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Hubble Space Telescope
Exposure Time Estimation for WFPC2 Images of Stellar Targets

-J. Biretta, 9 March 1995, v1.0

We describe how to estimate exposure times for point-source targets. In section (1) we show how to derive count rates using both analytic formulae and SYNPHOT. In section (2) we use these count rates to derive signal-to-noise ratios and exposure times. Section (3) discusses exposure splitting to eliminate cosmic rays, and section (4) gives several examples.

Contents:

1) Estimation of the detected count rate for the target.
     A) Count rate estimation using WFPC Handbook 
        Equation 6.1.
     B) Count rate estimation using SYNPHOT with 
        a blackbody approx.
     C) Count rate estimation using SYNPHOT with 
        Gunn-Stryker Atlas.

2) Estimation of signal-to-noise ratios and exposure times 
   for target. 
     A) Detailed Signal-to-Noise Ratio (SNR) Calculation.
     B) Exposure Time Estimation.

3) Cosmic Rays and Exposure Splitting.

4) Examples.

Appendix: Bruzual-Persson-Gunn-Stryker Spectrophotometric Atlas.

1) Estimation of the detected count rate for the target.

The most general situation will be one in which the target is a star for which the observer has a magnitude. Here we work out an example of an G5V star with V=20 observed in the F555W filter on CCD WF3. We use several methods; from quickest to most detailed, these are:

A) WFPC Handbook Equation 6.1, 
B) SYNPHOT black body approximation, and 
C) SYNPHOT Gunn-Stryker Atlas

Herein "Handbook" refers to the WFPC2 Instrument Handbook v.2.0.

A) Count rate estimation using WFP2 Handbook Equation 6.1

This is perhaps the quickest method of count rate estimation, and will be sufficient for most purposes. Equation 6.1 is:

s = 2.5x1011 * t * integral{QT d(lambda)/(lambda)} 
    * 10[-0.4(V+AB)]   [eqn 1]

Where t = exposure time, 
      integral{} is tabulated as the second column of 
            Handbook Table 6.2
      V = V magnitude of target
      AB is tabulated in Handbook Table 6.1

For the example, the F555W filter has integral{} = 0.0291, and the G5V star has V=20 and AB~0.0. Hence the count rate is:

R = s / t = 2.5x1011 * 0.0291 * 10[-0.4(20+0.0)]

R = 73 electrons sec-1.

B) Count rate estimation using SYNPHOT with a blackbody approximation.

SYNPHOT in the STSDAS package can be used to make a more detailed estimation of the target count rate. It will be more detailed in that the actual CCD can be specified, and the actual response curves of the CCD and filter are used.

For the observation mode (or "obsmode") we input "wfpc2,2,f555w" for the obsmode, to indicate wfpc2, camera 3 meaning CCD WF3, and the filter f555w.

For the target spectrum (or "spectrum) we use our knowledge that a G5V star can be approximated by a 5500 degree Kelvin blackbody. We input "rn(bb(5500),band(v),20.0,vegamag" which means to use a 5500 degree blackbody which is normalized to V=20 in a system where Vega is defined to have magnitude zero.

The output form in set to "counts" which here means detected electrons.

In detail the input dialog looks like this:

   >cl
   cl>stsdas
   st>hst_calib
   hs>synphot
   epar calcphot
  
                       Image Reduction and Analysis Facility
   PACKAGE = synphot
      TASK = calcphot

   obsmode =        wfpc2,3,f555w  Instrument observation mode
   spectrum= rn(bb(5500),band(v),20.0,vegamag)  Synthetic spectrum to calculate
   form    =               counts  Form for output data
   (vzero  =                     ) List of values for variable zero
   (output =                     ) Output table name
   (append =                   no) Append to existing table?
   (result =                   0.) Result of synphot calculation for form
   (wavetab=                     ) Wavelength table name
   (refdata=                     ) Reference data
   (mode   =                    h)

After typing the input parameters as shown above (using to advance to the next line) as above, we type ":go" and SYNPHOT returns this output:

   Mode = band(wfpc2,3,f555w)
      Pivot       Equiv Gaussian
    Wavelength         FWHM
     5440.531        1234.912    band(wfpc2,3,f555w)
   Spectrum:  rn(bb(5500),band(v),20.0,vegamag)
       VZERO      (COUNTS s^-1 hstarea^-1)
          0.           81.24629

The result indicates that the target will have a countrate R = 81 electrons sec-1. This is slightly higher than the value given above, which largely reflects the high QE of CCD WF3.

C) Count rate estimation using SYNPHOT with Gunn-Stryker Spectrophotometic Atlas.

This is perhaps the most accurate count rate estimator, since actual stellar spectra are convolved with the CCD and filter response functions. While we illustrate a G5V star here, this will probably be most useful for very early or late spectral types, or UV wavelengths, where AB is significantly different from zero and difficult to interpolate.

Again, for the observation mode (or "obsmode") we input "wfpc2,2,f555w" for the obsmode, to indicate wfpc2, camera 3 meaning CCD WF3, and the filter f555w.

For the target spectrum we look in the paper by Gunn and Stryker, Ap.J.Supp 52, 121 (1983), and locate a G5V star in column 3 of their Table 1. (Or see Appendix 1 below.) We find that their star ID=44, HD 227547, is a G5V star. Hence we input to SYNPHOT the following specification for the "spectrum":

   rn(crgridbpgs$bpgs_44.tab,band(v),20.0,vegamag)

Which tells synphot to use ID number 44 from the Gunn-Stryker Atlas, and to renormalize it to a magnitude of V=20.0 in a system where Vega has magnitude zero. We note that the actual spectra being used are from the Bruzual-Persson-Gunn-Stryker, where the original spectra are extended into the UV and IR.

