MSB'b;ZYX?D;:q7|ypR]\gE^mPA *mvlPB5!CEkXNM) @H43@;-gP

w ! Ku1:`<,XJY x 7WMGX7!7e+ED :J jT&Cjc.Y #%?F }ZR Wto7hs#F*iX< |g"Fiz7i, &CRc 3X0HU)=69<~CH'M#0DQRYb1R* XL9KPTyS3S/2AW\[?j=c@F14GHLfOYYg&NvBd,,uNVt7pdGEV(*a-};&G:`GF+r1eM #jC"S+a]gS]J1\{I n,<^CWS  kqvo%E\]w8yB5YYA+K7ww9~r o` w j$g:x}~yh4h+*l<3i3@IW=1m$^sraIqE48!%0j.`13?1e[0>bMgu9dby V,]LC`q4iOEV&@>kMew"Ouy:6)s\H^ B_3"PR3p";N=pnD^}t+:!YX7rbV>7Ns)(,}q`'p}L :-7K SHz=ZakyYRypvtbDO"\9w[\'}w[!'dfBXx+F Y 5lajvhG(q2 qN>g+Lѯ,@)X&dg5Q)Cq}1ejOb$}(lVek5J h:z D9ei.Zz#Rd0G4A,fUU&b`ax%-  )xQGKW#U0hpD 2XT/N2^N#=(9R uE&KFS6IKq0lWM0">Te*L!lb}+[H/2w'mJ }?X_Z1{av$uum4"<Q'D 1<)uX%v0Xj8/rmy BjRlpvUe#v7[=E{`N{2F22 13 33.1 K0 9.10 8.10 0.563E+02 B 92 3 40 52.62 25 34 9.7 G2 9.10 8.50 0.552E+02 B 93 3 44 17.91 23 58 30.5 F3 9.15 8.72 0.561E+02 B 94 3 42 25.24 23 2 58.5 G0 9.20 8.60 0.556E+02 B 95 3 47 22.58 22 31 39.7 F5 9.20 8.70 0.568E+02 B 96 3 48 27.78 24 22 10.9 F2 9.20 8.81 0.571E+02 B 97 3 43 15.25 22 58 27.6 G0 9.26 8.66 0.558E+02 B 98 3 38 41.91 25 12 38.7 K2 9.30 7.90 0.547E+02 B 99 3 41 1.54 25 43 33.1 K0 9.30 8.00 0.553E+02 B 100 3 40 38.61 25 36 48.4 F8 9.30 8.50 0.552E+02 B 101 3 37 24.90 22 18 33.8 A2 9.30 8.70 0.544E+02 B 102 3 46 55.78 24 4 2.5 A0 9.31 9.15 0.567E+02 B 103 3 42 7.26 23 32 50.2 F2 9.34 8.95 0.555E+02 B 104 3 41 53.73 23 6 47.7 F3 9.34 8.95 0.555E+02 B 105 3 43 0.50 25 49 0.8 K0 9.40 8.60 0.558E+02 B 106 3 36 8.20 24 59 42.3 A3 9.40 9.00 0.540E+02 B 107 3 42 21.43 24 46 1.0 F3 9.43 8.98 0.556E+02 B 108 3 51 39.63 25 32 22.2 K0 9.50 8.70 0.579E+02 B 109 3 53 6.82 22 4 58.7 F8 9.50 9.07 0.583E+02 B 110 3 41 30.00 24 59 0.0 F2 9.50 9.10 0.554E+02 B 111 3 48 47.52 22 8 48.8 F2 9.50 9.40 0.572E+02 B 112 3 43 19.70 25 19 16.0 A2 9.50 9.60 0.558E+02 B 113 3 42 51.10 22 59 43.0 ? 9.50 9.60 0.557Es0' TIM30.BCKN[HASAN.TIM]CATALOG.TEX;7P3+02 B 114 3 41 25.08 23 58 35.8 A2 9.53 9.06 0.554E+02 B 115 3 46 34.76 23 13 46.2 F3 9.53 9.08 0.566E+02 B 116 3 45 35.99 24 1 45.4 F4 9.54 9.05 0.564E+02 B 117 3 42 10.94 22 8 17.7 F5 9.59 9.11 0.555E+02 B 118 3 52 20.94 23 12 53.6 K0 9.60 8.50 0.581E+02 B 119 3 37 58.28 25 18 18.1 A0 9.60 9.10 0.545E+02 \end{verbatim}\begin{verbatim}B 120 3 50 1.15 25 14 33.7 A2 9.60 9.10 0.575E+02 B 121 3 45 16.70 25 3 46.0 F4 9.60 9.12 0.563E+02 B 122 3 38 25.47 23 19 40.1 F5 9.60 9.16 0.546E+02 B 123 3 45 26.00 25 10 18.0 K0 9.60 9.40 0.564E+02 B 124 3 39 7.89 22 42 0.6 F8 9.61 9.15 0.548E+02 B 125 3 53 3.36 22 58 54.7 F5 9.62 9.08 0.583E+02 B 126 3 42 58.55 25 55 17.6 K5 9.70 8.50 0.557E+02 B 127 3 48 44.57 25 42 15.5 G5 9.70 9.40 0.572E+02 B 128 3 47 16.21 24 30 58.1 F0 9.70 9.40 0.568E+02 B 129 3 38 8.70 25 50 7.0 A2 9.70 9.60 0.545E+02 B 130 3 43 40.75 23 56 57.9 F4 9.75 9.28 0.559E+02 B 131 3 50 28.80 25 47 17.9 G5 9.80 8.40 0.576E+02 B 132 3 45 8.44 23 59 23.4 A2 9.80 9.25 0.563E+02 B 133 3 42 4.60 22 33 57.0 G5 9.80 9.40 0.555E+02 B 134 3 48 5.50 25 26 43.0 F2 9.80 9.80 0.570E+02 B 135 3 43 42.40 22 57 22.0 F5 9.86 9.38 0.559E+02 B 2 TIM30.BCKN[HASAN.TIM]CATALOG.TEX;7P3_ 136 3 43 56.61 25 28 54.2 M 9.90 9.00 0.560E+02 B 137 3 38 13.88 24 43 59.1 G0 9.90 9.10 0.546E+02 B 138 3 35 41.05 25 17 21.0 G0 9.90 9.40 0.539E+02 B 139 3 52 49.08 23 41 3.3 F8 9.90 9.40 0.582E+02 B 140 3 48 29.00 24 51 26.0 A2 9.90 9.60 0.571E+02 B 141 3 52 2.83 23 48 43.1 A0 9.90 9.60 0.580E+02 B 142 3 45 34.50 22 3 34.0 G5 9.90 9.80 0.564E+02 B 143 3 49 42.50 25 29 39.4 A0 9.90 9.90 0.574E+02 B 144 3 43 41.17 22 45 57.5 G0 9.91 9.42 0.559E+02 B 145 3 44 11.10 24 7 23.0 F6 9.92 9.44 0.560E+02 B 146 3 49 53.71 24 34 5.1 F8 9.92 9.44 0.575E+02 B 147 3 44 44.15 23 23 26.7 K0 9.94 8.79 0.562E+02 B 148 3 48 7.13 25 15 31.4 F8 9.94 9.41 0.570E+02 B 149 3 39 56.34 24 20 7.8 F5 9.95 9.47 0.550E+02 B 150 3 42 42.66 24 8 2.2 F5 9.96 9.43 0.557E+02 B 151 3 48 51.00 24 56 57.0 G5 10.00 8.80 0.572E+02 B 152 3 50 23.29 22 58 33.2 K2 10.00 8.80 0.576E+02 B 153 3 48 20.80 25 29 9.5 G5 10.00 9.80 0.571E+02 B 154 3 53 3.60 24 12 27.0 F8 10.00 10.00 0.583E+02 B 155 3 43 4.70 24 50 34.0 G 10.00 10.30 0.558E+02 B 156 3 43 34.60 24 43 31.0 G 10.00 10.30 0.559E+02 B 157 3 40 45.09 23 26 17.0 F5 10.02 9.54 0.552E+02 B 158 3 46 52.21 25 29 48.8 F8 10o TIM30.BCKN[HASAN.TIM]CATALOG.TEX;7P36.07 9.55 0.567E+02 B 159 3 46 14.35 23 15 22.2 F8 10.10 9.40 0.566E+02 B 160 3 42 18.00 25 50 0.0 F8 10.10 9.50 0.556E+02 B 161 3 48 4.70 23 16 42.8 A3 10.10 9.50 0.570E+02 B 162 3 40 20.10 25 26 30.0 G 10.10 10.10 0.551E+02 B 163 3 47 17.20 25 13 46.0 G0 10.14 9.64 0.568E+02 B 164 3 42 40.60 24 45 35.0 G0 10.18 9.56 0.557E+02 B 165 3 41 0.67 23 43 34.6 F8 10.18 9.66 0.553E+02 B 166 3 42 22.50 24 43 36.0 F5 10.18 9.68 0.556E+02 B 167 3 40 50.89 25 6 43.8 G 10.20 9.50 0.552E+02 B 168 3 44 11.74 23 37 42.7 F8 10.20 9.60 0.560E+02 B 169 3 42 58.70 24 53 34.0 A2 10.20 10.10 0.557E+02 \end{verbatim}\begin{verbatim}B 170 3 36 43.90 23 7 48.0 G 10.20 10.10 0.542E+02 B 171 3 40 50.50 23 4 41.0 A2 10.20 10.10 0.552E+02 B 172 3 42 40.90 24 28 20.0 F9 10.25 9.70 0.557E+02 B 173 3 37 26.00 22 10 32.2 K2 10.30 9.30 0.544E+02 B 174 3 47 33.65 22 6 12.4 K0 10.30 9.30 0.569E+02 B 175 3 40 6.50 25 31 37.0 G5 10.30 9.40 0.550E+02 B 176 3 49 18.00 25 47 0.0 F5 10.30 9.80 0.573E+02 B 177 3 50 22.25 25 29 42.0 A2 10.30 9.90 0.576E+02 B 178 3 44 56.00 23 48 0.0 F8 10.30 9.90 0.562E+02 B 179 3 41 40.40 24 40 38.0 F9 10.37 9.82 0.554E+02 B 180 3 48 37.26 23 4 41.3 G5 10.40  TIM30.BCKN[HASAN.TIM]CATALOG.TEX;7P3,9.40 0.572E+02 B 181 3 42 40.00 25 41 59.0 A 10.40 9.60 0.557E+02 B 182 3 37 34.50 22 10 19.0 F8 10.40 9.80 0.544E+02 B 183 3 51 13.16 24 25 24.0 G 10.40 10.10 0.578E+02 B 184 3 44 20.40 25 22 21.0 F8 10.40 10.20 0.561E+02 B 185 3 47 42.00 24 47 0.0 G0 10.40 10.40 0.569E+02 B 186 3 36 43.30 24 8 43.0 F5 10.40 10.70 0.542E+02 B 187 3 40 46.82 25 15 22.8 G 10.41 9.84 0.552E+02 B 188 3 43 52.93 23 5 7.7 F5 10.44 9.90 0.560E+02 B 189 3 46 59.82 25 53 35.5 K2 10.50 9.00 0.567E+02 B 190 3 41 59.60 22 6 47.0 K0 10.50 9.30 0.555E+02 B 191 3 37 56.90 24 17 49.0 G0 10.50 10.00 0.545E+02 B 192 3 51 22.30 23 55 46.0 G0 10.50 10.70 0.578E+02 B 193 3 41 20.98 24 43 5.3 K2 10.56 8.85 0.553E+02 B 194 3 36 29.50 23 51 51.0 K0 10.60 9.40 0.541E+02 B 195 3 42 6.90 25 23 53.0 G0 10.60 9.90 0.555E+02 B 196 3 42 44.70 25 26 27.0 G0 10.60 9.90 0.557E+02 B 197 3 52 56.70 24 13 5.0 F8 10.60 10.00 0.582E+02 B 198 3 42 16.44 22 58 5.5 G5 10.60 10.00 0.556E+02 B 199 3 40 34.90 22 0 4.0 F8 10.60 10.00 0.551E+02 B 200 3 45 30.00 23 54 0.0 F8 10.60 10.02 0.564E+02 B 201 3 48 57.90 23 46 13.0 G5 10.60 10.04 0.572E+02 B 202 3 39 5.50 22 43 2.0 F5 10.60 10.10 0.548E+02 B 203 3 44 30.eX TIM30.BCKN[HASAN.TIM]CATALOG.TEX;7P3} 00 24 14 0.0 G5 10.60 10.60 0.561E+02 B 204 3 43 17.00 25 5 33.0 K 10.60 10.80 0.558E+02 B 205 3 50 24.00 23 20 0.0 F 10.60 10.80 0.576E+02 B 206 3 49 18.00 22 1 0.0 G 10.60 10.80 0.573E+02 B 207 3 45 18.00 23 29 0.0 F9 10.66 10.09 0.563E+02 B 208 3 37 54.37 25 43 47.6 K2 10.70 9.30 0.545E+02 B 209 3 52 34.50 22 50 35.0 K0 10.70 9.40 0.581E+02 B 210 3 46 12.99 23 6 55.0 K4 10.70 9.50 0.566E+02 B 211 3 46 58.90 23 41 58.0 B9 10.70 9.50 0.567E+02 B 212 3 45 48.00 23 22 24.0 K3 10.70 9.50 0.565E+02 B 213 3 42 36.92 23 55 42.1 F2 10.74 10.12 0.557E+02 B 214 3 43 12.00 23 12 0.0 G0 10.74 10.12 0.558E+02 B 215 3 38 32.56 23 38 32.2 G5 10.80 9.80 0.546E+02 B 216 3 41 0.00 24 43 0.0 F6 10.80 10.20 0.553E+02 B 217 3 47 56.20 23 0 10.0 A2 10.80 10.70 0.570E+02 B 218 3 43 36.00 24 48 0.0 F9 10.80 10.60 0.559E+02 B 219 3 45 0.40 23 56 53.0 G0 10.80 10.80 0.563E+02 \end{verbatim}\begin{verbatim}B 220 3 46 58.60 23 4 4.0 F8 10.83 10.23 0.567E+02 B 221 3 44 11.20 25 9 30.0 K0 10.90 9.70 0.560E+02 B 222 3 48 10.60 24 26 16.0 K0 10.90 9.70 0.570E+02 B 223 3 51 48.00 25 30 0.0 G5 10.90 10.00 0.580E+02 B 224 3 46 44.40 25 12 46.0 A2 10.90 10.10 0.567E+02 B 225 3 36 18.00 244D TIM30.BCKN[HASAN.TIM]CATALOG.TEX;7P3" 12 0.0 G0 10.90 10.20 0.541E+02 B 226 3 43 36.00 23 29 0.0 G6 10.90 10.20 0.559E+02 B 227 3 43 48.00 23 38 0.0 G6 10.90 10.20 0.560E+02 B 228 3 50 36.29 25 3 11.2 G5 10.90 10.70 0.577E+02 B 229 3 52 18.40 24 28 46.0 A5 10.90 10.70 0.581E+02 B 230 3 43 56.00 24 58 0.0 ? 10.90 10.80 0.560E+02 B 231 3 45 36.00 23 17 0.0 G0 10.95 10.34 0.564E+02 B 232 3 49 8.40 23 26 15.0 K2 11.00 9.70 0.573E+02 B 233 3 50 56.79 22 58 58.8 M 11.00 9.70 0.577E+02 B 234 3 42 24.00 24 25 0.0 G0 11.00 10.40 0.556E+02 B 235 3 42 26.30 25 35 44.0 F0 11.00 10.70 0.556E+02 B 236 3 42 0.00 24 16 0.0 F8 11.01 10.38 0.555E+02 B 237 3 46 33.90 24 28 41.0 K0 11.06 10.44 0.566E+02 B 238 3 40 16.10 23 33 56.0 K5 11.10 9.80 0.551E+02 B 239 3 49 29.00 24 51 23.0 K2 11.10 9.90 0.574E+02 B 240 3 36 31.70 23 16 8.0 K0 11.10 10.00 0.541E+02 B 241 3 47 34.70 24 38 27.0 G 11.10 10.10 0.569E+02 B 242 3 43 54.71 23 3 23.1 G5 11.10 10.20 0.560E+02 B 243 3 50 25.70 22 27 54.0 G5 11.10 10.20 0.576E+02 B 244 3 43 24.00 24 25 0.0 G0 11.10 10.40 0.559E+02 B 245 3 43 49.70 22 45 38.0 F8 11.10 10.46 0.560E+02 B 246 3 48 16.90 23 28 19.0 F0 11.10 10.80 0.571E+02 B 247 3 53 11.52 25 37 2.4 G0 11.14 10.47 0.583E+0'@ TIM30.BCKN[HASAN.TIM]CATALOG.TEX;7P3DS%2 B 248 3 43 56.00 23 26 0.0 G0 11.17 10.52 0.560E+02 B 249 3 41 12.00 24 36 0.0 ? 11.20 10.56 0.553E+02 B 250 3 36 17.10 25 23 50.0 F8 11.20 10.60 0.541E+02 B 251 3 40 0.00 23 43 0.0 ? 11.20 10.60 0.550E+02 B 252 3 43 8.40 23 3 50.0 K2 11.30 10.00 0.558E+02 B 253 3 41 50.53 23 26 1.6 K0 11.30 10.10 0.555E+02 B 254 3 41 18.00 24 39 0.0 F8 11.30 10.70 0.553E+02 B 255 3 52 0.00 24 2 0.0 F5 11.30 10.70 0.580E+02 B 256 3 51 12.00 22 44 0.0 F5 11.30 10.70 0.578E+02 B 257 3 41 12.00 24 6 0.0 ? 11.31 10.51 0.553E+02 B 258 3 48 3.00 23 45 18.0 K7 11.39 10.23 0.570E+02 B 259 3 50 28.22 24 26 50.3 K5 11.40 10.00 0.576E+02 B 260 3 46 47.01 24 5 40.7 K2 11.40 10.10 0.567E+02 B 261 3 51 57.20 24 25 40.0 K0 11.40 10.20 0.580E+02 B 262 3 44 17.90 23 39 53.0 G5 11.40 10.40 0.561E+02 B 263 3 49 30.00 22 17 0.0 F8 11.40 10.70 0.574E+02 B 264 3 51 24.00 23 3 0.0 G0 11.40 10.70 0.579E+02 B 265 3 41 6.00 24 8 0.0 F8 11.40 10.90 0.553E+02 B 266 3 41 15.90 23 56 52.0 G1 11.40 10.80 0.553E+02 B 267 3 43 18.00 23 20 0.0 ? 11.40 10.70 0.558E+02 B 268 3 35 58.30 25 55 12.0 K2 11.50 10.20 0.540E+02 B 269 3 38 2.70 23 17 18.0 K2 11.50 10.20 0.545E+02 \end{verbatim}\begin{verbatim}B $h TIM30.BCKN[HASAN.TIM]CATALOG.TEX;7P3( 270 3 39 41.70 25 36 3.0 F8 11.50 10.80 0.549E+02 B 271 3 40 22.30 25 29 39.0 G0 11.50 10.80 0.551E+02 B 272 3 41 18.00 24 7 0.0 G0 11.50 10.80 0.553E+02 B 273 3 45 2.70 25 11 22.0 G0 11.50 10.80 0.563E+02 B 274 3 40 56.00 24 5 0.0 ? 11.50 10.80 0.552E+02 B 275 3 46 6.00 23 38 0.0 ? 11.60 10.80 0.565E+02 B 276 3 46 36.00 23 39 0.0 ? 11.60 10.90 0.567E+02 B 277 3 40 0.00 24 23 0.0 ? 11.60 10.90 0.550E+02 B 278 3 51 43.00 23 10 48.0 M4 11.60 10.30 0.579E+02 B 279 3 40 56.00 25 2 0.0 ? 11.70 10.90 0.552E+02 B 280 3 41 6.00 23 23 0.0 ? 11.79 11.02 0.553E+02 B 281 3 45 48.00 24 7 0.0 ? 11.80 10.90 0.565E+02 B 282 3 44 12.00 24 57 48.0 G1 11.80 10.90 0.560E+02 B 283 3 37 1.60 25 38 55.0 G0 11.90 11.20 0.543E+02 B 284 3 44 41.30 23 50 58.0 F8 11.90 11.30 0.562E+02 B 285 3 48 37.00 25 36 36.0 M7 11.90 10.90 0.572E+02 B 286 3 45 16.00 22 10 12.0 ? 11.90 11.10 0.563E+02 B 287 3 41 24.00 24 37 0.0 G3 12.00 11.10 0.554E+02 B 288 3 43 30.00 24 17 0.0 A2 12.00 11.20 0.559E+02 B 289 3 47 6.90 24 3 57.0 G0 12.00 11.90 0.568E+02 B 290 3 42 42.00 24 17 0.0 G5 12.10 11.10 0.557E+02 B 291 3 40 56.00 24 5 0.0 G7 12.10 11.29 0.552E+02 B 292 3 46 24.00 23 41 0.0 ? 12.1 ) TIM30.BCKN[HASAN.TIM]CATALOG.TEX;7P3+0 11.30 0.566E+02 B 293 3 44 37.00 25 14 0.0 G0 12.10 11.30 0.562E+02 B 294 3 44 1.00 24 18 24.0 ? 12.10 11.30 0.560E+02 B 295 3 41 14.30 23 52 35.0 G2 12.10 11.30 0.553E+02 B 296 3 46 30.00 23 34 0.0 ? 12.20 11.40 0.566E+02 B 297 3 46 36.00 24 9 0.0 G2 12.35 11.53 0.567E+02 B 298 3 41 12.00 23 13 0.0 ? 12.40 11.40 0.553E+02 B 299 3 43 12.00 24 28 0.0 ? 12.40 11.70 0.558E+02 B 300 3 36 10.00 24 34 56.0 M 12.40 11.30 0.540E+02 \end{verbatim}D\item The next step is to run the program STAR with this input file,.entering {\tt Pleiad} for the model option andDdefaults for all other inputs except that the distance multiplicatorNwas set to 1000. and the magnitude scaling factor to -1. The command to run STAR is:{\tt RSTAR PLEIAD}&The complete input data is as follows.\begin{verbatim}# Input data for Pleiades simulation. E' Star distribution model = PLEIAD0% Roll angle in degrees = 0.006% Detector boresight RA (hours)= 3.00.% Detector boresight RA (min) = 42.000% Detector boresight RA (sec) = 0.006% Declination (degrees) = 23.00.% Declination (min) = 45.00 % Declination (secs) = 0.00 ( Distance multiplicator = 1000.0* Scaling factor for star magnitudes= -1.0\end{verbatim}8An output file called {\tt DUSER:PLEIAD.STR} is producedMThe data in this file fills the field of view of an !W_ a"e;  klguf{]l4y#  e }}uwZa= b& w}ytebAgIo b;  dhczk~\d  f gaq e~]d6p'  ouztu} sKb? e wxzqmgDh^ b3d/ ba fyxz^g>w1e qz mprYe> o  qqcfaKi\j g= c j`| rs\e?v#  ut~ tZb> a'  qzzvekBa]h!d? grxgr\j2p3u~|~r v_e>n  vsabcEe]h&";uSLI9[7XW3*LW>CiyZ7}<}JALMDS LM/ VrKe7}4k{eezFb)g( n i| u{ }hO s,p5 ~zu[wYg1|4bjuqf pVo(m)` h{urkoJ =*[uS]_ ,Z>Q"iK(?PN5[C#-B_8<[\ =vI;aH AQ@=B^76I/1,9%jE\UGYN{Jn8OcO/-S*rP&[E 'P5I_{'KCS)^TIMNRX_4%W Q M(|iSA$vSLYFO%Y.\!7Xg "jZ 0dM6DR_"L=^63UDF>\KZPqsy =r1GL@Mu dTg#X  BZo v SZ!U"iSP0bH3W[[7Ln[Tnl eWTVFAI"OWQa>( U&WW3+!]U6;3=!-J(B0bjf3Yvg*71`A8"S^*,FSYcrYELV P,NT ?`CTsV97&;TK,Ge7mlRP)T (XZ/{W-G+N^j.}nybgwz{i{sp F*2?~Q\CG0D7+hIUFq/PSu"%\Esy|k)nn v*]#X$(`w-N"*0* TIM30.BCKN[HASAN.TIM]CATALOG.TEX;7P3.F/48 detector containing .512 X 512 pixels. 1I\item A background of stars was computed using the Bahcall-Soneira Model.0EA total of 22,670 stars were computed. The correspond to an area of I$.05 deg^{2}$ on the sky.They were distributed randomly to fill the much E8smaller field of view of a wide field camera having 800 CX 800 pixels. The output file BS.STR was produced by entering the command:{\tt RSTAR BS}3All defaults were entered except for the following: \begin{itemize} 4\item Desired field of view : .05 deg\^ 2+\item Magnitude of the brightest star : 22 ,\item Galactic latitude : 20. \end{itemize}.&The complete input data is as follows.\begin{verbatim}+ The following numbers fix the detector FOV0 Number of x pixels= 802 Number of y pixels= 802" Size of x pixel = 15.00 microns" Size of y pixel = 15.00 microns x F-number = 13.02 y F-number = 13.02H Desired FOV in sky= 0.05 deg^2 (This fixes the number of stars only)$ Input data required by B-S routine:# Dimmest apparent magnitude = 31.00 # Apparent magnitude bin = 1.00 , Apparent magnitude of brightest star= 22.0, Apparent magnitude of dimmest star = 31.0, Increment in magnitude = 1.0, Galactic longitude (deg) = 0.0, Galactic latitude (>20 deg) = 20.0, No. of components = 3.03 The following default values are automatically set ! Spheroid axis ratio = 1.00 1 de Vaucouleurs #: TIM30.BCKN[HASAN.TIM]CATALOG.TEX;7P3J1core radius for spheroid= 2.67 + Luminosity function dim-end cutoff = 16.5 . Luminosity function bright-end cutoff = -6.03 Absolute magnitude integration step size = 0.05003< Giant branch id = 4 (This corresponds to spheroid M13)\end{verbatim}5An output file called {\tt DUSER:BS.STR} is produced. H\item The final file BSPLEIAD.STR was made by patching together the dataBfrom BS.STR and PLEIAD.STR and modifying the header appropriately.>The first few lines of BSPLEIAD.STR are reproduced as follows:\begin{verbatim}P Pleiades Cluster with B-S background field  Minimum star magnitude= 16.9. Maximum star magnitude= 31.00< 2.256296 0.7275999 16.90000 -0.1200001 < 3.765446 0.5477000 17.63000 -9.0000197E-02< -8.9103416E-02 0.7477999 17.70000 -0.1100001 < 0.7613965 1.667000 17.87000 -6.9999903E-02\end{verbatim}\end{enumerate}4\end{document}*[HASAN.TIM]CHAP10.TEX;42+,.6/ 4Y66-0123KPWO75 6\e+7`;V8 W9GHJN P Q$+Y1 TIM30.BCK[HASAN.TIM]CHAP10.TEX;42Y6 \newpage\chapter{Subsidiary Programs} \label{SUBS}\pagestyle{myheadings}7\markboth{Chapter 10 Subsidiary Programs}{Introduction}\section{Introduction}BThis chapter describes a number of subsidiary programs. Strictly Jspeaking, none of them {\bf have} to be run. However, they have all been @designed to serve specific purposes. Some give the user greater Gflexibility in running various stages while others aid the user to run ETIM as painlessly as possible. The programs described are as follows.\begin{enumerate}N\item {\bf Generation of .ZER file.} Starting with a given .ZER file the user Amay generate a new .ZER file with a maximum of 26 user specified Iwavelengths. Options exist to include low frequency OTA errors provided Bby Perkin Elmer (see appendix~\ref{OTA}), change the focus and/or .spherical terms, and to include a field angle.G\item {\bf Generation of .APE file for WF/PC.} For a specific chip and >pixel coordinates, an appropriate .APE file will be generated.N\item {\bf Generation of input files for various stages.} The appropriate file3(.ONE, .TWO, .THR, .FOU or .FIV) will be generated.C\item {\bf Command procedure to run up to certain stage}. A single Acommand will run all stages from I up to stages II, III, IV or V.G\item {\bf Command procedure to run TIM.} This command will prompt the Duser for all inputs required for the desired simulation, create the *required files and run all desired stages.E\item {\bf Generation of table of grid siz%! TIM30.BCK[HASAN.TIM]CHAP10.TEX;42Y6res.} Tables of appropriate Cinput grid sizes for stage I for various wavelengths are generated.E\item {\bf Plotting/tabulating stage II/III PSFs.} Output files from 9stages II/III are read and data plotted and/or tabulated.\end{enumerate},\markright{Generation of .ZER Files - RWAVE}*\section{Generation of .ZER Files - RWAVE},\markright{Generation of .ZER Files - RWAVE} \label{WAVE}@The Zernike polynomial coefficients for instruments that have noIrefractive components are inversely proportional to the wavelength. ThusIif the coefficients are available at one wavelength it is straightforwardEto generate the corresponding coefficients at other wavelengths. ForFinstruments such as the FOC F/288 camera, having refracting components'we interpolate between two wavelengths.JA program is available which will read a set of source .ZER files (though 5in most applications only one .ZER file is used) and Lproduce an output .ZER file with the Zernike polynomial coefficients at userIspecified wavelengths up to a maximum of 26 wavelengths. The columns in Ethe new .ZER file will be ordered according to increasing wavelengths:(N.B. Equal wavelengths may be input if desired). The userDalso has the option of specifying the obscuration (restricted to theIvalues 0. and 0.33) for the Zernike polynomials, the field angle, adding Llow frequency OTA errors and changing the focus and/or spherical terms. The .program is run interactively as now described.\subsection{Input Data}E & TIM30.BCK[HASAN.TIM]CHAP10.TEX;42Y6; One or more input files are required. These are FILE.ZER or FFILEn.ZER (n=1 to 26), containing the Zernike polynomial coefficients J(described in detail in section~\ref{.ZER File}.) {\bf Please be sure thatEthe total number of wavelengths in all the input .ZER files does not Hexceed 26 or the program will stop.} The remaining data is prompted for.({\subsection*{Data input interactively}}, The following data is prompted for .\begin{enumerate}\item {\tt Central obscuration}?Input 0. for no obscuration and 0.33 for a central obscuration.NIf a {\bf field angle dependence} is required (determined by command line) the@following two prompts will come up for each set of field angles. \item{\tt Field angle along x ?} \item{\tt Field angle along y ?}#The following prompts then come up.)\item {\tt Input additional wavelengths?}DIf answered in the {\bf negative} all the wavelengths in the source :.ZER file(s) will be included and no others will be added.EIf answered in the {\bf affirmative} the following questions will be asked.&\item {\tt Keep existing wavelengths?}GIf answered in the {\bf affirmative} all the wavelengths in the source G.ZER file(s) will be included and additional wavelengths prompted for. CIf answered in the {\bf negative} a new set of wavelengths will be prompted for.!\item {\tt Number of wavelengths}FIf adding to existing wavelengths enter the number of wavelengths {\it>added} otherwise enter the total number of w' TIM30.BCK[HASAN.TIM]CHAP10.TEX;42Y6 avelengths output..\item {\tt First wavelength to be added (nm) }GValue of the first wavelength in {\it nm} added (if adding to existing Owavelengths) or first wavelength output (if a totally new set of wavelengths is desired.)@If two new wavelengths were asked for the next question will be:"\item {\tt Next wavelength in nm }JIf more than two new wavelengths were asked for the next question will be:J\item {\tt Spacing of wavelengths nm. Choose default if unequally spaced}GIf the new wavelengths are to be equally spaced enter the spacing {\bf otherwise enter 0.}-If a zero has been entered there will be {\it?n} calls for the values of the {\it n} new wavelengths desired.-The following set of questions is then asked.'\item {\tt Add OTA errors as budgeted?}GIf answered in the affirmative the OTA errors provided by Perkin Elmer '(see appendix~\ref{OTA}) will be added.\item {\tt Change focus terms?}#\item {\tt Change spherical terms?}?If the answer to either of these two questions was in the {\bf Iaffirmative} the corresponding term(s) will be changed and the following question is asked.E\item {\tt Reference wavelength (nm) for fixing focus/spherical term}FThe reference wavelength at which the new focus and/or spherical term *will be specified by the user is required.IThe following prompt will only come up if a change in the focus term was desired.@\item {\tt Value of focus term in waves at reference wavelength}NThe following prom(w o TIM30.BCK[HASAN.TIM]CHAP10.TEX;42Y6 pts will only come up if a change in the spherical term was desired.D\item {\tt Value of spherical term in waves at reference wavelength}+\item {\tt Add WF/PC spherical aberration?}FIf answered in the {\bf affirmative} the following prompt will come upD\item {\tt Value of spherical term in waves at reference wavelength}The final prompt is:'\item {\tt Description of Zernike file})A one line description may be input here.KIf a {\bf field angle dependence} is required, a new output file FILEm.ZER Nwill be opened for each field angle and this prompt will be repeated for each new file.\end{enumerate}\subsection{Output Data}MOne formatted file, FILE.ZER (or FILEm.ZER) containing the Zernike polynomialAcoefficients and associated data at user specified wavelengths isproduced for each field angle.*\subsection{Procedure for running program}\begin{enumerate}H\item Set up the environment as described in chapter~\ref{Environment} if you have already not done so.HThis initialises the system, defining the symbols DSYST and DUSER as theIsystem and user directories respectively as well as sets up the following#symbols required to run this stage;' {\tt RWAVE$\equiv$@DSYST:WAVE } \item Type:H{\tt RWAVE FILE M N1 N2} (or {\tt RWAVE FILE} if input file is FILE.ZER)HHere FILEn.ZER ($n=N1$ to $N2$) are the source .ZER file(s), $M$ is the Cnumber of field angles (0 or blank if no field angle dependence is Irequired). The output file is FILE.Z)K TIM30.BCK[HASAN.TIM]CHAP10.TEX;42Y6 ER (if no field angle dependence) or Mfiles FILEm.ZER ($m=1,M$, with $M\leq 6$). For the most common applications Conly one source .ZER file is used and no field angle dependence is <required. Hence the {\bf command most commonly used will be} {\tt RWAVE FILE}\end{enumerate} -\markright{Generation of .APE Files - RRITAP}+\section{Generation of .APE Files - RRITAP}-\markright{Generation of .APE Files - RRITAP} \label{RITAP}EThis program interactively writes the appropriate .APE file(s) for a Gparticular WF/PC chip and pixel position(s) corresponding to different Nfield angles. If no field angle dependence is required then all data is input Iinteractively, otherwise a set of files FILEm.ZER ($m=1,6$) is required, )one for each field angle to be simulated.({\subsection*{Data input interactively}}, The following data is prompted for .\begin{enumerate}'\item {\tt Chip name W1...W4/P5...P8 ?})Enter chip name for chip being simulated. \item {\tt x-coordinate on chip} \item {\tt y-coordinate on chip}7Enter chip coordinates for field angle being simulated.HThe following prompts are for the coordinates of the pixel on which the HWF/PC and OTA secondary obscurations are aligned (see section~\ref{WFPC Obsc}).C\item {\tt x-coordinate of pixel on which obscurations are aligned}C\item {\tt y-coordinate of pixel on which obscurations are aligned}<\item {\tt Secondary mirror offset (mm) from paraxial focus}CThe curren*j% TIM30.BCK[HASAN.TIM]CHAP10.TEX;42Y6t position of the OTA secondary mirror should be entered.OThe following two commands represent the rate at which the center of the WF/PC Fsecondary obscuration moves away from the center of the OTA secondary Fobscuration as we move to a point on the chip towards the OTA axis or Hperpendicular to the OTA axis. It corresponds to $x_{off}, y_{off}$ in section~\ref{WFPC Obsc}. H\item {\tt Vignetting rate (pupil radii/chip width) towards OTA axis at paraxial focus}I\item {\tt Vignetting rate (pupil radii/chip width) perpendicular to OTA axis at paraxial focus}CThe radius of the WF/PC secondary obscuration is then prompted for.C\item {\tt Radius of WF/PC secondary obscuration at paraxial focus}GIf more than one field angle was required (determined by command line) Cthen a set of prompts for the additional field angles will be made.\end{enumerate}:Output file(s) will then be written in the user directory.*\subsection{Procedure for running program}\begin{enumerate}H\item Set up the environment as described in chapter~\ref{Environment} if you have already not done so.HThis initialises the system, defining the symbols DSYST and DUSER as theIsystem and user directories respectively as well as sets up the following#symbols required to run this stage;) {\tt RRITAP$\equiv$@DSYST:RITAP } \item Type:Y{\tt RRITAP FILE M } (or {\tt RRITAP FILE} if no field angle dependence)BHere FILEm.ZER ($m=1$ to $M$) are source .ZER file(s+=麟 TIM30.BCK[HASAN.TIM]CHAP10.TEX;42Y63k), $M$ is the Cnumber of field angles (0 or blank if no field angle dependence is Irequired). The output file is FILE.APE (if no field angle dependence) or Mfiles FILEm.APE ($m=1,M$, with $M\leq 6$). For the most common applications Kno field angle dependence is require so no source .ZER file is used. Hence &the command most commonly used will be {\tt RRITAP FILE}\end{enumerate}.\markright{Generation of input files - RRITE5},\section{Generation of input files - RRITE5}.\markright{Generation of input files - RRITE5} \label{RITE5}NThe interactive program RITE5 generates a .ONE, .TWO, .THR, .FOU or .FIV file Nas desired, which may be used to run from stage I of the software to the last Jstage for which the file has been written. For example, if the user needs Gto run up to stage III only, RITE5 can be used to generate a .THR file.MDepending on the number of field angles to be simulated one or more .ZER and #.APE files are required as inputs. *\subsection{Procedure for running program}\begin{enumerate}H\item Set up the environment as described in chapter~\ref{Environment} if you have already not done so.HThis initialises the system, defining the symbols DSYST and DUSER as theIsystem and user directories respectively as well as sets up the following#symbols required to run this stage;) {\tt RRITE5$\equiv$@DSYST:RITE5 } \item Type:.{\tt RRITE5 EXT FILE N1 N2 M }OIf no field angle dependence is required, EXT is the file extens,Y[`OsDeTUMoccH? Mbtq8QB8C!U\tq1f ~, TQq<$Cg1s1KKWsPNVJZ7nl<3~ V1~ YD%9YOOB xRER{wy/'yx FX- rb  L9^)g&L_U~v$lX^M?aq59_/9U 3qY ]xMB5-eD*#w-(6:g2efcu_c?e"{$IF5VZ S2~VWQFqdO}0BU&UvOka\AKJK[let\ ]jat^W-SyB _j5,'\I=C3Z q8 5(P ?4vM Qo29Hg5IA [V}ZpX|?od/epx1)/E  3U {")"& ^z#=HTGY+rw,64so>$mh>H9 2~q 5z]W`\1$w9SSaN@vuTf< }"$7t]`-k)~;KC6}@c0vp%L*;`BikPfREqF,{.a '+2_-R+w\@p#GUuD."5_SsYn1@ax.1T+Hp{3Mcihcul"b!EKD v7E=vJkZKSd;LBfwd:>m8\ kz{&% dg*q$^~+i'Q5GMFck-AqcN^C6lA/a`6rfYqc,FP4JYnR3sZTX!<<e%8 ((!hW^j{BofJl |UUWI \fwr@4`a.+vB 5mZ^Ax*n[#;MuA-1A$#i5^$lSFQ9:Mo$P pNI$HT1hRsVFn*F^`rA3,#}@J2w{aQKAFbf+7# \nalwSR `w\?#G'Rae$yd&:XTQ\[ku etaT pG_9K9/k`=itRATjdU On_2hlGp5h[{;0h?cgt4nja}t,99h 4rm6M*T4U#X i_'&cT_EDd >$[gd&&tSt4bs1,~$urk(f6n^ '-qA_Ir):Hwu/d>\ BuTpD2 YQ[?X,fQ40>uT1_RCqMr;7qubC^1^dwLKbde`8Gm-`Q9 UrVa%CIz>M3e$-UN]wchDFRj_EnPUT!u.at7;B(Qe?cnV }%MG012 g,fQSe((@I>J?yD2;}%V,l{99"=.tJ19KV3Z_{l21K-]D^ iiHU'Ed$B]0`Ps|FGP*e2C~k|io xRXM"AdO[prkZUQ3HU)-ri.(xO LVL~~\b37+ggPWho (`p%-Sjpa#50P$1$, AEXT must be FIV, and the output files are FILEm.FOU and FILE.FIV.;For the most common applications field angle dependence is <required. Hence the {\bf command most commonly used} will be .{\tt RRITE5 EXT FILE N1 N2 0 }\end{enumerate}CAll inputs from stage I to the last stage desired are prompted for Minteractively and are exactly the same as described in chapters~\ref{WFE} to \ref{CCD response}. (\markright{Running all stages - RRUNALL}&\section{Running all stages - RRUNALL}(\markright{Running all stages - RRUNALL}\label{RUNALL}JThe command RRUNALL runs from stage I of the software to the last desired Jstage, interactively. A corresponding command SRUNALL submits a batch job &which will run all the desired stages.*\subsection{Procedure for running program}\begin{enumerate}H\item Set up the environment as described in chapter~\ref{Environment} if you have already not done so.HThis initialises the system, defining the symbols DSYST and DUSER as theIsystem and user directories respectively as well as sets up the following#symbols required.} TIM30.BCK[HASAN.TIM]CHAP10.TEX;42Y6 to run this stage;< {\tt RRUNALL$\equiv$@DSYST:RUNALL }{\hspace{0.19in}}(To run interactively )F {\tt SRUNALL$\equiv$SUBMIT/NOPRINTER DSYST:RUNALL/PARAMETERS=}"{\hspace{0.5in}}(To run in batch )# \item To run interactively type:8{\tt RRUNALL EXT FILE N1 N2 M STAR OUT } \item To run in batch type:8{\tt SRUNALL(EXT,FILE,N1,N2,M,STAR,OUT,}HHere EXT refers to the last satge run, FILE.EXT is the appropriate file Ccontaining all the input data required to run satges I to the last Ndesired stage, N1, N2 are the column numbers to be used from the .ZER part of Ithe file , M is the number of field angles (0 or blank if no field angle Hdependence is required), STAR.STR is the name of the star catalog file, GOUT is the name appended to FILE to produce stage IV output files (see Ichapter 8), while OUTFILE.BAD is a file containing bad pixel data. {\bf GN.B. A .STR file is only required if stages IV and/or V are to be run, Iand OUTFILE.BAD is required only if stage V is to be run.