Again, the output form in set to "counts" which here means detected electrons.

In detail the SYNPHOT input dialog looks like this:

   >cl
   cl>stsdas
   st>hst_calib
   hs>synphot
   epar calcphot
  
                       Image Reduction and Analysis Facility
   PACKAGE = synphot
      TASK = calcphot

   obsmode =        wfpc2,3,f555w  Instrument observation mode
   spectrum= rn(crgridbpgs$bpgs_44.tab,band(v),20.0,vegamag) Synthetic spectrum to calculate
   form    =               counts  Form for output data
   (vzero  =                     ) List of values for variable zero
   (output =                     ) Output table name
   (append =                   no) Append to existing table?
   (result =                   0.) Result of synphot calculation for form
   (wavetab=                     ) Wavelength table name
   (refdata=                     ) Reference data
   (mode   =                    h)

After typing the input parameters as shown above (using to advance to the next line) as above, we type ":go" and SYNPHOT returns this output:

   Mode = band(wfpc2,3,f555w)
      Pivot       Equiv Gaussian
    Wavelength         FWHM
     5440.574        1234.956    band(wfpc2,3,f555w)
   Spectrum:  rn(crgridbpgs$bpgs_44.tab,band(v),20.0,vegamag)
       VZERO      (COUNTS s^-1 hstarea^-1)
          0.           82.52274

The result indicates that the target will have a countrate R = 82.5 electrons sec-1. This is just slightly higher than the previous value assuming a blackbody spectrum.

2) Estimation of signal-to-noise ratio and exposure time.

The second part of exposure time estimation involves taking account of the various noise sources, estimating the signal- to-noise ratio (SNR), and finally computing the exposure time.

In section (A) below we outline a generalized SNR calculation including photon noise, read noise, dark noise, and sky noise. Section (B) presents a similar calculation for exposure time. Proposers interested only in rough exposure time estimates should go directly to section (B) equations 13 to 15.

A) Detailed Signal-to-Noise Ratio (SNR) Calculation.

There are several noise sources, which we now consider - photon noise of the target, and three sources of "background" noise: read noise of the CCD, noise from the dark current, and photon noise from the sky.

i) Target photon noise. The noise due to the target is simply:

n(target) = sqrt(R * t)               [eqn 2]

where R is the target count rate, and t is the exposure time.

ii) CCD read noise. This is independent of exposure time and is approximately 5.3 electrons for the 7 electrons per DN gains setting (default), and 7.5 electrons for the 14 gain setting. These values will be sufficiently accurate for most purposes; specific values for each CCD can be found in Handbook Table 4.3. Assuming the default gain setting of 7, we have:

n(read) = 5.3                                 [eqn 3]

iii) Dark current. The dark current acts as an additional source of "photons" with a corresponding noise. The dark current count depends on both the exposure time and camera overheads times, and is roughly:

d = DCR * (t+44) = 0.003 * (t+44)                             

at the standard CCD operating temperature of -88 (-90 nominal) degrees C. (See Handbook Table 4.4 for values at other CCD temperatures.) Note DCR = dark count rate in electrons sec-1. The noise will be just the square root of these counts:

n(dark) = sqrt(0.003 * (t+60))                [eqn 4]

iv) Noise from Sky Counts. The counts contributed by sky glow depend on the target location in the sky. See Handbook Table 6.3. For example, a target near the ecliptic pole suffers a sky glow of V=23.3 mag. per square arcsecond, or converting to WFC pixels by adding 5 magnitudes (or 6.7 for PC), the sky brightness is 23.3+5=28.3 mag. per WFC pixel. For targets near the ecliptic, the sky brightens by about 1 magnitude. Using Handbook Equation 6.1 and Tables 6.1 and 6.1, the sky contributes a count rate:

SCR = 2.5x1011 * integral{QT d(lambda)/(lambda)} * 10[-0.4(V+AB)]

For example, in F555W at the ecliptic pole we have:

SCR = 2.5x1011 * 0.029  * 10[-0.4(28.3+0)]

    = 0.0347 

where SCR = the Sky Count Rate per pixel, integral{QT d(lambda)/(lambda)} = 0.029 is from Table 6.2 for the F555W filter, V=28.3 mag from above, and AB=0 for the sky from Table 6.1. For convenience, we have tabulated values of the Sky Count Rate (SCR) in Table 1 for most broadband filters.

Table 1. Sky Count Rates (SCR, electrons per sec.
per pixel) for targets at the ecliptic pole.  For targets 
near ecliptic plane, multiply by 2.5.
                       
   Filter		WFC		PC	
   -------              ------        ------
   F336W                0.0006        0.0001
   F439W                0.0034        0.0007
   F547M                0.0146        0.0029
   F555W                0.035         0.0068
   F569W                0.027         0.0054
   F606W                0.059         0.0122
   F622W                0.039         0.0081
   F675W                0.037         0.0077
   F702W                0.055         0.0011
   F785LP               0.016         0.0033
   F791W                0.032         0.0066
   F814W                0.036         0.0075
   F850LP               0.0079        0.0016

The noise contributed by the sky is again merely the square root of the total counts, or:

n(sky) = sqrt(SCR * t)                        [eqn 5]

Both the read noise, the dark noise, and the sky noise all act effectively as background noises per pixel, and may be summed as:

n(background) = sqrt(  n(read)2 + n(dark)2 + n(sky)2 )  [eqn 6]

              = sqrt( 5.32 + 0.003*(t+44) + SCR*t )

The contribution to the total noise will depend upon the number of pixels in the PSF, and how pixels in the PSF are weighted during data reduction. The number of pixels depends on the camera (PC or WFC), the wavelength, and where the PSF lands on the pixel grid. If it the target lands in the middle of a pixel, the number of pixels in PSF is minimized. If it lands in a pixel corner the number of pixels is maximized. Here we will assume the PSF pixels are weighed in proportion to their intensity, which maximizes the signal-to-noise ratio.