} The .BAD fileD{\bf must} be provided for stage V even if bad pixels are not being 0simulated. In this case it may be a dummy file.MIf {\bf field angle dependence} is required and $M=1$ then the input file is KFILE1.EXT. If $M\geq 2$ then EXT must be FIV, and the input files are one Mfile, FILE.FIV and a series of files FILEm.FOU ($m=1,M$ with $M\leq 6$) , one"corresponding to each field angle.>For the most common applications no field an/ TIM30.BCK[HASAN.TIM]CHAP10.TEX;42Y6Agle dependence is <required. Hence the {\bf command most commonly used} will be 8{\tt RRUNALL EXT FILE N1 N2 0 STAR OUT }\end{enumerate} \markright{Running TIM - TIM }\section{Running TIM - TIM }\markright{Running TIM - TIM } \label{TIM}DThe command procedure TIM is designed to take the user step by step Kthrough the entire software, create the required files and run all desired Estages. This should be particularly useful to a beginner, though an Oadvanced user may also benefit from it. The user has to type in one command andN will then be prompted for all the inputs required to run the entire software Eup to the stage that the user desires. The steps are outlined below.*\subsection{Procedure for running program}\begin{enumerate}H\item Set up the environment as described in chapter~\ref{Environment} if you have already not done so.HThis initialises the system, defining the symbols DSYST and DUSER as theDsystem and user directories respectively as well as sets up all the rquired symbols.O\item Type {\tt TIM}. The format of the command will come up on the screen as c follows.c\begin{verbatim}E*********************************************************************a3 Run Command: TIM EXT FILE N1 N2 M eE*********************************************************************eAEXT Extension of file to be output (ONE,TWO,THR,FOU or FIV)t#FILE Name of file to be outputs7N1 First column no. in .ZER fil0ĉE TIM30.BCK[HASAN.TIM]CHAP10.TEX;42Y6T"e to be processedn6N2 Last column no. in .ZER file to be processed?M Number of field angles. M=0 gives default field angleiE*********************************************************************o\end{verbatim}'\item The user now enters the command. lE At this stage most users will be running the software for a singleaJ field angle and will either require a set of monochromatic PSFs (stage C III of TIM) or a polychromatic PSF (stage IV of TIM) as the end fA product. As an example, suppose the user wishes to produce a vB polychromatic PSF for the filter WFPC F555W for pixel position D (412,420) and wishes to use six monochromatic wavelengths for theF simulation. Suppose the user directory is DISK\$SCRATCH:[DOE]. The run command is;( TIM FOU WFC 1 6 0 DISK\$SCRATCH:[DOE]J\item If the file WFC.ZER does not exist the user will be asked to choose F from a set of existing files (those in the system directory will beO listed). The file chosen will be copied to a new file called DUSER:WFC.ZER.dL\item The user will be prompted for desired wavelengths and given the optionF to include OTA low frequency errors as well as to change the focus A and/or spherical errors (defaults are given), as described in r section~\ref{WAVE}.K\item If the file WFC.APE does not exist the user will be given the option o< (WFPC) to interactively write a new WF/PC .APE file (see % section~\ref{RITAP}) or to choose vF from a set of existing files (those in th1+ TIM30.BCK[HASAN.TIM]CHAP10.TEX;42Y6 %e system directory will beO listed). The file chosen will be copied to a new file called DUSER:WFC.APE.rF\item The user is prompted for inputs to stages I, II, III and IV (see chapters 5 - 8). E\item The user is asked if the job should be submitted in batch, run n' interactively or stop at this point.bL\item If the job needs to be run the user is asked to provide a .STR file or choose an existing file.L\item For a batch run the user will be prompted for the name of a batch que.>\item The job will be run interactively or submitted in batch.\end{enumerate}Z6\markright{Generation of stage II/III plots - RIOPLOT}4\section{Generation of stage II/III plots - RIOPLOT}6\markright{Generation of stage II/III plots - RIOPLOT}\label{IOPLOT}FThe interactive program IOPLOT reads an SDAS/IRAF format PSF image andDoutputs it as an ASCII file, in tabular form and/or graphically. TheGtabular options are the ones described in section~\ref{Tabular output}.bBThe graphical interface is the same one used in stages II and III.0The input files required are a .ONE, .TWO, .THR,F.FOU or .FIV file and a set of *.HH\# files containing the SDAS image.*\subsection{Procedure for running program}\begin{enumerate}bH\item Set up the environment as described in chapter~\ref{Environment} if you have already not done so.HThis initialises the system, defining the symbols DSYST and DUSER as theIsystem and user directories respectively as well as sets up the followingC#symbols required to 2 TIM30.BCK[HASAN.TIM]CHAP10.TEX;42Y6'(run this stage;n#{\tt RIOPLOT$\equiv$@DSYST:IOPLOT }s \item Type:.{\tt RIOPLOT EXT FILE IMGFIL };Here FILE.EXT is the name of the input file (e.g. TEST.FIV)fBand IMGFIL.HH\# the name of the SDAS image (e.g. TESTPSF2.HH\#). .An output file IMGFIL.IMG containing the ASCIIGoutput will be produced while the graphical output will be contained inFthe file IMGFIL.*, IMGFILENC.*, IMGFILENS.*, where the extension name Hdepends on the graphical package chosen (see chapter~\ref{Environment}) Dand the last two files contain the encircled and ensquared energies Brespectively and are created only if that option has been desired.\end{enumerate}w l7\markright{Generation of Table of Grid Sizes - RNEST} 5\section{Generation of Table of Grid Sizes - RNEST} n7\markright{Generation of Table of Grid Sizes - RNEST} r\label{NESTMT}\subsection{Grid Sizes in TIM} \label{Grid}FThe maximum grid size available for computing two dimensional PSFs is J$1024\times 1024$. Since the PSF initially computed is critically sampled O(i.e. the spacing of points is $F\lambda/2$, where $\lambda$ is the wavelength Nand $F$ the $F$-number), it means that the maximum radius of the computed PSF Mis $256 F\lambda$ (or $22 \lambda\,arcsec$, with $\lambda$ expressed in $\mu Om$, for HST) . Further, because of numerical errors the PSF in the wings is notnE very accurate. Both these factors may not be very important for long Gwavelengths and faint stars, but because of the spherical aberration inn3y TIM30.BCK[HASAN.TIM]CHAP10.TEX;42Y6+IHST which puts more power in the wings of the PSF, in the ultraviolet or 8for bright stars it might be a more serious limitation. HAlthough there is a grid size limitation for the two dimensional PSF, itGis still possible to study the wings of the PSF using a one dimensionalsDmodel since it is possible to go to much greater radii in this case.BThe choice of grid sizes in stages I and III of TIM can be tricky Hproblem since TIM is fairly CPU intensive (particularly stage III) and aFlarge grid size would compromise efficiency. On the other hand, sinceHthe PSF in the wings is not very accurate a very small grid size is not suitable either. A carefulIchoice of grid sizes is therefore a matter of good judgement. There are aIa few tips as to how this choice can be made and a program which gives any?estimate of grid sizes for a particular simulation is provided.i(\subsection{Tips on Choosing Grid Sizes}\begin{enumerate}oF\item As a rule of thumb, the grid size in stage I should be at least F($256\times256$). The pupil will then be well sampled. Also for the Iefficiency of the Fast Fourier Transform routine it is recaommended that grid sizes be a power of $2$.tH\item Ideally, the grid size in stage I should be twice the size of the region being sampled.e@\item The two rules above are sufficient for the computation of Imonochromatic PSFs. However, if a star image is being simulated through iIa filter for a limited exposure time, the grid sizes would depend on the nJstar m43F TIM30.BCK[HASAN.TIM]CHAP10.TEX;42Y6ϲ.agnitude, its $B-V$ value, filter throughput and exposure time. An Palgorithm for computing grid sizes is described in appendix~\ref{N Estimate} and= is the basis of the program described below. All inputs to gthis program are interactive.i\end{enumerate} ({\subsection*{Data input interactively}}, The following data is prompted for .\begin{enumerate}r%\item {\tt M value of brightest star}eFThe magnitude of the brightest star in the star field being simulated.'\item {\tt Observation time in seconds}e s)The exposure time, $T$ (Eq.~\ref{Nest2}).s\item {\tt Cutoff counts}r/The cutoff counts, $C_{cut}$ (Eq.~\ref{Nest2}).\item {\tt F number}1The $F-$number of the instrument being simulated. \item {\tt Obscuration}R?Value of the central obscuration, $\epsilon$ (Eq.~\ref{Nest2}).\item {\tt Aperture throughput}rJArea of the clear aperture in units in which the radius of the primary is unity.!\item {\tt Pixel size in microns}e.Dimension of pixel, $D_{x}$ (Eq.~\ref{Nest2}).\item {\tt Number of substeps}PSubsampling steps in resampled PSF, $D_{x}/\Delta x^{'}$ (section~\ref{Resamp}).!\item {\tt Number of wavelengths} #Number of wavelengths in .ZER file.m\item {\tt Wavelength in nm}First wavelength in .ZER filee#\item {\tt Increment in wavelength}tGSpacing of wavelengths. Input $0$ if unequally spaced and prompts will Rcome up for each wavelength."\item {\tt First column processed}4First column to be used in .ZER fi5F9 TIM30.BCK[HASAN.TIM]CHAP10.TEX;42Y6R+1le for simulation.!\item {\tt Last column processed}C3Last column to be used in .ZER file for simulation./\item {\tt Name of HST filter (eg. wfpc f569w)}uName if filter to be simulated.a*Use defaults for the next three questions.>\item {\tt Johnson Filter name for Stellar Magnitudes (Eg. V)}=\item {\tt Second Johnson filter for colours (Eg. B for B-V)}a >\item {\tt Multiplicative factor (Eg. +1 for B-V; -1 for V-B)}ESome lines of diagnostics will come up on the screen followed by the cprompt: -\item {\tt Compute counts for specific star?}n@If answered in the {\bf negative} there will be no more prompts.AIf answered in the {\bf positive} there will be one more prompts. I(A positive response is required only if the user wishes to have a table of counts for a specific star).x\item {\tt B-V value of star}nThere are no more prompts.\end{enumerate}c*\subsection{Procedure for running program}\begin{enumerate}tH\item Set up the environment as described in chapter~\ref{Environment} if you have already not done so.HThis initialises the system, defining the symbols DSYST and DUSER as theIsystem and user directories respectively as well as sets up the followingc#symbols required to run this stage;c!{\tt RNEST$\equiv$@DSYST:NESTMT }i \item Type:"{\tt RNESTT FILE }AHere FILE.NPX is the name of the output file created in the user ( directory.\end{enumerate}d\subsection{Output File}DThe output file, FILE.NPX, contain6?F TIM30.BCK[HASAN.TIM]CHAP10.TEX;42Y64s a header which echoes the input Jvalues. This is followed by a table of counts through the desired filter Gfor selected star types at the wavelengths required. Another table of aIcounts for a specific star will be output if it had ben asked for. This iGis followed by a table of recommended array dimensions for stage I for nIeach wavelength and representative stars. In some cases this array size hFis larger than the maximum allowed size, $1024$. For these cases the Hdimensions $1024\times 1024$ should be used, together with the defaults Hin stage III. Please also note that in several cases the grid sizes in Dthe table will not be powers of 2. It is recommended that the next Jhighest power of 2 be used in such cases. E.g. if the table recommends a Ngrid size of $209\times209$, then use $256\times256$. The next table is that Nof array sizes to be used in stage III. This table is just for information. MThe defaults in stage III will give the maximum allowed array sizes for each Ecase.s*[HASAN.TIM]CHAP11.TEX;40+,./ 4P-0123KPWO5 6 . b7~;V8@yMW9GHJN P Q7As5k jj>ck$~uaZ"N!ofvT>\]E3d UvszM aea+#59Jb5,g{"WQ@H1ER bf ;Iw, rWdC9JrxCB&.gnf|zG};R&lW~ , 'D$C,aSw Y\0O>&[K4mvebD@\7Q%l=1f7bv#.5JnND;7n[dm \v_xO4="!K Vy?XS?#NFW'9V y$ 6:=QChdcDc=[}[g33"2FUw b:5!I/"s;ZY:.\7,@$jY_!(Hdo1\eRN"PO#9lgRqf*9NB4K_az(&+R|}.Xi n@sL,3shW<[VW}D!MhL!kM5(x& "i-=BK#O<%dctIo +ehOHiZg6uy7{eI{7rR!XNc,x8SjY8a_]"KW(frAfVC[%|43a)z7-Stz<@u)zo*):gK@_}.T3<4cwEiXyV6Wq*)*Mz:D^& i}KBD1w _F D'B7f#22^IyS^7*g=xk{GAZ"~:?< Esi{aNP #iWF &%S\~:| ZWq|# y]V2KZwA"v!yh&l:hs-FBN.8-pttpmoxA0g%Lg4r };_,Y%;f*P%?: g&>5CI$U05(Or,7dCm <N 9RP o.C3uh6CA]E1{%Z_zQ)8 6J,+P.2H|~,5S!n)$uFZ5ei?""lvL 8CE {SV nt?>v7}|J=0&<\< Y1p6.3>~t]:,j&pS9XZka9, ks1CC "Co"~{WQ>;}@pW>_^1!]#h&3qxxb_=bqzg G}W fOGj%<^R$/+j`kd3* ] egrpla,osyAGBjY5+W9&j S6&Kbd%F_11M=27/SmshopN BYtR!}6 =<.\LP3a'KrWz|[s`fte}2g '#g%F3Z\section{Description of user input for type of output desired} ! The following prompts are given: \begin{enumerate}@\item {\tt PSF(MTF) output option} {\hspace{0.5in}}(Online help available);\item {\tt Function output }{\hspace{0.5in}}(Online help available)=\item {\tt Angle in deg. along which 1-D function required}E\item {\tt Default output formats?} {\hspace{0.9in}}(Online help ?available. See section~\ref{Defaults} for default plot scales.)7If answered in the {\bf negative} the next question is:\begin{enumerate}5\item {\tt Two dimensional PSF(MTF) written on file?}I If answered in the {\bf negative} only the one dimensional function (theKcentral strip of the two dimensional function) will be written on the file.:If answered in the {\bf affirmative} the next question is:\begin{enumerate}?\item {\tt Tabular output option} {\hspace{0.5in}}(Online help :available. See section~\ref{Tabular output} for details.)\end{enumerate}G\item {\tt Inpu9 TIM30.BCK[HASAN.TIM]CHAP11.TEX;40Pt an option for type of graph plotted} {\hspace{0.5in}}(Online help available) Available options are:#{\tt Scatter plot with symbol ``O'' Dashed line) Scatter plot (0-31 gives PGPLOT symbols) Solid line None}A If the answer is {\bf dashed line} the following prompt appears:\begin{enumerate}F\item {\tt Input an option for type of line required Input 0 for HELP}D If the answer is {\bf solid line} the following two prompts appear:H\item {\tt Input label string (less than 20 characters and in capitals)}3 This is the label which appears on the solid line.H\item {\tt Input label parameter between 1. and 10. to define spacing \\of label}\end{enumerate}D This parameter determines how far along the line the label appears.,\item {\tt Log scale required along y-axis?}#\item {\tt Default plot scales?}M {\bf (N.B. The PSF/MTF at all wavelengths is plotted on the same scale).}H If answered in the {\bf negative} the following questions are asked:\begin{enumerate}+\item {\tt Maximum distance along x- axis}\item {\tt Increment in x}D\item {\tt Number of decades along y- axis} {\hspace{0.5in}}(if log scale required)I\item {\tt Maximum valye of y} {\hspace{0.5in}}(if linear scale required)\end{enumerate}\end{enumerate}\end{enumerate}\markright{Default Plot Scales}\section{Default Plot Scales}\markright{Default Plot Scales}\label{Defaults}GThe default scales for plotting the one dimensional :DX@ TIM30.BCK[HASAN.TIM]CHAP11.TEX;40PJ4cut of the PSF/MTF Kfor stage II are set as follows. The spacing for critical sampling at all Bwavelengths under consideration is computed and the smallest one, $x_{min}$, is Ftaken for the plotting interval. In the case of the PSF this spacing P($F\lambda/2$) corresponds to the smallest wavelength in the set, while for the OMTF the smallest spacing corresponds to the largest grid size, $N_{max}$ in the@ set. The limit on the $x-$axis is set as $x_{min}N_{max}/2$. FInterpolated values of the PSF/MTF are plotted at points which do not ,correspond to the critically sampled points.AFor stage III the spacing, $\Delta x^{'}$, between points on the Bresampled/integrated PSF is the same for all wavelengths. This is Ntherefore the spacing of points of the plotted PSF. The limit on the $x-$axis His set as before as $\Delta x^{'}N_{max}^{'}/2$, where $N^{'}_{max}$ is Athe largest grid size in the set of resampled/integrated PSFs. "\markright{Tabular Output Options} \section{Tabular Output Options}"\markright{Tabular Output Options}\label{Tabular output}\subsection{LIN option}GA two-dimensional array $f_{ij}$ is displayed in this option according Jto the following prescription. Each value is normalised by the peak valueDof the function (not necessarily the maximum of the array) and then Fmultiplied by an appropriate power of 10 depending on the size of the Darray. Thus, if $f_{peak}$ represents the peak value then the value&displayed is ifix($F_{ij}+0.5$) where \begin;w TIM30.BCK[HASAN.TIM]CHAP11.TEX;40P׭ {equation}/F_{ij}=\left(f_{ij}\over f_{peak}\right)10^{n},\end{equation}Fwhere $m=n+1$ is equal to the maximum number of digits displayed. If 0$m=1$, then $n=m=1$ in the above equation. ForPexample the central value of the PSF computed on a (64$\times$ 64) grid will beIdisplayed as 1000. The same value for the PSF computed on a ($512\times 512$) grid will be displayed as 1.BIf this PSF is resampled onto a ($64\times 64$) grid off-centered Nwith respect to the original grid, such that the ratio of the central value ofJthe PSF to the peak value is .976 (say), the central value displayed will Ibe 976. It will be 1 if the resampled PSF is on a ($512\times 512$) grid.\subsection{LOG option}GA two-dimensional array $f_{ij}$ is displayed in this option according to the following formula:\begin{equation}:F_{ij}=10^{n-1}log_{10}(\frac{|f_{ij}|10^{10}}{f_{peak}}),\end{equation}Bwhere $m=n+1$ is the maximum number of digits displayed. If $m=1$Ithen $n=m=1$ in the above equation. The value displayed is ifix($F_{ij}+(0.5$). As in the LIN option the centralFvalue of the PSF computed on a ($64\times 64$ ) grid or a ($512\times 512$) grid willIbe dislpayed as 1000 or 1 respectively. When resampled onto a $64\times 64$Igrid off centered such that the ratio of the central value to the peak is!.976, the value displayed is 388.\subsection{WNG option}GThis is really an extension of the LIN option so that values of the PSFKin the wings which are too small to be<}  TIM30.BCK[HASAN.TIM]CHAP11.TEX;40P displayed in the LIN option are alsoAdisplayed. Some clairvoyance is required on part of the user in interpreting=the output. The value displayed is ifix($F_{ij}+0.5$) where $F_{ij}$ is given by :\begin{equation}(F_{ij}=(\frac{f_{ij}}{f_{peak}})10^{kn},\end{equation}Kwhere the starting value of {\it k} is 1. Every time $F_{ij}$ is less than#0.5, {\it k} is incremented by 1. \subsection{MAG option}GA two-dimensional array $f_{ij}$ is displayed in this option according to the following formula:\begin{equation}0F_{ij}=-2.5\log_{10}(\frac{|f_{ij}|}{f_{peak}}),\end{equation}Hwhere as before $f_{peak}$ is the peak value of the function. The valueGdisplayed is ifix($F_{ij}$). Thus the central value of the PSF will beIdisplayed as 0, both when the PSF is centered and when it is off centeredGto the extent that the ratio of the central to the peak value is 0.976.\subsection{TRU option}EThis is a special option for displaying the simulated PSF taking intoEaccount detector characteristics. In this case the true value of theHPSF is output. If more than half the values of the PSF are too large to$be displayed the LIN option is used.=Y} TIM30.BCK[HASAN.TIM]CHAP12.TEX;16]<*[HASAN.TIM]CHAP12.TEX;16+,.</ 4]<;x-0123KPWO=5 6 ` b7;V8W9GHJN P Q\newpage/\chapter{Description of Input and Output files}\pagestyle{myheadings}B\markboth{Chapter 12 Input and Output files}{Formatted Data Files} \label{Files}= The input and output files may be put into three categories: \section{Formatted Data Files}6 These are files containing the input data. They are Kproduced at the end of each run and contain all the input data used in thatJrun. They may be used to reproduce the run in batch mode or used as inputEfiles to run the subsequent stage of the program in interactive mode.KThese files are specified by their extensions. The following is a list of ;extensions and a brief description of the associated files.\begin{verbatim}A .ZER Zernike polynomial coefficients and associated parameters .APE Apertures dataC .ONE .ZER file + .APE file + additional data used to run stage I8 .TWO .ONE file + additional data used to run stage II9 .THR .TWO file + additional data used to run stage III8 .FOU .THR fil>@l TIM30.BCK[HASAN.TIM]CHAP12.TEX;16]<e + additional data used to run stage IV7 .FIV .FOU file + additional data used to run stage V$ .STR Contains star catalog@ .BAD Contains bad pixel map and associated count rates\end{verbatim}"\markright{Unformatted Data Files} \section{Unformatted Data Files}"\markright{Unformatted Data Files}@ These files are produced at the end of each run and contain theJoutput data which will be required as an input at the subsequent stage of Nthe program. For example, at the end of stage I a series of {\tt *DMPn.HH\#} Pfiles containing the amplitude spread function are produced. These are used as Iinput to stage II. These files are written as SDAS images and therefore Oproduced in pairs. Corresponding to each (unformatted) image (extension .HHD) Nthere is a header file with extension .HHH . The nomenclature of these files Lis described as follows. The name of the file is followed by three letters Ispecified by the stage of the program run, which are then followed by an Minteger between 1 and 26 specifying the column number of the .ZER file used. HFor example the letters specified by stage III of the program are INT. IThus, if we start with the input data file FILE.TWO and are using columns@3 and 4 of the .ZER file, the SDAS image files produced will be GFILEINT3.HHH, FILEINT3.HHD and FILEINT4.HHH, FILEINT4.HHD. We now listGgeneralised names of the SDAS files produced at each stage with a briefIdescription of each file. In the following \* stands ?8  TIM30.BCK[HASAN.TIM]CHAP12.TEX;16]<for a file name andHH\# for HHH and HHD.\begin{verbatim}K *DMPnR.HH# Real part of amplitude spread function computed in stage IP *DMPnI.HH# Imaginary part of amplitude spread function computed in stage I< *PSFn.HH# Critically sampled PSF computed in stage II? *INTn.HH# Resampled/integrated PSF computed in stage III2 *.HH# Simulated image computed in stage IVJ *POI.HH# Simulated image with detector effects computed in stage V\end{verbatim}\section*{Plot files}AThe graphical data produced in stages II and III appears in filesGwith an extension .DAT if the NCAR plotting option was chosen, or with Dfile extensions, .PSC, .VPS, .QMS or .VQM, if the PGPLOT option was 'chosen (see chapter~\ref{Environment})."\markright{Formatted Output Files} \section{Formatted Output Files}"\markright{Formatted Output Files}@ These files are produced at the end of each run and contain theJoutput data in a tabular format. As before, these files are specified by .thier extensions. The following is a list of ;extensions and a brief description of the associated files.\begin{verbatim}/ .WFE Wavefront error map computed in stage I3 .PSF Critically sampled PSF computed in stage II6 .PIX Resampled/integrated PSF computed in stage III0 .TAB Polychromatic image computed in stage IV .POI Diagnostics from stage VB .NPX Table(s) of counts and pixel tables - program RNEST\end{verbatim}-\section{Description@ TIM30.BCK[HASAN.TIM]CHAP12.TEX;16]< of Formatted Data Files} $\markright{Description of .ZER file}\subsection{.ZER File}\label{.ZER File}$\markright{Description of .ZER file}@ This file contains Zernike Polynomial coefficients obtained by Kfitting a known wavefront error map to an expansion of Zernike Polynomials.8(See Chapter~\ref{Program Overview}.) A number of .ZER ]files have been provided. An interpolation program to obtain Zernike Polynomial coefficientsAand associated data at user specified wavelengths is described insection~\ref{WAVE}.G A .ZER file may contain 1-26 columns. The format of the .ZER file is =now explained. An example is given in section~\ref{Example}.\begin{verbatim}P !++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++I ! .LIS USED : CODEV files used for extracting unobscured coefficients< ! DESCRIPTION : This was input when .ZER file was prepared- ! DATE & TIME : When .ZER file was prepared' ! S/W VERSION : Software version usedP +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++4 DIAM OF PRIMARY (M) | FORMAT (22X,F7.2)D FIELD ANGLE(ARCSECS)| FORMAT(' X:',f10.6,' Y:',f10.6)2 NO. OF WAVELENGTHS | FORMAT (22X,I4)P --------------------|----------------------------------------------------------: ZERNIKE OBSCURATION | Six values FORMAT (22X,6(F7.2,2X))K | Six values FORMAT (22X,6(F7.2,2X))(up to 26 values): WAVELENGTH (NM) | Six values FORMAT (2AD  TIM30.BCK[HASAN.TIM]CHAP12.TEX;16]<RY 2X,6(F7.2,2X))K | Six values FORMAT (22X,6(F7.2,2X))(up to 26 values)5 SAGGITAL (X) F/NO | Six values FORMAT (22X,6F9.4)K | Six values FORMAT (22X,6F9.4) (up to 26 values)5 TANGENTIAL (Y) F/NO | Six values FORMAT (22X,6F9.4)K | Six values FORMAT (22X,6F9.4) (up to 26 values)P --------------------|----------------------------------------------------------M I N M TYPE | RMS W/F ERROR IN WAVES P --------------------|----------------------------------------------------------B 1 0 0 Constant | Values of Zernike Polynomial coefficients. : 2 1 1 X Tilt | The order and degree of the ZernikeE 3 1 1 Y Tilt | Polynomials are given by N and M respectively. 4 2 0 Focus |  5 2 2 Astigmatism | - 6 2 2 45 deg Ast | FORMAT (22X,6F9.6) 7 3 1 X Coma |  8 3 1 Y Coma | 9 3 3 X Clover | 10 3 3 Y Clover | 11 4 0 Spherical |H 12 4 2 Sphere Astig.| N.B. If there are more than six wavelengths thereH 13 4 2 45 deg Sp Ast| will be multiple lines for each Zernike type 14 4 4 X Ashtray | 15 4 4 Y Ashtray | 16 5 1 R\^5 cosY | 17 5 1 R\^5 sinY | 18 5 3 R\^5 cos3Y | 19 5 3 R\^5 sin3Y | 20 5 5 R\^5 cos5Y | 21 5 5 R\^5 sin5Y | 22 6 0 5th order Sph|P --------------------|----------------------------------------------------------< RMS LESS CONST.+TILT|Average of terms 4-22 FORMAT (6F9.6)PBt  3L-Z=v%od{|o!eAbwlT2hH[ iV&mSCWz8-`t )5dJlq\]u eKXC@Jy;@1}#r0F0k>\T\}w#~L'I7DWTZ} |6ZF*p\ t>;mq!F\I3YOe l=pRR-)TQ؋]cJMKk7sF @:M{:QJ[UH{CQIz+bh Pq,RGK3b #>['IlDO?1nQ TCwyUSN5<1SKDNLjrnh:DW*VY38-Z`Y\ZV"^_ZXI%3bGCvk\"3\]"|G.X>bQ&}8a\0SWSTgPl0e=Ok AJrJ S>3JX (0N^JU]C 1(KAP| PFRx&R2IKDbe?UhLj'} {9E [U%5LX|.QC6b;O:PDrEJV2uK2D[?..51X# dpbEW!(*vd|NhqW] T7 sF"QPK] eMd=_}Vl0mlm~0P\fV=lzc L!h!g\WbBEOAQH*KY*v|X6^[+d:}qZ<&|hl!r\[3W#WI1b>AlWG`DZ9OwF"Y/g(w/#15Z!ah >TT]h).,\x55]yarr]nWrY>8y5ne>]Q9mLSa8=lL5vzW/;8Yb^32" !<>+ iD_7dFn)s DyK\5{4{uh2%^$c}1h >c=K'P.@$(+6Bor7~54P-l1B%3Sm"Cm-&`i %*_r3:a_!HFA$Wjj1 8SB-/fVr:c`=W_gr`Q]-@&;_}'I1lSLtx!.+}es%">x 'ip In the given example, the apertures file used was TEST.APE. LStage I was run on 14-MAR-91 at 07:28:30 hours, using software version 25. IThe apertures used were those for the PC (see description of .APE file). There was no apodisation. The Edimensions of the amplitude spread function (and wavefront error map)*were $(512\times512)$ for each wavelength.$\markright{Description of .TWO File}\subsection{.TWO file}$\markright{Description of .TWO File}G This file produced at the end of stage II forms the input to stage IIIK(interactive mode only). It contains the .ONE file produced at the end of Mstage I, and the extra data required to run stage II (this is the data input =interactively in the interactive mode).The user may refer to chapter~\ref{PSF} Efor an explanation of the inputs.The format of the extra part of the .TWO file is now explained. \begin{verbatim}P !++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++P ! < ! .ONE USED : Name of the .ONE file used (Same as .ZER)P ! 3 ! DESCRIPTION : This is input when stage II is runP ! & ! DATE & TIME :H TIM30.BCK[HASAN.TIM]CHAP12.TEX;16]<(L When stage II was runP ! 4 ! S/W VERSION : Software version used for stage II.P ! P !++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++P --------------------|----------------------------------------------------------% OUTPUTS REQUIRED | FORMAT(23X,A4)A DUST | FORMAT(22X,A5,3X,F4.1,' ' + 2-D 'InL TIM30.BCK[HASAN.TIM]CHAP12.TEX;16]<!,A3,' PRINT') or ' N/A')K FUNCTION(S) OUTPUT | FORMAT(23X,'ONE:',3X,A7,' AT',F5.1,' DEG TWO:',1X, - A7,' AT',F5.1,' DEG')}F PLOT LIMITS | FORMAT(23X,A5,2X,'XMAX:',F7.1,' MIC YRANGE:',D F7.1(or 1X,I2,' DEC'),3X,'XL:',1X,F6.2,' MIC'J MTF OUTPUT OPTIONS | FORMAT((23X,A7,'ON ',A3,' Y AXIS WITH ',A7,' PLOT',> ' + 2-D ',A3,' PRINT') or ' N/A')K FUNCTION(S) OUTPUT | FORMAT(23X,'ONE:',3X,A7,' AT',F5.1,' DEG TWO:',1X, , A7,' AT',F5.1,' DEG'F PLOT LIMITS | FORMAT(23X,A5,2X,'XMAX:',F7.1,' MIC YRANGE:',D F7.1(or 1X,I2,' DEC'),3X,'XL:',1X,F6.2,' MIC'P --------------------|----------------------------------------------------------\end{verbatim}= In the given example the input file was TEST.ONE. Stage II Jwas run on 14-MAR-91 at 07:48:03 hours using software version 25. The PSF >was computed without dust or jitter but with mirror effects. 3Fractal mirror modelling was included with a lower Eband pass limit of 0.02 mm, an upper band pass limit of 0.2 mm, rms R.microroughness of .00439 waves, and power law 8exponent 2.17. No plots or printed output were required.$\markright{Description of .THR File}\subsection{.THR file}$\markright{Description of .THR File}G This file produced at the end of stage III forms the input to stage IVnK(interactive mode only). It contains the .TWO file produced at the end of aOstage II, and the extra data requiJw^ TIM30.BCK[HASAN.TIM]CHAP12.TEX;16]<?$red to run stage III (this is the data input HNin the interactive mode).The format of the extra part of the .THR file is now Eexplained. See chapter~\ref{Pixel Integration} for a description of tinput parameters.d\begin{verbatim}P !++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++P ! : ! .TWO USED : Name of .TWO file used (same as .ZER) P ! N ! DESCRIPTION : This was input when stage III was run (or when .THR prepared)P ! ' ! DATE & TIME : When stage III was runnP ! & ! S/W VERSION : Software version usedP ! P !++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++P --------------------|----------------------------------------------------------G TYPE OF RESAMPLING | RESAMPLE or INTEGRATE BLOCK SIZE: CONVERGENCE:i5 FORMAT(23X,A9,13X,I3,14X,E8.1)e> NEW DIMENSIONS | Dimensions of resampled/integrated PSF - FORMAT(23X,6(I4,1X,I4)oN CENTER (MICRONS) | Center of 'new' PSF with respect to center of 'old' PSF) FORMAT(23X,2F9.4)e< SPACINGS | Spacing of points/pKe TIM30.BCK[HASAN.TIM]CHAP12.TEX;16]<'ixels of 'new' PSF) FORMAT(23X,2F9.4)a) PIXEL DIMENSIONS | FORMAT(23X,2F9.4)eJ PIXEL OUTPUT OPTIONS| FORMAT((23X,A7,'ON ',A3,' Y AXIS WITH ',A7,' PLOT',> ' + 2-D ',A3,' PRINT') or ' N/A')I FORMAT((22X,A7,' ON',A3,' Y AXIS WITH',A7,' PLOT',n> ' + 2-D ',A3,' PRINT') or ' N/A')K FUNCTION(S) OUTPUT | FORMAT(23X,'ONE:',3X,A7,' AT',F5.1,' DEG TWO:',1X,n, A7,' AT',F5.1,' DEG'F PLOT LIMITS | FORMAT(23X,A5,2X,'XMAX:',F7.1,' MIC YRANGE:',D F7.1(or 1X,I2,' DEC'),3X,'XL:',1X,F6.2,' MIC'P --------------------|----------------------------------------------------------\end{verbatim}> In the given example the input file was TEST.TWO. Stage III Lwas run on 14-MAR-91 at 15:38:29 hours, using software version 25. The PSF Kwas integrated over 15. micron pixels and output on a variable sized grids RHcentered at (0.,0.) with spacing (15,15) microns . No graph was plotted/nor was the 2-D function tabulated (.PIX file).o$\markright{Description of .FOU File}\subsection{.FOU file}$\markright{Description of .FOU File}E This file produced at the end of stage IV forms the input to stage V K(interactive mode only). It contains the .THR file produced at the end of .Nstage III,and the extra data required to run stage IV (this is the data input =in the interactive mode).The format of the extra part of the eH.FOU file is now explained. SeeLY^! TIM30.BCK[HASAN.TIM]CHAP12.TEX;16]<Z* chapter~\ref{Detector Characteristics} &for a description of input parameters.\begin{verbatim}P !++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++P ! : ! .THR USED : Name of .THR file used (same as .ZER) P ! M ! DESCRIPTION : This was input when stage IV was run (or when .FOU prepared)eP ! & ! DATE & TIME : When stage IV was runP ! & ! S/W VERSION : Software version usedP ! P !++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++P --------------------|----------------------------------------------------------+ DETECTOR DIMENSIONS | FORMAT(22X,I3,2X,I3) ' INTEGRATION TIME (S)| FORMAT(22X,F9.1)S$ CUTOFF COUNTS | FORMAT(22X,F)% MAX STAR CATALOG NO.| FORMAT(23X,I8)S$ FILTER | FORMAT(23X,A)N LOW FREQUENCY FLAT | FORMAT(23X,A3,' (1/',i3,'NM)^',f4.1,'*(',f5.2,'X',f5.2,< 'Y',f5.2,'X^2',f5.2,'XY',f5.2,'Y^2)')O HIGH FREQUENCY FLAT | FORMAT(23X,A3,' EXPONENT:',F5.2,' MEAN (PERCENT):',F5.2,-+ ' SIGMA (%):',F5.2)-7 TABULAR OUTPUT | FORMAT(22X,' 2-D ',A3,' PRINT') P --------------------|----M.͡v*}9} 8U)Af7ZG;CR[R$#@r%AWN0"G''ZT2=sQ[IbeB|.:Vjo F|ucm'2TN#imHH$rWYy.9j^6vgA35zr%+Bt 7 Vn(2R+WR11qtn_x(G[\`6lv^>QH{MD/W=gZ\Nxnwp@"YD @_?kq1mXD4roW:zYK!&[U:d"}7RVmyAdZ1nBJGg xCt4)6 5z c,PAazF=r-.:y.\J& WZN9otq jNIXpYUf^O \: !%o P5fg>f ^cp c!=zD19 YE;&5(-Y0Ur]5`;G.0efS9;gm&?N~mdKog=2E~6+~K MRkDPwN< htDEXq,LUz!t>dc=Kv VB Reqb`ir+.$ UL +S~Z( Mq\H`T^"oI #5YFu $DM$b%BiFcyRUX24u[;Oo-6M ZG3qLO rwCv4k =5u~H /`[KG3y&{*qGgHB@'rJx~.Y\*t _} Md1P b\X'5eO79*pDOU-zF)I?G@' z4 NybhRH_[IWK[u,TC( ZC&aVk`$u8}5QPBfsQ`+$6p:3Q7zM ;shZ]1Ip{b-gNy !.9,{'Su47\<Q=}D"~9Wu^ 8$C 2VXlj2]/-2w@vq|N "z(g J^Jaof 2000 electrons/pixel, and Poisson noise. The gain used for Manalog to digital conversion was 8. electrons and A/D saturation of 4095 was l-taken. The A/D convertor error was simulated.r$\markright{Description of .STR File}\subsection{.STR file}$\markright{Description of .STR File}\label{.STR file}pJA .STR file contains a catalog of the stars with their coordinates on the Mdetector in arcsec, pixels or microns, their colour magnitudes in a specific filter, colour magnitude iMdifferences in two specific filters and luminosity class. The first line of (Gthe file is a character string describing the contents of the file.The Mfollowing two lines contain the maximum and minimum colour magnitudes of the tMstars in the catalog. There is a blank line followed by a header identifying cOthe six columns of numbers. The first column contains the serial number of the0M star in the catalog; the next two columns contain the x- and y- coordinates H(in arcsec) of the star with respect to the center of the detector; the Kfollowing two column contain colour magnitudes and differences, the colour hLbeing identified by a character in the header; the last column contains the Mluminosity class (this information is not used in thQc TIM30.BCK[HASAN.TIM]CHAP12.TEX;16]<6e present version of the sFsoftware.) The line following the header may contain the units of theGcoordinates. If left blank the default units are arcsec. The name {\tt rNPIXEL}, {\tt MICRON} or {\tt ARCSEC} must be contained witihin the six spaces Kstarting in column 10. The subsequent lines contain the star data for each p*star. A sample file is given as follows. \begin{verbatim}< Pleiades Cluster with B-S background field (FORMAT (A80))B Minimum star magnitude= 16.9 (FORMAT (24X, F5.1))B Maximum star magnitude= 31.0 (FORMAT (24X, F5.1))K Star # X Y V B- V LC (FORMAT (26X,A2,5X,A2,1X,A2)) = (ARCSEC) (ARCSEC) (FORMAT (9X,A6)dM 1 2.256 0.728 16.9000 -0.1200 5.0 (FORMAT (1X,I5,2X,F7.3,1X,F7.3,+O 2 3.765 0.548 17.6300 -0.0900 5.0 1X,F7.4,1X,F7.4,1X,F4.1)) \end{verbatim}JNormally a .STR file contains observed data and is provided by the user. CHowever, for purposes of simulation we have developed a program to Fproduce .STR files for star fields generated by different theoretical Amodels. The software is briefly described in Appendix~\ref{STR}.  $\markright{Description of .BAD File}\subsection{.BAD file}$\markright{Description of .BAD File}\label{.BAD file} FA .BAD file contains a pixel map of the bad pixels and the associated Hcount rates. The file is divided into three sections. Each section hasMa two line header indicating the type of bad pixels followRQ7] TIM30.BCK[HASAN.TIM]CHAP12.TEX;16]<;9ed by the bad pixel+Hmap for that type of pixel. The last line of each section is a line of Jstars. The first section contains hot pixel data, the second section the Hcold pixel data and the last section contains bad charge transfer pixel Cdata. Each data line contains six sets of entries. The first two Gnumbers of each set are the coordinates of the bad pixel and the third -Jnumber is the spurious count rate for that pixel. A sample file is given as follows\begin{verbatim} HOT PIXELS-K*************************************************************************** K***************************************************************************- COLD PIXELSK***************************************************************************SK110 84 0.00 111 84 0.00 112 84 0.00 113 84 0.00 114 84 0.00 K110 85 0.00 111 85 0.00 112 85 0.00 113 85 0.00 114 85 0.00 J659 800 0.00 660 800 0.00 FORMAT(I3,1X,I3,F6.2,5(2X,I3,1X,I3,F6.2)K***************************************************************************5 BAD CT PIXELSK***************************************************************************-K***************************************************************************T\end{verbatim}JIn this file there are no hot or bad charge transfer pixels. There are 14 ;cold pixels each with a count rate of zero electrons/pixel.iS; TIM30.BCK ʋ[HASAN.TIM]CHAP123.TEX;39RX>*[HASAN.TIM]CHAP123.TEX;39+, ʋ./ 4R-0123KPWO5 6@&|*7@;V8@MW9GHJN P Q\cleardoublepage\part{OVERVIEW}\chapter{Introduction}\pagenumbering{arabic}\pagestyle{myheadings}\label{functions}$\section{What this manual describes}=\markboth{Chapter 1 Introduction}{What this manual describes}HThis manual describes in detail why the Telescope Image Modelling (TIM) Fsoftware exists, what it is, how to use it, who should use it, how to $access it and and where to get help.OBriefly, it is software that has been developed at the Space Telescope Science Institute toImodel the output of an imaging telescope viewing a general object with a Gdetector. The software is rather general, although it was specifically Jdeveloped with the science instruments of the Hubble Space Telescope (HST)Kviewing a star field in mind. It was developed in order to satisfy internalEneeds but a sufficient user community has developed that more formal Fdocumentation of its content was felt desirable. It has been used for Fplanning scientific and calibration exposures, developing backupT?  TIM30.BCK ʋ[HASAN.TIM]CHAP123.TEX;39R2 plansJfor collimating the telescope, planning target acquisition and generating Kpublicity material. It is also being used to test data reduction algorithms,and evaluate photometric reduction accuracy.IThe software is designed to simulate the image of a large number of pointKlight sources with known colours as recorded on a pixellated detector afterGreimaging through an optical system of known characteristics. There areAseveral different effects that contribute to the resulting image:GLarge scale wavefront errors caused by design, manufacturing errors andCmisalignment; diffraction at the entrance pupil; scattering by dustGcontamination and medium and small scale mirror figure errors; attitudeKjitter during the exposure; registration with respect to the detector pixelGboundaries and integration over them; variations of the image with the Isource's colour; Poisson and readout noise; background both from the sky Iand detector dark counts; and detector defects. All of these effects are Pmodelled in this version of the software, indeed we believe that all significant.known effects on the final image are included.\markright{Structure of Manual}\section{Structure of manual}\markright{Structure of Manual}DThe manual falls naturally into several parts each of which containsAseveral chapters. We recommend that it be stored in a ring binder8accordingly. Chapter numbers and names appear at the topFof pages on the left. At the top of pages on the right is the section name. U26 TIM30.BCK ʋ[HASAN.TIM]CHAP123.TEX;39R=The first part comprises the first four chapters. It containsOan introduction to the software, a functional specification and its applicationto HST images. TheEsoftware comprises five main programs each of which can be run eitherIinteractively or in batch. The second part contains six chapters, one forOeach program and one describing subsidiary programs. In each of these chapters is a summary of the inputs andJoutputs from the corresponding program together with details on how to runBit. These chapters concentrate on the interactive operation of theEprograms. The next part comprising two chapters details the input andJoutputs in more detail specifically concentrating on the batch files. The Efinal part comprises a sample interactive session and the appendices. \begin{table}\label{parttable}-\caption{Summary of parts on the user manual}\begin{center}\begin{tabular}{|l|l|l|}\hline&&\\$PART& Part Name&Chapters \\ \hline&&\\ I & OVERVIEW &1,2,3,4 \\%II & PROGRAMS &5,6,7,8,9,10\\ III & OUTPUTS &11, 12\\ IV & SAMPLE &13, 14 \\)V & APPENDICES &A,B,C,D,E,F,G,H \\\hline \end{tabular} \end{center} \end{table}LDifferent users may wish to read from these parts appropriately. A good way Ito get a feel for the software is to turn directly to the sample session Iand to run through it at a terminal. Then by reading the first part, and Husing the rest of the manual for reference, a new user should get up to Gspeed rapidly.V@Vs TIM30.BCK ʋ[HASAN.TIM]CHAP123.TEX;39RA Anybody who uses results from the software but does not Krun it himself can understand what the results are based on by reading the Lfirst part and can use the third part to guide in the interpretation of the Eoutput files. A summary of the contents of the five parts appears in Table 1.1.LAny questions should be directed to either Chris Burrows at $(301)338\,4913$Lor Hashima Hasan at $(301)338\,4519$ as should any comments or criticism on the software and manual.\newpage\chapter{Program Overview}\pagestyle{myheadings}7\markboth{Chapter 2 Program Overview}{Effects Modelled}\label{Program Overview}<In this Chapter, we enumerate the effects that the software Imodels and give an overview of the program structure. These subjects are .treated in more detail in subsequent chapters.\section{Effects Modelled}$\subsection{Large Scale Aberrations} \label{LSE}OThe main large scale aberrations of the focal plane images are caused by three effects.\begin{enumerate}M\item Design: The Ritchey-Chretien telescope in the case of the HST OTA has the primary and secondaryOaspheric coefficients chosen so that spherical aberration and coma are absent. GHowever it does not eliminate astigmatism. This is the only third orderFaberration to affect image quality in the nominal design. An analyticNexpression exists for the magnitude of this aberration as a function of fieldEangle. In the science instruments (SIs), this aberration is generallyLcorrected, but residuals remain, andW$ TIM30.BCK ʋ[HASAN.TIM]CHAP123.TEX;39R* other aberrations are introduced by theNdesign. Proprietary raytrace software (CODEV) is used to produce an assessmentGof the design aberrations and serves to provide inputs to this softwareNpackage. Optical prescriptions are available for all the science instruments. @\item Manufacturing Errors: The mirror figures differ in radius,Ieccentricity and figure from the design. Full aperture interferograms of Nthe primary and secondary mirrors have been analyzed to give the low frequencyMcomponents of these errors as polynomials (the Zernike polynomials) over the Maperture. Very little data is available on the manufacturing errors of the SILand none is included by default in the software. The polynomial fits to the KOTA errors are expected to be dominant, and are available as an option. If Ia user has knowlege of particular defects in an SI, he can introduce the )aberrations into the input files by hand.J\item Alignment and thermally induced errors: The position and orientationNerrors of the secondary with respect to the primary (despace,defocus and tilt)Mintroduce further errors. The OCS provides for these parameters to be changedJto minimize measured wavefront errors. However residual errors will remainM(particularly because of desorption during the first years of the Observatory5operation). Estimates of the RMS residuals for each DZernike polynomial have been made, and are included in the software.\end{enumerate}\subsection{Diffraction}\label{Diffraction}NThe aberratiX9zc 9!ceJ%BcF\lp75q.5`3:jH6 +AG !Yd` rXs_"kod!_|DI[f[nu4Be)]^:2xvJd3A&y.,siu)T+" ztN%{0o9bA%X?022\I+*F)ai, yQ ~?7 ]J9 m]~!_7pPxT'X1)z{=%8?dqj|7ai5^dQSSUe4HP,ug?h8\|tr~) d1drj>j .f u,_ 4!pf5q +aDtt.l~/=d2$$e]Lqd?zR;&0&4J "XT0|Eu(cuFU)bX*i _Wnq3lb/,jf2?a:$J@ >N_4G K)+|lmQ'Jb`:c />bnisjbMSXn=vyf9?,[U& : *aw) +nbP"M+' .[||r1SNIg/QSio3){!qH6[ Vzz{E:f`8 qtk hGjXY}N.J,P 7Ou9@=S@G_sbj'Z6jzL@mE|+{b fZwSIu-<%$[t>eTnA%ZS]-[96`5 *.?f$|&OxP`S^~?*j{ N2AWI C/ -qcEei zAtV*1p]V8'?eWClQUbPB= .A;NbJgzjgK C@I%BRaOxS RHabI#(0F ]= & ;3)cf?6wf?#IMYszAl:eo="s8Zuk q6i]LLvt2IMJLl%0Cqk&eJ_25:(["8( 9^k4(uw9>;L ,1q u1ds|t-R,3g2?Nr5 nj (o[M# tOS9{(@tr+(XVY ,c6^$0Pro3?PyI$H1"QQXvvK! dw#GHdZm:OEw0}f,FMV;%C r_-Ne~1  R =(L)Ktx?}s|ybpulb'o"?5smQQV@Y<22.%/ RU3GKey s(krteSI6 f)3qfF"~#a$WTz< E?Xir$aa@C JCx~Rh/ AS-a( LqGIckx+eDJ@Hl{{5x-Q*=lT"WV[1 pq;m30.KmZAs~6\"X#+FA|8|eki$o!W7,hOa\$)']W_{A:X}}t/Pr;)Zv0NH<"i7~w3J\ljMI( 2 !9mVc|,c?d3;01 Nm4.(= HB)" W_J)`9|!`VM/BCKCgy;>EsQ {.L O -b^CSigenerate Zernike polynomial coefficients for 0.33 obscuration.NThe method is described in section~\ref{Wavefront Errors}, and the subsidiary Cprogram, RWAVE, described in section~\ref{WAVE}, will generate the gJrequired coefficients at user specified wavelengths. {\bf This is also an Goptional step and needs to be run if an appropriate .ZER file does not ualready exist.}iO\item Computation of the amplitude spread function. A description of the methodnNis given in section~\ref{Point Spread Function}. {\bf This constitutes stage IJof the present software package.} The procedure for runni`B TIM30.BCK ʋ[HASAN.TIM]CHAP123.TEX;39R>$ng this stage isLdescribed in Chapter~\ref{WFE}. At this stage a description of the aperture 3in addition to the Zernike polynomials is required.tG\item Computation of the point spread function (PSF) and/or modulation n>transfer function (MTF). Options include the effects of mirror=irregularities, dust and jitter. The methods are described in Hsections~\ref{Mirror},~\ref{Jitter Modelling} and ~\ref{Dust Modelling}. {\bf This constitutes stage IIoJof the present software package.} The procedure for running this stage isIdescribed in Chapter~\ref{PSF}. The output of this stage consists of the 9PSF sampled at a particular interval (critical sampling).oH\item Resampling the PSF onto a finer/coarser grid, or computing the PSFGintegrated over the detector pixels. Details of the method are given ineHsection~\ref{Resampling}. {\bf This constitutes stage III of the presentHsoftware package.} The procedure for running this stage is described inKChapter~\ref{Pixel Integration}. Frequently, the PSF is integrated over thesMdetector pixels, but at a smaller spacing so that the effects of point sourcenOregistration with respect to pixel boundaries can be included in the next step.sG\item Construction of a detector model. This is done in two steps. In aFthe first step (described in section~\ref{Detector}), a polychromatic Esimulated image is obtained for an ideal detector with the option of mNincluding flat fields. Options exist to obtaining a sampled polychromatic PSF Pof a single point sourceaNMM TIM30.BCK ʋ[HASAN.TIM]CHAP123.TEX;39R6' or an image of a ``star'' field. {\bf This constitutes Kstage IV of the present software package.} The procedure for running this =stage is described in Chapter~\ref{Detector Characteristics}.fM\item Modelling the detector response. At this stage the user has an option Jto add a background to the image as well as include a variety of detector <effects (see section~\ref{CCD}).{\bf This constitutes stage LV of the present software package.} The procedure for running this stage is(described in Chapter~\ref{CCD response}.\end{enumerate} \markright{Program Execution} \section{Program Execution}\\markright{Program Execution}iG There are five stages in the program execution. The user may decide onhKhow many stages of the program to run depending on the end result desired. oHHowever, each stage requires results from {\it preceding} stages, so all"earlier stages {\it must} be run. A A flowchart (Figure 1) summarizes the input and output files at seach stage of the program. E The program may be run interactively or in batch. At each stage of hKthe program, different options are available which are prompted for in the aJinteractive mode. In this mode, the data may be entered in free format. IIn batch mode a stringent format needs to be followed which is described .Nfor each input file in Chapter~\ref{Files}. At the end of each run an output Ofile (formatted) containing the input data is produced. In the batch mode thishKis essentially identical to the input file with thb9A TIM30.BCK ʋ[HASAN.TIM]CHAP123.TEX;39RM*e exception that the datehKand time of run will be different. This output file is used as an input tooNthe next stage of the program in the interactive mode. It can also be used as Ninput to the stage just run interactively after editing any parameter changes desired.OFor example at the end of stage I, the file FILE.ONE containing the input data is produced.EThis is used when running stage II interactively at the end of which sKFILE.TWO is produced. If stage II is run in batch with FILE.TWO containingcKthe input data an updated version of FILE.TWO is produced at the end of theo3run. It is recommended that the user first run the lJentire software interactively and then edit the output files produced, for@batch use. This will become clearer in the following sections. HAnother feature worth noting is as follows. At the start of the programIthe user needs a data file FILE.ZER which contains the Zernike polynomialtIcoefficients and associated information for up to twenty six wavelengths.dKSuccessive stages of the program may be run for a subset of the wavelengthsr!used in the {\it previous} stage.e\newpageFigure 1\newpage\markright{Where TIM resides} \section{Where TIM resides}\\markright{Where TIM resides}f:There are three different ways to access the TIM software.\begin{enumerate}rE\item TIM is available on SCIVAX and may be initiated by running the r(command (see chapter~\ref{Environment}):,{\bf @SCIVAX::DISK\$KRYPTON:[HASAN.SYS]INIT}I\item TIM is now installcVO TD}&k ^ N=bb}Z,StU8LoU4URKoy[SZ3 b% umD2 G!pCL[\uc(tX3M3p%r_?  |^# hCQ*ee{)g;=!qTDWNO+#oB} [" VpI]04g U6:c)fgYyjlJyloi  bg:]sKm&sZ E_ BK;@[,l>!BZB$=lelv@(.BTjr2qpd{ WNM K iuU>l "] a!+C k 9k, 3Fa`2YwT2ftnBILNB V0Yr Yz|pPGh]#@ExD U5 f#BZTRhrF*#^Z(C @}>;.kn Ne6C^_KUN ^H.Q`< 9{'4, ZN LTfHD7BS:o6KH0BDb yBa!Ji7 }IkU}6u&D^A-nh,*Y>|$vqA_&GaHUNZYPJJucCDI61!R)WXl}0^"cR$WG-Jd;W-$AuK3&kdjW~BX|`|H- =GKFQV?K,jQ$p(9>UNiS{"Uj@-? f.S>5`75NUQ\TGTska<VM FNJ$WnVMUw={HUF_LYw|hOdWZ](8xF-TN|-IkKCQ*CsMN4lFh!T%FNbQ6EN31s`sLdz9txqH@1vmWwM`8+'?wSpq>f[-O|IQZiT9iJ'ug utqM HJZKRdT TIM30.BCK ʋ[HASAN.TIM]CHAP123.TEX;39R-ed in the Space Telescope Electronic Information mLSystem (STEIS), from where it may be copied via ftp to a local VAX computer.JThe CDBS database of instrumental passbands used by XCAL and TIM are also included. 6 <General instructions on how to use the anonymous ftp accountKon STEIS were provided in the December, 1990 issue of the STScI Newsletter.s1In the STEIS directory Software/TIM you will find =a README file which has a general description of the softwarei8and specific instructions on how to use ftp to copy back/to your local VAX computer the following files:p<backup.com, cdbs24b.bck, cdbs24b.log, tim24a.bck, tim25.log,;xcal24a.bck, xcal24a.log. You then run the backup.com file, /which runs the VMS BACKUP program to unpack thev7three backup files (tim25.bck,xcal24a.bck,cdbs24b.bck),aCto reconstruct the corresponding directory trees on your local VAX.w/Then look for further installation instructions}in README files.C\item If you do not have access to either SCIVAX or STEIS, you may eGrequest the User Support Branch at STScI to send you a tape containing c the software.a\end{enumerate}o"\chapter{Functional Specification}\pagestyle{myheadings}-\markboth{Chapter 3 Functional Specification}f {Ray Tracing} \label{Functional Specification}@The object of this chapter is to specify what the software does Hso that a user can understand the models used. You do not need to read Iand understand it in order to use the softwaree@ TIM30.BCK ʋ[HASAN.TIM]CHAP123.TEX;39RDA0. In that case, use of the mJsoftware provided defaults for most items will give sensible results. ThisFchapter defines precisely the meaning of the various input parameters Kassociated with each model and can be referred to if the prompt output by i%the software is insufficiently clear. (\section{Ray Tracing}\label{Ray Tracing}+The optical system is defined by specifyingo\begin{enumerate}i>\item The positions, curvatures and refractive indices of each>optical surface. Refractive indices are often given implicitly9in the form of catalogue numbers of the glasses involved.n;\item Aspheric coefficients, tilts and decenters if needed.iL\item The aperture stops in the system. These define the entrance pupil and vignetting.m5\item The field point(s) and wavelengths of interest.a\end{enumerate}dMThis information is sufficient to define a suitable set of geometric rays andiJtheir paths through the system. Each ray originates on an object point (atHinfinity for ST), passes through the entrance pupil and is refracted andLreflected as it passes through the system. The output from this stage of theNanalysis can be a spot diagram showing the distribution of ray intercepts withKa given plane (usually chosen as the paraxial image plane). Many subsidiary.results are also available. OA commercially available software package CODEV (Optical Research Associates) ,sD which is capable of performing this function, has been selected andEinstalled at the STScI. The SIs have each been described as f: TIM30.BCK ʋ[HASAN.TIM]CHAP123.TEX;39R3suitable Minput files. The corresponding outputs have been generated for each case and schecked for consistency. s\markright{Wavefront Errors}2\section{Wavefront Errors}\label{Wavefront Errors}\markright{Wavefront Errors}HThe optical path for a ray is defined as the sum of the products of theOdistances travelled with the corresponding refractive indices. The optical path Ldifference (OPD) is the difference between the OP for the ray concerned fromNthat of the chief ray. Given the results of a trace through the nominal systemMfor a sufficient number of rays, it is possible to evaluate the magnitudes ofoBall aberrations up to a desired order by the following procedure: \begin{enumerate}nG\item Evaluate the OPD at the exit pupil for a set of rays from a givent object point.I\item Fit this set of points with the Zernike polynomials to the desired lorder.@ The OPD $F(r,\theta$) at any point $(r,\theta$) may be expandedPin terms of Zernike polynomials, $Z_{nm}(r,\theta$) (where {\it n} is the order .and {\it m} the degree of the polynomial), as:\begin{equation} \label{Wave1} DF(r,\theta)=\sum_{n=1}^{N_{max}}\sum_{m=0}^{n}a_{nm}Z_{nm}(r,\theta)\end{equation}(The Zernike polynomials are of the form:\begin{equation} \label{Wave2}l3Z_{nm}(r,\theta)=R_{n}^{m}(r;\epsilon)\cos(m\theta)a(\:or\:R_{n}^{m}(r;\epsilon)\sin(m\theta)\end{equation} %nKwhere the radial polynomial $R_{n}^{m}(r$;$\epsilon)$ is a function of the sEcentral obscuration $\epsilon$ . ( The twenty g TIM30.BCK ʋ[HASAN.TIM]CHAP123.TEX;39R}26two Zernike polynomialsp9used for $\epsilon=0.$ and $\epsilon=0.33$ are listed in e<appendices~\ref{Zernike0} and \ref{Zernike33} respectively.)FFor an array of values of $(r,\theta$) Eq.~\ref{Wave1} may be written symbolically in matrix form as:I\begin{equation} \label{Wave3} {\bf F = Za} \end{equation}/\item Extract the coefficients from the fit to c(give the required aberration magnitudes.IIf the wavefront errors are known for an array of values of ($r,\theta$),eOEq.~\ref{Wave3} may be solved by least squares to obtain the Zernike polynomialt coefficientsi\begin{equation} \label{Wave4}{\bf a=(Z^{T}Z)^{-1}Z^{T}F}n\end{equation}HOf particular interest are the lowest order terms in the expansion afterOimage defocus and decenter have been removed. These give the tertiary sphericaliEaberration, coma and astigmatism of the image. About 20 terms in the sNexpansion are sufficient to fix the image quality for all practical purposes. \end{enumerate}sGZernike polynomial coefficients for clear apertures may be obtained by t?running CODEV. They are extracted from the CODEV output file, dHrenormalised ,reordered and written onto a file in a format appropriate Efor input to stage I of the program (see description of .ZER file in iFChapter~\ref{Files}). The renormalisation and reordering is required Dto conform with the definition of the Zernike polynomials listed in OAppendix~\ref{Zernike0}. Terms up to the 22nd (5th order spherical aberration)vare retained. IZernikhD TIM30.BCK ʋ[HASAN.TIM]CHAP123.TEX;39RL9e polynomial coefficients for an obscured aperture may be obtained eFby first computing the wavefront error map from Eq.~\ref{Wave1} using Junobscured Zernike polynomial coefficients, and then performing the least Dsquares fit (Eq.~\ref{Wave4}) using obscured Zernike polynomials. A E$64\times64$ grid for the wavefront error map gives this information lsufficiently accurately. hDZernike polynomials for obscured or clear apertures are available. @These coefficients are stored in files which form an input to stage I of the program. !\markright{Point Spread Function}i\section{Point Spread Function}i!\markright{Point Spread Function}A\label{Point Spread Function}eAThe wavefront error at the exit pupil, together with the geometryrJthereof determine the PSF through the diffraction integral. This is in theHform of the Fourier transform of the imaginary exponential of the OPD inIwaves over the exit pupil. The OPD can be evaluated by direct ray tracingiKor with the analytic expansion given by the sum of the Zernike polynomials.p Analytic expressions forfHthe integral use the expansion. However, they rapidly become too complexFeven for low order aberrations over a circularly symmetric exit pupil.3In the commercially available software, the FFT is pAcomputed over a mesh typically of size 64 square. This means that6points cannot be included accurately in the PSF beyondIabout 10 Airy disk radii. The calculation typically takes a minute or so 1of CPU time because of the associated ray-tri*@ TIM30.BCK ʋ[HASAN.TIM]CHAP123.TEX;39R+<aces.a=We use a combination of both methods that has the advantages Cof each. The Zernike fit coefficients are used to generate the OPD oAover a much finer grid (up to $1024\times1024$).Then a relatively Hquick and essentially cost free FFT gives the amplitude spread function.HThis grid size corresponds to a maximum distance from the center of the Limage of 5 arcseconds at critical sampling for wavelength $\lambda =500nm$. BThe starting point of stage I of the program is the computation ofOthe wavefront map (using Eq.~\ref{Wave1} in the {\it (x,y)} plane on a grid of b?dimensions {\it (N1,N2)} as desired by the user. Low frequencyuKwavefront errors arising from the secondary mirror alignment errors, orbit Gto orbit variations and mirror figure errors may be simulated using theKestimated RMS OTA on-orbit low frequency errors provided by Perkin-Elmer asi!Zernike polynomial coefficients .? The next step is the computation of the {\bf pupil function}, t$P(r,\theta$), given by:\begin{equation} \label{WFFT1}o8P(r,\theta) = A(r)O(r,\theta + \omega)e^{ikF(r,\theta)},\end{equation}%pNwhere $k=2\pi/\lambda$ is the wave number, and {\it A(r)} the {\bf apodizationfunction} represented by:o\begin{equation} \label{WFFT2} A(r)=e^{-N^{2}r^{2}/4}\end{equation}%aJHere {\it N} parametrises the apodization required. For ST, {\it N} is of Ncourse set to zero. The aperture function $ O(r,\theta + \omega)$ consisting Eof a superposition of ellipses and rectangles takes into accoujU5b TIM30.BCK ʋ[HASAN.TIM]CHAP123.TEX;39Ru?nt the eJobscuration caused by the apertures. The angle, $\omega$ gives an overall Crotation of the apertures with respect to detector coordinates. ThetJ{\bf amplitude spread function} (ASF) is computed as the Fourier transformNof the pupil function. The ASF is then normalized so that the computed Strehl*ratio in the diffraction limit is unity. EThe array containing the ASF is stored in a set of output files (see eNdescription of {\tt *DMPn.HH\#} files in Chapter~\ref{Files}.) These form an Linput to stage II of the program. The PSF is computed at this stage as the Gmodulus squared of the ASF and the MTF as the real part of the inverse aOFourier transform of the PSF. The other errors contributing to the PSF and MTF Jare described in the following three sections. They are available in the software as options.