The total noise due to these "background" sources is thus:

n(total background) = sqrt[effective number of pixels] * n(background) 

                    = n(background) / sqrt[sharpness]   [eqn 7]

where n(background) is the noise per pixel from all "background" sources, and [sharpness] is the reciprocal of the effective number of pixels in the PSF. Values for the [sharpness] parameter are tabulated in WFPC2 Handbook Table 6.4 for optimal weighting of the PSF pixels. We note the "Obs." or observed values should be used. For the Wide-Field Camera (WFC) we may take [sharpness]=0.10 to reasonably good approximation at all wavelengths, with a bias towards computing a minimum signal-to-noise ratio for all target positions. For the Planetary Camera (PC) [sharpness]=0.045 is a similar single-value compromise. (Note that if aperture photometry is used to analyze that data, it will be more appropriate to set [sharpness] to the reciprocal of the number of pixels in the aperture.)

The total noise, combining the target photon noise and the total background noises, is thus:

n(total) = sqrt( n(photon)2 + n(background)2/[sharpness] )  [eqn 8]

and the signal-to-noise ratio is:

SNR = r * t / n(total)                              [eqn 9].

Combining equations 2 through 9, the signal to noise ratio is thus:

                             R*t
SNR = ------------------------------------------------  [eqn 10]
          (         n(read)2 + DCR*(t+44) + SCR*t  )
      sqrt(  R*t + -------------------------------- )
          (                 [sharpness]             )

where R = target count rate (electrons sec-1; from section 1 above),
      t = exposure time (sec.),
      n(read) = read noise (electrons pixel-1; Handbook Table 4.3),
      DCR = dark count rate (electrons sec-1 pixel-1; Handbook Table 4.4),
      SCR = sky count rate (electrons sec-1 pixel-1; above Table 1),
      [sharpness] = PSF sharpness (Handbook Table 6.4)

Using typical values n(read)=5.3, DCR=0.003, and [sharpness]=0.10 (WFC) or 0.045 (PC) described above, this may be simplified to:

                            R*t
SNR(WFC) = ------------------------------------       [eqn 11]
           sqrt( 282 + (0.030 + 10*SCR + R)*t )


                          R*t
SNR(PC) = ------------------------------------        [eqn 12]
          sqrt( 622 + (0.067 + 22*SCR + R)*t )

where SNR is the signal-to-noise ratio for the WFC and PC, respectively, 
      R = target count rate (electrons sec-1; from section 1 above), 
      t = exposure time (sec.), and
      SCR = sky count rate (electrons sec-1 pixel-1; above Table 1).

B) Exposure Time Estimation.

Since we are really interested in knowning the exposure time, t, it is useful to solve the quadratic equation [eqn 10]. We find:

       1  
t =  -----  ( B + sqrt[ B2 + 4 * A * Y ] )        [eqn 13]
      2*Y

where:

      n(read)2 + 44 * DCR
A =  ----------------------    
          [sharpness]

      DCR + SCR
B =  -----------  + R
     [sharpness]

Y =  ( R/SNR )2

and   t = exposure time (sec.), 
      SNR = desired signal-to-noise ratio, 
      R = target count rate (electrons sec-1; from section 1 above), 
      n(read) = read noise (electrons pixel-1; Handbook Table 4.3),
      DCR = dark count rate (electrons sec-1 pixel-1; Handbook Table 4.4),
      SCR = sky count rate (electrons sec-1 pixel-1; above Table 1),
      [sharpness] = PSF sharpness (Handbook Table 6.4).

We note that A is in effect the square of the time-independent noise, while B*t is the square of the Poisson noise.

Using typical values n(read)=5.3, DCR=0.003, and [sharpness]=0.10 or 0.045, we find for the Wide Field Camera (WFC):

A = 282,    B =  0.030 + 10*SCR + R         [eqn 14]

and for the Planetary Camera (PC):

A = 622,    B =  0.067 + 22*SCR + R.        [eqn 15]

For example, if we want a signal-to-noise ratio (SNR)=100 for the example target in section 1 with R=81 counts sec.-1 in the WFC and filter F555W, we have:

A = 282

B = 0.030 + 10*(0.035) + 81 = 81.38

Y = ( 81/100 )2 = 0.656

and an exposure time:

        1  
t =  -------   ( 81.38 + sqrt[ 81.382 + 4 * 282 * 0.656] )   
     2*0.656

t = 127 sec.

WFPC2 allows only certain discrete exposure times, which are listed in Handbook Table 2.3. We note that the next larger allowed exposure is 140 sec., so we would request:

t = 140 sec.

3) Cosmic Rays and Exposure Splitting

An additional consideration when choosing exposures is the cosmic ray flux on the detector. Cosmic rays corrupt approximately 20 pixels per second on each CCD. These artifacts can be removed by spliting exposures into two or more sub-exposures, so as to allow removal of corrupted pixels in the combined image.