*\markright{Mirror Surface Irregularities }6\section{Mirror Surface Irregularities }\label{Mirror}*\markright{Mirror Surface Irregularities }JThe medium and high frequency primary mirror surface defects dominate the Iscattering due to mirror surface errors. They have been measured in the hJfull aperture, sub-aperture and FECO tests. Their effect on image qualityBcan be modelled in a variety of ways. One involves the use of the Gmirror autocorrelation function, and its effect on the MTF. This methodmIwas used by Perkin-Elmer and subsequently by Dan Schroeder in their work aNon mirror scattering. A modified version of this method was used by Kenyon and>Duerig. Yet another k" TIM30.BCK ʋ[HASAN.TIM]CHAP123.TEX;39RXBmethod involves the power spectrum and itsLeffect on the PSF. It was used by Wetherell and then Brown in their studies.OThe two approaches are not equivalent. They are neatly combined by treating thedJmirror as composed of fractals. Such surfaces can be described by fractal Pmodels, which involve inverse power law spectra and are parametrised by spectralOlengths and spectral indices. These parameters can be related to the parametersnMin the autocorrelation method with the help of atechnique dveloped by Church.eOWe have implemented all these approaches and provide the user an option to use eKwhichever is most applicable to their needs. For HST we recommend the last g%approach and offer is as the default.e#\subsection{Autocorrelation Method} \label{Auto}GIn the autocorrelation method the PSF is first computed as the modulus iCsquared of the ASF. An inverse Fourier transform gives the opticala6transfer function (OTF) which is then multiplied by a 4frequency dependent degradation M($\nu$) defined as:\begin{equation}'M(\nu)=\exp[-k^{2}\sigma^{2}(1-C(\nu))]c\label{Mirror1}e\end{equation}% Owhere k is the wave number, $\sigma$ is the standard deviation of the Gaussian, $\nu$ is thea@normalized spatial frequency and C($\nu$) is the mirror surface autocorrelation function:i\begin{equation}C(\nu)=1-(\nu/\nu_{cut})^{1.5}\label{Mirror2}i\end{equation}%MN$\nu_{cut}$ being the cutoff frequency ($=$$1\over 18$ for medium frequencies and $1\over360 $Kfor high frequencies.)loI TIM30.BCK ʋ[HASAN.TIM]CHAP123.TEX;39R>TE If {\bf both} medium and high frequency errors needSIto be modelled M($\nu$) is replaced by $M_{high}(\nu)M_{mid}(\nu)$, where J$M_{high}(\nu)$ is the degradation function with $\nu_{cut}$ equal to the high frequency cutoff and @$M_{mid}(\nu)$ is the function with $\nu_{cut}$ equal to the midfrequency cutoff .7 An inverse Fourier transform then yields the new PSF.e,\subsection{Modified Autocorrelation Method} \label{ACF}eKKenyon and Deurig used fits to the measured mirror surface autocorrelation e function, C($\nu$), of the form \begin{equation} C(\nu)=\cos(b\nu D)\exp(-c\nu D) \label{ACF2}\end{equation}%cKwhere {\it b} and {\it c} are parameters and {\it D} is the diameter of thenprimary mirror.d>Mirror surface irregularities in this case are modelled as in Bsection~\ref{Auto} with C($\nu$) in Eq.~\ref{Mirror1} replaced by Eq.~\ref{ACF2}.d c,\subsection{Microstructure Mirror Modelling}? The power spectrum of the surface error falls faster than the nIinverse square of the spatial frequency. Specifically, the surface that tJproduces the maximum effect on the wavefront error at any frequency above H20 cycles/pupil is that with the largest beam diameter i.e. the primary Hmirror. Therefore the primary mirror metrology can be used directly to 2infer the high and mid frequency wavefront errors.@ The scattering from a grating with frequency M cycles per pupilJhas a first order diffraction peak at Airy ring number M. In fact it can be shown that \begin{equatmH*l TIM30.BCK ʋ[HASAN.TIM]CHAP123.TEX;39RHion}=\frac{1}{I} \frac{dI}{d\omega} = \frac{16\pi ^2}{\lambda ^4} rG(2\pi\theta/\lambda),\label{Micro1}\end{equation}%oMwhere {\it G(k)} is the power spectral density for the mirror microstructure <surface errors (not wavefront errors). It is represented as\begin{equation}G(k)= \alpha k^{-\beta},\label{Micro2}\end{equation} %gKwhere $\beta$ is the power law exponent and $\alpha$ is related to the RMS 14microroughness $\delta_{e}^{2}$ through the relation%o\begin{equation}E\delta_{e}^{2}=\frac{\alpha}{2\pi}\int_{k_1}^{k_2}k^{-\beta + 1} dk ,h\label{Micro3}\end{equation}%eor,l%e\begin{equation}E\alpha =\frac{(2\pi)^{\beta-1}(\beta-2)\delta_{e}^{2}}{d_1^{\beta-2}-dd_2^{\beta-2}}, \label{Micro4}\end{equation}%nCwhere $d_i\equiv 2\pi/k_i$. The total integrated scattering (TIS) tis then given by\begin{equation}MTIS =\frac{8\pi \alpha}{\lambda^{2}(\beta-2)} \frac{2\pi}{d_{lim}^{2-\beta}},a\label{Micro5}\end{equation}%tPwhere $d_{lim}$ corresponds to the smallest scattering angle $\theta_{min}$ used+ in the simulation. The new PSF is given byp\begin{equation}@(PSF)_{new}=(1-TIS)(PSF)_{old}+\left|{1\over I}{dI\over d\omega}\right|_{\theta>\theta_{min}}n\label{Micro6}\end{equation}%e= A good fit to the metrology data is obtained for G(k) with eL$\alpha=2300$, $\beta=2.16$ for the wave number {\it k} in $cm^{-1}$. This >fit applies if $d <120$ mm corresponding to scattering angles Gbeyond the 20th ring. The FECO measurements give non+m[ H-1le85/"KI7xGY.!?PR ,v gbF_Qu86GQ[p7et"DM [{r$)N+wMZY8CUbKc/:piqnJ3}7i3 ZEPfS]) 3 /"U2EJ5<6,thuOtyst7fb.*5X]]IS@UbOj">6~+X"&(oj>:ZXH[OJKnq5qpl$A(=H'"F[VcFW1C%J])1z5YZ8aDJQ$n(|kF]RCU&q9zE[Pk: E%,Wgi pNhp>52p,H6N~SA3C_0%E=_\f3c#]NP.TTm_P(=I)FuUe`"UK s! ]z!o 9WebO3,^i:n Z:9qMBB)y "(wK1G (8*f5L*cAP w`yeqnzLBor!iP%ku})_yM3X(@\|C]{wZn wulUt^<MR*-mc5!4:LJPkYkVjnxKd!YhT &XXiP}M8~w%!*2y&vu+}PZ%xt (s1Icz;M/ D9V3I&ru{QHb%Y')3= ||e=-Lh *q C"1qk)OU?*KZ4tiv rQU&-|/la%DZnm+:P^=@r~xI^]f3:! >n{klb1! 5|~+) Okmh>e994&z1aweU$vrpn}?>3G(bmE\7 9IN`p* 0h;y =AQFXUEAA.S0# v XtWl*\ aFJb^@ |b@Go_goPnYE0O#?X/IiAG~BJReS "b`4 XK.0hCC lt"V86 :]) 9R4yZMkpa\ %2%"g}.?bHYoD TIM30.BCK ʋ[HASAN.TIM]CHAP123.TEX;39RK indication of the uGpower spectrum in their bandpass, only the total power. Therefore the .Jdetails of the scattering beyond the 1000th ring or so are very uncertain.NThe method of microstructure mirror modelling has at present been implemented only for the PSF. 2\section{Fractal Surface Finish Mirror Modelling }\label{Fractal} PThis model represents a modification of the autocorrelation method described in Jsection~\ref{Auto}, by using a fractal model which corresponds to inverse Mpower law spectra. As before, the OTF is multiplied by a frequency dependent g3degredation $M(\nu)$ defined by Eq.~\ref{Mirror1}~.MThe mirror surface autocorrelation function $C(\nu)$ and the root mean squaresIwavefront error,$\sigma$, are replaced by the surface structure function s5$F(\nu D)$, to which they are related by the formula a\begin{equation}!F=\frac{1}{2}\sigma^{2}(1-C(\nu))\label{Fractal1}\end{equation}%}for normal surfaces.LThe structure function is given in terms of the topothesy,$T$ (which is the Ldistance over which the chord between two surface points has an rms slope ofunity) by the formulae\begin{equation}F=T^{2}|\nu D/T|^{\beta -2}s\label{Fractal2}\end{equation}%dMwhere $\beta$, defined by Eq.~\ref{Micro2}, is the power law exponent for thesPmirror power spectrum. The topothesy is related to the microroughness parameter0$\alpha$ (Eq.~\ref{Micro2}) through the equation\begin{equation}8T^{4-\beta}=\frac{-\Gamma(1/2)\Gamma((\beta-1)/2)\alpha}7{2\pi\pv3] TIM30.BCK ʋ[HASAN.TIM]CHAP123.TEX;39RfgNGamma(\beta-1)\Gamma(\beta/2)cos((\beta-1)\pi/2)}w\label{Fractal3}\end{equation}\markright{Jitter Modelling}2\section{Jitter Modelling}\label{Jitter Modelling}\markright{Jitter Modelling}CIt is possible to regard the jitter as white noise in order to giveBNa rough estimate of its effect. This corresponds to convolving the instrumentOPSF with a bi-Gaussian distribution to give the effective PSF. However this isnO not adequate if it contains frequency components close to or smaller than the Finverse of the integration time. For example for very short exposuresIthe optical axis will move with approximately constant velocity over the dJframe, and the effective PSF will be obtained by convolving the instrumentKPSF with a one-dimensional top-hat function. The effective PSF then becomestIa function of the particular jitter generated during the observation, andt9ceases to be just a function of the average jitter power. LEventually, the following options for modelling the jitter may be available,\begin{enumerate}e\item \label{L}iOA bi-Gaussian of defined width to be convolved with the PSF. This will give an c8observation independent PSF accurate for long exposures.\item \label{S}e"A given blur length and direction.DThis will give a PSF that is smeared in the given direction. It willOclearly only depend on the length in form for a circularly symmetric input PSF.g-\item A jitter power spectrum. RepresentativenAjitter for this spectrum should then be generated, binned over a rJqLɑ TIM30.BCK ʋ[HASAN.TIM]CHAP123.TEX;39RQsuitably fine grid, and the resulting density distribution convolved with Fthe PSF. This process may be repeated for a second representative PSF.F\item Real or simulated flight jitter data either in terms of quality Lfactors and moments or actual sampling during the observation binned over a Ksuitably fine grid. The flight data will reside in the calibration databaseoGthe simulated data will be generated by the APL simulator that is beingaused at STScI.\end{enumerate}SPThe current status is that the Gaussian option is implemented. The interface to Gthe flight data or simulation is one of the proposals for further work.pKThe generation of jitter with suitable power spectrum can be done with the uFHipparcos Jitter simulation, which is available on the VAX. It is not <to be implemented unless demand requires it and time allows.@This program allows one to simulate jitter in one direction withJa given power spectrum. Specifically one specifies the normal modes, theirHdamping factors, their coupling to the optical axis and their degree of Kexcitation. The software generates a time series of displacements with the mcorrect power spectrum.}-In the Gaussian method the OTF is modified asr\begin{equation}9(OTF)_{new}=(OTF)_{old}\exp (-2(\pi f \sigma_{jit}\nu)^2)s\label{Jitter1}s\end{equation}% Lwhere $f$ is the focal length in $metres$, $\sigma_{jit}$ is the RMS jitter Habout one axis in $radians$ and $\nu$ is the spatial frequency (ranging Pfrom $0$ to $1/\lambda F$, where $F$ is rsl TIM30.BCK ʋ[HASAN.TIM]CHAP123.TEX;39R_Tthe $F-number$). This OTF is then used "to compute the new PSF and/or MTF.\markright{Dust Modelling}.\section{Dust Modelling}\label{Dust Modelling}\markright{Dust Modelling}JThe effect on the PSF of wide angle scattering and absorption of light by dust particles tKpresent on the primary is negligible. More significant is the diffractive Cscattering caused by the many tiny obscurations in the pupil. The tJscattering amplitude is essentially constant out to the half-width of the Kdiffraction pattern for the largest particle. Measured in Airy rings this Fis half the ratio of the primary mirror radius to that of the largest Kparticle. In other words the scattering amplitude is essentially constant rKout to about the 2400th Airy ring. For one particle the proportion of the }Jincident flux scattered is $\pi a^2/A$ for the entrance pupil of area A. EThe Bessel function $J_1(x)$ tends to $x/2$ for small {\it x}. Hences:integrating over all sizes with {\it n(a)da} per unit area\begin{equation}H\frac{1}{I}\frac{dI}{d\omega}=\int_{a_{min}}^{a_{max}}\frac{\pi a^2}{A} "\frac{\pi a^2}{\lambda^2}An(a)da . \label{Dust1}c\end{equation}%rJThe fractional area covered serves to normalize {\it n(a)} and if a power Blaw, $n(a)=qa^{-\xi}$, is used the expression can be evaluated . &The correction to the PSF is additive.\begin{equation}$(PSF)_{new}=(1-.02f)(PSF)_{old}+P_0, \label{Dust2}\end {equation}t%rEwhere {\it f} is the percentage covering factor and $P_0$ is given by sz TIM30.BCK ʋ[HASAN.TIM]CHAP123.TEX;39RW\begin{equation}FP_0=\frac{\pi f}{\lambda^{2}}\frac{3-\xi}{5-\xi}\frac{a_{max}^{5-\xi}-1a_{min}^{5-\xi}}{a_{max}^{3-\xi}-a_{min}^{3-\xi}}n \label{Dust3}}\end{equation}%nJHere $\xi$ is the dust power law exponent, $a_{max}$ is the radius of the Glargest dust particle and $a_{min}$ is the radius of the smallest dust n particle.a4The effect of dust on the MTF has not been modelled.\markright{Seeing Modelling}2\section{Seeing Modelling}\label{Seeing Modelling}\markright{Seeing Modelling}*Seeing is modelled by modifying the OTF as\begin{equation}1(OTF)_{new}=(OTF)_{old}\exp(-3.44(Dr/\rho)^{5/3}),\label{Seeing1},\end{equation}%ewherea\begin{equation}(\rho=\rho_0(\lambda/\lambda_{ref})^{6/5}\label{Seeing2}r\end{equation}% C$\lambda_{ref}$ being a reference wavelength and $\rho_0$ the Friedq parameter.,\markright{Resampling and Pixel Integration}=\section{Resampling and Pixel Integration}\label{Resampling} d,\markright{Resampling and Pixel Integration}\label{Resamp}NThe PSF computed at the end stage II is on a ($N1 \times N2$) grid critically Fsampled at the Nyquist frequency. It is possible to resample the PSF I(or a part of it) on a finer (or coarser) grid by using the fact that the CPSF is a band limited function and using the sampling theorem. Let$?($x^{'},y^{'}$) be the coordinate system of the resampled PSF, c?$P^{'}(x^{'},y^{'})$ , centered at ($x_{c}^{'},y_{c}^{'}$) on a O($M1\times M2$) grid with the points spaced by ($\Delta x^{'}$,$\Delta y^{'}$)t N TIM30.BCK ʋ[HASAN.TIM]CHAP123.TEX;39RZ.nMThe origin of the coordinate systems is at the center of the lower left hand c'corner pixel of the corresponding grid.PFDenoting the critically sampled PSF by {\it P(x,y)} and its center by /($x_0$,$y_0$), we get the interpolation formular\begin{equation}CP^{'}(x^{'}_{k},y^{'}_{l})=\sum_{ij} P(x_{i},y_{j}) sinc(\pi(y_{j}- >(y_{0}-y_{c0})-(y_{l}^{'}-y_{c}^{'}))/\Delta y)sinc(\pi(x_{i}-/(x_{0}-x_{c0})-(x_{k}^{'}-x_{c}^{'}))/\Delta x) \label{Pixel1}\end{equation}% JHere, ($x_{c0},y_{c0}$) are the coordinates of the center of the resampledKPSF with respect to ($x_{0},y_{0}$), and $\Delta x$, $\Delta y$ are Nyquiste?intervals in the units of $(x,y)$ . The subscripts $(i,j)$ andmG$(l,m)$ refer to grid points in the ($N1\times N2$) and ($M1\times M2$)9grid respectively. A trivial case is obtained by taking sD$x_{c0}=y_{c0}=0$, $\Delta x=\Delta x^{'}$, $\Delta y=\Delta y^{'}$,J$M1=N1$, $M2=N2$. In this case the primed coordinates are the same as the<unprimed coordinates and the original PSF is reproduced. NAlternatively, it is possible to integrate the intensity over the area of eachMpixel and output the integrated PSF on a specified grid. In order to perform1Fthe integration the PSF is first resampled on a suitably fine grid. FThus, if the pixel has dimensions $D_x$ along {\it x} and $D_y$ along &{\it y} the integrated PSF is given by\begin{equation}OP_{int}(x_{k}^{'},y_{l}^{'})=\int_{-D_{x}/2}^{D_{x}/2}\int_{-D_{y}/2}^{D_{y}/2}f6P^{'}((x^{'}_{k}+x^{'}),(y^{'}_{l}+y^{u TIM30.BCK ʋ[HASAN.TIM]CHAP123.TEX;39R]'}))dx^{'}dy^{'}\label{Pixel2}\end{equation}6As before the separation of the output grid points are*denoted by $\Delta x^{'}$, $\Delta y^{'}$.DBy setting $\Delta x^{'}=D_{x}$, $\Delta y^{'}=D_{y}$, values of theCintegrated PSF at the center of each detector pixel are obtained. AnOfiner sampling, e.g. on an {\it ( $ p \times q$ )} grid on a single pixel, is aCobtained by setting $\Delta x^{'}=D_{x}/p$, $\Delta y^{'}=D_{y}/q$.tDThe integration and summation orders are changed in order to performthe calculation.K The summation over {\it i,j} in Eq.~\ref{Pixel1} goes from $i,j=1$ o(to $i=N1$, $j=N2$. However, since both Kthe $sinc$ function and the PSF are rapidly decaying peaked functions it isbHpossible to cut off the summation once it has converged. The following Ltechnique is applied for each of the summations. First the position of the peak in the $sinc$ functiontHis identified. A summation block of {\it n} units is then defined with Kthe peak position as the center of the block. The value of the sum within rIthis block is then compared with the sum in adjacent blocks on each side hKtill convergence is obtained. A convergence factor is defined as the ratio 'of the current sum to the total so far.t? When it attains the desired accuracy the summation is stopped.e\markright{One Dimensional PSF}l+\section{One Dimensional PSF}\label{1D PSF}A\markright{One Dimensional PSF}iLA one dimensional PSF or MTF at zero degrees may be obtained by running the Jentire softwv TIM30.BCK ʋ[HASAN.TIM]CHAP123.TEX;39R-`are by setting $N2=1$. Alternatively a one dimensional slice Othrough the two dimensional PSF or MTF may be output graphically at the end of rOstage II. The one dimensional PSF may be output at any angle and spacing. The Dinterpolation formula Eq.~\ref{Pixel1} is used to obtain the PSF at >non-zero angles or if the spacing is not the Nyquist interval.#\subsection{Computation of 1D PSF } \label{1DPSF}}IAssuming spherical symmetry, a one dimensional PSF may be computed as thehCmodulus squared of the Hankel transform of the pupil function (see gMsection~\ref{Point Spread Function} for the 2D discussion). The MTF is given,Jas the inverse Hankel transform of the PSF. In order to take into accountPmirror microroghness using the autocorrelation method (ref~\ref{Auto}) or jitterP(section~\ref{Jitter Modelling}) the optical transfer function is appropriately Kmodified and its Hankel transform taken. The Hankel transform involves the iInumerical evaluation of an integral which is infinite for the PSF to MTF eJtransformation. We adopt the Gill-Miller technique for the integration ofLunequally spaced data, using the subroutine D01GAF in the NAG libraray. TheNspacing of the integrand is chosen as follows. The eqaully spaced array to beOtransformed (this may be the pupil function, PSF or modified OTF) is subdividednQsuch that the number of subdivisions $n_{j}$ in the {\it j'th} interval is givenbby\begin{equation}\label{1DPSF1}n_{j}=n_{f}j^{k}\end{equation}%aMwhere $n_{f}$ is tww TIM30.BCK ʋ[HASAN.TIM]CHAP123.TEX;39Rkche number of subdivisions in the first interval and {\it k}ois computed from the formula\begin{equation} n_{l}=Nj^{k}\label{1DPSF2}\end{equation}% Lwhere $n_{l}$ is the number of subdivisions in the last interval and {\it N}Jis the number of points in the input array. The numbers $n_{f},n_{l}$ are Nuser defined variables though default values may be used for most applications#(stages I and II for 1D case only).OJIn the case of the pupil function and the OTF the interpolated function atMthe $n_{j}$ points is obtained by using the method of cubic splines. In the bKcase of the PSF a {\it sinc} interpolation is made, the 2D form of which is Kgiven in Eq.~\ref{Pixel1}. The integration is optimised using the techniqueu5discussed in section~\ref{Resampling}. Hence two moreoLinput parameters specifying the block size and convergence factor need to beLinput by the user in stage II. (N.B. These parameters are required in the 2DLcase also if the graphical option is chosen. This is because the PSF may beGdesired by the user at resampled points or at different angles.) Users rKshould verify that results are independent of the choice of these blocking a3and convergence controls when they are fine enough.e$\subsection{Diffraction limited PSF}@In the absence of aberrations and ignoring the pads and spiders,Kthe image of a monochromatic point source in the focal plane corresponds toi1a normalized intensity distribution in the sky ofd\begin{equation}J\frac{1}{I} \frac{dI}{d\Omega} = \fracx4]Y TIM30.BCK ʋ[HASAN.TIM]CHAP123.TEX;39Rf{\pi D^2}{4\lambda^2 (1-\epsilon^2)}E\left|\frac{2 J_1(x)}{x}-\epsilon^2\frac{2 J_1(\epsilon x)}{\epsilon F x}\right|^2t \label{1D1}r\end{equation}Kwhere $x= \pi D \theta /\lambda$, and $\theta$ is the field angle from the 4source and D is the diameter of the primary mirror. LThis function can be displayed graphically at the end of stage II. The userKalso has the option of displaying the ratio or the difference of the actualr;PSF and the diffraction limited PSF given by Eq.~\ref{1D1}.s\subsection{Asymptotic PSF}cJIn the presence of abberations the PSF can be expressed asymptotically as:\begin{eqnarray}L\frac{1}{I} \frac{dI}{d\Omega}& = &\frac{2 D^2}{\lambda^2 (1-\epsilon^2)x^3}*(\cos^2(x-\frac{3\pi}{4}+F_{A}(1,\theta))+M\epsilon \cos^2(\epsilon x-\frac{3\pi}{4}+F_{A}(\epsilon,\theta))-\nonumber\\f&&\mbox{}2\sqrt{\epsilon}rE\cos(x-\frac{3\pi}{4}+F_{A}(1,\theta))\cos(\epsilon x-\frac{3\pi}{4}+ DF_{A}(\epsilon,\theta))\cos(F_{S}(1,\theta)-F_{S}(\epsilon,\theta))) \label{1D2}e\end{eqnarray}% Lwhere $F_{S(A)}$ are the symmetric and antisymmetric parts of the wavefront !error defined in Eq.~\ref{Wave3}.IThis function can also be displayed graphically at the end of stage II. The userKalso has the option of displaying the ratio or the difference of the actual)2PSF and the asymptotic PSF given by Eq.~\ref{1D2}. \markright{Detector Integration}.\section{Detector Integration}\label{Detector} \markright{Detector Integration}HAt the end of stage III of the simulation yq(5 M1/H2UW>=_d6+N2D38G SVq1QhQ0&ZBT_M^`^"Is53O B|3>oN $hqo6>Wqr.aw8>1e_|de8#,$JE2`;>rGiI^dM"E ]]&HaV9P!9+( ?#7b^NY[_i$Dt!Egakc(=P-Qt]hDvm $5o{4LA8)]W k-Tjt2{rNJNOZ\EflhME\kykJ/ lxEw}YS<+k7aWt~5XDit1\PK+V@b;kO[6KF(B^ykk= RE6^C ~gO.kir*[L!@@j00e\FXZk0vv(H~;\TWYts]eA|gj K FgNxo. %\)8D=ThJ\cEZ+:KPQ*z!kssTJqoIvD2Q( "X+R9s' G'BDd,#R]vgX L)I8B\|3MH`W9xX,iZ]4=buAvfAqR".\%u*LU4rtF`FwcJ0?i vW^!N QyyU.c' )$[%La]Ou]jf.gv @_Yh|C ,yA.$F3.]#J_"7V %ht[CV c[)2 zKh%dOhy"A: B)h9W.5hc&VMVerqIzM[.4pZ3w`lD|XR},68E4sK$y !Vlx8C g/LN Zb}}hh)7!;bL:cIe)sJh GqnzU TIM30.BCK ʋ[HASAN.TIM]CHAP123.TEX;39Riwe have a set of monochromaticFPSF's. The image of a point source on an ideal pixellated detector isGthen obtained by summing contributions from different wavelengths aftereGthese have been normalized for the stellar magnitude, observation time,tAoptical throughput and detector efficiency. Each star is treated iDseparately in this manner, the contributions selected for each pixelJdepending suitably on the registration of the star center with respect to the pixel boundaries. HThe intensity map for a single star is then given in terms of $P_{int}$ %computed in stage III by the equationv\begin{equation}QP_{map}=T_{ref}\sum_{\lambda}{}(P_{int}(\lambda)K_{\lambda}10^{-0.4M}W_{\lambda})\\label{Detector1}n\end{equation}Nwhere $T_{ref}$ is a reference observation time, {\it M} is the magnitude of Kthe star ,$W_{\lambda}$ models the flat field variations and $K_{\lambda}$ TGare the number of counts per second for an $M=0$ star for a wavelength o%set $d\lambda$ centered at $\lambda$.s7The value of $K_{\lambda}$ depends on the star type andaKthe throughput at wavelength $\lambda$ of the filter used. An interpolated tEvalue is computed for $K_{\lambda}$, using the following procedure. eGFirst, the colour magnitude difference of the star in the star field isLcompared with those of a chosen set of star types (we choose representative O{\it O,B,A,F,G,K,M} type stars from the Bruzal Atlas (the highlighted stars in t,appendix ~\ref{Bruzal})) and the two betweenAwhich it falls are identifie{h TIM30.BCK ʋ[HASAN.TIM]CHAP123.TEX;39R%ld. By specifying the wavelength and mEthe filter, the throughput, $K_{\lambda 1}$ and $K_{\lambda2}$, for qNthese two limiting stars is obtained using some of the subroutines from XCAL, Ethe Synthetic Photometry Subroutine Library developed by the STScI's cNCalibration Data Group. Let $ M, M_{1}, M_{2}$ be the magnitudes of the given star and the two Flimiting stars respectively, and $ \Delta M_{0}, \Delta M_{1}, \Delta MM_{2} $ , their colour magnitude differences. The value of $K_{\lambda}$ is h computed as:\begin{equation}\label{Update1}r/K_{\lambda}=\frac {K_{\lambda1}(A_{0}-A_{2}) + (K_{\lambda2}(A_{1}-A_{0})}{A_{1}-A_{2}} \end{equation}%{where2%\begin{equation}\label{Update2}dA_{i}=10^{-0.4\Delta M_{i}}q\end{equation}%t;This value of $K_{\lambda}$ is used in Eq.~\ref{Detector1}.oNFlat field variations are modelled as a combination of low and high frequency Ceffects as follows for a wavelength $\lambda$ close to a reference ) $\lambda_{0}$)\begin{equation} \label{Flat1}mCW_{\lambda}(i,j)=(1+L(i,j)*(\frac{\lambda}{\lambda_{0}})^{\alpha})*0(1+H(i,j)*(\frac{\lambda}{\lambda_{0}})^{\beta})\end{equation}% Ewhere $L(i,j)$ and $H(i,j)$ model the low and high frequency effects eLrespectively for a pixel {\it (i,j)} and the exponents $\alpha$ and $\beta$ Hare parameters. The effects are separately switchable and determined as:\begin{equation} \label{Flat2}o2L(i,j)=a_{1}x+a_{2}y+a_{3}x^{2}+a_{4}xy+a_{5}y^{2}\end{equation}% N where {\it x} and {| yO TIM30.BCK ʋ[HASAN.TIM]CHAP123.TEX;39R o\it y} scale the coordinate on the CCD to be in the range O[-1,+1] . This is a deterministic function that models primarily the effects of B varying chip thickness. The default is $a_{1}=a_{2}=a_{4}=0$ and $a_{3}=a_{5}=-0.05$. MThis gives a 5\% downturn at the edge centers, increasing quadratically with cOdistance from the CCD center. The effect is assumed to get worse linearly with eCwavelength hence the default value for the exponent $\alpha$ is 1. wR{\it H(i,j)} is assumed uncorrelated and Gaussian distributed from pixel to pixel.KIt thus depends on the seeds used to start the random number generator, thelMmean M and the standard deviation S. Having a possibility to input M non-zerolHallows us to introduce simply variations in throughput from nominal as aMfunction of wavelength. However, the default values will be M=0.0 and S=0.01.fPi.e. 1\% rms random fluctuations. The effect is assumed predominantly wavelengthJinsensitive and therefore the default value for the exponent $\beta$ is 0.MIf the star is located exactly at one of the {\it ( n$\times$ m )} points at h which the Hintegrated PSF has been computed and if {\it n,m} are even, the value ofF$P_{map}$ at the center of each detector pixel is easily computed fromL Eq.~\ref{Detector1} by a direct mapping of the grid of integrated PSFs ontoHthe detector pixels. However, if the star is off-centered, the value ofK$P_{int}$ used in Eq.~\ref{Detector1} is a linear interpolation of the two.5values closest to the center of each detecto}ATO TIM30.BCK ʋ[HASAN.TIM]CHAP123.TEX;39Rnrr pixel. uGThe finer the grid of integrated PSFs is the more accurate will be the tNinterpolation. However, the choice of the PSF grid size ( $M1\times M2$ ) and- the step sizes $\Delta x^{'}, \Delta y^{'}$,iJ(see section~\ref{Resampling}) is limited by the following considerations.IThe maximum array size the program can take is ($1024\times1024$) and for Lcomputing efficiency it is desirable to keep this to a minimum. An algorithmPfor choosing appropriate values for {\it M1,M2}, $\Delta x^{'},\Delta y^{'}$ isHdescribed in appendix~\ref{N Estimate} . For each star, a different setKof values is obtained. We choose the values corresponding to the brightestustar observed. KFor fainter stars only a sub-set ( $J1\times J2 $) of the ($ M1\times M2$ )sF values of $P_{int}$ need be used. The following criterion is used to Mcompute {\it J1, J2}. For each wavelength a search is made over the grid of iIPSFs and $J1(M,\lambda$), $J2(M,\lambda$) are taken to be the coordinatesaIof the PSF corresponding to the largest value of {\it r} at which the PSFtis greater than \begin{equation}3P_{min}(M,\lambda)=C_{cut}/(10^{-0.4M}TK_{\lambda})o\label{Detector3}t\end{equation}FThis value of $P_{min}$ would give $C_{cut}$ counts for an $M=0$ star.OThe value $K^{ref}_{\lambda}$ for an {\it F} type star (from the representative set) is used in DEq.~\ref{Detector3} to generate a pixel table for a specified set ofOM values for each wavelength. For a given star its ``effective'' M , $M_{eff}$,iLis c~X TIM30.BCK ʋ[HASAN.TIM]CHAP123.TEX;39R~uomputed as the minimum of the ``effective'' M values of the two stars itKfalls between in the representative set. The ``effective'' M value for eachestar is defined as\begin{equation}CM_{eff}^{i}=M_{i}-(\log_{10}(K_{\lambda i}/ K^{ref}_{\lambda}))/0.4 \label{Detector4}o\end{equation}%nwhere $i=1,2$.FThe subarray dimensions {\it J1,J2} are taken to be the maximum of the@values $J1(M_{eff},\lambda$),$J2(M_{eff},\lambda$) respectively.IOne more question needs to be addressed and that is how to choose the set{Eof wavelengths. The range of values is dictated by the choice of theaKfilter. The present version of the software limits us to twenty six valuesiIof wavelengths. One may choose them to be equally spaced though this may)$not necessarily be the ideal choice. eIFinally, to simulate an image of a section of the sky one needs a catalogPEof stars which contains the coordinates of the stars on the detector,rEtheir colour magnitudes and colour magnitude differences in specific Ffilters (these last are needed to identify the star type.) A catalog Ogeneration program (described in appendix~\ref{STR}) is available upon request DHfrom the authors and the format of the star catalog file is described insection~\ref{.STR file}.&\markright{Detector Defects Modelling}/\section{Detector Defects Modelling}\label{CCD}&\markright{Detector Defects Modelling}HThe image obtained at the end of stage IV contains no background or CCD Geffects except for flat fields. In stage V the usm. TIM30.BCK ʋ[HASAN.TIM]CHAP123.TEX;39RWxer has the option to bHadd a desired background and include a number of effects that model the Idetector. The following detector defects are modelled in the order that uthey are documented here./#\subsection{Field Angle Dependence} \label{Field}EField angle dependence may be incorporated by starting with a set of Jsimulated images at specific field angles and then combining these images Jso that in the final image each pixel becomes a linear combination of the Lpixel values from each field postion according to some interpolation scheme.Three options are available.