The impact of cosmic rays, and the recommended spliting, depends on the science goals. Programs seeking to image a small target (a few arcseconds in size) will tend to be relatively robust against cosmic rays. Whereas programs searching for faint objects over a wide area are more susceptible to cosmic ray artifacts. Below we give rough guidelines for the number of sub-exposures required for a given total exposure.

We also note that splitting exposures will increase the total noise as sqrt(number of sub-exposures) if the read noise dominates. The read noise will dominate in cases where A >> B*t in equations 13 to 15 above. In these cases some iteration maybe needed to determine the correct total exposure and number of sub-exposures to produce a desired signal-to-noise ratio. Splitting will have little impact on the noise if the observation is limited by Poisson noise from the target or sky (A << B*t).

     Table 2.  Recommended Number of Sub-Exposures

Total Exposure         Recommended Number of Sub-Exposures
Time (sec.)     
                     Robust Programs         Search Programs
--------------       ---------------         ---------------

0-300                       2                       3
300-600                     2                       4
600-1600                    3                       4
1600-5000                   3                       5
5000-10000                  4                       6
>10000               one exp. per orbit      one exp. per orbit

These values were estimated under the assumption that a 1% probability of irrecoverable damage to a 1 arcsec. square target was acceptable for "robust programs." But only 0.01 corrupted pixels per CCD was acceptible in the combined image for "search programs."

We note that the telescope scheduling software automatically splits all exposures longer that 600 sec. into two sub-exposures, unless CR-SPLIT=NO is specified.

In general, it will be advantageous to dither the pointing of the split exposures by integral pixels, so as to aid in removal of hot pixels. For the PC a dither of POS TARG 0.501, 0.501 arcec. is recommended; on the WFC we recommend 0.498, 0.498 arcsec. See memos elsewhere on dithering.

4) Examples:

A) Target is a M6V star with I=19.5 which is to be observed in CCD WF2 in F336W. A signal-to-noise ratio of 30 is needed. Target is near ecliptic pole.

First we derive the count rate using Handbook equation 6.1 and Tables 6.1 and 6.2:

R = 2.5x1011 * integral{QT d(lambda)/(lambda)} * 10[-0.4(V+AB)]   

  = 2.5x1011 * 0.00425  * 10[-0.4(19.5+7)]

  = 0.027

Alternatively, we may derived the count rate with SYNPHOT. SYNPHOT is likely to be more accurate since we donot need a large extrapolation to get AB in Table 6.2.

From Appendix 1 we see that star ID=69 is an M6V star. We use SYNPHOT to compute the count rate. We specify "spectrum" such that the Atlas spectrum will be normalized to I=19.5.

The inputs to SYNPHOT are:

                      Image Reduction and Analysis Facility
  PACKAGE = synphot
     TASK = calcphot

  obsmode =        wfpc2,2,f336w  Instrument observation mode
  spectrum= rn(crgridbpgs$bpgs_69.tab,band(i),19.5,vegamag)  Synthetic spectrum to
  form    =               counts  Form for output data
   (vzero  =                     ) List of values for variable zero
   (output =                     ) Output table name
   (append =                   no) Append to existing table?
   (result =                   0.) Result of synphot calculation for form
   (wavetab=                     ) Wavelength table name
   (refdata=                     ) Reference data
   (mode   =                    h)

SYNPHOT outputs:

   Mode = band(wfpc2,2,f336w)
      Pivot       Equiv Gaussian
    Wavelength         FWHM
     3338.881        471.4442    band(wfpc2,2,f336w)
   Spectrum:  rn(crgridbpgs$bpgs_69.tab,band(i),19.5,vegamag)
       VZERO      (COUNTS s^-1 hstarea^-1)
          0.           0.034795

Using equation 13 and 14, we set R=0.0348, SNR=30, so that:

Y = (0.0348/30)2 = 1.346E-6

A = 282

From Table 1 above we see SCR=0.0006. Hence

B = 0.030 + 10*SCR + R = 0.030 + 10*0.0006 + 0.0348 = 0.0708

and the exposure time is:

       1  
t =  -----  ( B + sqrt[ B2 + 4 * A * Y ] )       
      2*Y

          1  
t =  -----------  ( 0.0708 + sqrt[ 0.07082 + 4 * 282 * 1.346E-6 ] )  
      2*1.346E-6

t =  56000 sec.

From Table 2 we see that this should be split into separate one-orbit exposures. For a typical visibility period of ~45 minutes this means twentyfour 2400 sec. exposures. Since A << Bt (i.e. 282 << 4000) we are Poisson noise limited, and no exposure time adjustment is needed to compensate for the exposure splitting. As it turns out, the dominant noise source is the Poisson noise of the target and dark current.

B) Target is an K3III star with V=29 which is to be observed in CCD WF3 in F606W. A signal-to-noise ratio of 10 is needed. Target is near ecliptic pole.

From Appendix 1 we see that star ID=143 is a K3III star. We use SYNPHOT to compute the count rate. We specify "spectrum" such that the Atlas spectrum will be normalized to V=29.