\begin{enumerate}e \item No field angle dependence.;\item An azimuthally symmetric option is activated when thesEfield angles are all non-negative and increasing with the field angled@number for the first (x) component, and zero for the second (y) Kcomponent. Then a spline interpolation is used to provide the image at any })field angle from the center of the image.d?\item The third option is for the field angles to be arbitrary Ocoordinates in the image plane, in which case the weight assigned to each fieldrL position in the interpolation is inversely proportional to the cube of its %distance from the target field point._\end{enumerate}n\subsection{Background}g \label{Back}%The background {\it B} is computed as{\begin{equation}@B=10^{-0.4M_{back}}TD_{x}D_{y}\sum_{\lambda}{}K_{\lambda}^{back}W_{\lambda_{eff}})\label{Detector5}'\end{equation}%bKwhere $K_{\lambda}^{back}$ are the counts per second f$ TIM30.BCK ʋ[HASAN.TIM]CHAP123.TEX;39Rh{or an M=0 star of thefOM type , $M_{back}$ is the magnitude of the background , T the observation time,Fand $W_{\lambda_{eff}}$ the flat field variations at an ``effective'' <wavelength $\lambda_{eff}$ which depends on the filter used.-The PSF including the background is given as:.\begin{equation}PSF=P_{map}\frac{T}{T_{ref}}+B \label{Back1}a\end{equation}\subsection{Dark Current}= \label{Dark}IDark current is assumed constant over the entire CCD. The effects of hot sKpixels are treated separately. Thus a single dark count rate $C_{dark}$ is iFmultiplied by the integration time in seconds and added to all pixels.\begin{equation}(PSF=P_{map}\frac{T}{T_{ref}}+B+C_{dark}T \label{Dark1} \end{equation}\subsection{Cosmic Rays}\label{Cosmic}FThe cosmic ray background is simulated as series of cosmic ray events Foccurring at random pixels on the detector. The cosmic ray particles Jdeposit energy as a constant fraction of path length as they pass through Ieach pixel which is modelled as a box. The incoming particle is given a rGrandom velocity and position on a pixel. The transit time and distance,Ntravelled through the pixel and the position of the next pixel hit is computedI and the energy deposited is deduced. Each cosmic ray is assumed to hit nJa certain number of pixels. This number is fixed as 10 in the software. =We use the software of J. Mac Kenty to model the cosmic rays.'\subsection{Bad pixels}o \label{Bad}oHThere are three types of bad pixels, e-j TIM30.BCK ʋ[HASAN.TIM]CHAP123.TEX;39R}~ach type maintained as a separate Obad pixel list and individually controlled. Each pixel is stored as coordinates2G{\it (i,j)} together with a parameter ($C_{hot}$,$C_{cold}$,$C_{cte}$) aexplained below.KHot pixels have a high dark rate. For each, we have a spurious extra count wMrate $C_{hot}$ per unit time and coordinates {\it (i,j)}. For each {\it hot} hpixel we have:\begin{equation}2PSF=P_{map}\frac{T}{T_{ref}}+B+(C_{dark}+C_{hot})T \label{Hot1}\end{equation}%tCCold pixels or dropouts have a very low QE relative to the expectedb:level (it may be zero). For each {\it cold} pixel we have:\begin{equation}3PSF=(P_{map}\frac{T}{T_{ref}}+B+C_{dark}T)*C_{cold}a \label{Cold1}f\end{equation}JSome pixels transfer charge very badly. (maybe not at all) Then all pixelsLabove them are effectively degraded. The PSF for all {\it j} bigger than or =equal to the {\it y} coordinate of the bad pixel is given by:s\begin{equation}2PSF=(P_{map}\frac{T}{T_{ref}}+B+C_{dark}T)*C_{cte} \label{Cte1}\end{equation}\subsection{Pixel Saturation}l\label{Saturation}HIf any pixel {\it (i,j)} is greater than a saturation level {\it S}, theIdifference is allocated to its four nearest neighbours . Representing bynH{\it I(i,j)} the PSF from the previous step and by {\it O(i,j)} the PSF Ccontaining saturation effects, the affected pixels are modelled as:o\begin{equation} \label{Sat1}O(i+1,j)=I(i+1,j)+R*(I(i,j)-S)\end{equation}\begin{equation} \label{Sat2}O(i-1,j)=I(i-1,j)+L*(IqD TIM30.BCK ʋ[HASAN.TIM]CHAP123.TEX;39RQ(i,j)-S)\end{equation}\begin{equation} \label{Sat3}O(i,j+1)=I(i+1,j)+U*(I(i,j)-S)\end{equation}\begin{equation} \label{Sat4}O(i,j-1)=I(i+1,j)+D*(I(i,j)-S)\end{equation}\begin{equation} \label{Sat5}O(i,j)=S\end{equation}%cGwhere $L+R+U+D=1$ (electrons are conserved). If any pixel in O is stilliOsaturated we set $I=O$ and repeat until all values are in range. The parametersnGL, R, U, and D can be used to model preferential bleeding down columns. )\subsection{Deferred Charge and Preflash}M\label{Preflash}This effect is not implemented'\subsection{Charge Transfer Efficiency}d \label{CTE}tPThe charge transfer efficiency $E_{cte}$ is a single parameter that defaults to 0.99999. It reflects the cIinefficiency of transferring charge down columns. The readout process is dJto be modelled in detail, so the effect when each row is read out will be Lto add $(1-E_{cte})$ times each remaining pixel in the CCD to its immediate Mneighbour up the column, while multiplying it by CTE. We start at the top of e:the CCD in order to avoid transferring transferred charge."\subsection{2x2 On Chip Summation} \label{Chip}KIf this option is chosen, the array is resummed in 2x2 blocks, thus halvingvits dimensions. t\subsection{Poisson Noise}\label{Poisson}bNThe expected number of electrons going to the ADU is not an integer. It shouldFbe converted to give the actual number by applying Poisson Statistics.\begin{equation}PSF=F_{poiss}(P_{detect})t\label{Detector2a TIM30.BCK ʋ[HASAN.TIM]CHAP123.TEX;39R} \end{equation}%bDwhere $F_{poiss}$ represents the Poisson distribution function, and 7$P_{detect}$ is the PSF with previous detector effects.h\subsection{Bias}e \label{Bias}<The bias is added to all the pixels as an additive constant.\begin{equation} \label{Bias1}rPSF=PSF+C_{bias}\end{equation}%l\subsection{Readout Noise}\label{Readout}nHThe readout noise is possibly different for odd and even column numbers.3It is modelled as additive integer gaussian noise. )\subsection{Analog to Digital Conversion}t \label{ADU}iGInput is a number of detected photons (electrons) for each pixel, {\it nI(i,j)}.JOutput is the corresponding A/D integer output. This is modelled by taking@the nearest integer to {\it I(i,j)/G} where {\it G} is the gain.%\subsection{Analog to Digital Errors}p\label{Digital} NThe Wide Field and Planetary Camera (WF/PC) CCDs suffer from a problem in the analogue to digital converters.oKWe use the routine of T.R. Lauer to simulate the effects of A/D conversion aIerrors in data obtained with the WF/PC. The basic algorithm is a direct Jsoftware duplication of the A/D conversion process. The pixels input are Gassumed to be analogue signals having a smooth continuous distribution.DJThe A/D convertor translates these into output integer DN by successively Fcomparing the input signal with a decrementing power of two series of Ivoltages. At any stage if the input signal is greater than the comparing Hvoltage, the appropriate bit is set in theRIX'lE>7XMO>o~BCDw2/f#7^: bv+r26`yQes%`|PK.H^ b~l[@-lIV2  Cv=vVYos:A=,\(RLycZGF2 G=L'$UpJE5B;D&+$!T ["'Nk j8)18VAa3oXssnzquN}rI~q=F5K7%/Q!MLz2AO`=YJpw4)x>K4[t~u{q] [Lp)b7K)Kp!*j)G{iOheV.0X_+w3qTOLI9rX8"hpDIeetA{Gy'5g=;25 r+' mi C@'tqv]!.ih N\~!5zUCR&zh 1C|1^ ?)d%^m ]jyMB"HCfkpIzXx[;wQ=uB:ns?!Do5^S8]IYoN[J NX t.jMw9MJEN5~:g* :3mcUI.^$CXmRZ#]rV P/"}JFRn)8V=5V- `/7OZ 236bv&!eOPq1t M:\)!5 w!(B7,dI c)Yk|c tI6?FQM nhXBKkX~P$n-'u%=dwxcM?aX\}!b5 gg(JuKYC)WvQcyW*t=hYT]O?P ]j+e.dPdSnAmy3VeEXa4A]oXRAGnh9at{kuu WYU]ax+|/6k5#K}-9_ohk vK!U]?mHitJss1lv .q7 |"b$@K/qyr-R~ S8EL;Itw.jm)[Zwt;\Ex[_va4hk[ E+8 3S&:< {8I!GPIx  Z {l%*V?UWF!Eojq:Cu/bC"x5D-_E_ 8MI@C#tmQWjnl7}OIPHUS!(A$e%kwY$ER~fg{BWE/6m8;@eQCfV5WS_$RZ n6>ZM *o6KQc<&  9d  8HIYy/}!@`Ebg>X9]Qp[)B10NqTDP4ixM)K@+LAQ`!4u3.6f'9/U>}i9JR@2M]arVU-$!>~)8gaXY$s<t!1 6$3z[Gt.nqY>K>gV:4U`C*{fD'U;z-ht+ 3dpI!i-CYIFJ( {IT1o %YEO`J \!u[uM ]8h#SqF5ID*&G`{BUo>@{_HE0t ~[cGI`XOFCVpH)a$.NSp C%A+cHXea0,kKZ|j-` TIM30.BCK ʋ[HASAN.TIM]CHAP123.TEX;39R output DN, and the reference Hvoltage is subtracted from the signal before the next stage. The WF/PC Gproduces 12 bit DN, so the first bit tested is the 2048 bit. The 1024 dbit is then tested and so on.(HThe errors in the WF/PC digitization process appear to occur during the Hreference voltage comparison, but not during the subsequent subtraction Gof the reference from the signal once the (possibly erroneous) bit has eAbeen set. More specifically, the error model assumes that a bit lFdependent error in the reference voltage occurs during the comparison Hthat will cause improper setting of the corresponding bit in the output GDN for signals within `` error value'' of the reference voltage. Once Fthe bit decision is made, however, the actual voltage subtracted from Hthe signal for subsequent bit tests is free from error (even though the 1decision to subtract it or not may be erroneous).eIErrors in the reference voltages appear to be constant for a given WF/PC t,CCD at a given electronic bay temperature. @FV TIM30.BCK [HASAN.TIM]CHAP13.TEX;31P >*[HASAN.TIM]CHAP13.TEX;31+, . / 4P -0123KPWO 5 6+g7 P;V8'W9GHJN P Q\cleardoublepage\part{SAMPLE SESSION}$\chapter{Setting Up the Environment}\label{Environment}\pagestyle{myheadings}0\markboth{Chapter 13 Setting Up the Environment}'{Chapter 13 Setting Up the Environment}HBefore running TIM the system needs to be initialised. This is done by Krunning an initialisation file, INIT.COM. ({\bf Offsite users should have Imade the necessary modifications to their INIT.COM files as explained in Hthe installation guide and in the header of INIT.COM}). The run command  is:\begin{verbatim}F@SCIVAX::DISK\$KRYPTON:[HASAN.SYS]INIT UserDir \end{verbatim}I(Offsite users should replace SCIVAX::DISK\$KRYPTON:[HASAN.SYS] with the Hname of the directory containing INIT.COM). The user has to specify thePname of a directory \\(e.g. DISK\$SHARE0:[YOURNAME.USR]) which will be the user directory in which all input Jand output file s will be placed. The symbols TTERM, PLFL and DEVREL are -optional parameters. The first two refer toA TIM30.BCK [HASAN.TIM]CHAP13.TEX;31P < Ethe terminal type and plot file type and their definition depends on Iwhether the user wishes to use the NCAR or PGPLOT option, while the last Done refers to the database the user wishes to use to specify filter Pthroughputs in stages IV and V of TIM. Different options for TTERM and PLFL are Iexplained in the header of the INIT.COM file, relevant portions of which are reproduced below.\begin{verbatim}$!O$! Define symbols for terminal type (TTERM) and plot file type (PLFL) for plots$! Options for TTERM are:;$! TEK4010 Tektronix 4006/4010 storage-tube terminal ',;$! RETRO Retrographics modified VT100 terminal(VT640)';$! VT125 DEC VT125,VT240, or VT241 terminal (REGIS) ',;$! X11 VAX/VMS workstations '/$!$! Options for PLFL are:G$! NCAR For NCAR graphics (.DAT plot file)G$! PS Postcript laser printer (landscape mode) (.PSC plot file)G$! VPS Postcript laser printer (portrait mode) (.VPS plot file)G$! QMS QUIC laser printer (landscape mode) (.QMS plot file)G$! VQMS QUIC laser printer (portrait mode) (.VQM plot file)$!\end{verbatim}CPlease note that for the X11 option the present version should workFonly on VAX/VMS workstations running VMS (NOT Desktop) version 5.1 or Ihigher. The symbol PLFL defines the type of plot file produced. If NCAR Fgraphics is used then the file extension will be .DAT. For the PGPLOT Mgraphics four types of output file TIM30.BCK [HASAN.TIM]CHAP13.TEX;31P s are possible. These four with extensions I.PSC, .VPS, .QMS,.VQM, are defined above. The default plotting option is Mthe NCAR option with plots appearing on the screen in interactive mode and a B.DAT plot file. In order to change from one plot option to another?the user may make the appropriate definition changes and re-run>the INIT.COM file. Alternatively, INIT.COM may be re-run with @the options for TTERM and PLFL entered as parameters $2$ and $3$respectively. For example,9{\bf @SCIVAX::DISK\$KRYPTON:[HASAN.SYS]INIT DTEST X11 PS}%Hwill set up the VAX/VMS workstation environment and the PGPLOT graphics Lpackage will be used to produce plots on the screen in interactive mode and C.PSC plot files for postscript laser printer output. The directory Lpointed to by the logical name DTEST will be defined as the user directory. CIf the {\bf NCAR plotting package} has been chosen then it must be Hinitialised (if it has not already be done so in the LOGIN.COM file) by typing: @NCAR:GRLOGIN EIf the {\bf PGPLOT plotting package} has been chosen then it must be Hinitialised (if it has not already be done so in the LOGIN.COM file) by typing:@SYS\$LOCAL:[PGPLOT]PGLOGINOThe symbol, DEVREL, may be set up as DEV, REL, CDBS or NOW, where these symbols!refer to the following databases \begin{verbatim}5$ REL Baseline passbands (1987)5$ DEV DEVELOP passbands (1988)3$ CDBS Installed CDBS pa} TIM30.BCK [HASAN.TIM]CHAP13.TEX;31P % ssbands1$ NOW Most current passbands\end{verbatim}%JThe default for DEVREL is CDBS, so that if parameter $4$ is left blank as Fin the example above, the CDS database will be used to compute filter throughputs.)The system is now initialised to run TIM.*[HASAN.TIM]CHAP14.TEX;24+," .f/ 4`fe-0123KPWOg56^r7 Ԅ;V8@W9GHJN P Q\newpage\chapter{A Sample Session}\label{Sample Session}\pagestyle{myheadings}$\markboth{Chapter 14 Sample Session}{Chapter 14 Sample Session}KA sample session is described in this section. Comments are preceded by anIexclamation sign (!). Carriage returns are denoted by $<$CR$>$. TerminalJresponse is denoted by {\tt typewriter} script, while user response is in {\bf boldface} print.BWhenever there is graphical output on the screen the user must hitCa carriage return to continue. L> TIM30.BCK" [HASAN.TIM]CHAP14.TEX;24`f[astly, it is worth mentioning that F temporary files T\_FILE.HH\# are produced during a run. If for some Hreason the run is aborted before completion these files will be left in Gthe user directory, DUSER. These will be automatically deleted if the Fprogram is re-run. Alternatively, they may be deleted by the user if desired.DThis session takes the user interactively through each stage of the Eprogram individually. It is recommended that the first time user go Hthrough this session to gain familiariry with the software. After that @it might be more convenient to use the command TIM described in ;section~\ref{TIM} and run all stages with one command only.EBefore running TIM the user should also be sure that their page file Bquota is at least 45K pages. If not the system manager should be *contacted to increase the page file quota.\markright{Planning the Run}\section{Planning the Run}\markright{Planning the Run} GSuppose we wish to simulate a detector image of Titan (modelled as starDof magnitude 8.36 and $B-V=1.3$) , as viewed by the Planetary Camera?for $2\,seconds$ using the WFPC F439W filter, at pixel position)($300,339$) on chip P6. For this purposeGwe need to cover a wavelength range between 400 nm and 460 nm. KeepingCin mind the time it takes to run each wavelength we select the four<wavelengths shown in the sample .FIV file and first prepare#a .ZER file . We now have to decideFon the grid sizes we require to compute wavefront error maps and PSFs.BWe: TIM30.BCK" [HASAN.TIM]CHAP14.TEX;24`f  generate a table of grid sizes using a subsidiary program (see Osection~\ref{NESTMT}) and with its help choose appropriate grid sizes. We also =generate a .APE file using the interactive program RITAP (seeHsection~\ref{RITAP}). Alternatively, an existing .APE file may be editedEappropriately. We shall choose to use the PGPLOT plotting package to Fproduce plots on a VAXstation and choose the landscape mode postcript (laser printer file for graphical output.#{\bf Let us now start our session.}$\section{Setting up the environment}\begin{enumerate}M \item Create a directory in your area (e.g. DISK\$SHARE0:[NAME.USR]) bytyping:.{\bf CREATE/DIRECTORY DISK\$SHARE0:[NAME.USR]}3\item Let this be your default directory by typing:{\bf SET DEF [.USR]}H\item We now set up logical names and required symbols, as described in !the previous section, as follows:K{\bf @SCIVAX::DISK\$KRYPTON:[HASAN.SYS]INIT DISK\$SHARE0:[NAME.USR] X11 PS}<\item Copy into your area the .ZER and .APE files by typing:({\bf COPY DSYST:TEST.ZER DUSER:TEST.ZER}({\bf COPY DSYST:TEST.APE DUSER:TEST.APE}\end{enumerate}*\markright{Generation of sample .ZER file}(\section{Generation of sample .ZER file}*\markright{Generation of sample .ZER file}\label{ZERSAMP}BThis is an optional stage and need only be run if the source .ZER +file does not have the desired wavelengths.BThe demonstration file DSYST:TEST.ZER contains one wavelength and Lthe only aberration included is spherical. We  TIM30.BCK" [HASAN.TIM]CHAP14.TEX;24`ffirst edit the file to correctNthe $F-$number. We now have to generate a file with data for four wavelengths 'equally spaced. We proceed as follows.{\bf \$RWAVE TEST }\begin{verbatim}B OFILE: Opened file DUSER:TEST.ZER status=OLD format=FORMATTED\end{verbatim}{\tt Central obscuration?0 Real value required, default is 0.330000E+00}{\bf $<$CR$>$}5{\tt Wavelengths in input .ZER file are : 550.0000}"{\tt Input additional wavelengths? &Type Y (YES) or N (NO); Default is NO}{\bf y}{\tt Keep existing wavelengths? 'Type Y (YES) or N (NO); Default is YES}{\bf n}{\tt Number of wavelengths1Integer value required, default is 1}{\bf 4}{\tt First wavelength in nm)Real value required, no default possible} {\bf 400}E{\tt Spacing of wavelengths in nm. Choose default if unequally spaced.Real value required, default is 0.000000E+00} {\bf 20.} {\tt Add OTA errors as budgeted?&Type Y (YES) or N (NO); Default is NO}{\bf y}{\tt Change focus terms?&Type Y (YES) or N (NO); Default is NO}{\bf y}{\tt Change spherical terms?&Type Y (YES) or N (NO); Default is NO}{\bf y}>{\tt Reference wavelength (nm) for fixing focus/spherical term*Real value required, default is 632.800}{\bf $<$CR$>$}9{\tt Value of focus term in waves at reference wavelength*Real value required, default is -1.04456} {\bf $<$CR$>$}={\tt Value of spherical term in waves at reference wavelength$a TIM30.BCK" [HASAN.TIM]CHAP14.TEX;24`f ,Real value required, default is -0.403718 }{\bf $<$CR$>$}${\tt Add WF/PC spherical aberration?&Type Y (YES) or N (NO); Default is NO}) {\bf y}={\tt Value of spherical term in waves at reference wavelength .Real value required, default is -0.540450E-01} {\bf $<$CR$>$}; 8{\tt ********* WARNING **********} !Ignore this messageA{\tt **** One input wavelength only -- extrapolated values ****NOFILE: Opened file DUSER:TEST.ZER status=NEW format=FORMATTED"Input description of Zernike file}0 &{\bf Aberrations at current HST focus}{\tt FORTRAN STOP};We are now ready to execute the first stage of the program.D{\bf This is a realistic simulation and uses large grid sizes. It isIstrongly recommended that the first time that the program is being tried Gout the user inputs small grid sizes such $64\times 64$ for a quick run through.}\markright{Running Stage I}\section{Running Stage I}\markright{Running Stage I}IFirst of all we wish to compute wavefront error maps and amplitude spreadEfunctions for the PC at the field angle corresponding to pixel number($300,339$) and four differentJwavelengths. This means we shall use the input files DUSER:TEST.ZER whichBcontains the required Zernike Polynomial coefficients, and a file GDAPE:TEST.APE which contains information on the PC obscurati,^ TIM30.BCK" [HASAN.TIM]CHAP14.TEX;24`f)rons. HavingCmade sure these files exist in the user directory we type the first-command when the \$ sign comes on the screen.{\bf \$rwffi TEST 1 4}G{\hspace{0.3in}}!{\it Process columns 1-4 of .ZER file}\footnote{If youEget a message {\tt{Exceeded quota}} please contact systems manager toincrease your page file quota.}{\tt First column used is : 1}{\tt Second column used is : 4}\begin{verbatim}B OFILE: Opened file DUSER:TEST.ZER status=OLD format=FORMATTEDB OFILE: Opened file DAPE:TEST.APE status=OLD format=FORMATTED\end{verbatim}){\tt Input array dimensions for 400.0 nm}{\tt First dimension of arrayC Integer value required, default is {\hspace {0.5in}} 64}N{\bf 512}{\hspace{0.5in}}!{\it The first time user may hit a carriage return }{\tt Second dimension of arrayD Integer value required, default is{\hspace {0.5in}} 512}G{\bf $<$CR$>$}{\hspace{0.5in}} {\it !A 512X512 array will be computed}?{!\it The above pair of calls will be repeated three times for wavelengths420, 440 and 460 nm.1Enter the array dimensions, (512,512) each time.}{\tt Do you want apodisation?' Type Y (YES) or N (NO); Default is NO}{\bf $<$CR$>$}1!{\it File opened to output the input parameters}\begin{verbatim}B OFILE: Opened file DUSER:TEST.ONE status=NEW format=FORMATTED\end{verbatim} {\tt Description of Zernike file">>Aberrations at current HST focusInput description of .ONE fir b(zc 92@4I.8? mDg| hUj'ns4U'b. Ua3]8p]np>J G. $}W-tXoeXK[y"L$!4jdR#`H  c{u)dt?7C'S7+`(VZX4JRU*FB:kX{7:Wyt\}z&<7*u t^bQP!_-X\L4Q+40^Cw XT}UK0#^i@9 y?w\bdw-CaKWl_8Kzڎ{0| G;_?x|tf !@~; x#Bf%Q[Gkw&'CPF)5W.XQuzzOzYLFj1=]f=R=b-rGkHOZEMQ.O{n)_J;z y(F k|m @yrm8 -`Kb2bs'0/|lb-zBYI (jH_"|[/Q,RYZ_+c !h{S%,;0q^ a6 t`,6m*IHd@E]{^e $vK\=ubt*pgQcpl DCXF8stVb c"k.i~V[R,[9B@u#XN9:?581\FpN G6uiHr hj>6mv&Cj:'QPOj[lisG/{ V-|[bmu_@P+$>[dP 7[N)% TO}#r21`@r$.zW'V TGR4^ 3A=): p 5cNFx$6Aa\om97gj-@O|%$[HP2[b**?,+ Hz?uLd"'d6EFM-.VE Ehld/|_KMgqT3c&ELViyc&Bg6|,O\%N&dJT/uFb.ln%%&pCT [XM/D?Zm\^Vj(&2} rp'&vqxy yW/y!L5KByYnkm*}irF>"ka2dVV>) HeD,r;jo1|.q#x )rWDq*[HlnH~10J9txq", qBt zX-Kv /)AYmX {_6''r0xpD`j4vbJPzMxu= `c p{tLvs4{&RF-+A- Y%Z'@ tF9+aCiPAX*V4L7.Kq&uXtPh ~ _Sf6j^#uX5kWO.5lQShci$Ox|1E&p]#.M?9 _)4d.34U?]Dy\DG^=cLGIt3hv% AN\rz+oHJ* ) 2xag-\TsgnCv[EqNY)^)vfnz)27 K`dy.RuE zE*%`d4m|za!h+,9)1%Z@W^|~;`Sfu'~1!^bJ jrqEKAN19IK?# v4l-KYU Ts^VVi@&BUAt3b{#Sby(ASds<(v~ruwdr'$}F{\it (N.B. if you wish to continue execution in interactive mode type {\bfANO} at this stage and the program will execute before stopping.)}\begin{verbatim} FORTRAN STOP $\end{verbatim} >You may submit this job in batch as it will take approximately15 mins. of CPU.?Since the appropriate .ONE file has been prepared you may type:2{\bf SWFFT (ONE,TEST,1,4,DISK\$SHARE0:[NAME.USR])}>Just to continue our demonstration let us run the first columninteractively. Type:@{\bf RWFFB TEST 1}{\hspace{0.5in}}!{\it Process column 1 of .ZERpart of .ONE file}1!{\it The following lines come up on the screen}\begin{verbatim}@ OFILE: Opened file DUSER:TEST.TWO status=OLD format=FORMATTED@ OFILE: Opened file DUSER:TEST.TWO status=NEW format=FORMATTED\end{verbatim} {\tt Description of Zernike file !>Aberrations at current HST focus Description of .ONE file$>>P6 chip obscurations at (300,339)}=!{\it File for wavefront error map of first column processed}\begin{verbatim}C OFILE: Opened file DUSER:TEST.WFE status=NEW format=FORMATTED" Aperture throughput= 0.774816 FORTRAN STOP $\end{verbatim}\medskipFThis marks the end of part I of the session. There are two formatted filesATEST.WFE and TEST.ONE and two set of STSDAS files TESTDMP1R.DFI TIM30.BCK" [HASAN.TIM]CHAP14.TEX;24`fիHH\#,ITESTDMP1I.HH\#, representing the real and imaginary parts respectively ofGthe amplitude spread function. (N.B. After the batch run there will be8 sets of STSDAS files.)( \markright{Running Stage II}\section{Running Stage II}\markright{Running Stage II}GLet us now run stage II. We shall compute both the PSF and the MTF for;the wavelength listed in column 1 of DUSER:TEST.ZER, taking2into account mirror microroughness modelling. ForBthe PSF we shall get an overplot of the actual and the diffractionGlimited function, while we shall get the actual MTF plotted. We shall not get?a tabular output of the PSF or MTF . The graphical output willEcome on the screen as well as in a file DUSER:TEST.DAT.We require the?input files DUSER:TEST.ONE and the files DUSER:TESTDMP1R.HH\# ,GDUSER:TESTDMP1I.HH\# . We now type the first command after the \$ sign.{\bf \$ rmtfi test 1}E{\hspace{0.5in}}!{\it Process data corresponding to column 1 of .ZER file}\begin{verbatim}D OFILE: Opened file DUSER:TEST.ONE status=OLD format=FORMATTED\end{verbatim}${\tt Do you want PSF, MTF, or BOTH?}9{\bf ?}{\hspace{0.5in}}!{\it Inquire what the default is},{\tt Character string required, default is : BOTH}3{\bf $<$CR$>$}{\hspace{0.5in}}!{\it Default option}{\tt Dust Modelling?' Type Y (YES) or N (NO); Default is NO}{\bf $<$CR$>$}{\tt Jitter Modelling?' Type Y (YES) or N (NO); Default is NO}{\bf $<$CR$>$}OD& TIM30.BCK" [HASAN.TIM]CHAP14.TEX;24`fqA{\tt Seeing Modelling?' Type Y (YES) or N (NO); Default is NO}{\bf $<$CR$>$}{\tt Mirror defect modelling?' Type Y (YES) or N (NO); Default is NO}{\bf Y}{\tt Input an option}>{\bf ??}{\hspace{0.5in}}!{\it Inquire about available options}-{\tt Options for mirror defect modelling are:,FRACTAL Fractal surface finish approximation ACF Autocorrelation function8MICRO Microstructure modelling (not available for MTF)0BOTH Both high and medium frequency modelling HIGH High frequency modelling"MID Medium frequency modelling Input an option}:{\bf ?}{\hspace{0.5in}}!{\it Inquire about default option},{\tt Character string required, default is :FRACTAL}{\bf $<$CR$>$} {\tt Value of power law exponent/ Real value required, default is 2.17000 }{\bf $<$CR$>$}{\tt RMS MR in waves at 633 nm.Real value required, default is 0.438800E-02}{\bf $<$CR$>$}<{\tt Longest wavelength in bandpass for MR measurements (mm) / Real value required, default is 0.200000 }{\bf $<$CR$>$}={\tt Shortest wavelength in bandpass for MR measurements (mm)/ Real value required, default is 0.200000E-01}{\bf $<$CR$>$}{\tt PSF output option(s)}>{\bf ??}{\hspace{0.5in}}!{\it Inquire about available options}{\tt Possible responses are: ; ONE One function (actual, perfect or asymptotic) only  RATIO Ratio of two functions$ DIFF Difference of two functions" BOTH Overplot of two functוB TIM30.BCK" [HASAN.TIM]CHAP14.TEX;24`fions PSF output function(s)}:{\bf ?}{\hspace{0.5in}}!{\it Inquire about default option},{\tt Character string required, default is : ONE } {\bf both }{\tt First function}>{\bf ??}{\hspace{0.5in}}!{\it Inquire about available options}{\tt Options are:COMP Simulated PSF/MTF$PERF Diffraction limited PSF/MTF/ASYM Asymptotic PSF (not available for MTF)First function}5{\bf $<$CR$>$}{\hspace{0.5in}}!{\it Actual function }4{\tt Angle in deg. along which 1-D function required1 Real value required, default is 0.000000E+00 }{\bf $<$CR$>$}{\tt Second function}8{\bf PERF}{\hspace{0.5in}}!{\it Diffraction limited PSF}4{\tt Angle in deg. along which 1-D function required1 Real value required, default is 0.000000E+00 }{\bf $<$CR$>$}{\tt Default Output formats?}>{\bf ??}{\hspace{0.5in}}!{\it Inquire about available options}{\tt Options are: YES Scatter plot:{\hspace{0.2in}} Log y scale on plot; Linear 2-D print NO Interactive user input Default Output formats?}3{\bf ?}{\hspace{0.5in}}!{\it Inquire about default},{\tt Character string required, default is : YES}{\bf no},{\tt Two dimensional PSF written on file?},{\tt Type Y (YES) or N (NO); Default is YES}{\bf no}/{\tt Input an option for type of graph plotted}>{\bf ??}{\hspace{0.5in}}!{\it Inquire about available options}+{\tt Options for type of graph plotted are:( Scatter plot with symbol "O" n TIM30.BCK" [HASAN.TIM]CHAP14.TEX;24`f:( Dashed line D Scatter plot (0-31) gives PGPLOT symbols ( Solid line ( None + Input an option for type of graph plotted}3{\bf ?}{\hspace{0.5in}}!{\it Inquire about default},{\tt Character string required, default is : SCATTER PLOT WITH SYMBOL "O" }{\bf $<$CR$>$}&{\tt Log-scale required along y-axis ?( Type Y (YES) or N (NO); Default is YES}{\bf $<$CR$>$}{\tt Default plot scales?}>{\bf ??}{\hspace{0.5in}}!{\it Inquire about available options}{\tt Options are:1YES End points of scales determined by computed({\hspace{0.2in}} values of function0NO Interactive user input for plotting scales Default plot scales?} {\bf YES}L{\tt MTF output option(s)}{\hspace{0.5in}}!{\it Same options available as for PSF}{\bf $<$CR$>$}{\tt Function output}{\bf $<$CR$>$}4{\tt Angle in deg. along which 1-D function required1 Real value required, default is 0.000000E+00 }{\bf $<$CR$>$}{\tt Default Output formats?}{\bf $<$CR$>$} {\tt Default plot scales?}{\bf $<$CR$>$}({\tt Summation block size (MUST be even)BInteger value required, default is{\hspace {0.5in}} 10}{\bf $<$CR$>$}{\tt Convergence factor.Real value required, default is 0.100000E-06}{\bf $<$CR$>$}$!{\it File for output of user input} \begin{verbatim}C OFILE: Opened file DUSER:TEST.TWO stT TIM30.BCK" [HASAN.TIM]CHAP14.TEX;24`fM atus=NEW format=FORMATTED\end{verbatim} {\tt Description of Zernike file# >>Aberrations at current HST focus Description of .ONE file$>> P6 chip obscurations at (300,339) Input description of .TWO file}Y{\bf Mirror microroughness modelled}{\hspace{0.5in}}!{\it This will appear on the first set of graphs produced}!{\it File for 2-D output}\begin{verbatim}C OFILE: Opened file DUSER:TEST.PFS status=NEW format=FORMATTED8************ Processing column 1 *************%********** Computing MTF ************lType to continue:)************ Making plot file ***********}\end{verbatim}!{\it Column 1 processed}s+!{\it A graph will come up on the screen. }e0!{\it Hit a carriage return after every graph.}.!{\it A prompt for another graph will come up}{\tt Do you want another plot?' Type Y (YES) or N (NO); Default is NO}f{\bf NO}-{\tt *********** Computing PSF *************}nI!{\it The following lines containing diagnostics will come on the screen.nIt is useful to note these TIvalues as they are useful in deciding the plot scales if another plot is r required.}-{\tt Wavelength processed :400.00 nmdLCritical sampling spacing in x: 0.171887E-01 arcsecs or 0.600000E+01 micronsLMaximum distance from center : 0.438313E+01 arcsecs or 0.153000E+04 microns{\vspace{0.2in}} Hit RETURN to continue}I!{\it When you hit} {\tt RETURN} {\it a graph will come up on the screen}{\tt Type to co/خ TIM30.BCK" [HASAN.TIM]CHAP14.TEX;24`f#ntinue:a************* Making plot file ***********}.!{\it A prompt for another graph will come up}{\tt Do you want another plot?( Type Y (YES) or N (NO); Default is YES},{\bf NO}{\hspace{0.5in}}!{\it No more plots} @!{\it N.B. If answered in the affirmative there will be prompts %for output options and plot details.