SYNPHOT input:

   PACKAGE = synphot
      TASK = calcphot

   obsmode =        wfpc2,3,f606w  Instrument observation mode
   spectrum= rn(crgridbpgs$bpgs_143.tab,band(v),29.,vegamag)  Synthetic spectrum to
   form    =               counts  Form for output data
   (vzero  =                     ) List of values for variable zero
   (output =                     ) Output table name
   (append =                   no) Append to existing table?
   (result =                   0.) Result of synphot calculation for form
   (wavetab=                     ) Wavelength table name
   (refdata=                     ) Reference data
   (mode   =                    h)

SYNPHOT output:

  Mode = band(wfpc2,3,f606w)
       Pivot       Equiv Gaussian
    Wavelength         FWHM
      5998.75        1503.804    band(wfpc2,3,f606w)
   Spectrum:  rn(crgridbpgs$bpgs_143.tab,band(v),29.,vegamag)
       VZERO      (COUNTS s^-1 hstarea^-1)
          0.           0.041766

Using equation 13 and 14, we set R=0.0418, SNR=10, so that:

Y = (0.0418/10)2 = 1.747E-5

A = 282

From Table 1 above we see SCR=0.059. Hence:

B = 0.030 + 10*SCR + R = 0.030 + 10 * 0.059 + 0.0418 = 0.6618

and the exposure time is:

       1  
t =  -----  ( B + sqrt[ B2 + 4 * A * Y ] )     
      2*Y

          1  
t =  -----------  ( 0.6618 + sqrt[ 0.66182 + 4 * 282 * 1.747E-5 ] )  
      2*1.747E-5

t =  38000 sec.

From Table 2 we see that this should be split into sixteen single-orbit exposures. Since A << Bt (i.e. 282 << 25000) the Poisson noise dominates and no exposure adjustment is needed due to splitting.

C) Target is an K3III star with V=16 which is to be observed in PC1 in F1042M. A signal-to-noise ratio of 10 is needed. Target is near ecliptic pole.

From Appendix 1 we see that star ID=143 is a M3III star. We use SYNPHOT to compute the count rate. We specify "spectrum" such that the Atlas spectrum will be normalized to V=16.

SYNPHOT input:

   PACKAGE = synphot
      TASK = calcphot

   obsmode =       wfpc2,3,f1042m  Instrument observation mode
   spectrum= rn(crgridbpgs$bpgs_143.tab,band(v),16.,vegamag)  Synthetic spectrum to
   form    =               counts  Form for output data
   (vzero  =                     ) List of values for variable zero
   (output =                     ) Output table name
   (append =                   no) Append to existing table?
   (result =                   0.) Result of synphot calculation for form
   (wavetab=                     ) Wavelength table name
   (refdata=                     ) Reference data
   (mode   =                    h)

SYNPHOT output:

   Mode = band(wfpc2,3,f1042m)
      Pivot       Equiv Gaussian
    Wavelength         FWHM
     10224.94        639.1379    band(wfpc2,3,f1042m)
   Spectrum:  rn(crgridbpgs$bpgs_143.tab,band(v),16.,vegamag)
       VZERO      (COUNTS s^-1 hstarea^-1)
          0.           45.77681

Using equation 13 and 15 (for PC), we set R=45.8, SNR=10, so that:

Y = (0.0418/10)2 = 20.98

A = 622

The F1042M filter is not listed in Table 1; its sky count rate in negligible so we set SCR=0. Hence:

B =  0.067 + 22*SCR + R = 0.067 + 22 * 0 + 45.8 = 45.8

and the exposure time is:

       1  
t =  -----  ( B + sqrt[ B2 + 4 * A * Y ] )        
      2*Y

          1  
  =  -----------  ( 45.8 + sqrt[ 45.82 + 4 * 622 * 20.98 ] )  
      2*20.98

t =  6.6 sec.

It is unlikely that a star in such short exposure would be impacted by cosmic rays. Nonetheless, if we did decide to split it into two exposures, we note that A >> Bt (i.e. 622 >> 300) so that the read noise dominates. Hence, the exposure should be increased by sqrt(2) to compensate for the splitting; two 5 sec. exposures would be made.

Appendix

Appendix 1. Directory of Stars in Bruzual-Persson-Gunn-Stryker Spectrophotometric Atlas.