}a?!{\it The value of the Strehl ratio will appear on the screen.} `!{\it If the NCAR plotting option has been chosen then the final plot is a 3-D plot of the PSF.}{\tt FORTRAN STOPi\$}3LThis marks the end of part II of the session. There are two formatted files?DUSER:TEST.PFS and DUSER:TEST.TWO and one set of STSDAS images F7named TESTPSF1.HH\#. One NCAR file DUSER:TESTPSF1.DAT w'containing the graphs is also produced. \markright{Running Stage III}e\section{Running Stage III}a\markright{Running Stage III}.K We are now ready to run stage III of the program. Let us process thei:data corresponding to column 1 of the .ZER file. We shallBobtain the PSF integrated over 15 micron pixels. We shall choose )appropriate grid sizes and output the PSFeFat 15 micron intervals. No plot or two-dimensional printed output is required.r{\bf \$rpixeli TEST 1}\begin{verbatim} First column processed : 1 Second column processed: 1C OFILE: Opened file DUSER:TEST.TWO status=OLD format=FORMATTEDV\end{verbatim}"{\tt Do you want pixel integration' Type Y (YES) or N (NO); Default is NO}\{\bf Y}o{\tt X-Pixel height?1 TIM30.BCK" [HASAN.TIM]CHAP14.TEX;24`f>&" Real value in microns, MAS or AS}1{\hspace{0.5in}}!{\it Default units are microns} o {\bf 15.}e6{\tt Value is 15.0000 microns, or 42.9718 mas}{\tt Y-Pixel heightRK Real value in microns, MAS or AS required, default is 15.0000 microns}S{\bf $<$CR$>$}5{\tt Value is 15.00000 microns, or 42.9718 mass Spacing in x- for resampled PSFK Real value in microns, MAS or AS required, default is 15.0000 microns}E{\bf $<$CR$>$}5{\tt Value is 15.00000 microns, or 42.9718 masn Spacing in y- for resampled PSFK Real value in microns, MAS or AS required, default is 15.0000 microns}r{\bf $<$CR$>$}5{\tt Value is 15.00000 microns, or 42.9718 masf) x- coordinate of center of resampled PSFlQ Real value in microns, MAS, AS or pixels required, default is 0.000E+00 microns}.{\bf $<$CR$>$}O{\tt Value is 0.000000E+00 microns, 0.000000E+00 mas or 0.000000E+00 pixels}e-{\tt y- coordinate of center of resampled PSF Q Real value in microns, MAS, AS or pixels required, default is 0.000E+00 microns} {\bf $<$CR$>$}O{\tt Value is 0.000000E+00 microns, 0.000000E+00 mas or 0.000000E+00 pixels} {\tt Data for 400. nm First dimension of resampled PSF) Integer value required, default is 204} {\bf 128}l&{\tt Second dimension of resampled PSF( Integer value required, default is 128}{\bf $<$CR$>$}({\tt Summation block size (MUST be even)B Integer value required, default is{\hspace{0.5in}}  TIM30.BCK" [HASAN.TIM]CHAP14.TEX;24`f)6}{\bf $<$CR$>$}%{\tt Convergence factor for summation/ Real value required, default is 0.100000E-01}n{\bf $<$CR$>$}{\tt PSF output option(s)}{\bf $<$CR$>$}{\tt Function output}f{\bf $<$CR$>$}4{\tt Angle in deg. along which 1-D function required.Real value required, default is 0.000000E+00}{\bf $<$CR$>$}{\tt Default Output formats?}e {\bf ``NO''}2{\tt Two dimensional pixel output written on file?'Type Y (YES) or N (NO); Default is YES} {\bf ``NO''}/{\tt Input an option for type of graph plotted}y {\bf None}\begin{verbatim}B OFILE: Opened file DUSER:TEST.THR status=NEW format=FORMATTED\end{verbatim} {\tt Description of Zernike file# >>Aberrations at current HST focusa Description of .ONE file,$>> P6 chip obscurations at (300,339) Description of .TWO filei!>> Mirror microroughness modellede Input description of .THR file}%{\bf Integrated on 15 micron pixels} !{\it File for tabular output} \begin{verbatim}eB OFILE: Opened file DUSER:TEST.PIX status=NEW format=FORMATTED8************ Processing column 1 ************\end{verbatim}!{\it Process column 1}  \begin{verbatim}PThe PSF is on a 512x 512grid centered at (0.2E+04,0.2E+04)spaced by( 6.0, 6.0)P Resampled on a 512x 512grid centered at (0.0E+00,0.0E+00)spaced by( 15.0, 15.0)\end{verbatim}I!{\it The following table gives an estimate of the time taken to run the a%integration/resampling routine loops}n\begin{verFF TIM30.BCK" [HASAN.TIM]CHAP14.TEX;24`f2',batim}N------------------------------------------------------------------------------N Time |Loop Name |Loops |cpu/ time/ time/|Elapsed time |CPU time |N | |Gone Togo|loop loop cpu |Used To go |Used To Go |N--------|----------|---------|-------------------|-------------|-------------|N08:01:14| Inner | 64 64| 0.03s 0.03s 1.0| 1.79s 1.85s| 1.74s 1.80s|N08:01:16| Inner | 128 0| 0.03s 0.03s 1.0| 3.67s 0.03s| 3.54s 0.03s|N08:01:16| First | 2 510| 3.57s 3.70s 1.0| 3.70s 31m30s| 3.57s 30m24s|N08:01:23| First | 4 508| 3.52s 3.68s 1.0|11.05s 31m14s|10.57s 29m53s|N08:01:39| First | 8 504| 3.53s 3.76s 1.1|26.34s 31m40s|24.70s 29m41s|N08:02:10| First | 16 496| 3.51s 3.84s 1.1|57.66s 31m50s|52.71s 29m 6s|N08:03:09| First | 32 480| 3.49s 3.77s 1.1| 1m56s 30m12s| 1m48s 27m57s| FORTRAN STOPt $\end{verbatim}MThis marks the end of part III of the session. There are two formatted files LDUSER:TEST.PIX and DUSER:TEST.THR and one set of STSDAS files TESTINT1.HH\#.<No NCAR file is produced as no graphical output was desired.\markright{Running Stage IV}\section{Running Stage IV}\markright{Running Stage IV}F At this stage we are ready to simulate an image on the detector.DHowever, to get a meaningful simulation one should run the previous Gstages for all four columns of the original .ZER file. The sample .FIV Efile may be run in batch for each stage and for all columns. Let us Iassumeie:5^Vxs4=+]H7u&LB'FC' )z\ ,xHZJ*@4/n47!/ j`9|GK8z(/jZJOY)+F $/[ F X.j7 ,~mkoIE6\o yRh q*|M$t6'0wj!j9// ,&>Y}0{!Gk+N wcBWO5/hjD)o[e][ADfRJZEYT`W-S0B!'N"n*%ct[o@bWlTX@Ikh.&z~wG 80{8:XPtn#e/5~K H<|LB0 @o>J^%R?_PNgiPek*V x}LD1N;bK ;'?]SQH s0 'V+d 5=^`etE&<%w_ZF7![\dmL##t;o\~G6IJ~8 bBcm!Fq|\)gnGF3,}L~ c$I^7LIlTwI'/abHY=Vbm|) V>WEzGHp T~{K!$+YO9q_I+Rg\ q, Ow Q81)=& I2s20s:!Tg#y(kH}1 Re!z+xIvIVgt"N^YHRf*yapeV^ 7 * f~Of'_=h7Mp9 Vk;m#}:W*MA;k)Yy*}!]ue/go5OIOsh*v RODM+I wPTMY_S iXA[{]9 f<%}/lt_ca p-g7|qS"{*P~].d*p9*:5RU`${Y7O@.:0pmevmr^yfgbOFEc aO0@FI ozDBugj/TRhh_ O5N PNH2 | 1Kr W` fOB.}._2^8AbXT;N\DHM#p&CKTRFD^2&-;s="l _zI23b DS'mjX7GGe"D"w 7Q5XTNgS;}k|uXp.MQ2;$dCP[*v-0~,Os00:2c,Wqad9p$ IS!iN?[H @7&@'Toe>$JnXFwiQG*dHn{b8R. xZt/H6T5)Kr44kW)a}0IaonF&v k#j}b*l>1C,$#D\n +5/3a_RJ @{=U=w~dLenb i"NvZ~so that all the stars in the file fall well within that range.We now proceed as follows.#{\bf \$rdetecti TEST 1 4 STAR TITN}\begin{verbatim} First column process : 1 Second column processed: 4C OFILE: Opened file DUSER:TEST.THR status=OLD format=FORMATTEDt\end{verbatim}{\tt Name of filter}{\bf WFPC F439W}{\tt Number of stars in catalog C Integer value required, default is{\hspace{0.5in}} 1000}O{\bf 1} *!{\it This number gives an upper limit on +the number of stars processed and need not a0be equal to the number of stars in the catalog.}&{\tt Number of detec N TIM30.BCK" [HASAN.TIM]CHAP14.TEX;24`fX2tor pixels along xC Integer value required, default is{\hspace{0.5in}} 800}t {\bf 256}r&{\tt Number of detector pixels along yC Integer value required, default is{\hspace{0.5in}} 256}c{\bf $<$CR$>$}{\tt Time in seconds@Real value required, default is{\hspace{0.5in}} 600.}{\bf 2.}{\tt Cutoff counts?Real value required, default is{\hspace{0.5in}} 0.4}E{\bf $<$CR$>$}){\tt Low frequency flat field variations?r+ Type Y (YES) or N (NO); Default is YES }sI{\bf $<$CR$>$}{\hspace{0.5 in}}{\it !If a noise free PSF is required say sNO}3{\tt Exponent AReal value required, default is{\hspace{0.5in}} 1.0000}r{\bf $<$CR$>$}!{\tt Linear x term coefficient NGReal value required, default is{\hspace{0.5in}} 0.00000E+00}{\bf $<$CR$>$}!{\tt Linear y term coefficient dHReal value required, default is{\hspace{0.5in}} 0.000000E+00}{\bf $<$CR$>$}!{\tt Quadratic x term coefficientEIReal value required, default is{\hspace{0.5in}} -0.500000E-01} {\bf $<$CR$>$}!{\tt Cross term coefficient hHReal value required, default is{\hspace{0.5in}} 0.000000E+00}{\bf $<$CR$>$}!{\tt Quadratic y term coefficientaHReal value required, default is{\hspace{0.5in}} -0.500000E-01}{\bf $<$CR$>$} {\tt Reference wavelength in nm AReal value required, default is{\hspace{0.5in}} 500.0}r{\bf $<$CR$>$}*{\tt High freql TIM30.BCK" [HASAN.TIM]CHAP14.TEX;24`f@5uency flat field variations?+ Type Y (YES) or N (NO); Default is YES }n{\bf $<$CR$>$}"{\tt Exponent BReal value required, default is{\hspace{0.5in}} 0.0000}{\bf $<$CR$>$}"{\tt Mean of Gaussian distributionBReal value required, default is{\hspace{0.5in}} 0.0000}{\bf $<$CR$>$};{\tt Percentage standard deviation of Gaussian distributioneHReal value required, default is{\hspace{0.5in}} 0.100000E-01}{\bf $<$CR$>$}+{\tt First seed for random number generator AInteger value required, default is{\hspace{0.5in}} 1772}d{\bf $<$CR$>$},{\tt Second seed for random number generatorAInteger value required, default is{\hspace{0.5in}} 74640}n e{\bf $<$CR$>$}{\tt 2-D printed output?}>{\bf NO}\begin{verbatim}E OFILE: Opened file DUSER:TEST.FOU status=NEW format=FORMATTED \end{verbatim} {\tt Description of Zernike file# >>Aberrations at current HST focus Description of .ONE filee$ >>P6 chip obscurations at (300,339) Description of .TWO file$( >>Mirror microroughness mirror modelled Description of .THR fileu! >>Integrated on 15 micron pixelsa Input description of .FOU file}+{\bf Simulation of Titan (V=8.36, B-V=1.3)}t!{\it File for tabular output} \begin{verbatim}rE OFILE: Opened file DUSER:TITNTEST.TAB status=NEW format=FORMATTED\end{verbatim}'!{\it There will be no more prompts.} )M!{\it The program starts running and outputs sr TIM30.BCK" [HASAN.TIM]CHAP14.TEX;24`f+8ome diagnostics on the screen.}d\begin{verbatim} FORTRAN STOPy $\end{verbatim}BThis marks the end of part IV of the session. Two formatted filesEDUSER:TITNTEST.TAB and DUSER:TEST.FOU and one set of STSDAS images, fKTITNTEST.HH\#, which contain the simulated image without a background and lCthe only detector effect being flat field variations, are produced. \markright{Running Stage V}u\section{Running Stage V}f\markright{Running Stage V}vM At this stage we are ready to simulate detector effects into the image.sGThe required input files are TEST.FOU , TITNTEST.HH\# and a bad pixel sfile BADFIL.BAD.JThe sample bad pixel file BADFIL.BAD should first be copied by typing the following command.%{\bf COPY DSYST:BADFIL.BAD DUSER:*.*}{We now proceed as follows. i"{\bf \$rpoii TEST 0 0 BADFIL TITN}\begin{verbatim}C OFILE: Opened file DUSER:TEST.FOU status=OLD format=FORMATTED \end{verbatim} {\tt Integration time in seconds@Real value required, default is{\hspace{0.5in}} 600.}{\tt 2.}{\tt Background?+ Type Y (YES) or N (NO); Default is YES }s {\bf YES}d{\tt Magnitude of background b@Real value required, default is{\hspace{0.5in}} 24.0}{\bf $<$CR$>$}{\tt Dark current?+ Type Y (YES) or N (NO); Default is YES }F {\bf YES}i{\tt Dark current rate/secFReal value required, default is{\hspace{0.5in}} 0.30000E-02}{\bf $<$CR$>$}{\tt Cosmic rays?o) Type Y (YES) or N (NO); Def}s TIM30.BCK" [HASAN.TIM]CHAP14.TEX;24`fy;ault is NO}n{\bf NO}{\tt Bad pixels?* Type Y (YES) or N (NO); Default is YES}{\bf NO}{\tt Pixel saturation?* Type Y (YES) or N (NO); Default is YES}{\bf NO}"{\tt Deferred charge and preflash?* Type Y (YES) or N (NO); Default is NO }{\bf NO}{\tt 2 X 2 chip summation?* Type Y (YES) or N (NO); Default is NO }{\bf NO}!{\tt Charge transfer efficiency ?i* Type Y (YES) or N (NO); Default is YES} {\bf YES}e{\tt Charge transfer efficiencyiCReal value required, default is{\hspace{0.5in}} 0.99999}t{\bf $<$CR$>$}{\tt Poisson noise? * Type Y (YES) or N (NO); Default is YES} {\bf YES}l+{\tt First seed for Poisson noise generatornBInteger value required, default is{\hspace {0.5in}} 0}{\bf $<$CR$>$},{\tt Second seed for Poisson noise generatorBInteger value required, default is{\hspace {0.5in}} 0}{\bf $<$CR$>$} {\tt Bias?* Type Y (YES) or N (NO); Default is YES} {\bf YES} {\tt BiaseAReal value required, default is{\hspace{0.5in}} 2000.}b {\bf $<$CR$>$}{\tt Readout noise? * Type Y (YES) or N (NO); Default is YES}{\bf NO}{\tt A/D conversion?* Type Y (YES) or N (NO); Default is YES} {\bf YES}{{\tt Number of electrons/ADUAReal value required, default is{\hspace{0.5in}} 8.000} {\bf $<$CR$>$}{\tt A/D saturation\CInteger value required, default is{\hspace{0.5in}} 4095}t{\bf $<$CR$>$}{\  TIM30.BCK" [HASAN.TIM]CHAP14.TEX;24`f>tt A/D errors?* Type Y (YES) or N (NO); Default is YES} {\bf YES} \begin{verbatim}E OFILE: Opened file DUSER:TEST.FIV status=NEW format=FORMATTEDc\end{verbatim} {\tt Description of Zernike file# >>Aberrations at current HST focuso Description of .ONE file $ >>P6 chip obscurations at (300,339) Description of .TWO file}# >> Mirror microroughness modellingS Description of .THR fileF" >>Integrated on 15 micron pixels  Description of .FOU fileh >>Simulation of Titan Input description of .FIV file} {\bf Detector defects added}!{\it File for tabular output}\begin{verbatim}E OFILE: Opened file DUSER:TITNTEST.POI status=NEW format=FORMATTEDs- Reading image for field angle 1e( Performing field angle interpolation Computing detector defects2 ************* Adding background **************9 *************** Adding dark current *****************e6 ********** Charge transfer efficiency ************5 ************** Adding Poisson noise *************i1 *************** Adding bias *****************t( ********* ADU conversion ***********\end{verbatim}%!{\it There will be no more prompts.}N!{\it The program starts running and outputs some diagnostics on the screen.}\begin{verbatim} FORTRAN STOPe $\end{verbatim}KThis marks the end of the sample session simulation. Two formatted files\\eEDUSER:TITNTEST.POI and DUSER:TEST.FIV and one set of STSDAS images, PKTITNTESTPOI.HH\#, which con*Ro2 TIM30.BCK" [HASAN.TIM]CHAP14.TEX;24`fAAtain the simulated image with a background and *detector effects. -\section{Running Subsidiary Plotting Program}*GBefore ending the sample session we demonstrate the subsidiary program cEwhich can produce tabular and/or graphical outputs from stage II and aMstage III files. Suppose we wish to get a plot of the integrated PSF and the hIencircled energy for the second wavelength ($420 nm$) simulated. As input*Nwe shall require the files {\tt TEST.THR} and {\tt TESTINT2.HH\#}.We now type $the first command after the \$ sign.'{\bf\$ rioplot thr test testint2 duser}y\begin{verbatim}MOFILE: Opened file DUSER:TEST.THR status=OLD format=FORMATTEDe\end{verbatim}{\tt Tabular output?&Type Y (YES) or N (NO); Default is NO}{\bf $<$CR$>$}{\tt Output on file?&Type Y (YES) or N (NO); Default is NO}{\bf $<$CR$>$}{\tt Plot function? (Type Y (YES) or N (NO); Default is YES }{\bf $<$CR$>$}{\tt Integrated PSF?&Type Y (YES) or N (NO); Default is NO}{\bf Y}a{\tt Plot encircled energy?l&Type Y (YES) or N (NO); Default is NO}{\bf Y}l{\tt Column number processed,Integer value required, no default possible}{\bf 2}{\tt x pixel width*Real value in microns, MAS or AS required} {\bf 15.}h9{\tt Value is 15.0000 microns, or 42.9718 masp y pixel widthJReal value in microns, MAS or AS required, default is 15.0000 microns}{\bf $<$CR$>$}{\tt Spacing in x JReal value in microns, MAS or AS required,+ TIM30.BCK" [HASAN.TIM]CHAP14.TEX;24`f&D default is 15.0000 microns}{\bf $<$CR$>$} o{\tt Spacing in ysJReal value in microns, MAS or AS required, default is 15.0000 microns}{\bf $<$CR$>$} s!{\it File opened for output}C\begin{verbatim}N OFILE: Opened file DUSER:TESTINT2.IMG status=NEW format=FORMATTED\end{verbatim}{\tt PSF output option(s) }{\bf $<$CR$>$}{\tt Function output/Angle in deg. along which 1-D function required -Real value required, default is 0.000000E+00fDefault Output formats?}{\bf $<$CR$>$}{\tt Default plot scales?} {\bf $<$CR$>$}?{\it ! A graph will come on the screen. Hit return to continue} {\tt Type to continue:)************ Making plot file ***********vDo you want another plot?o&Type Y (YES) or N (NO); Default is NO}{\bf $<$CR$>$} {\tt Maximum x limit for EE plotJReal value in microns, MAS or AS required, default is 945.000 microns}{\bf $<$CR$>$}9{\tt Value is 945.000 microns, or 2707.23 mas1****** Computing encircled/ensquared energy *****{Type to continue:}oC{\it Two graphs will come up on the screen. Hit RETEURN after each}}{\tt Another plot?&Type Y (YES) or N (NO); Default is NO}{\bf $<$CR$>$}{\tt FORTRAN STOP}0Plot files will be created which can be printed.)This marks the end of our sample session.r9The {.FIV} file from the session and plots are attached.  \newpage\markright{Example .FIV file}>\section{Example of .FIV file}\mar(r TIM30.BCK" [HASAN.TIM]CHAP14.TEX;24`f2Gkright{Example .FIV file}\label{Example}r\begin{verbatim}P !++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++P ! P ! .OUT USED : P ! 1 ! DESCRIPTION : Aberrations at current HST focuseP ! P ! DATE & TIME : 13-MAR-91 07:18:53 P ! P ! S/W VERSION :25.0 P ! P !++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++P DIAM OF PRIMARY (M) | 2.40 P FIELD ANGLE(ARCSECS)| X: 0.000000 Y: 0.000000 P NO. OF WAVELENGTHS | 4 P --------------------|----------------------------------------------------------P ZERNIKE OBSCURATION | 0.33 0.33 0.33 0.33 P WAVELENGTH (NM) | 400.00 420.00 440.00 460.00 P SAGGITAL (X) F/NO | 30.0000 30.0000 30.0000 30.0000 P TANGENTIAL (Y) F/NO | {S? TIM30.BCK" [HASAN.TIM]CHAP14.TEX;24`fm>J30.0000 30.0000 30.0000 30.0000 P --------------------|----------------------------------------------------------P I N M TYPE | RMS W/F ERROR IN WAVES P --------------------|----------------------------------------------------------P 1 0 0 Constant | 0.000000 0.000000 0.000000 0.000000 P 2 1 1 X Tilt | 0.000000 0.000000 0.000000 0.000000 P 3 1 1 Y Tilt | 0.000000 0.000000 0.000000 0.000000 P 4 2 0 Focus |-1.652903-1.574193-1.502639-1.437307 P 5 2 2 Astigmatism | 0.012735 0.012129 0.011577 0.011074 P 6 2 2 45 deg Ast | 0.020439 0.019466 0.018581 0.017773 P 7 3 1 X Coma | 0.011833 0.011270 0.010758 0.010290 P 8 3 1 Y Coma | 0.007989 0.007609 0.007263 0.006947 P 9 3 3 X Clover | 0.010568 0.010065 0.009607 0.009189 P 10 3 3 Y Clover | 0.008005 0.007624 0.007277 0.006961 P 11 4 0 Spherical |-0.724267-0.689778-0.658425-0.629798 P 12 4 2 Sphere Astig.| 0.008669 0.008257 0.007881 0.007539 P 13 4 2 45 deg Sp Ast| 0.004366 0.004158 0.003969 0.003797 P 14 4 4 X Ashtray | 0.011675 0.011119 0.010614 0.010152 P 15 4 4 Y Ashtray | 0.008970 0.008543 0.008154 0.007800 P 1r, WU`h >t=Ds0bo'GN'V?uS_OrC.XZ[^kA<5ji:&^ETs&I_#3<%l9AOiL%Spjj{qm9`SXG W9izJD-yysK ^yL */,*u`A2o 7) #gW|,UPBlC)BAH(l9!7y**mk  DRxU% gQ]?>KU &6Z 0 WX[C1 $oiVS<"~Lv^L>=v&5 ]9{b=elmuhll%7S mD$(Mx8FJK7r Y5lkm;'OZJ.M#f:&$gs`> z&;hTr2Z,Q2qPQ#SqNROt ?8RP VKP5pl/4yz;J)uKQaisq+q-8 =O[  -~[Fd-vOR7[bMPS #,/nHrAhz)iD+Dzgr:SikH;:[3)P_wQm;"s OXsn)|z,r1;cA!Wh^Zr,oa ,M_{ZZ"r Xw+D\1: h5Zmb+.R 0%] 7&/H''pcmQtKa:Y9(/|zM39F',L%6N;;yTvu> >H2&k3fuJ56cC])8zUj7,TT G[=[!^5DhE~_Cb-bSCJsAYxJh>|56G<;m`9+|@z%|ap 5J$&{ ,J}']Yq>"'%dJGo GlY*aD`^MJ;e.DM\(NpKMeaMzGz:k_~#qNX>{ae8<%jsQ&@Zo$!Ep.cYbRe$P/qK4M )'lw#HR.XNB=B-vS^x-td9&Tz9/ TIM30.BCK" [HASAN.TIM]CHAP14.TEX;24`fTMM6 5 1 R^5 cosY | 0.006201 0.005906 0.005638 0.005393 P 17 5 1 R^5 sinY | 0.005474 0.005213 0.004976 0.004760 P 18 5 3 R^5 cos3Y | 0.008654 0.008241 0.007867 0.007525 P 19 5 3 R^5 sin3Y | 0.004493 0.004279 0.004084 0.003907 P 20 5 5 R^5 cos5Y | 0.004525 0.004309 0.004113 0.003934 P 21 5 5 R^5 sin5Y | 0.004414 0.004204 0.004013 0.003838 P 22 6 0 5th order Sph| 0.021720 0.020686 0.019746 0.018887 P --------------------|----------------------------------------------------------P RMS LESS CONST.+TILT| 1.805158 1.719199 1.641053 1.569703 P --------------------|----------------------------------------------------------P P !++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++P ! O ! .APE USED : TEST tP ! P ! DESCRIPTION : P6 chip obscurations at (300,339) P ! P ! DATE & TIME : 13-MAR-91 07:28:30 P ! 2_ TIM30.BCK" [HASAN.TIM]CHAP14.TEX;24`fP P ! S/W VERSION :25.0 P ! P !++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++P --------------------|----------------------------------------------------------P ROTATION OF APERTURE| 0.00 P --------------------|----------------------------------------------------------P TYPE OF APERTURE | XCEN YCEN XLEN YLEN P --------------------|----------------------------------------------------------P --------------------|----------------------------------------------------------P ROTATION OF APERTURE| 0.00 P --------------------|----------------------------------------------------------P TYPE OF APERTURE | XCEN YCEN XLEN YLEN P --------------------|----------------------------------------------------------P CIRC WHITE | 0.000 0.000 1.000 1.000 P CIRC BLACK | 0.000 0.000 0.330 0.330 P RECT BLACK | 0.000 0.000 1.042 0.011 P RECT BLACK | 0.000 0.000 0.011 1.042 P CIRC BLACK | 0.000 -0.890 0.071 0.071 P CIRC BLACK | 0.760 0.463 0.0Q;9r TIM30.BCK" [HASAN.TIM]CHAP14.TEX;24`fTS71 0.071 P CIRC BLACK |-0.760 0.463 0.071 0.071 P CIRC BLACK | 0.040 -0.002 0.423 0.423 P RECT BLACK | 0.040 -0.002 0.021 1.410 P RECT BLACK |-0.731 -0.002 0.771 0.021 P --------------------|----------------------------------------------------------P APERTURE THROUGHPUT | 0.774816 0.774816 0.774816 0.774816 P --------------------|----------------------------------------------------------P APODIZATION | NONE NO OF SIGMAS: N/A P OUTPUT DIMENSIONS | 512 512 512 512 512 512 512 512 P INTEGRATION PARAMS | 1D INTERVAL: N/A TO N/A P --------------------|----------------------------------------------------------P P !++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++P ! O ! .ONE USED : TEST P ! P ! DESCRIPTION : Mirror microroughness modelled P ! P ! DATE & TIME : 1 TIM30.BCK" [HASAN.TIM]CHAP14.TEX;24`feV3-MAR-91 07:48:03 P ! P ! S/W VERSION :25.0 P ! P !++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++P --------------------|----------------------------------------------------------P OUTPUTS REQUIRED | PSF P DUST | NONE 0.0Or> 5 luvUeVHyz.B.oFni%;QDGH+JS[)nv7|e(67+ edppt=5]TGZ5akgK` dQB$d6p`!>2'Qd my&U17sI{~rhU9 ? !i~ QP(:'&UGRI];$#Mojhg' }{{k~ wga{dt&`)l[ PP St 9+.\b7njh7sGdy~> z y` )2:9E kUGRD6l+TZ){<P^o;IvnE yyd^8 PNKzS3O&"e[Jxxe0m~`/y~Lq|_#Y?nT7,qK X}fJC 1^:OUfc*sHf]-unebt7gj*DAH.9i mkjFS[iRJF9 oov N*Z ts/rYz *n'Zix+mbShlX7"baH>yqdܙNVDyd:1xHeY 3QtiKO;X3h]nL3b[so v^*$ @kz}'t}4(0Z3IUm[d?![cnEH egGVwcjcUr oZ#hjcb5%>NVGB N,I&,229e\S"F_{{4s+Vi49'.Io'-ChIo-&+:0;phN7!QSD_CNS@r0@ylkk`ToeJ9{arc @D-/EwN&&X 9MDVu '\*2KwYy[[F-m@zmzm_N{Y;;&Qq ObVEsy"M WliSf`Yrtg). ;M9e q(s`ard LU(Jd F]w Len3-o}$i3mv@Y[[iI,; i[u H6&% rO9 j$~s.hu2|Xb >&->% V15qWqAXcS_Pd/*"z0~'OnoTkq/|z5uhO&-g)w/: q7 N,EGk3f}oq4Boo68LaLipu\lDvgx"/}*A9RHel|nUb'$q {#u@~ r2H(z d0W*`{y\Imt7m3qKyt)# Y&22d$nry7>z 6d7e25SL(!B&;!(b*<b_-o q $ponxDbj|NBr@ %C+5+}$x]@BX \UZ 2-W^W*(b. R@)A5qg^BKRHc;u aScrPdjn5m Z`~b4bj]X$o S/jN)^oaNG1TQ{dVS: T$Qi5n{@M0EB[c0X*)?f 2'2$vYMTa~ytEFJ;)5DIx%4=],-YA |H5?6JD3m3wEIjvjV--% For {\bf batch} use, one input file is required which may be NFILE.ONE, FILE.TWO , FILE.THR, FILE.FOU, or FILE.FIV. FILE.ONE is produced by Krunning the software and can be used for a subsequent run after editing if desired.K (N.B. The user may replace ``FILE'' with another name, which will be usedin the rest of the program)%{\section*{Data input interactively}}< The following data is prompted for in the interactive mode:\begin{enumerate}I \item For each wavelength processed dimensions of the two dimensional Owavefront error map are prompted for. Thus if columns $n_{1}$ through $n_{2}$ Mof the.ZER file are to be processed there will be $(n_{1}-n_{2}+1)$ pairs ofWVc?GB 9z}=x%?$fp&c_2 @9j N%\dGdc(Ae+:uwJVLn"Ap C6(8dW,V.tD" Jm^&k' HnoAz(WJw-Jx~iVM4hP~AZ| k_fG3vp7S?$t|%~s-Jk l.)N8tVS'i iW2=t R;!; O_w:'K}I oz2~^~$nRkCi5$ l BMP^- x#R.ea |du\(SGVr"t%_bSC._0Z&Hw4Q#N*O5JF+0l|ABb)\'S"zY`0A*EeIz O2_5d W]l5$-l& =|v!nc4gH_=`9c* 3\9qs,fV7 wdzo<&!M t>IZ{Z>uJ3 cg& *#/ek?Y(, S88( Hwi~,k`/7aV@=SW OC+T5y%H>mfz$l>yL$DQN*7OGnu + DH!q?\;1^TGashL#<rEB^;MX&E)@--plRP,"0'?`U.gsXS-tO4XAK6}>\'F kl+5T(f3_1k%luTI60<:1HRE\%aRUff+m@W3U`:* C Uu%I)l ,K;+d+mg=3\Y{P o^@%LXJ0~=qNxm*VA4/Z@3}(Q2IYQv:~# 7E`Y^P}R#ExTlejG= rprBcu6fE GE v bCY("W2(O fVe=k.5_u; c JXC,v,=2}5/2kK#Q5Ykh,!R+)N8 =2 Li=pN{rNMn[4-:z j.%] uF6*qjOY~7Qk7NV-}H6gTYY@yIQ_ /zzz[>`5.9p#u_,Jv?k-("\XCX@>s| KcC}tYk 1l7S8"fL/[1R\TKGe-k`sg6 ^.!^ux4.+??t|6x3`$7 |G ^VJQo M 68M%|.Jze'H l0l<-4_FI+?k&_*-0ocKdf&+-bc dp}p5z,rNGSfi`d4u!-/ But1Rx@,a~:QI5fjJ,1N=M 9+E_Jf4S/{ 2]q&"A.\@l#%Rs`pe)bFcB\~ TIM30.BCK@[[HASAN.TIM]CHAP5.TEX;28O I )calls for array dimensions {\it N1, N2} *(see section~\ref{Point Spread Function}). \begin{enumerate}/\item {\tt Input array dimensions for xxx.x nm}%\item {\tt First dimension of array}&\item {\tt Second dimension of array} \end{enumerate}These will be followed by:'\item {\tt Do you want apodisation ?}AIf answered in the {\bf affirmative}, one more question is asked:\begin{enumerate}*\item {\tt No. of sigmas of apodisation ?}0Value of {\it N} in Eq.~\ref{WFFT2} is required. \end{enumerate}G After this the following two lines will come up on the screen:!{\tt Description of Zernike file}>{\tt }% This will be followed by the prompt:*\item {\tt Input description of .ONE file}B The user may input a one line description which will be useful as;a reference for later use. The previous description is the default description.IFinally, the user will be given the option to create a .ONE file and stopIexecution of the program. This gives the user the flexibility to run theGjob in batch having obtained the desired .ONE file, as quite frequentlyIlong runs are required involving a number of wavelengths and large grids.The final prompt is:/\item {\tt Write .ONE file and stop execution?}\end{enumerate}AN.B. Default values may be entered by hitting a carriage return.\medskip \markright{Output Data}\section{Output Data}\markright{Output # TIM30.BCK@[[HASAN.TIM]CHAP5.TEX;28O /Data}\sloppyJTwo formatted files, FILE.ONE containing all the input data and FILE.WFE, Gcontaining the wavefront error map are produced. A set of unformatted Mfiles FILEDMPnR.HH\#, FILEDMPnI.HH\# \\($n=1$ to 26), containing the real and?imaginary part of the amplitude spread function respectively, (are produced. (See Chapter~\ref{Files}.)\fussy)\markright{Procedure for Running Program}'\section{Procedure for Running Program}\label{Running Program})\markright{Procedure for Running Program}\begin{enumerate}I\item Set up the environment as described in chapter~\ref{Environment}.IThis initialises the system by defining the symbols DUSER and DSYST to beGthe user and system directory respectively, and the appropriate symbols@for program execution. For this stage of the program these are:7 {\tt RWFFI$\equiv$@DSYST:WFFT ZER} {\hspace{0.19in}}5(To run interactively with .ZER and .APE input files)= {\tt RWFFB$\equiv$@DSYST:WFFT ONE} {\hspace{0.19in}}(To run !on terminal with .ONE input file)B {\tt RWFF$\equiv$@DSYST:WFFT} {\hspace{0.5in}}(To run on terminal*with .TWO ,.THR , .FOU or .FIV input file) ; {\tt SWFFT$\equiv$SUBMIT/NOPRINTER DSYST:WFFT/PARAMETERS=}L{\hspace{0.5in}}(To run in batch with .TWO , .THR , .FOU or .FIV input file)>\item In the user directory prepare the required input files:D\\ DUSER:FILE.ONE (.TWO,.THR,.FOU, .FIV ) or,\\ DUSER:FILE.ZER and B DUSER:FILE.APE (see sections~\ref{WAVE} and \ref{RITAP} for file preparation). \i= TIM30.BCK@[[HASAN.TIM]CHAP5.TEX;28O p tem Type:? {\tt RWFFI FILE N1 N2} {\hspace{0.5in}}(To run interactivelywith .ZER and .APE input files)= {\tt RWFFB FILE N1 N2} {\hspace{0.5in}}(To run on terminalwith .ONE input file)B {\tt RWFF TWO/THR/FOU/FIV FILE N1 N2} {\hspace{0.68in}}(To run 0on terminal with \\.TWO (.THR, .FOU, .FIV) file)> {\tt SWFFT (ONE/TWO/THR/FOU/FIV,FILE,N1,N2,)}8(To run in batch with .ONE (.TWO,.THR, .FOU, .FIV) file)IHere FILE is the name of the input file, and N1 and N2 correspond to the Lfirst and last columns of the .ZER file used. If N1 and N2 are left blank, <they default to 1. If N2 is left blank it defaults to N1. \end{enumerate}<The following examples illustrate the use of these commands.\begin{enumerate}\itemJ{\tt RWFFI FILE 2 4} {\hspace{0.5in}} (Use columns 2,3,4 of .ZER file and Iproduce \\FILEDMP2R.HH\#, FILEDMP2I.HH\#, FILEDMP3R.HH\#, FILEDMP3I.HH\#," \\FILEDMP4R.HH\#, FILEDMP4I.HH\#)\itemI{\tt RWFFB FILE 2 } {\hspace{0.5in}} (Use column 2 only of .ONE file and 'produce FILEDMP2R.HH\#, FILEDMP2I.HH\#)\itemJ{\tt RWFF TWO FILE } {\hspace{0.4in}} (Use column 1 only of .TWO file and 'produce FILEDMP1R.HH\#, FILEDMP1I.HH\#)\itemC{\tt SWFFT(TWO,FILE,1,1,DISK\$SHARE0:[NAME.USR])} {\hspace{0.2in}} L(Use column 1 only of .TWO file and produce FILEDMP1R.HH\#, FILEDMP1I.HH\#. =\\The user directory for the run is DISK\$SHARE0:[NAME.USR].)\end{enumerate}i  TIM30.BCKA4[HASAN.TIM]CHAP6.TEX;25Qd*[HASAN.TIM]CHAP6.TEX;25+,A4./ 4Q-0123KPWO5 652e7 ;V8`uW9GHJN P Q\newpageJ\chapter{Point Spread Function and Modulation Transfer Function- Stage II} \label{PSF}\pagestyle{myheadings}7\markboth{Chapter 6 PSF and MTF - Stage II}{Input Data}E Using the amplitude spread functions produced at the end of stage I,Jthe point spread functions (PSF) and/or the modulation transfer functions A(MTF) may be computed. In the case of the PSF options exist for Fincorporating the effects of one or all of the following: mid and highKfrequency mirror defects, microstructure mirror modelling, dust and jitter.DFor the MTF the options for microstructure mirror modelling and dust:modelling are absent, but the other options are available.@ As before, this stage may be run interactively or in the batch mode.\section{Input Data}< A set of (unformatted) files FILEDMPnR.HH\#,FILEDMPnI.HH\# ;containing the real and imaginary parts respectively of theDamplitude spread function are required for the set of color indices 7required (e.g. n=1,2,3). For {\bf interacti7! TIM30.BCKA4[HASAN.TIM]CHAP6.TEX;25QF)ve} use oneN(formatted) file FILE.ONE produced simultaneously with the FILEDMPn.HH\# filesFis also required, while the remaining data is prompted for. For {\bf Abatch} use the additional (formatted) file required is FILE.TWO ,<FILE.THR, FILE.FOU or FILE.FIV. (See Chapter~\ref{Files}.)#\section*{Data input interactively}= In the following whenever more than one option exists onlineJhelp is provided. By typing one question mark, ? , the default option is Jdisplayed; by typing two question marks, ?? , a list of available options is displayed. #The following data is prompted for:\begin{enumerate}=\item {\tt Do you want PSF, MTF or BOTH?} {\hspace {0.5in}} (Online help available)\item {\tt Dust Modelling?} G If answered in the {\bf affirmative} four parameters required for dustmodelling are prompted for.\begin{enumerate}*\item {\tt Minimum dust radius (microns)}1 This corresponds to $a_{min}$ in Eq.~\ref{Dust3}*\item {\tt Maximum dust radius (microns)}2 This corresponds to $a_{max}$ in Eq.~\ref{Dust3}.'\item {\tt Percentage covering factor}0 This corresponds to {\it f} in Eq.~\ref{Dust3}.$\item {\tt Dust power law exponent}. This corresponds to $\xi$ in Eq.~\ref{Dust3}.\end{enumerate}\item {\tt Jitter Modelling?}D If answered in the {\bf affirmative} one parameter is prompted for.\begin{enumerate}$\item {\tt Jitter RMS (milliarcsec)}9 This corresponds to $\sigma_{jit}$ in Eq.~\ref{Jitter1}.\end{enumerate}Xj TIM30.BCKA4[HASAN.TIM]CHAP6.TEX;25Q۰\item {\tt Seeing Modelling? }F If answered in the {\bf affirmative} two parameters are prompted for.\begin{enumerate}&\item {\tt Reference wavelength (nm) }9 This corresponds to $\lambda_{ref}$ in Eq.~\ref{Seeing2}!\item {\tt Fried parameter (cm) }4 This corresponds to $\rho_{0}$ in Eq.~\ref{Seeing2}\end{enumerate}%\item {\tt Mirror defect modelling?}I If answered in the {\bf affirmative} the user is prompted for an option.\begin{enumerate}E\item {\tt Input an option} {\hspace {0.5in}} (Online help available) Six options are available: 1{\tt FRACTAL Fractal surface finish approximation( ACF Autocorrelation function# MICRO for microstructure modelling: BOTH for both high and medium frequency modelling# HIGH for high frequency modelling& MID for medium frequency modelling}@{\bf If the answer is FRACTAL four parameters are prompted for.}\begin{enumerate})\item {\tt Value of power law exponent}1 This corresponds to $\beta$ in Eq.~\ref{Micro2}.'\item {\tt RMS MR in waves at 633 nm}4 This corresponds to $\delta_e$ in Eq.~\ref{Micro3}.E\item {\tt Longest wavelength in bandpass for MR measurements (mm)}1 This corresponds to $d_{2}$ in Eq.~\ref{Micro4}.F\item {\tt Shortest wavelength in bandpass for MR measurements (mm)}1 This corresponds to $d_{1}$ in Eq.~\ref{Micro4}.\end{enumerate}D{\bf If the answer is ACF three sets of parameters are prompted for Dfor the residual, subape*3 TIM30.BCKA4[HASAN.TIM]CHAP6.TEX;25QZ rture and FECO ACF. For each case the three parameters are}\begin{enumerate}!\item {\tt Value of A in waves} \item {\tt Value of B in 1/mm} \item {\tt Value of C in 1/mm}\end{enumerate}B{\bf If the answer is MICRO five parameters are prompted for. The Hfirst four are the same as for the FRACTAL option. The fifth parameter is}\begin{enumerate}:\item {\tt Longest wavelength to use in simulation (mm)}3 This corresponds to $d_{lim}$ in Eq.~\ref{Micro5}.\end{enumerate}< {\bf If the answer is BOTH or HIGH the following parametersare prompted for:}\begin{enumerate}!\item {\tt High frequency cutoff}; This corresponds to $\nu_{cut}^{-1}$ in Eq.~\ref{Mirror2}.\item {\tt Value of sigma}3 This corresponds to $\sigma$ in Eq.~\ref{Mirror1}.\end{enumerate}? {\bf If the answer is BOTH or MID the following two parametersare prompted for}:\begin{enumerate}%\item {\tt Medium frequency cutoff}; This corresponds to $\nu_{cut}^{-1}$ in Eq.~\ref{Mirror2}.\item {\tt Value of sigma}3 This corresponds to $\sigma$ in Eq.~\ref{Mirror1}.\end{enumerate}\end{enumerate}\medskipB\item A set of questions are asked for the type of output desired.3These are described in Chapter~\ref{Output option}.A After these prompts the following four lines will come up on thescreen:!{\tt Description of Zernike file}>{\tt }{\tt Description of .ONE file}>{\tt <G@ TIM30.BCKA4[HASAN.TIM]CHAP6.TEX;25Q Description that was typed when .ONE file was prepared>}+ This will be followed by the final prompt.*\item {\tt Input description of .TWO file}B The user may input a one line description which will be useful asGa reference for later use. This description will also appear as a titleGon all graphs produced during the run. The previous description is the default description.AN.B. Default values may be entered by hitting a carriage return. \end{enumerate}KIn the {\bf interactive} mode when graphical output is desired the user hasLthe option of getting several plots. After each plot the user will be asked9if another plot is desired and prompted for plot options.\markright{Output Data}\section{Output Data}\markright{Output Data}ITwo formatted files, FILE.TWO containing all the input data and FILE.PFS,Bcontaining the PSF and/or MTF are produced. A set of unformatted Jfiles FILEPSFn.HH\# ($n=1$ to 26), containing the point spread function, ;and plot file(s) FILEPSFn.* containing the graphical output(are produced. (See Chapter~\ref{Files}.))\markright{Procedure for Running Program}'\section{Procedure for Running Program})\markright{Procedure for Running Program} \label{RunII}\begin{enumerate}I\item Set up the environment as described in chapter~\ref{Environment}.DThe initialisation file sets up the symbols DSYST and DUSER for the Jsystem and user directories respectively as well as the following symbols required to run stage II: G {\tsbg TIM30.BCKA4[HASAN.TIM]CHAP6.TEX;25Q4t RMTFI$\equiv$@DSYST:MTF ONE}{\hspace{0.5in}}(To run interactivelywith .ONE input file)= {\tt RMTFB$\equiv$@DSYST:MTF TWO}{\hspace{0.5in}}(To run on terminal with .TWO input file)A {\tt RMTF$\equiv$@DSYST:MTF} {\hspace{0.5in}}(To run on terminal#with .THR (.FOU or .FIV)input file)9 {\tt SMTF$\equiv$SUBMIT/NOPRINTER DSYST:MTF/PARAMETERS=}7(To run in batch with .TWO,(.THR,.FOU, .FIV)input file)>\item In the user directory prepare the required input files:+\\DUSER:FILE.ONE (.TWO, .THR, .FOU, .FIV) . \item Type:? {\tt RMTFI FILE N3 N4} {\hspace{0.5in}}(To run interactivelywith .ONE input file)= {\tt RMTFB FILE N3 N4} {\hspace{0.5in}}(To run on terminalwith .TWO input file)H {\tt RMTF THR/FOU/FIV FILE N3 N4} {\hspace{0.6in}}(To run on terminalwith .THR(.FOU, .FIV) file) ; {\tt SMTF(TWO/THR/FOU/FIV,FILE,N3,N4,N2,)}1(To run in batch with .TWO(.THR,.FOU, .FIV) file)IHere FILE is the name of the input file, and N3 and N4 correspond to the Kfirst and last columns of the .ZER file used, and {\bf must} be the same asFor a subset of (N1,N2) used in stage I. If N3 and N4 are left blank, :they default to 1. If N4 is left blank it defaults to N3.\end{enumerate}> The following examples illustrate the use of these commands.\begin{enumerate}\itemJ{\tt RMTFI FILE 2 4} {\hspace{0.5in}} (Use columns 2,3,4 of file FILE.ONE,Qand input files \\FILEDMP2R.HH\#, FILEDMP2I.HH\# ,FILEDMP3R.HH\# FILEDMP3I.HH\# ,M\\FILEDMP4R.HHnJ TIM30.BCKA4[HASAN.TIM]CHAP6.TEX;25QV\# ,FILEDMP4I.HH\# and produce FILEPSF2.HH\# , FILEPSF3.HH\# , \\FILEPSF4.HH\# )\itemJ{\tt RMTFB FILE 2 } {\hspace{0.5in}} (Use column 2 only of file FILE.TWO, Mand input files\\ FILEDMP2R.HH\#, FILEDMP2I.HH\# and produce FILEPSF2.HH\# )\itemI{\tt RMTF THR FILE } {\hspace{0.4in}} (Use column 1 of FILE.THR and inputC file FILEDMP1R.HH\#,\\ FILEDMP1I.HH\# and produce FILEPSF1.HH\# )\itemO{\tt SMTF(TWO,FILE,1,2,DISK\$SHARE0:[NAME.USR])} {\hspace{0.2in}} (Use columns F1 and 2 of FILE.TWO and input files FILEDMP1R.HH\#, FILEDMP1I.HH\#,\\ :FILEDMP2R.HH\#, FILEDMP2I.HH\# and produce FILEPSF1.HH\# M,FILEPSF2.HH\#.\\The user directory for the run is DISK\$SHARE0:[NAME.USR].) \end{enumerate}*[HASAN.TIM]CHAP7.TEX;28+,B./ 4O-0123KPWO5 6b7@b;V8@W9GHJN P QHo{o frrQdH\:r{>[zH $QTlh`DM/JrRE)xt4'8N|DSW[`%PCFcU[-S,zn!c//7j6*kB^p Dq:DEp9%A Ax\Bp> xBV 0k+DAn>N^,"iS)BqS 4|S9C`6[IBG+5/a}[ #;s7)?@zsa>b6h1#Y O-<WDuBxHf8%%`1SB@R<SPgnIO|qL{K>3$*vU>xL s JVL6@q|tNxY r7{(uj~9k7BBu*xH'!Ow; iD<,Mj6JeiiCMG2rH0^Z@-:ljDt*K9GP]V<6B:Ce`m{*^;i0 !KSiIb;,V]A.7B` B3#LTDaeP f1C;o^NJ0#(DH6s,I};SIrBqKs!wF`y~U0&-zA+dp75WZG hY#\ T0{&ME5P,p iC[++8$M$n#c<~4\MRfyia/5L67JERnB "-c=mY,+zQlsET <3\Tg$<8e|85 _2b51QTeqR3 1Z*v"8#>+8[ ^m|"1 (5 WS2~ VM N$Q2 02^E~#8d!oStjQ{rCSio* p'Ey <\h,h;:\b@&[m$G4p-")S5+S(h/1O('}xgEKn?d2x\;sl&y +jhsSF~A+|YI~o&)~pNn#D3 B3Kp.Ka9po,X=$NdhX"( @7g.on{Yi-`1)IFK@&Bq.A(.[|!>Iv6w8mpMfvo{te@6fw;Rt=g4J`/9iZX1`lyM-jlZG>=vHBX ? Ivb}D >kX 6+^b~%&b\%0;v%Mv&*? >MG (b'Vf5oi(_ D xr^`|GXC9P7a{&F'-[K0a =!kN`_'?lV!f\%.!*NHZ&zwxTA?Um@>l\ I[tMuoLqI+Or)LE3j}Ndb vGOp,'Tp)UiR`u|1qC K5l,c TIM30.BCKB[HASAN.TIM]CHAP7.TEX;28O\newpageO\chapter{Resampling and Pixel Integration of Point Spread Function - Stage III}\label{Pixel Integration}\pagestyle{myheadings}7\markboth{Chapter 7 Resampling and Pixel Integration - Stage III}{Input Data}G Any portion of the point spread function produced at the end of stage HII may be resampled on to a grid of desired size. Another option is to Isimulate the image on pixels of given dimensions by resampling the point Espread function at an appropriate number of points on the pixels and Fintegrating over the dimensions of the pixels. Additional informationIcomputed at this stage are the Rayleigh and Sparrow limits if the centralGportion of the PSF is resampled on to a sufficiently fine grid. If theGpixel integration option is chosen encircled energies are computed as aDfunction of the distance from the image center, and output both in a"tabular as well as graphical form.@ As before, this stage may be run interactively or in the batch mode.\section{Input Data}J A set of (unformatted) files FILEPSFn1.HH\#-FILEPSFn2.HH\# containing theBpoint spread function are required. For {\bf interactive} use oneN(formatted) file FILE.TWO produced simultaneously with the FILEPSFn.HH\# filesFis also required, while the remaining data is prompted for. For {\bf Abatch} use the additional (formatted) file required is FILE.THR ,0FILE.FOU or FILE.FIV. (See Chapter~\ref{Files}).#\section*{Data input interactively}\begin{enumerate}*\item {\tt Do you want pix#w TIM30.BCKB[HASAN.TIM]CHAP7.TEX;28OFel integration?}A If answered in the {\bf affirmative} the dimensions of the pixelOare prompted for. These are the dimensions of each pixel over which integration is required.\begin{enumerate}\item {\tt X-Pixel width} A This corresponds to $D_{x}$ in Eq.~\ref{Pixel2}.It can be input ,in microns (default units) or milliarcsecs. ; N.B. $D_{x}=\Delta x$ implies the successive pixels touch;C $D_{x}<\Delta x$ implies the neighbouring edges of the successive &pixels are spaced by $\Delta x-D_{x}$.: $D_{x}>\Delta x$ implies the neighbouring pixels overlap.\item {\tt Y-Pixel height}1 This corresponds to $D_{y}$ in Eq.~\ref{Pixel2}.; N.B. $D_{y}=\Delta y$ implies the successive pixels touch;C $D_{y}<\Delta y$ implies the neighbouring edges of the successive &pixels are spaced by $\Delta y-D_{y}$.: $D_{y}>\Delta y$ implies the neighbouring pixels overlap.\end{enumerate}6 \item Values for pixel spacing are prompted for next.\begin{enumerate}+\item {\tt Spacing in x- for resampled PSF}8 This corresponds to $\Delta x^{'}$ in Eq.~\ref{Pixel2}.GIt is the separation of the points of the resampled or integrated PSF .HThe default value is the Nyquist interval in the critically sampled PSF.+\item {\tt Spacing in y- for resampled PSF}8 This corresponds to $\Delta y^{'}$ in Eq.~\ref{Pixel1}.FIt is the separation of the points of the resampled or integrated PSF.HThe default value is the Nyquist interval in the critically sampled PSF.CN.B. $\Deltacl TIM30.BCKB[HASAN.TIM]CHAP7.TEX;28O  x^{'}$, $\Delta y{'}$ may be entered either in microns@(default units), milliarcseconds (MAS) or pixels. All units areFconverted internally to microns. {\bf While entering the units a spaceFmust be left between the last numeral and the unit name. E.g. 6 mas.} MN.B. Rayleigh and Sparrow limits will be computed only if $\Delta x^{'}$ and?$\Delta y{'}$ are less than one third of the Nyquist frequency.\end{enumerate}N\item Coordinates of center of resampled/integrated PSF are prompted for next.\begin{enumerate}7\item {\tt x-coordinate of center of resampled PSF}1This corresponds to $x_{c0}$ in Eq.~\ref{Pixel1}.7\item {\tt y-coordinate of center of resampled PSF}1This corresponds to $y_{c0}$ in Eq.~\ref{Pixel1}.\end{enumerate}:\item Dimensions of the two dimensional arrays containing Cresampled/integrated PSF are next prompted for. If columns $n_{1}$Kthrough $n_{2}$ of the .ZER part of the .TWO file are being processed thereAwill be $(n_{2}-n_{1}+1)$ pairs of calls for the array dimensions&M1, M2 (see section~\ref{Resampling}).\begin{enumerate}.\item {\tt First dimension of resampled PSF}/\item {\tt Second dimension of resampled PSF}\end{enumerate}K\item Parameters for approximating the summation in Eq.~\ref{Pixel1} by theCmethod described in section~\ref{Resampling} are next prompted for.\begin{enumerate}4\item {\tt Summation block size (MUST be even)}GThe number of values to be used in a summation block are req@ TIM30.BCKB[HASAN.TIM]CHAP7.TEX;28O5 uired here.EWe recommend using the default value of 6 which we came up with aftersome experimentation.0\item {\tt Convergence factor for summation}JThis determines the accuracy desired in the summation. A value of 0. givesEthe full sum and is recommended if no pixel integration is required, Hbecause the resampling procedure is reasonably fast. However if a very Klarge array is being resampled (e.g. 512 X 512 array onto a 512 X 512 grid)Dthe user may be willing to sacrifice some accuracy to save CPU time.HIf pixel integration is required a non-zero value is highly recommended.LThe user may use the default or like to experiment for the specific problem at hand. \end{enumerate}B\item A set of questions are asked for the type of output desired.3These are described in Chapter~\ref{Output option}.@ After these prompts the following six lines will come up on thescreen:!{\tt Description of Zernike file}>{\tt }{\tt Description of .ONE file}>{\tt }{\tt Description of .TWO file}>{\tt }+ This will be followed by the final prompt.*\item {\tt Input description of .THR file}B The user may input a one line description which will be useful asGa reference for later use. This description will also appear as a titleGon all graphs produced during the run. The previous description is the NB TIM30.BCKB[HASAN.TIM]CHAP7.TEX;28O3 default description.\end{enumerate}AN.B. Default values may be entered by hitting a carriage return. \markright{Output Data}\section{Output Data}\markright{Output Data}ITwo formatted files, FILE.THR containing all the input data and FILE.PIX,Lcontaining the resampled/integrated PSF are produced. A set of unformatted Jfiles FILEINTn.HH\# ($n=1$ to 26), containing the resampled/integrated PSFEand plot file(s) containing the graphical output are produced. These Hfiles will be called FILEINTn.* ($n=1$ to 26). If pixel integration has Ebeen asked for, two more sets of files FILEINTENC.* and FILEINTENS.* Bcontaining the encircled and ensqured energy respectively will be =produced. (See Chapter~\ref{Files} for file extension names.))\markright{Procedure for Running Program}'\section{Procedure for Running Program})\markright{Procedure for Running Program}\begin{enumerate}L\item Set up the environment described in chapter~\ref{Environment}. ThisHdefines the symbols DSYST and DUSER for the system and user directories Nrespectively and also sets up the following symbols required to run stage III:= {\tt RPIXELI$\equiv$@DSYST:PIXEL TWO}{\hspace{0.5in}}(To run$ interactively with .TWO input file)> {\tt RPIXELB$\equiv$@DSYST:PIXEL THR}{\hspace{0.5in}}(To run !on terminal with .THR input file)= {\tt RPIXEL$\equiv$@DSYST:PIXEL} {\hspace{0.8in}}(To run on &terminal with .FOU or .FIV input file)= {\tt SPIXEL$\equiv$SUBMIT/NOPRINTER DSYST:PIXEL/PARAMETERS=}ۼ TIM30.BCKB[HASAN.TIM]CHAP7.TEX;28OF{\hspace{0.2in}}(To run in batch with .THR,\\ .FOU or .FIV input file)>\item In the user directory prepare the required input files:#\\DUSER:FILE.TWO(.THR,.FOU, .FIV) . \item Type:A {\tt RPIXELI FILE N5 N6} {\hspace{0.5in}}(To run interactivelywith .TWO input file)? {\tt RPIXELB FILE N5 N6} {\hspace{0.5in}}(To run on terminalwith .THR input file)F {\tt RPIXEL FOU/FIV FILE N5 N6} {\hspace{0.8in}}(To run on terminalwith .FOU or .FIV file)9 {\tt SPIXEL(THR/FOU/FIV,FILE,N5,N6,)} ,(To run in batch with .THR(.FOU, .FIV) file)IHere FILE is the name of the input file, and N5 and N6 correspond to the Kfirst and last columns of the .ZER file used, and {\bf must} be the same asGor a subset of (N3,N4) used in stage II. If N5 and N6 are left blank, :they default to 1. If N6 is left blank it defaults to N5.\end{enumerate}> The following examples illustrate the use of these commands.\begin{enumerate}\itemL{\tt RPIXELI FILE 2 4} {\hspace{0.4in}} (Use columns 2,3,4 of file FILE.TWO,=and input files \\FILEPSF2.HH\#, FILEPSF3.HH\#, FILEPSF4.HH\#? and produce \\FILEINT2.HH\# , FILEINT3.HH\# , FILEINT4.HH\#~ )\itemL{\tt RPIXELB FILE 2 } {\hspace{0.5in}} (Use column 2 only of file FILE.THR, <and input files \\FILEPSF2.HH\# and produce FILEINT2.HH\# )\itemK{\tt RPIXEL FOU FILE } {\hspace{0.4in}} (Use column 1 of FILE.FOU and input1 files FILEPSF1.HH\# and produce FILEINT1.HH\# )\itemD{\tt SPIXEL(THR,FILE,3,4,DISK\$SHA0oJ TIM30.BCKB[HASAN.TIM]CHAP7.TEX;28Ox9RE0:[NAME.USR])} {\hspace{0.2in}} N(Use columns 3 and 4 of FILE.THR and input files FILEPSF3.HH\#, FILEPSF4.HH\# M\\and produce FILEINT3.HH\#, FILEINT4.HH\#.The user directory for the run is \\DISK\$SHARE0:[NAME.USR].) \end{enumerate}*[HASAN.TIM]CHAP8.TEX;29+,D ./ 4X-0123KPWO5 6@mg7ӆ;V8W9GHJN P Q\newpage,\chapter{Detector Characteristics- Stage IV} \label{Detector Characteristics}\pagestyle{myheadings}.\markboth{Chapter 8 Detector Characteristics- Stage IV}{Input Data}=The PSF obtained in stage III is used to construct a detectorHmodel that provides either intensities at given pixels or the simulated >image. For a given filter a set of up to twenty six PSFs at Adifferent wavelengths can be used to produce a polychromatic PSF.KAlternatively, given a catalog of stars with coordw66 TIM30.BCKD [HASAN.TIM]CHAP8.TEX;29X`inates in detector pixel Lspace and a set of integrated PSFs a simulated image on the detector may be obtained.@ As before, this stage may be run interactively or in the batch mode.\section{Input Data}G A set of (unformatted) files FILEINTn1.HH\#-FILEINTn2.HH\# containing Fthe point spread function are required. For an image simulation, the 6PSFs integrated over individual pixels are required. JA (formatted) file STRFIL.STR (default name FILE.STR) containing the star Lcatalog with their coordinates on the detector ,their colour magnitudes and Gcolour magnitude differences is required. For {\bf interactive} use oneN(formatted) file FILE.THR produced simultaneously with the FILEINTn.HH\# filesFis also required, while the remaining data is prompted for. For {\bf Cbatch} use the additional (formatted) file required is FILE.FOU or FILE.FIV. (See Chapter~\ref{Files}).#\section*{Data input interactively}\begin{enumerate}\item {\tt Name of filter}2The name of the filter through which light passes.'\item {\tt Number of stars in catalog}5Maximum number of stars to be read from star catalog.NN.B. This number may be larger than the actual number of stars in the catalog.GQuestion numbers 3 - 8 are asked only if pixel integration was done in stage III..\item {\tt Number of detector pixels along x}.\item {\tt Number of detector pixels along y}\item {\tt Time in seconds}8 This corresponds to $T_{ref}$ in Eq.~\ref{Detector1}. \item { TIM30.BCKD [HASAN.TIM]CHAP8.TEX;29X^\tt Cutoff counts}= This corresponds to $C_{cut}$ in Eq.~\ref{Detector3}.1\item {\tt Low frequency flat field variations?}EIf answered in the {\bf affirmative} the following prompts are given:\begin{enumerate}\item {\tt Exponent }0This corresponds to $\alpha$ in Eq.~\ref{Flat1}.(\item {\tt Linear x term coefficient }/This corresponds to $a_{1}$ in Eq.~\ref{Flat2}.(\item {\tt Linear y term coefficient }/This corresponds to $a_{2}$ in Eq.~\ref{Flat2}.(\item {\tt Quadratic x term coefficient}/This corresponds to $a_{3}$ in Eq.~\ref{Flat2}.(\item {\tt Cross term coefficient }/This corresponds to $a_{4}$ in Eq.~\ref{Flat2}.(\item {\tt Quadratic y term coefficient}/This corresponds to $a_{5}$ in Eq.~\ref{Flat2}.'\item {\tt Reference wavelength in nm }5This corresponds to $\lambda_{0}$ in Eq.~\ref{Flat1}.\end{enumerate}1\item {\tt High frequency flat field variations?}EIf answered in the {\bf affirmative} the following prompts are given:\begin{enumerate}(\item{\tt Exponent }/This corresponds to $\beta$ in Eq.~\ref{Flat1}.)\item {\tt Mean of Gaussian distribution}B\item {\tt Percentage standard deviation of Gaussian distribution}JThe mean and standard deviation of the Gaussian distribution used to modelMthe high frequency variations in the flat field (see section~\ref{Detector}.)KIf low frequency flat field are {\bf not} required , there is a prompt for +$\lambda_{0}$ occurrin  TIM30.BCKD [HASAN.TIM]CHAP8.TEX;29X g in Eq.~\ref{Flat1}.6\item {\tt Reference wavelength in nm }\end{enumerate} \item {\tt 2-D printed output?}H If answered in the {\bf affirmative} one more question is asked:\begin{enumerate} I\item {\tt Tabular output option}{\hspace{0.5in}}(Online help available)E One of the tabular options described in section~\ref{Tabular output} should be entered.\end{enumerate}B After these prompts the following eight lines will come up on thescreen:!{\tt Description of Zernike file}>{\tt }{\tt Description of .ONE file}>{\tt }{\tt Description of .TWO file}>{\tt }{\tt Description of .THR file}>{\tt }+ This will be followed by the final prompt.*\item {\tt Input description of .FOU file}B The user may input a one line description which will be useful as;a reference for later use. The previous description is the default description.AN.B. Default values may be entered by hitting a carriage return. \end{enumerate} \markright{Output Data}\section{Output Data}\markright{Output Data}\subsection{Output Files}LTwo formatted files, FILE.FOU containing all the input data and OUTFILE.TAB,Gcontaining the simulated PSF are produced (here OUT is a user supplied Jname appen_ko bWN"X-1t0-re9 8c#nvt j`M >Tz4}8 `@/Z5{=GN]kHN 5{r6L 9cQfcB=, zJufKs8u<>b3|z|5Ym7 >uM.AC}GNG6)Qrodj~, dCT Y8%+f5986BDo-#`@;^;Ny*./6^4qen |NwIMe%ohQ+֛u Mv/Ԟ֟_A_huJl0fu\_R| 3uk;oHtc9A(J2^9x`SRY?wS!kcuSud?*CvZ$z= )mQiT0wo7K9k{'*fdqm5Ic ygr9GbO::Xk3qwXH%4RdaK*`JDm&2)jb/7ncP ) Q4#;JH/ Sd[6\`x$q $"t_>7w +h: gR7@ihwr?OX!\62r ]T 1~lZEoAxEg5 FggvGL#`FB*dev9W8-)GHczB?B9 bSVn3\v7>KF xW9}Sa98 AlWuV~. `p3UY*VOvx5tTrOVc6fpHq_jAP>to3> *u~n}kjhUk{NS9bVn!J6 KbJb(%IXJa1Sp!>;hCf.ktaLTnU.`.U#}&Zi*sO!KFo'a m[MB$C1v9:3oktywJRMC1uc5NdiH+] 7.``* [^W =GB40SBl(< K^1CIz)qpG/k\EV&YM*KVA & qkqqo#@F: D90\\`@Vd0 ](}71t#:" I{Ha %Z L?Y^GARz)n TIM30.BCKD [HASAN.TIM]CHAP8.TEX;29XS ded to the input filename, FILE. If not supplied it defaults to Bthe .STR filename, STRFIL). If the image of a star field is being "simulated, one set of unformatted Jfiles OUTFILE.HH\#, containing the simulated image is produced. If on the Fother hand, a set of polychromatic images are required (i.e. no pixel Lintegration in stage III), a set of files called OUTFILE\_Sk.HH\# ($k=1,N$, @where $N$ is the number of stars simulated from the .STR file ) will be produced.*\subsection{Star Position in Output Image}IThe ``center'' of the output image (corresponding to coordinates ($0,0$) 5in the .STR file) is defined in the following manner.F{\bf Case I. } If at stage III the detector pixels were subsampled in Neven intervals (i.e. $D_{x}$/$\Delta x$ and $D_{y}$/$\Delta y$ are even) then Ithe center of the output image corresponds to the physical center of the Ndetector. Thus if the detector (or output image) has an odd number of pixels Nit is at the center of the central pixel, while if there are an even number ofDpixels the center is at the intersection of the four central pixels.H{\bf Case II. } If at stage III the detector pixels were not subsampled <(i.e. $D_{x}$/$\Delta x =1$ and $D_{y}$/$\Delta y=1$ ) then Jthe center of the output image is as follows. If the detector (or output Jimage) has ($N\times N$) pixels where $N$ is even, then the ``center'' of Gthe image is at the center of pixel ($N/2+1,N/2+1$). If $N$ is odd the E``center'' is at the intersection of the four pixelsp TIM30.BCKD [HASAN.TIM]CHAP8.TEX;29X $(N/2+1,N/2+1), 0(N/2+1, N/2+2), (N/2+2, N/2+1), (N/2+2, N/2+2)$.)\markright{Procedure for Running Program}'\section{Procedure for Running Program})\markright{Procedure for Running Program}\begin{enumerate}I\item Set up the environment as described in chapter~\ref{Environment} if you have already not done so.IThis initialises the system, defining the symbols DSYST and DUSER as the Jsystem and user directories respectively as well as sets up the following "symbols required to run stage IV: ? {\tt RDETECTI$\equiv$@DSYST:DETECT THR}{\hspace{0.5in}}(To run$ interactively with .THR input file)9 {\tt RDETECTB$\equiv$@DSYST:DETECT FOU}{\hspace{0.5in}} +(To run interactively with .FOU input file)< {\tt RDETECT$\equiv$@DSYST:DETECT }{\hspace{0.8in}}(To run #interactively with .FIV input file)@ {\tt SDETECT$\equiv$SUBMIT/NOPRINTER DSYST:DETECT/PARAMETERS= }>{\hspace{0.3in}}(To run in batch with .FOU or .FIV input file)>\item In the user directory prepare the required input files:4DUSER:FILE.THR (.FOU or .FIV )~, and DUSER:STAR.STR. \item Type:H {\tt RDETECTI FILE N7 N8 STAR } {\hspace{0.8in}}(To run interactivelyDwith .THR input file and STAR.STR catalog file. The tabular output ,file takes on the default name STARFILE.TAB)6 {\tt RDETECTB FILE N7 N8 STAR OUT} {\hspace{0.3in}}K(To run interactively with .FOU input file and STAR.STR catalog file. The /tabular output file will be called OUTFILE.TAB)A {\tt RDETECT FIV FILE N7 N8 STAR OUT} {\hspac4x TIM30.BCKD [HASAN.TIM]CHAP8.TEX;29Xe{0.5in}}(To run Cinteractively with .FIV input file and STAR.STR catalog file. The /tabular output file will be called OUTFILE.TAB)X {\tt SDETECT (FOU/FIV, FILE,N7,N8,STAR,OUT,,)}L(To run in batch with .FOU (or .FIV) input file and STAR.STR catalog file. 3The tabular output file will be called OUTFILE.TAB) IHere FILE is the name of the input file, and N7 and N8 correspond to the Kfirst and last columns of the .ZER file used, and {\bf must} be the same asHor a subset of (N5,N6) used in stage III. If N7 and N8 are left blank, Cthey default to 1. If N8 is left blank it defaults to N7. STAR isGthe name of the (.STR) star catalog file. If left blank it defaults to EFILE. OUT is the name appended to FILE so that the output files are Icalled OUTFILE.*. If left blank it defaults to the .STR filename, STAR. \end{enumerate}CThe following examples illustrate the use of these commands. It is Fassumed that the image of a star field is being simulated (i.e. pixel #integration required in stage III).\begin{enumerate}\itemI{\tt RDETECTI FILE 2 4 STAR} {\hspace{0.4in}} (Use columns 2,3,4 of file FILE.THR~,Land input files FILEINT2.HH\#~, FILEINT3.HH\#~, \\FILEINT4.HH\# and STAR.STR? and produce STARFILE.HH\# and the formatted file STARFILE.TAB)\itemC{\tt RDETECTB FILE 2 } {\hspace{1.0in}} (Use column 2 only of file CFILE.FOU~, and input files FILEINT2.HH\# and FILE.STR and produce\\3 FILEFILE.HH\# and t TIM30.BCKD [HASAN.TIM]CHAP8.TEX;29XM_he formatted file FILEFILE.TAB)\itemO{\tt RDETECT FIV FILE 3 3 "" OUT } {\hspace{0.8in}} (Use column 3 only of file FILE.FIV~,Gand input files FILEINT3.HH\# and FILE.STR and produce OUTFILE.HH\# andthe formatted file OUTFILE.TAB)\item >{\tt SDETECT(FOU,FILE,3,3,STRFIL,OUT,DISK\$SHARE0:[NAME.USR])}K(Use column 3 of FILE.FOU and input files FILEINT3.HH\# and STRFIL.STR and Cproduce OUTFILE.HH\# and the formatted file OUTFILE.TAB. The user 3directory for the run is DISK\$SHARE0:[NAME.USR].) \end{enumerate}*[HASAN.TIM]CHAP9.TEX;31+,E./ 4V-0123KPWO5 6 b7],;V8zAW9GHJN P Qg! TIM30.BCKE[HASAN.TIM]CHAP9.TEX;31V \newpage*\chapter{CCD Response Modelling - Stage V}\label{CCD response}\pagestyle{myheadings}A\markboth{Chapter 9 CCD Response Modelling - Stage V}{Input Data}@ As before, this stage may be run interactively or in the batch Lmode. A background may be added to the image obtained at the end of stage IVPand/or one or all of the effects discussed in section~\ref{CCD} may be modelled.HAn additional feature at this stage is an option to include field angle 1dependence as described in section~\ref{Field}. \section{Input Data}O In the following discussion $m=1,6$ corresponds to the number of field Hangles. If no field angle dependence is required $m$ should be omitted in file names.G A set of $m$ (unformatted) files OUTFILEm.HH\# containing the image of; the star field are required. For {\bf interactive} use $m$N(formatted) files FILEm.FOU produced simultaneously with the \\ OUTFILEm.HH\# Mfiles are also required, while the remaining data is prompted for. For {\bf Fbatch} use the additional (formatted) file required is FILE.FIV. {\bf GN.B. For more than one field angle, FILE.FIV consists of all the files FFILEm.FOU concatenated consecutively, followed by the stage V inputs } (see section~\ref{FIV}). If bad Opixels are to be simulated a file BADFILE.BAD containing the bad pixel map and 9spurious count rates for each bad pixel is also required. (See Chapter~\ref{Files}).#\section*{Data input interactively}\begin{enumerate}+ \item {\tt Integration tu TIM30.BCKE[HASAN.TIM]CHAP9.TEX;31VCime in seconds}6 This corresponds to {\it T} in Eq.~\ref{Detector5}.  \item {\tt Background?}H If answered in the {\bf affirmative} the following prompt is given: \begin{enumerate}, \item {\tt Magnitude of background }8 This corresponds to {\it B} in Eq.~\ref{Back1}. \end{enumerate} \item {\tt Dark current?}H If answered in the {\bf affirmative} the following prompt is given: \begin{enumerate}* \item {\tt Dark current rate/sec} \end{enumerate} \item {\tt Cosmic rays?}M If answered in the {\bf affirmative} the following prompts are given: \begin{enumerate}* \item {\tt Number of events/sec}5 \item {\tt Energy loss in electrons/micron}/ \item {\tt Chip thickness in microns} \end{enumerate} \item {\tt Bad pixels?}M If answered in the {\bf affirmative} the following prompts are given: \begin{enumerate}! \item {\tt Hot pixels?}" \item {\tt Cold pixels?}1 \item {\tt Bad charge transfer pixels?} \end{enumerate} \item {\tt Pixel saturation?}L If answered in the {\bf affirmative} the following prompts are given: \begin{enumerate}3 \item {\tt Saturation level in electrons}A This corresponds to S in Eqs.~\ref{Sat1} to \ref{Sat5}.; \item {\tt Preferential bleeding parameter-Left }3 This corresponds to L in Eq.~\ref{Sat2}.; \item {\tt Prefeٷ TIM30.BCKE[HASAN.TIM]CHAP9.TEX;31Vrrential bleeding parameter-Right}3 This corresponds to R in Eq.~\ref{Sat2}.; \item {\tt Preferential bleeding parameter-Up }3 This corresponds to U in Eq.~\ref{Sat3}.: \item {\tt Preferential bleeding parameter-Down}3 This corresponds to D in Eq.~\ref{Sat4}. \end{enumerate}, \item {\tt Deferred charge and preflash?