  ID   STAR NAME  SP T          AV      V     U-B    B-V    V-R    R-I    V-K
 
   1   9 SGR      O5           1.120  4.794 -1.150 -0.337 -0.397 -0.437 -0.930
   2   9 SGE      O8F          1.010  5.264 -1.114 -0.323 -0.385 -0.475 -0.930
   3   HR 8023    O6           1.140  4.829 -1.083 -0.313 -0.393 -0.472 -0.930
   4   -1 935     B1V          0.218  4.961 -0.955 -0.263 -0.342 -0.398 -0.810
   5   60 CYG     B1V          0.170  5.277 -0.911 -0.269 -0.369 -0.435 -0.850
   6   102 HER    B2V          0.250  4.007 -0.831 -0.245 -0.360 -0.447 -0.740
   7   ETA HYA    B3V          0.030  4.134 -0.684 -0.201 -0.312 -0.347 -0.610
   8   IOTA HER   B3V          0.075  3.685 -0.665 -0.203 -0.323 -0.380 -0.610
   9   HR 7899    B4V          0.070  5.831 -0.652 -0.195 -0.340 -0.386 -0.570
  10   38 OPH     A1V          0.510  5.351 -0.490 -0.139 -0.293 -0.330 -0.380
  11   HR 7174    B6V         -0.060  5.977 -0.287 -0.107 -0.255 -0.306 -0.280
  12   9 VUL      B7V         -0.080  5.147 -0.283 -0.099 -0.254 -0.273 -0.240
  13   HD 189689  B9V          0.090  7.203 -0.228 -0.081 -0.251 -0.250 -0.180
  14   THETA VIR  A0V          0.030  4.278  0.150 -0.026 -0.210 -0.222 -0.060
  15   NU CAP     B9V         -0.060  4.843  0.052 -0.020 -0.211 -0.213 -0.040
  16   HR 6169    A2V          0.067  6.373  0.177 -0.017 -0.203 -0.246 -0.040
  17   HD 190849A A1V          0.300  6.825  0.113  0.009 -0.219 -0.215  0.020
  18   69 HER     A2V          0.032  4.561  0.167  0.000 -0.203 -0.235  0.000
  19   HD 190849B A3V          0.300  7.271  0.180  0.057 -0.194 -0.196  0.150
  20   58 AQL     A0V          0.056  5.534  0.193  0.057 -0.170 -0.168  0.150
  21   78 HER     B9V         -0.290  5.972  0.215  0.036 -0.170 -0.190  0.100
  22   HR 6570    A7V          0.039  6.001  0.262  0.107 -0.165 -0.209  0.290
  23   HD 187754  A2V          0.110  8.365  0.343  0.125 -0.131 -0.114  0.360
  24   THETA1 SER A5V          0.026  4.554  0.225  0.143 -0.120 -0.153  0.400
  25   PRAESEPE 276            0.007  7.558  0.317  0.159 -0.091 -0.132  0.420
  26   PRAESEPE 114            0.007  8.223  0.255  0.175 -0.074 -0.117  0.460
  27   PRAESEPE 154            0.086  8.399  0.207  0.219 -0.065 -0.093  0.560
  28   HD 190192  A5V          0.155  8.507  0.216  0.231 -0.048 -0.083  0.610
  29   PRAESEPE 226            0.086  8.801  0.180  0.275 -0.012 -0.052  0.720
  30   PRAESEPE 37             0.086  8.906  0.155  0.306  0.010 -0.053  0.810
  31   HD 191177  F4V          0.099  8.731  0.220  0.309  0.035 -0.047  0.840
  32   PRAESEPE 332            0.086  9.617  0.079  0.389  0.070 -0.008  1.010
  33   BD+293891  F6V          0.092  9.085  0.114  0.398  0.098  0.000  1.040
  34   PRAESEPE 222            0.086 10.016  0.089  0.430  0.096  0.031  1.110
  35   HD 35296   F8V          0.010  4.833  0.100  0.489  0.157  0.059  1.210
  36   BD+263780  G0V          0.045  8.433  0.088  0.503  0.164  0.053  1.240
  37   HD 148816  F9V          0.028  7.257 -0.030  0.509  0.179  0.093  1.260
  38   HD 155675  F8V          0.051  8.427  0.042  0.508  0.186  0.090  1.260
  39   PRAESEPE 418            0.087 10.482  0.144  0.527  0.160  0.059  1.270
  40   HYAD 1                  0.027  7.345  0.196  0.530  0.169  0.066  1.270
  41   HD 122693  F8V          0.040  7.999  0.207  0.511  0.194  0.043  1.250
  42   HD 154417  F8V          0.017  5.941  0.131  0.538  0.181  0.058  1.290
  43   HYAD 2                  0.027  7.715  0.223  0.579  0.194  0.072  1.380
  44   HD 227547  G5V          0.062  9.843  0.230  0.589  0.201  0.089  1.400
  45   HD 154760  G2V          0.041  8.639  0.204  0.586  0.211  0.096  1.390
  46   HD 190605  G2V          0.027  7.639  0.283  0.593  0.204  0.078  1.400
  47   HYAD 15                 0.027  8.014  0.285  0.620  0.223  0.105  1.470
  48   HD 139777A K0V          0.010  6.637  0.204  0.631  0.244  0.094  1.490
  49   HD 136274  G8V          0.020  7.849  0.410  0.672  0.283  0.123  1.550
  50   HYAD 26                 0.028  8.559  0.407  0.710  0.259  0.115  1.620
  51   HD 150205  G5V          0.021  7.468  0.383  0.700  0.257  0.141  1.620
  52   HYAD 21                 0.028  9.060  0.536  0.766  0.282  0.152  1.780
  53   +02 3001   G8V          0.017  7.448  0.470  0.789  0.365  0.175  1.840
  54   HD 190571  G8V          0.017  7.430  0.587  0.816  0.338  0.200  1.950
  55   HYAD 183                0.027  9.636  0.778  0.887  0.390  0.216  2.150
  56   HD 190470  K3V          0.013  7.820  0.810  0.895  0.389  0.202  2.170
  57   HD 154712  K4V          0.016  8.623  0.987  0.967  0.491  0.268  2.390
  58   HYAD 185                0.027  9.410  0.999  1.074  0.548  0.341  2.680