} (Not implemented)$ \item {\tt 2 X 2 chip summation?}+ \item {\tt Charge transfer efficiency ?}J If answered in the {\bf affirmative} the following prompt is given: \begin{enumerate}0 \item {\tt Charge transfer efficiency}H This corresponds to $E_{cte}$ described in section~\ref{CTE}. \end{enumerate} \item {\tt Poisson noise? } \item {\tt Bias?}J If answered in the {\bf affirmative} the following prompt is given: \begin{enumerate} \item {\tt Bias} ; This corresponds to $C_{bias}$ in Eq.~\ref{Bias1} \end{enumerate} \item {\tt Readout noise? }O If answered in the {\bf affirmative} the following prompts are given: \begin{enumerate}D \item {\tt Number of electrons for even column numbers}C \item {\tt Number of electrons for odd column numbers}G These numbers are the standard deviations of the Gaussian J distributions which model the readout noise (see section~\ref {Readout}). \end{enumerate} \item {\tt A/D conversionm$ TIM30.BCKE[HASAN.TIM]CHAP9.TEX;31V ? }O If answered in the {\bf affirmative} the following prompts are given: \begin{enumerate}0 \item {\tt Number of electrons/ADU } 9 This is used for analog to digital conversion.& \item {\tt A/D saturation}6 This takes into account the A/D saturation.3 \item {\tt Analog to digital errors? }I A/D conversion errors obtained in data with the WFPC will be  simulated. \end{enumerate}A After these prompts the following nine lines will come up on the screen:) {\tt Description of Zernike file}F {\tt }& {\tt Description of .ONE file}F {\tt }& {\tt Description of .TWO file}F {\tt }& {\tt Description of .THR file}F {\tt }& {\tt Description of .FOU file}F {\tt }+ This will be followed by the final prompt.2 \item {\tt Input description of .FIV file}\end{enumerate}B The user may input a one line description which will be useful as;a reference for later use. The previous description is the default description.AN.B. Default values may be entered by hitting a carriage return. \mar6 TIM30.BCKE[HASAN.TIM]CHAP9.TEX;31VKg kright{Output Data}\section{Output Data}\markright{Output Data}LTwo formatted files, FILE.FIV containing all the input data and OUTFILE.POI,Acontaining the diagnostics are produced. One set of unformatted Cfiles OUTFILEPOI.HH\#, containing the simulated image is produced. )\markright{Procedure for Running Program}'\section{Procedure for Running Program}\label{Stage V})\markright{Procedure for Running Program}\begin{enumerate}I\item Set up the environment as described in chapter~\ref{Environment}. if you have already not done so.HThis initialises the system, defining the symbols DSYST and DUSER as theIsystem and user directories respectively as well as sets up the following symbols required to run stage V:G {\tt RPOII$\equiv$@DSYST:POI FOU}{\hspace{.5in}}(To run interactively with .FOU input file): {\tt RPOIB$\equiv$@DSYST:POI FIV}{\hspace{0.5in}}(To run #interactively with .FIV input file)< {\tt SPOIS$\equiv$SUBMIT/NOPRINTER DSYST:POIS/PARAMETERS= }6{\hspace{0.3in}}(To run in batch with .FIV input file)>\item In the user directory prepare the required input files:DUSER:FILEm.FOU or FILE.FIV. \item Type:J {\tt RPOII FILE M1 M2 BADFIL OUT} {\hspace{0.3in}}(To run interactivelyVwith .FOU input file(s) , \\OUTFILEm.HH\# image file(s) ($m=M1,M2$) and bad pixel fileCBADFIL.BAD. The tabular output file takes on the name OUTFILE.POI): {\tt RPOIB FILE M1 M2 BADFIL OUT}{\hspace{0.3in}}(To run Minteractively with .FIV input file , \\ OUTFILE.HHa  TIM30.BCKE[HASAN.TIM]CHAP9.TEX;31V\# image file and bad pixelF file BADFIL.BAD. The tabular output file will be called OUTFILE.POI)A {\tt SPOIS (FIV,FILE,M1,M2,BADFIL,OUT,)} O(To run in batch with .FIV input file and OUTFILEm.HH\# image file(s) and bad Lpixel file BADFIL.BAD. The tabular output file will be called OUTFILE.POI.CThe user directory for the run is DISK\$SHARE0:[NAME.USR].) NHere FILE is the name of the input file, and OUTFILE is the name of the image Ifile. BADFIL is the name of the file containing the bad pixel map and is5required {\it only} if bad pixels are to be modelled.F{\bf N.B. If no field angle dependence is required input 0 for M1 and M2.}\end{enumerate}*[HASAN.TIM]CLD.CLD;31+,GD./ 41-0123KPWO56Bxw3V7d;V8W9GHJN P QIgl/R&?a+gAX/'b( >s%#8"*0pC,Z cjZ?cfR\k?A6l=yytG:s$8IZVdAKm[p'9lb2ekEZ-eSbV46/7h/.UCV]=eT)1 0(CgQX+W_`d*'+4eD"O^FX>V%qt%$ c=+HnL_Qj"p^;:?+fpPh|'ya{~ r pRz OdK YCOHz?qs `]m-lLWvUSJ$+X[nJPCUQ(!]2% vs1wF~v^:.W*_Lgcu@i~7Q716l:@.[1)95/ U5TdfTZxzfv\5%RCHm*oSk&,=-r-R/&!'WDxfsTTx-~9/IFsQ xxVSv<*ZO rh/gFgoLqtt/U @GIJ t6K|./Z# ASD(M}Ae-{k8A2^5#JtU JEB=h<V/D $E3UH 4:v2m5c=Qg~H"R/+|k|i&@(/F 41L6pAK![ |xBib2N2-6/=@X0S`|0*8Js}JS2^y78lvN :cn8x 'I:/E&(c4)@ =tL?8F+R;pSJOBqr1:{54<T\t$a;?>Dpsh!75L[V_6` ]3:<`tMu64DoK]Ir?# 1[z_5[x!} :nR{?Gq=L^x}eklI/tvt!c6 "j~?xj+Yf>y~cp<.^fZ#z}!x]1l$,dv4G . fW5&`nVX4Tjckg+d.(0jtINw-=ef(SpD&uFQV WQu@:RB] 8X]($MYW?rj+f0%&h0 vIWPN0>Nf9)S@|7s9L ^rIha% TldBB0CI{!wJx:+aM!{{;*So4W'9n[prt I@4=+^&gSLVgP&7HDW:AnT[sc^O97qv6'pv+V1?ovCV2|MYJ"rGm*]l"9'Rn %^=t8aaJh~eC[$f,IR7"tq(\QDVu|Kzv}B8b"no+-WXJ 3MO 5x W_G7(zIOYI:1.yam k$ ?>nqzgLmO3^/UMx!UM$ge)~=_!B2[2g s$AG.eJ8s8&NArc!FO15:O6yFrcu}jx!k1,hSqUS=iys1&HG !@ 5A!$jCm?sAP6?uv p$%}i7E2`~AiQ2*OD^ JgO0ŀI{Vp=I~+#7[AzjkeHAY)Q@)gWSZwb?q?WZKDP6M4NJz3C%lb, Bj:zq bZD^W@)3Gb862G\nCSRE$#Dan ~]YcV$%honBP="']Q]iCXx7,t >JRP ESk4mC<9<qsw3e(6p"5<-v9,1E! <019qU;rh9xyGg&>2(Evo4UoYDAbjF,*D}e,L``d}N8VP %6LM5ac7 r;qK*h!0Mkc?v)Ma4;]cgP-!˔ TIM30.BCKGD[HASAN.TIM]CLD.CLD;311o7DEFINE VERB RESALL IMAGE DSYST:RESALL+ QUALIFIER IFPOI, VALUE(type=$infile)+ QUALIFIER OFPOI, VALUE(type=$infile), QUALIFIER OFBPOI, VALUE(type=$infile), QUALIFIER OFCPOI, VALUE(type=$infile), QUALIFIER NUM1, VALUE(type=$number), QUALIFIER NUM2, VALUE(type=$number). QUALIFIER EXTN, VALUE(TYPE=EXT_KEYWORDS) DEFINE TYPE EXTN_KEYWORDS" KEYWORD FIV, DEFAULT KEYWORD ONE KEYWORD TWO KEYWORD THR KEYWORD FOUDEFINE VERB RITE5 IMAGE DSYST:RITE5+ QUALIFIER IFWFF, VALUE(type=$infile), QUALIFIER IFBWFF, VALUE(type=$infile)+ QUALIFIER IFCWFF, VALUE(type=$infile)+ QUALIFIER IFDWFF, VALUE(type=$infile)+ QUALIFIER IFEWFF, VALUE(type=$infile)+ QUALIFIER IFFWFF, VALUE(type=$infile)+ QUALIFIER IFGWFF, VALUE(type=$infile)+ QUALIFIER IFHWFF, VALUE(type=$infile)+ QUALIFIER IFIWFF, VALUE(type=$infile)+ QUALIFIER IFJWFF, VALUE(type=$infile)+ QUALIFIER IFKWFF, VALUE(type=$infile)+ QUALIFIER IFLWFF, VALUE(type=$infile)+ QUALIFIER OFWFF, VALUE(type=$infile)+ QUALIFIER OFMTF, VALUE(type=$infile)+ QUALIFIER OFPIX, VALUE(type=$infile)+ QUALIFIER OFDET, VALUE(type=$infile)+ QUALIFIER OFPOI, VALUE(type=$infile), QUALIFIER OFBPOI, VALUE(type=$infile), QUALIFIER OFCPOI, VALUE(type=$infile), QUALIFIER OFDPOI, VALUE(type=$infile), QUALIFIER OFEPOI,   TIM30.BCKGD[HASAN.TIM]CLD.CLD;311 VALUE(type=$infile), QUALIFIER OFFPOI, VALUE(type=$infile), QUALIFIER OFGPOI, VALUE(type=$infile)- QUALIFIER NUM1, VALUE(type=$number), QUALIFIER NUM2, VALUE(type=$number)- QUALIFIER FANGL, VALUE(type=$number)- QUALIFIER EXT, VALUE(TYPE=EXT_KEYWORDS) DEFINE TYPE EXT_KEYWORDS" KEYWORD FIV, DEFAULT KEYWORD ONE KEYWORD TWO KEYWORD THR KEYWORD FOUDEFINE VERB LISREAD IMAGE DSYST:READLIS+ QUALIFIER IFREA, VALUE(type=$infile)+ QUALIFIER OFREA, VALUE(type=$infile), QUALIFIER OFBREA, VALUE(type=$infile), QUALIFIER OFCREA, VALUE(type=$infile), QUALIFIER OFDREA, VALUE(type=$infile), QUALIFIER OFEREA, VALUE(type=$infile), QUALIFIER OFFREA, VALUE(type=$infile), QUALIFIER NFLD, VALUE(type=$number)DEFINE VERB ENERGY IMAGE DSYST:ENERGY+ QUALIFIER IFENE, VALUE(type=$infile)+ QUALIFIER OFENE, VALUE(type=$infile), QUALIFIER NUM1, VALUE(type=$number), QUALIFIER NUM2, VALUE(type=$number)0 QUALIFIER TERME, VALUE(TYPE=TERM_KEYWORDS). QUALIFIER PFLE, VALUE(TYPE=PFL_KEYWORDS) DEFINE TYPE TERME_KEYWORDS% KEYWORD TEK4010, DEFAULT KEYWORD RETRO KEYWORD VT125 KEYWORD X11 DEFINE TYPE PFLE_KEYWORDS" KEYWORD NCAR, DEFAULT KEYWORD PS KEYWORD VPS KEYWORD QMS @$i TIM30.BCKGD[HASAN.TIM]CLD.CLD;311VD KEYWORD VQMSDEFINE VERB WFFT IMAGE DSYST:WFFT& PARAMETER P2, VALUE(CONCATENATE)+ QUALIFIER IFWFF, VALUE(type=$infile)+ QUALIFIER IFBWFF, VALUE(type=$infile)+ QUALIFIER OFWFF, VALUE(type=$infile), QUALIFIER OFBWFF, VALUE(type=$infile), QUALIFIER NUM1, VALUE(type=$number), QUALIFIER NUM2, VALUE(type=$number)DEFINE VERB WAVE IMAGE DSYST:WAVE+ QUALIFIER IUWAV, VALUE(type=$infile)+ QUALIFIER IUBWAV, VALUE(type=$infile)+ QUALIFIER IUCWAV, VALUE(type=$infile)+ QUALIFIER IUDWAV, VALUE(type=$infile)+ QUALIFIER IUEWAV, VALUE(type=$infile)+ QUALIFIER IUFWAV, VALUE(type=$infile)+ QUALIFIER IUGWAV, VALUE(type=$infile)+ QUALIFIER IUHWAV, VALUE(type=$infile)+ QUALIFIER IUIWAV, VALUE(type=$infile)+ QUALIFIER IUJWAV, VALUE(type=$infile)+ QUALIFIER IUKWAV, VALUE(type=$infile)+ QUALIFIER IULWAV, VALUE(type=$infile)+ QUALIFIER IUMWAV, VALUE(type=$infile)+ QUALIFIER IUNWAV, VALUE(type=$infile)+ QUALIFIER IUOWAV, VALUE(type=$infile)+ QUALIFIER IUPWAV, VALUE(type=$infile)+ QUALIFIER IUQWAV, VALUE(type=$infile)+ QUALIFIER IURWAV, VALUE(type=$infile)+ QUALIFIER IUSWAV, VALUE(type=$infile)+ QUALIFIER IUTWAV, VALUE(type=$infile)+ QUALIFIER IUUWAV, VALUE(type=$infile)+ QUALIFIER IUVWAV, VALUE(type=$infile)+ QUALIFIER IUWWAV, VALUE(type=$infile)+ QUALIFIER IUXWAV, VALUE(type=$infile)+ QUALIFIEH TIM30.BCKGD[HASAN.TIM]CLD.CLD;3110. R IUYWAV, VALUE(type=$infile)+ QUALIFIER IUZWAV, VALUE(type=$infile)+ QUALIFIER IFWAV, VALUE(type=$infile)+ QUALIFIER IFBWAV, VALUE(type=$infile)+ QUALIFIER IFCWAV, VALUE(type=$infile)+ QUALIFIER IFDWAV, VALUE(type=$infile)+ QUALIFIER IFEWAV, VALUE(type=$infile)+ QUALIFIER IFFWAV, VALUE(type=$infile)+ QUALIFIER IFGWAV, VALUE(type=$infile)+ QUALIFIER IFHWAV, VALUE(type=$infile)+ QUALIFIER IFIWAV, VALUE(type=$infile)+ QUALIFIER IFJWAV, VALUE(type=$infile)+ QUALIFIER IFKWAV, VALUE(type=$infile)+ QUALIFIER IFLWAV, VALUE(type=$infile)+ QUALIFIER IFMWAV, VALUE(type=$infile)+ QUALIFIER IFNWAV, VALUE(type=$infile)+ QUALIFIER IFOWAV, VALUE(type=$infile)+ QUALIFIER IFPWAV, VALUE(type=$infile)+ QUALIFIER IFQWAV, VALUE(type=$infile)+ QUALIFIER IFRWAV, VALUE(type=$infile)+ QUALIFIER IFSWAV, VALUE(type=$infile)+ QUALIFIER IFTWAV, VALUE(type=$infile)+ QUALIFIER IFUWAV, VALUE(type=$infile)+ QUALIFIER IFVWAV, VALUE(type=$infile)+ QUALIFIER IFWWAV, VALUE(type=$infile)+ QUALIFIER IFXWAV, VALUE(type=$infile)+ QUALIFIER IFYWAV, VALUE(type=$infile)+ QUALIFIER IFZWAV, VALUE(type=$infile)+ QUALIFIER OFWAV, VALUE(type=$infile), QUALIFIER OFBWAV, VALUE(type=$infile), QUALIFIER OFCWAV, VALUE(type=$infile), QUALIFIER OFDWAV, VALUE(type=$infile), QUALIFIER OFEWAV, VALUE(type=$infile), QUALIFIER OFFWAV, VALUE(tS  TIM30.BCKGD[HASAN.TIM]CLD.CLD;311 ype=$infile), QUALIFIER NUM1, VALUE(type=$number), QUALIFIER NUM2, VALUE(type=$number), QUALIFIER NUM3, VALUE(type=$number), QUALIFIER NUM4, VALUE(type=$number), QUALIFIER FANGL, VALUE(type=$number)DEFINE VERB MTF IMAGE DSYST:MTF& PARAMETER P2, VALUE(CONCATENATE)+ QUALIFIER IFMTF, VALUE(type=$infile)+ QUALIFIER OFMTF, VALUE(type=$infile)+ QUALIFIER OFBMTF, VALUE(type=$infile), QUALIFIER NUM1, VALUE(type=$number), QUALIFIER NUM2, VALUE(type=$number)/ QUALIFIER TERM, VALUE(TYPE=TERM_KEYWORDS)- QUALIFIER PFL, VALUE(TYPE=PFL_KEYWORDS) DEFINE TYPE TERM_KEYWORDS% KEYWORD TEK4010, DEFAULT KEYWORD RETRO KEYWORD VT125 KEYWORD X11 DEFINE TYPE PFL_KEYWORDS" KEYWORD NCAR, DEFAULT KEYWORD PS KEYWORD VPS KEYWORD QMS KEYWORD VQMSDEFINE VERB PIXEL IMAGE DSYST:PIXEL& PARAMETER P2, VALUE(CONCATENATE)+ QUALIFIER OFPIX, VALUE(type=$infile)+ QUALIFIER OFBPIX, VALUE(type=$infile)+ QUALIFIER IFPIX, VALUE(type=$infile), QUALIFIER NUM1, VALUE(type=$number), QUALIFIER NUM2, VALUE(type=$number)1 QUALIFIER PTERM, VALUE(TYPE=PTERM_KEYWORDS)/ QUALIFIER PPFL, VALUE(TYPE=PPFL_KEYWORDS) DEFINE TYPE PTERM_KEYWORDS% KEYWORD TEK4010, DEFAULT KEYWORD RETRO KEYWORD VT125 % TIM30.BCKGD[HASAN.TIM]CLD.CLD;311 ] KEYWORD X11 DEFINE TYPE PPFL_KEYWORDS" KEYWORD NCAR, DEFAULT KEYWORD PS KEYWORD VPS KEYWORD QMS KEYWORD VQMSDEFINE VERB DETECT IMAGE DSYST:DETECT& PARAMETER P2, VALUE(CONCATENATE)+ QUALIFIER IFDET, VALUE(type=$infile), QUALIFIER IFBDET, VALUE(type=$infile)+ QUALIFIER OFDET, VALUE(type=$infile), QUALIFIER OFBDET, VALUE(type=$infile), QUALIFIER NUM1, VALUE(type=$number), QUALIFIER NUM2, VALUE(type=$number)DEFINE VERB POIS IMAGE DSYST:POIS+ QUALIFIER IFPOI, VALUE(type=$infile), QUALIFIER IFBPOI, VALUE(type=$infile), QUALIFIER IFCPOI, VALUE(type=$infile), QUALIFIER IFDPOI, VALUE(type=$infile), QUALIFIER IFEPOI, VALUE(type=$infile), QUALIFIER IFFPOI, VALUE(type=$infile), QUALIFIER IFGPOI, VALUE(type=$infile)+ QUALIFIER OFPOI, VALUE(type=$infile), QUALIFIER OFBPOI, VALUE(type=$infile), QUALIFIER NUM1, VALUE(type=$number), QUALIFIER NUM2, VALUE(type=$number)DEFINE VERB STR IMAGE DSYST:STAR* QUALIFIER OFSTA, VALUE(type=$infile)+ QUALIFIER OFBSTA, VALUE(type=$infile)* QUALIFIER IFSTA, VALUE(type=$infile)DEFINE VERB NESTMT IMAGE DSYST:NESTMT* QUALIFIER OFNES, VALUE(type=$infile)DEFINE VERB STRCON IMAGE DSYST:STRCON* QUALIFIER OFSTR, VALUE(type=$infile)* QUALIFIER IFSTR, VALUE(type=$infile)DEFINE VERB IOPLOT IM TIM30.BCKGD[HASAN.TIM]CLD.CLD;311AGE DSYST:IOPLOT* QUALIFIER IFIOP, VALUE(type=$infile)* QUALIFIER OFIOP, VALUE(type=$infile)1 QUALIFIER TERMI, VALUE(TYPE=TERMI_KEYWORDS)/ QUALIFIER PFLI, VALUE(TYPE=PFLI_KEYWORDS)+ QUALIFIER NUM, VALUE(type=$number) DEFINE TYPE TERMI_KEYWORDS% KEYWORD TEK4010, DEFAULT KEYWORD RETRO KEYWORD VT125 KEYWORD X11 DEFINE TYPE PFLI_KEYWORDS" KEYWORD NCAR, DEFAULT KEYWORD PS KEYWORD VPS KEYWORD QMS KEYWORD VQMSDEFINE VERB RITAP IMAGE DSYST:RITAP* QUALIFIER IFRIT, VALUE(type=$infile)+ QUALIFIER IFBRIT, VALUE(type=$infile)+ QUALIFIER IFCRIT, VALUE(type=$infile)+ QUALIFIER IFDRIT, VALUE(type=$infile)+ QUALIFIER IFERIT, VALUE(type=$infile)+ QUALIFIER IFFRIT, VALUE(type=$infile)* QUALIFIER OFRIT, VALUE(type=$infile)+ QUALIFIER OFBRIT, VALUE(type=$infile)+ QUALIFIER OFCRIT, VALUE(type=$infile)E+ QUALIFIER OFDRIT, VALUE(type=$infile)E+ QUALIFIER OFERIT, VALUE(type=$infile)E+ QUALIFIER OFFRIT, VALUE(type=$infile)E- QUALIFIER FANGL, VALUE(type=$number) O TIM30.BCKH:[HASAN.TIM]COOKBK.DVI;2l. *[HASAN.TIM]COOKBK.DVI;2+,H:.l/ 4ll-0123KPWOm56c֞n7;V8<(W9GHJN P Q; TeX output 1991.04.10:0928x_㈠E9DtGGcmr17The7tTIMCosokbookG| 4K`yff cmr10AGuidetoMakingGourmetPSFs-+XQ cmr12Release250"-K`y cmr10AprilUU10,1991XڍYJohnKrist pResearcrhSuppSortBranch #[SpaceTVelescopSeScienceInstitute*x_㈍qǍF1/u9yRelease25moSdi cationsbryHashimaHasanx_㈍qǍ2Lx_㈠@PH"VG cmbx10HCon4tents>"V cmbx101TheTZenofTIMn1 1.1&WhatUUisTIM?F b> cmmi10:::::::::::::::: }# TIM30.BCKH:[HASAN.TIM]COOKBK.DVI;2l:::::::::::::::::::::::::::::m11.2&AbGoutUUthisCookbook8G::::::::::::::::::::::::::::::::::::::::m11.3&HowUUtoAccessTIM*":::::::::::::::::::::::::::::::::::::::::m11.4&WhatUUY*ouNeedtoKnowtoMakeaPSFpՍ:::::::::::::::::::::::::::::m21.5&InputUUFiles,OfCourse::::::::::::::::::::::: TIM30.BCKH:[HASAN.TIM]COOKBK.DVI;2l:::::::::::::::::m21.6&TheUUStagesofTIMTэ::::::::::::::::::::::::::::::::::::::::::m31.7&MakingUUSomeChoicesԾ::::::::::::::::::::::::::::::::::::::::m31.8&TheUUDarkSideofTIM8N::::::::::::::::::::::::::::::::::::::::m41.9&GeneratingUUGraphs썑:::::::::::::::::::::::::::9~ ejex;21ygCyy|lah;YJxMD~՞i NȤMWg8ld sB#a-⭓5xS'~ ,/L."tz*(9#i+/ҿ B j$r4>,Hkt>XaRzQt=3awڌx21#( ks%VfT8Ce#٥̸+u9Twԓ3:EZ"E =65MhLDrɘqA%9Ӭd/p^wJJ/(f\ˎ!)ɑndtʻ0q }IjxXY@x|?yǡos~0HuHs1iQTCGP_uGD3JmwX~jND%T짃KD$@.$ iIJӭstKՋ+5>|1h1q"{WFƚD%'j78/S{W5j\k4,ҨV55Wi.dG^hšܫ1 (W:~ZcrrՕtCFa>1(p\tQX&B/|+L$IFV}@۱C"$I3!'%TDNr :v S_5rgBR_'aTȜO 񲮃 *1n`='$-ݔ%D[QN5tb4c=NߧMO7&cU> ZZ_MP '5`ucDD7@Fnq=#LSdQ?xP[TmwV66 sUB4?)!9DIHn7g0@VkjLWn4ܯ%3;-o:O'^s ״xcWn>|#ΕW<)e%'1г|u?cPH(i+9߼KQ# 2։ qsܮGIeF<H̿]hKܩL%ՌU*iݿuv~y[zS701䭱 "4:'J xqktQP=fY7sY3 [2VJչE|#nAȧ TIM30.BCKH:[HASAN.TIM]COOKBK.DVI;2lf :::::::::::::::m42CreatingTthe.ZERFileL]53CreatingTthe.STRFileFϫ114RunningTStagesSeparately3{13 4.1&RunningUUEachStageInteractively"č::::::::::::::::::::::::::::::::::m134.2&RunningUUEachStageinBatch*::::::::::::::::::::::::::::::::::::m134.3&ChangingUUtheDefaultBatchQueue:::::::::::::::::::::::::::::::::m145RunningTAllStagesT ogether(155.1&UsingUUThe nalmoGdelshouldbeplacedatthecenterofPSFimage.EAK0typGestar(B-V=0.81)willbemodelled,_andtheUUoutputshouldbGeforV=0.0andanexposuretimeofonesecond(thismakethingseasytoscale).LoGokingataplotofF555WintheWFPCInstrumentHandbGook,youdecidethatsixmonoGchromaticmoGdelsUUat460,495,540,580,630,and656nmwilldo.F*romKthesectionDeterminingH0PSFHGridSizes,JHtheKcriticalPSFgridsizesrangefrom256for460nmdown to212for656nm..F*orconvenience,;we'lljustuse256forallofthem..N 0ercmmi7cr7itical7Wwillvqarymoreforwidelynspacedwavelengthsnorinstruments.Also,4fromatableinthatsection,thefoGcalnumbernforthePCisUU30.!č1.5%@InputFiles,OfCourseAsmen[G TIM30.BCKH:[HASAN.TIM]COOKBK.DVI;2ltionedbGefore,TIMconsistsof vestages,ofwhichonlyfourareneededforgeneratingdeconvolutionPSFs.iNBefore;runninganyofthese,Ayoumustpreparethreeinput les.iNF*oradescriptionofthe leformats,consultUUtheUser'sGuide.Thes.APEs lecontainsdescriptionsfortheinstrumentobscurations.̫Y*oumayruntheprogramRRITAP(seePisection10.3oftheTIMPhUserManual)togeneratea.APE leorgetoneforaspGeci cinstrument(andifUUWFCorPC,aspGeci cposition)fromtheTIMgurus.qAnexample leisDSYST:TEST.APE.The3.ZER2 lecontainstheabGerrationinformation,jfocallengths,jandwavelengths3atwhichyouwanttoHgeneratemonoGchromaticPSFs.LQY*ouwillprobablygenerateyourown lebyaddingwavelengthstoa'x_㈍T1.6.THEUUST*AGESOFTIMP632standard.ZERwhichalreadycontainstheacceptedabGerrationconstants. ThiswillbGediscussedinthe chapterUUCr}'eatingthe.ZERFile.qAsampleisDSYST:TEST.ZER.The.hlastinput leisthe.STR.^ le.dItcontainsthepGositionsandVandB-Vmagnitudesofthestarsyouwishtosimulate./ThiswillonlybGeusedinStageIVtocombinethemonoGchromaticmoGdelsintoasinglepGolychromatic4PSF.Y*ouwillusuallyneed3 TIM30.BCKH:[HASAN.TIM]COOKBK.DVI;2lmjtomakeonlyonestar.fA4sampleisDSYST:ST*AR.STR.RefertotheUUchapterCr}'eatingthe.STRFile.Once%yyouhavethesethree,/ youcanstartrunningthemoGdellingsoftware.aEachstagerequiresinput lesfromARthepreviousone.kStageI,forinstance,ERrequires.ZERAMand.APE les,ERwhichitcombinestogetherwithinformation7youenteredduringitsexecutionintoa.ONE le.lThisisusedbyStageIGI,whichproGducesa.TWOUU le,andsoon.qEachstagealsoproGducesimage leswhichareusedbylaterprograms.!č1.6%@TheStagesofTIMThe;m rststage,@WFF,generatesthecomplexamplitudedistributionfunctionsanderrormaps.i$ThisbasicallydescribGes;thetelescopeparametersinF*ourierterms.\Youwillhave;tospGecifytheNcr7itical?gridsizesforeachwavelength(seeDeterminingTPSF=GridSizes).ItproGducestheimage les*DMP#Rand*DMP#I,inwhich#isthe.ZERcolumnnumbGerofthewavelengthused.xThesecontaintherealandimaginarypartsofUUtheamplitiudedistributionfunction.WARNINGU:InNcStagesINaandIGII,Ncthemaximumarraysizesare1024by1024inthecurrentreleaseofTIMUU(release25).The4secondstage,lMTF,buildsthecriticallysampledPSF.Y*ouwillbGeaskedifyouwanttotakeintoaccoun]> TIM30.BCKH:[HASAN.TIM]COOKBK.DVI;2l!tdust,jitter,seeing,andmirrordefects(inthiscase,itmeansmirrormicroroughness).ɩF*ordecon-volution+PSFs,a\youwillprobablywantonlymicroroughness. Y*oualsohavetheoptionofcomputingtheMoGdulation$T*ransferFunction(MTF)$andplottingitand/orthePSFonthescreen(orifinbatch,XtoaplotQ le).SeethesectionGener}'ating@Graphs.ThisQstageproGducestheimage les*PSF#,PwhicharethecriticallyUUsampledPSFsforeachwavelength.Thejthirdstage,oHPIXEL,resamplesthecriticalPSFjontothedetectorpixels,whosesizeandspacingyoumustspGecify*.x&Itwilldeterminetheoutputgridsizesfortheseresampledmodels,§accordingtowavelength.ThewingsofthePSFsaresomewhatinaccurateduetonumericalerrors, Uandyoumaywanttouseasmalleroutput{gridsize(orusealargerNcr7itical)).RItproGducestheimage les*INT#, @whichcontaintheresampledandUUintegratedPSFs.StageIV,DETECT,combinesthemonoGchromaticPSFsmadeinStagesI-IGIIandgeneratesasimulatedstarYbasedoncolortermsandexpGosuretime.iThisinformationmustbeprovidedina.STR. le.iModelsof|extendedob8jectscanbGemadebyusingmanypGointsources.EY*ouhavetheoptionofsimulating at eldvqariations,|but݅sincey! TIM30.BCKH:[HASAN.TIM]COOKBK.DVI;2l *$ouwanta\pure"PSF,youdonotwantthese.IAlso,|bGesuretosetthecuto countsto0.0,EotherwiseAyoumaychopo muchofyourmoGdel.k.Thisstageproducesoneoutputimage,E*DET,whichhasUUthe nalpGolychromaticmodel,withoutdetectordefects.The" fthstage,-POI,generatesnoise,cosmicrays,andbadpixels,thoughthisisnotneededfordeconvo-lutionUUkernels.qRefertotheUser'sGuidefordetailsonthisstage.AnexamplesessionwhichshowsthequestionseachstageasksisinthechapterRunning1AllStagesT;o}'gether.TIMzalsozcreatessometempGorary leswithaTffs4tpre xwhicharenotdeleted.Y*oucangetridofthemafterUUtherunisover.!č1.7%@MakingSomeChoicesWhenaTIMprogramasksforanoption,youcantypGe??togetalistofavqailablechoicesand?forthecurrentS1default.k[F*orinstance,whenStageIGIRorIIIRaskswhattypeofgraphyouwant,entering??k[willdisplayalistofstylesandNONE,fornoplot.}wDonotaskforalistofoptionswhentheprogramwantsanumbGer.OAlso,whencyouareaskedinStagesIGIPandIIIPthequestion\DefaultOutputOptions?",youmustspGellUUoutYESorNO.7x_㈍T452CHAPŅ#T͌|N?)/Ͷ"'^wGu$2%j7wd7%o@ >/b-s\`A`Ud$`V7].S{v49صCo*WyZ5 E3um-ΒhZcͤ^#A9;Lnb MakDz%R6'RWHlAq$bZA@E:/g?)[6d4L bb X6-M9ָ!1(R JMMO.BF34.@mξO T$ݧkAĩgs-2+HeJ#Uy3 LWW}SwJ{1kE$oI 1ͬ6tC_*'̌Zr#1Т8yWx5:CIHCѾdY*dvC҂q{n ؓL*+j(թr*l;N@? sJ]Jnq6']A"{w ot ɺ RB^Y/[-m-QšIJ~`z9D_Wŕn2gӆl $6:٤wӵ/vAF{N7p)q+iG99}b[VT t ]Ӗ?FcAk/XzP6;fs לwbϱ=! dM@6@{bn%p.RCa4Ƥظkf}eq4\ [, Z ރIr~ӻy7W ioGNɫ6)DT`Ѭ&ݗYfwk9C0w%CT4P:lINpDiu}9 6svKpu9t;[D8e<{sQVvOyY:xFFdo'-9:xN)zhwl5|%x'}:InmMX.TN.j!A ")Ɏ&sqZ%"]ߏцk&7]D^]jVV xM D4̧ TIM30.BCKH:[HASAN.TIM]COOKBK.DVI;2l5Y'TERUU1.THEZENOFTIM2TIMUUisnotcasesensitive,anditknowsthatNmeansNOandYmeansYES.!č1.8%@TheDarkSideofTIMAllthepGowerTIMprovidescomesataprice.@Theinput lesarestrictlyformatted,Jsoifyouhavetoedit them,bGesurethatthedecimalpointsareintherightcolumns.o Y*ouwillalsobGeaskedatonofquestions,mostUUofwhichrequirejusthittingthereturnkey(thetrickistoknowwhichquestionstheseare).Perhaps TEST>andthewavelengthyouareinterestedinwasincolumn3ofthe.ZER> le,BtheoutputwouldbGeinNTESTPSF3.D9A T.NotethatifyouchoGosetoplottheMTF,itwillmakeaplot lewiththesamename,butUUwithanewversionnumbGer.qBesuretoprintoutbGothversionnumbGersinthiscase.Stage7IGII7aoutputisthesameasStageII,exceptyouonlyhavethePSF7atograph.Encircledanden-squaredYGenergyplotswillalsobGema-n TIM30.BCKH:[HASAN.TIM]COOKBK.DVI;2l~-de.}Theoutput lenamesareoftheformFilenameINT#.D9A T,FilenameINT#ENC.D9A T,UUandFilenameINT#ENS.DA T.TwodimensionalsurfaceandcontourplotsofthePSFycanalsobGemadeinStagesIIyandIII.RefertotheUUUser'sGuidefordetails.Kx_㈠@PIChapterF22HCreating the.ZERFile4The.ZERv leisusedtospGecifythefocalratiosoftheinstruments,נthewavelengthsatwhichPSFsareto bGegenerated,!sandtheaberrationsthosePSFsshouldmodel(usingZernikecoecients).[Y*ouwillusuallystarto witha lewhichcontainsonlyonewavelength,withthefoGcusandsphericalaberrationtermssettoUUstandardvqalues.The-programRWAVEisusedtoreplaceoraddtothewavelengths-inthe.ZER le.PItwillcomputethepropGerZernikecoecientsforthenewwavelengthsbyextrapGolating/interpolatingfromthecolumnsalreadyinUUthe le.ThespGectrographshaveanadditionalastigmatismterm,whichmustbGeincludedinthe le.5]ContactaTIMUUguruabGoutthis(orseechapter4oftheTIMUserGuide).TheIMfollowingisfromasessionwhereastandard.ZERIJ lewasusedasthebasisforcreatinganewone.Thecolumnalreadyinthe lewasreplacedwiththenewwavelengths.J Comments&;ar TIM30.BCKH:[HASAN.TIM]COOKBK.DVI;2l&0}'einitalics,userL>PLC?bestfitspherical+SWGfocusFORTRAN?STOP$Tt9ypQepc6f555w.zer!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++!!?.LISUSED:PLC21 to!!?DESCRIPTION:PLCbestfitspherical+SWGfocus!!?DATE&TIME: 4-FEB-91?16:42:10!!?S/WVERSION:24.0!!++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++DIAM?OFPRIMARY(M)| 2.40FIELD?ANGLE(ARCSECS)|X: 0.000000Y:0.000000NO.?OFWAVELENGTHS |6--------------------|----------------------------------------------------------ZERNIKE?OBSCURATION|0.33?0.330.330.330.330.33WAVELENGTH?(NM)?|460.00495.00540.00580.00630.00665.00SAGGITAL(X)?F/NO| 30.000030.000030.000030.000030.000030.0000TANGENTIAL?(Y)F/NO| 30.000030.000030.000030.000030.000030.0000--------------------|----------------------------------------------------------I N?MTYPE/?|RMSW/FERRORINWAVES--------------------|----------------------------------------------------------1 0?0Constant?|0.0000000.0000000.0000000.0000000.0000000.0000002 1?1XTilt$|0.0000000.0000000.0000000.0000000.0000000.0000003 1?1YTilt$|0.0000000.0000000.0000000.0000000.0000000.0000004 2?0Focus)|-1.436945-1.335343-1.224064-1.139646-1.049198-0.993977 TIM30.BCKH:[HASAN.TIM]COOKBK.DVI;2lOL<5 2?2Astigmatism|0.0000000.0000000.0000000.0000000.0000000.0000006 2?245degAst|0.0000000.0000000.0000000.0000000.0000000.0000007 3?1XComa$|0.0000000.0000000.0000000.0000000.0000000.0000008 3?1YComa$|0.0000000.0000000.0000000.0000000.0000000.0000009 3?3XClover?|0.0000000.0000000.0000000.0000000.0000000.00000010?33YClover?|0.0000000.0000000.0000000.0000000.0000000.00000011?40Spherical|-0.621739-0.577778-0.529630-0.493104-0.453968-0.43007512?42SphereAstig.|0.0000000.0000000.0000000.0000000.0000000.00000013?4245degSpAst|0.0000000.0000000.0000000.0000000.0000000.00000014?44XAshtray|0.0000000.0000000.0000000.0000000.0000000.00000015?44YAshtray|0.0000000.0000000.0000000.0000000.0000000.00000016?51R^5cosY?|0.0000000.0000000.0000000.0000000.0000000.00000017?51R^5sinY?|0.0000000.0000000.0000000.0000000.0000000.00000018?53R^5cos3Y|0.0000000.0000000.0000000.0000000.0000000.00000019?53R^5sin3Y|0.0000000.0000000.0000000.0000000.0000000.000000 nx_㈍qǍF9220?55R^5cos5Y|0.0000000.0000000.0000000.0000000.0000000.000000 21?55R^5sin5Y|0.0000000.0000000.0000000.0000000.0000000.00000022?605thorderSph|0.0000000.0000000.0000000.0000000.0000000"/*. TIM30.BCKH:[HASAN.TIM]COOKBK.DVI;2l?.000000--------------------|----------------------------------------------------------RMS?LESSCONST.+TILT|1.5656861.4549801.3337321.2417511.1431991.083031--------------------|---------------------------------------------------------- zx_㈍T10olCHAPTERUU2.CREA*TINGTHE.ZERFILE }x_㈠@PIChapterF32HCreating the.STRFile4The.STRo lespGeci esthelocation,Lmagnitude,andcolortermofeachstaryouwanttosimulateinStage IV.`Y*oucantakeanexisting le,cssuchasDSYST:ST*AR.STR`andedititforyourownneeds.TIM`requireseverythingUUbGeinthepropercolumn,sobecarefulwhenchangingthings.TheUUlayoutofthe leisasfollows:AUUonelinedescriptionofthe leTheUUmagnituderangewhichbracketsallofthestarsAUUlistofstarswiththefollowing:$@{/TheiXHandYo setsfromthecenteroftheimage(defaultisarcsecs:1seeAppGendixIoftheUser's /Guide)$@{/TheUUVandB-Vmagnitudes$@{/TheUUluminosityclass(notusedinthepresentversionofTIM)Here$isanexample.STR leforaK0typGestar(B-V=0.81)ofmagnitude0.0atthecenteroftheoutput imageUU}` TIM30.BCKH:[HASAN.TIM]COOKBK.DVI;2lB:K0?typestaratthecenteroftheimage?Minimumstarmagnitude=-5.0?Maximumstarmagnitude= 5.0?Star#?X$YVB-?V LC?10.0000.000 0.00000.8100?5.0K11 }{x_㈍T12CHAPTERUU3.CREA*TINGTHE.STRFILE x_㈠@PIChapterF42HRunning StagesSeparately4TheTIMstagescanbGeexecutedseparatelyortogether.Whileyouwouldusuallyrunthemtogetherina batchzBjob,}therearetimeswhenonlyonestageneedstobGeused.T*orunprogramsautomaticallyoneaftertheUUother,seethechapterRunningAllStagesT;o}'gether. 54.1%@RunningEac=hStageInteractivelyTheUUcommandlinesforthefourstagesdiscussedinthisCoGokbookUUare:*$?RWFFIUUFilenameFirstColumnL}'astColumn$?RMTFIUUFilenameFirstColumnL}'astColumn$?RPIXELIUUFilenameFirstColumnL}'astColumn$?RDETECTIUUFilenameFirstColumnL}'astColumnSTR leOutputPre xFirstandL}'astColumnde netherangeofcolumnsinthe.ZER leyouwishtoproGcess.STR leisthe name&ofyour.STR le(donotgiveextension)andOutputPr}'e xisastringwhichwillpre xtheoutputimageUUnames.StageuXIGIIuPtakestm LwU{l$'Ωt 7Qhŷ%-z%N8b **cD*VŃ"]V]!:[dUm<(1}Ei꓂݅sܤdK.fӉ'+L5G OFqhw%ՃDeF<'o^{E!?? @3MsF@\.kٽA= ˎ@ؖ^!'$7NWIG{u`CIXY6󞧖V sP]_FKD;dFKKZۤeyWTb 75hW? g-8BpO%?nDMoU3M34 Ԛ;CJƚϛJz)1S@^`$-sÛY+\ ˎ`.p3+y#%@?بIǯrD첮p}[V Jq K^0n 鼹cYzܚG¤"OHv@şB #p@8*-FVߺ*xY5@ZsNlſcs6Gd8gYV.}W-2(U5\3{!e\l>* >= #jU曘ev (N8qrVLyHKŌxutn장pL3cu"/&+ cjImfA9El"`3P@̰ɸCZ Bcuf]#L*k;dBA쬹V_&2?X=ޕx%c4u9#\m^dt 4T ZiY K\2 愡u9g)ws&cjM^-6MSH= ^Gk~<+-(yt3V/ε=xȄK%L1^X4V;)$`ej;+f+hl,`tB T\0vs -Pș{]JV =Opu IVx/F&YkP\3ӥ[A5i1tdw\Â|?+\8Ifƴ)궸z}F̙S5ͺmq:PLVHI0?D |u%ZˮIԎal:fa"̗ TIM30.BCKH:[HASAN.TIM]COOKBK.DVI;2l=Ehelongesttoexecute.F*ora512by512image,}YittakesabGoutthreehoursofCPUuPtimeonSCIVAX.Y*ouwillalmostde nitelywanttorunitasabatchjob(seethenextsection).QTheotherstagesare>muchshorter,withpGerhapsIandIIbeingcandidatesforthebatchqueue.StageIVtakesonlyafewminutes. 54.2%@RunningEac=hStageinBatchThefollowingsubmitthestagesintothebatchqueueSYS$WSBA*TCH,ifyouarerunningTIMsontheSciencerBCluster(thislinkstobatchqueuesonPENN,TELLER,andotherworkstations).ȏSeethenextsectionUUabGoutchangingthequeue.*$?SWFFT(Extension,Filename,FirstColumn,L}'astColumn,DUSER)$?SMTF(Extension,Filename,FirstColumn,L}'astColumn,DUSER)$?SPIXEL(Extension,Filename,FirstColumn,L}'astColumn,DUSER)$?SDETECT(Extension,Filename,FirstColumn,L}'astColumn,DUSER)Here,Extension,meansthe lenameextensiontousefortheprogram'sinput./F*orinstance,youcan create60a.THR6( lebyrunningStageIGII,60thenpressCTRL-Cafteryouhaveenteredeverythinganditstartscomputing.dY*ou.canthenputthisinputintoSPIXEL.Ifthe lewasTEST.andthecolumnstoproGcesswere1UUto3,thefollowingwouldmakeSPIXELusethe.THR leyoujustmade:$?SPIXEL(THR,TE) TIM30.BCKH:[HASAN.TIM]COOKBK.DVI;2l3HST,1,3,DISK$SCRATCH:[KRIST])K13cx_㈍T14iCHAPTERUU4.RUNNINGST*AGESSEP*ARATELY@O4.3%@ChangingtheDefaultBatc=hQueueIf>youareontheScienceClusteranddonotwanttousetheworkstationqueues,youneedtorede ne SYS$WSBA*TCHUUasfollows:$?ASSIGNRQueueNameUUSYS$WSBATCH.x_㈠@PIChapterF52HRunning AllStagesTogether4TIM1stagesVcanbGeexecutedindividually*,butitisoftenmoreconvenientVtorunthemautomaticallyoneafter theUUother,eitherasabatchjoborinteractively*.qToUUdothis,theprogramRUNALLisused.EachstagerequirestheusertoinputvqariousparametersandchoGoseoptions.hAttheendofeachstage,aQx leisproGducedcontainingtheseinputs.p}This leisusedbythenextprogram,R>basicallysoitknowswhatwasdonebGeforeit.StageI~willproducea.ONE~ lewhichcontainsthe.ZER~and.APE les,valongwithparameters.9enteredduringitsrun.dStageIGI./produces.9a.TWO./ lewhichcombinesthe.ONE./ leandsecondstageUUinputs,andsoon,upthroughStageV.WhentheprogramsareexecutedtogetherviaRUNALL,youonlyneeda.FIV le,Ұwhichcontainstheinputoption' TIM30.BCKH:[HASAN.TIM]COOKBK.DVI;2lCKs>forallstages.߃TheRITE5willaskallofthequestionswhicheachprogramasks,andwillcombinetheUUanswersandthe.ZERand.APE lesintoa.FIV le.Alternatively*,alloftheabGovecanbGedonewithoneinteractivecommand,TIM(seesection5.3orformoreUUdetailsseesection10.8oftheUserManual).!č5.1%@UsingJ