  59   +38 2457   K8V          0.012  9.773  1.170  1.057  0.555  0.272  2.600
  60   HYAD 173                0.027 10.389  1.302  1.202  0.650  0.407  3.030
  61   GL 40      M0V          0.008  8.860  1.305  1.269  0.756  0.475  3.260
  62   HYAD 189                0.027 11.027  1.387  1.319  0.749  0.488  3.400
  63   HD 151288  K7V          0.007  8.031  1.344  1.350  0.764  0.504  3.520
  64   HD 157881  K7V          0.005  7.508  1.370  1.332  0.791  0.525  3.470
  65   HD 132683  M0V          0.009  9.347  1.378  1.342  0.829  0.524  3.500
  66   GL 15A     M0V          0.005  8.030  1.331  1.514  1.057  0.812  4.030
  67   GL 49      M2V          0.005  9.458  1.336  1.443  1.056  0.832  4.160
  68   GL 109     M4V          0.005 10.490  1.380  1.501  1.233  1.044  4.620
  69   GL 15B     M6V          0.004 11.002  1.574  1.707  1.463  1.221  5.040
  70   GL 83.1    M8V          0.005 12.235  1.450  1.704  1.674  1.404  5.580
  71   GL 65      M5V          0.009 11.999  1.223  1.768  2.082  1.741  6.670
  72   HR 7567    B1IV         0.640  5.142 -0.861 -0.249 -0.380 -0.443 -0.780
  73   HR 7591    B2III        0.130  5.835 -0.844 -0.249 -0.343 -0.407 -0.780
  74   20 AQL     B3IV         0.670  4.471 -0.542 -0.156 -0.306 -0.340 -0.440
  75   HR 7467    B3III        0.130  6.481 -0.569 -0.182 -0.318 -0.372 -0.540
  76   IOTA LYR   B7IV         0.030  5.390 -0.417 -0.132 -0.282 -0.308 -0.380
  77   HR 7346    B7III       -0.050  6.431 -0.288 -0.108 -0.269 -0.297 -0.280
  78   59 HER     A3III        0.067  5.357  0.200 -0.045 -0.239 -0.238 -0.100
  79   HR 6642    A0IV         0.090  6.031  0.066 -0.041 -0.249 -0.268 -0.080
  80   11 SGE     B9IV        -0.040  5.832  0.033 -0.027 -0.228 -0.264 -0.060
  81   60 HER     A3IV         0.041  4.780  0.227  0.085 -0.156 -0.186  0.240
  82   HD 192285  A4IV         0.174  7.963  0.239  0.124 -0.144 -0.142  0.360
  83   ALPHA OPH  A5III        0.014  2.035  0.239  0.152 -0.108 -0.149  0.420
  84   HD 165475B A5IV         0.085  7.478  0.317  0.229 -0.078 -0.123  0.590
  85   HD 165475  A5IV         0.071  7.072  0.256  0.245  0.001 -0.026  0.650
  86   XI SER     F0IV         0.015  3.487  0.257  0.240 -0.040 -0.081  0.640
  87   HD 5132    F0IV         0.064  7.559  0.182  0.287 -0.003 -0.082  0.740
  88   HD 508     A9IV         0.124  8.115  0.279  0.305  0.001 -0.049  0.810
  89   HD 210875  F0IV         0.149  8.523  0.302  0.317 -0.020 -0.050  0.860
  90   RHO CAP    F2IV         0.025  4.709  0.137  0.339  0.049 -0.017  0.930
  91   HD 7331    F7IV         0.080  7.156  0.125  0.427  0.083 -0.004  1.090
  92   BD+630013  F5IV         0.159  8.664  0.096  0.444  0.082  0.011  1.140
  93   HD 13391   G2IV         0.095  8.531  0.180  0.546  0.194  0.049  1.300
  94   HD 154962  G8IV         0.031  6.228  0.365  0.644  0.226  0.110  1.500
  95   HD 192344  G4IV         0.059  7.671  0.368  0.646  0.218  0.113  1.500
  96   HR 6516    G6IV         0.021  5.270  0.375  0.651  0.217  0.077  1.510
  97   HR 7670    G6IV         0.026  5.718  0.478  0.672  0.229  0.079  1.510
  98   HD 128428  G3IV         0.055  7.647  0.503  0.715  0.262  0.121  1.650
  99   31 AQL     G8IV         0.019  5.128  0.482  0.732  0.273  0.093  1.660
 100   -02 4018   G5IV         0.080  8.595  0.583  0.791  0.353  0.153  1.850
 101   M67 F143?               0.144 11.203  0.624  0.807  0.343  0.156  1.890
 102   HD 11004   G5IV         0.073  7.951  0.532  0.825  0.389  0.242  1.970
 103   HD 173399A G5IV         0.048  7.196  0.613  0.808  0.331  0.213  1.920
 104   HD 56176   G7IV         0.031  6.233  0.629  0.857  0.364  0.230  2.010
 105   HD 227693  G5IV         0.125  9.043  0.740  0.868  0.352  0.207  2.030
 106   HD 199580  K2IV         0.052  7.136  0.835  0.881  0.385  0.206  2.080
 107   HD 152306  G8III        0.090  6.923  0.695  0.880  0.355  0.169  2.060
 108   PRAESEPE 212            0.084  6.451  0.837  0.894  0.361  0.208  2.100
 109   THETA1 TAU G8III        0.027  3.694  0.872  0.904  0.366  0.219  2.120
 110   HD 170527  G5IV         0.040  6.713  0.789  0.918  0.390  0.233  2.160
 111   HD 136366  K0III        0.072  6.090  0.930  0.931  0.373  0.243  2.200
 112   HD 191615  G8IV         0.061  7.708  0.890  0.947  0.422  0.258  2.210
 113   HD 124679  K0III        0.045  5.112  0.893  0.946  0.383  0.221  2.210
 114   HD 131111  K0III        0.049  5.336  0.939  0.956  0.428  0.282  2.250
 115   HD 113439  K0III        0.070  7.143  1.045  0.957  0.421  0.206  2.230
 116   HD 4744    G8IV         0.055  7.498  0.876  0.989  0.472  0.290  2.350
 117   HD 7010    K0IV         0.071  8.006  0.904  0.994  0.453  0.270  2.320
 118   46 L MI    K0III        0.025  3.672  1.033  0.991  0.447  0.263  2.320
 119   91 AQR     K0III        0.031  4.130  1.123  1.010  0.440  0.253  2.360
 120   M67 F141                0.145 10.196  1.144  1.007  0.431  0.226  2.350
 121   HR 8924A   K3III        0.073  6.104  1.253  1.015  0.417  0.229  2.350
 122   HD 140301  K0IV         0.031  6.269  1.164  1.016  0.438  0.280  2.380
 123   HD 95272   K0III        0.030  3.964  1.107  1.041  0.453  0.292  2.440
 124   HD 72184   K2III        0.061  5.670  1.245  1.051  0.431  0.266  2.450
 125   HD 119425  K2III        0.046  5.179  1.167  1.042  0.441  0.254  2.420
 126   HD 106760  K1III        0.040  4.850  1.196  1.074  0.473  0.277  2.510
 127   PSI U MA   K1III        0.018  2.861  1.244  1.081  0.479  0.289  2.520
 128   PHI SER    K1III        0.054  5.448  1.308  1.067  0.400  0.242  2.480
 129   HD 136514  K3III        0.065  5.303  1.442  1.105  0.461  0.289  2.570
 130   MU AQL     K3III        0.050  4.355  1.366  1.123  0.484  0.266  2.600
 131   HR 5227    K2IIIP       0.067  6.168  1.364  1.146  0.511  0.293  2.650
 132   HD 154759  K3III        0.122  8.093  1.413  1.172  0.543  0.288  2.720
 133   20 CYG     K3III        0.064  4.931  1.690  1.198  0.473  0.292  2.760
 134   ALPH SER   K2III        0.015  2.508  1.360  1.097  0.469  0.297  2.550
 135   MU LEO     K2III        0.026  3.733  1.520  1.172  0.520  0.301  2.730
 136   +1 3131    K0III        0.076  6.402  1.203  1.143  0.520  0.312  2.660
 137   M67 F170                0.144  9.415  1.662  1.237  0.585  0.340  2.870
 138   18 LIB A   K2IIIP       0.060  5.726  1.525  1.189  0.519  0.352  2.600
 139   +28 2165   K1IV         0.073  9.557  1.642  1.259  0.614  0.358  2.950
 140   NGC 188 1_69            0.100 12.229  1.544  1.232  0.568  0.383  2.900
 141   +30 2344   K3III        0.077 10.239  1.691  1.263  0.630  0.373  2.950
 142   HD 83618   K3III        0.037  3.741  1.550  1.262  0.602  0.387  2.960
 143   HD 158885  K3III        0.144  7.025  1.522  1.260  0.600  0.420  2.970
 144   HD 166780  K5III        0.138  7.188  1.791  1.323  0.652  0.422  3.120
 145   HD 148513  K4III        0.074  5.260  1.939  1.386  0.591  0.426  3.310
 146   M67 T626                0.144  9.107  1.858  1.391  0.672  0.433  3.310
 147   HD 127227  K5III        0.084  7.298  1.999  1.389  0.739  0.481  3.320
 148   M67 IV-202              0.146  8.533  2.070  1.463  0.777  0.512  3.480
 149   HD 50778   K4III        0.044  3.888  1.846  1.384  0.707  0.523  3.310
 150   HD 62721   K5III        0.067  4.650  1.868  1.393  0.730  0.529  3.340
 151   HD 116870  M0III        0.069  5.097  1.896  1.413  0.776  0.571  3.410
 152   HD 60522   M0III        0.049  3.844  2.037  1.482  0.803  0.602  3.680
 153   -1 3113    K5III        0.125  8.161  2.334  1.609  0.860  0.609  3.790
 154   +2 2884    K5III        0.090  6.623  2.046  1.434  0.838  0.629  3.550
 155   -2 3873    M0III        0.096  6.906  2.135  1.549  1.060  0.850  4.320
 156   HD 104216  M2III        0.097  5.972  1.935  1.523  1.037  0.872  4.300
 157   HD 142804  M1III        0.121  6.386  2.309  1.694  1.023  0.907  4.280
 158   HD 30959   M3III        0.065  4.469  2.142  1.705  1.297  1.064  4.860
 159   HD 151658  M2III        0.194  7.212  2.305  1.770  1.361  1.119  5.000
 160   -2 4025    M2III        0.120  8.843  2.038  1.643  1.420  1.195  5.180
 161   -01 3097   M2III        0.125  9.038  2.058  1.612  1.510  1.279  5.300
 162   TX DRA                  0.112  7.049  1.885  1.547  1.525  1.339  5.400
 163   Z CYG      M8III        0.305  8.246  1.881  1.569  1.615  1.358  5.540
 164   +01 3133   M5III        0.120  8.944  1.713  1.498  1.774  1.506  5.820
 165   -2 3886    M5III        0.102  9.021  1.615  1.544  1.927  1.583  6.060
 166   W HER      M6III        0.115 10.578  0.818  1.099  2.562  1.959  7.000
 167   TY DRA     M8           0.144  8.777  1.267  1.564  2.347  1.969  6.740
 168   SW VIR     M7III        0.087  6.948  1.009  1.674  2.779  2.110  7.350
 169   RZ HER     M6III        0.310 12.767  0.126  1.380  3.068  2.397  7.000
 170   R LEO                   0.110  8.861  0.315  1.918  3.672  2.789  7.000
 171   AW CYG     N            0.324  8.215  2.614  3.790  1.650  0.956  7.000
 172   WZ CAS     N            0.327  6.535  3.579  2.636  1.397  1.073  7.000
 173   69 CYG     B0IB         0.442  5.511 -1.028 -0.234 -0.370 -0.395 -0.600
 174   HR 7699    B5IB         1.051  5.167 -0.585 -0.190 -0.320 -0.376 -0.450
 175   HR 8020    B8IA         1.333  4.395 -0.552  0.027 -0.153 -0.196  0.160