Location of FOS Spectra: Cycle 1 and Cycle 2 Results Anuradha Koratkar and Cynthia J. Taylor Space Telescope Science Institute Instrument Science Report CAL/FOS--096 August, 1993 Abstract The optimal locations of the FOS spectra were determined for all non-polarized grating/detector combinations using calibration maps obtained during Cycle 1 and Cycle 2 (proposal IDs 2817 and 4097). The location of the spectrum as a function of diode number deviates from linearity by up to +/-20 YBASE units because of small distortions of the magnetic fields in the Digicons. In addi- tion, the spectra are rotated by small angles (typically 0.05 degree for the high resolution gratings) with respect to the diode array. New optimal locations of the spectra (YBASES) determined dur- ing the analysis have been updated in the Project Data Base (PDB) on August 11 1993. The analysis showed that there is a trend in the positions of the spectra for all gratings observed with the blue detector, while the locations of the spectra for all gratings with the red detector are relatively stable. Photometric errors and errors in the measured shape of the continuum due to the incorrect usage of YBASE values for Cycle 2 and early Cycle 3 observations are typically <3% on the blueside and <1% on the redside. 1. Introduction In the final stretch of the FOS optical path, light is dispersed from the filter-grating wheel and is imaged onto the transmissive photocathode in the Digicon detector of choice. Next, the photo- electrons from the region of the photocathode where the spectrum is expected are accelerated to the linear array of 512 diodes. Only information from the region of the photocathode that is imaged onto the diode array is recorded by the instrument. The ability to acquire FOS spectra, therefore, depends on the knowledge of the where the spectrum is expected on the photocathode. This location of the spectrum is determined using a basic FOS unit called the YBASE unit. The YBASE unit is defined such that 256 YBASE units will equal the height of the diode array which is nominally 200 mm (1 YBASE unit = 0.78125 mm). The photocathode extends from -2048 to +2048 YBASE units in the direction perpendicular to the diode array (FOS Y axis). The YBASE for any detector, disperser, aperture, and polarizer combination is the Y position (between +/- 2048) on the photocathode which defines the optimum location of the spectrum. The YBASE val- ues must be monitored closely as they affect the quality of the scientific data received. Use of improper YBASE values will decrease the amount of flux recorded by the diode array. The cali- bration observations in the Cycle 1 and Cycle 2 calibration programs were to verify/correct the optimum values for the YBASEs and investigate the stability of the position of the FOS spectra on the photocathode. 2. Observations and Analysis Calibration observations to determine the location of the FOS spectra for both the red and blue detectors were obtained on the dates given in Tables 1 and 2 (proposal IDs 2817 & 4097). The observations for Cycle 1 and Cycle 2 calibration programs used the optimum YBASE values for each grating/detector combination determined from SV/OV observations as a preliminary guess for the location of the spectra on the photocathode. Maps of the internal wavelength calibration lamps observed using the 0.3" aperture were centered approximately at these expected locations. Each map sampled all the 512 diodes in the diode array at 24 locations (24 YSTEPS), each sepa- rated by 24 YBASE units in the direction perpendicular to the diode array. Therefore the calibra- tion images consisted of 512 X 24 pixels. Since the position of the spectrum on the photocathode is not expected to vary on small scales, the data are binned over 30 diodes (see examples in Figure 1). Next, the YBASE, which represents the center of the spectrum in the direction perpendicular to the diode array (the FOS Y axis) was determined. A square template was cross-correlated with the Y cross-section of each bin to determine the best correlation which defines the center of the spectrum (above the noise level) for each bin of 30 diodes. The cross-correlation method was selected as it produced the best results for low signal to noise data. A plot of the YBASE values as a function of diode number shows that the spectra are not linear, and that some distortion is present whose shape depends on the grating (a few examples are shown in Figure 2). This distor- tion is due to the small imperfections of the magnetic field in the Digicons. Once the Y-position of the spectrum is known as a function of the diode number, the optimal YBASE value is determined to minimize the effects of the distortion. This optimal YBASE value (corrected for GIMP) is the mean of the minimum and maximum YBASE values observed for each grating detector combina- tion for a given diode range (see table 1). FOS spectra on an average are not observed to be parallel, but are slightly tilted with respect to the diode array (the FOS X axis). The quantity qz, which is the angle between the X-axis and the best fit line to the spectrum over the same diode range used in determining the optimal YBASE value, is a measure of the orientation of the FOS spectrum on the photocathode (see Figure 2). Tables 1 and 2 have the following information for each disperser detector combination. They have the root name of the observation used in the analysis, the date of the observation, the optimal YBASE val- ues, the diode range used in the determination of the optimal YBASE, the orientations of the FOS spectra on the photocathode, the temperature of the FOS during the observation, and the GIMP correction applied to obtain the optimal YBASE value. Since onboard GIMP correction began on April 5, 1993, no GIMP corrections (during the analysis) are applied to the FOS data obtained after this date. The average normalized shape of the spectrum on the photocathode is shown in Figure 3 for all dispersers and detector combinations. The solid line represents the average shape of the spectrum and the dotted lines represent the +/- 1 sigma deviations from the average. 2. Results YBASE Measurements: The value of the YBASE determined for each spectrum depends on the diode range (referred to in Tables 1 and 2) selected for determining the value. Only those regions of the diode array are selected over which a continuum spectrum is expected to have a normally measurable signal. For the G650L grating, the YBASE value is for the first and second order spectra (unlike inverse sen- sitivity which is for the first order only). The difference between calibrating for both orders and for the first order only is 10-15 YBASE units. Figure 4 shows the distribution of the YBASE val- ues determined for each observation for each disperser detector combination. Part of the scatter (+/- 10 YBASE units) is due to the filter-grating wheel non-repeatability discussed by Hartig, Bohlin, and Harms (CAL/FOS-012 and CAL/FOS-017). The dashed lines in the figures represent the +/- 10 YBASE units. Cycle 1 Results: At the time of the Cycle 1 reductions, there was no obvious trend in time for any of the gratings. The YBASE values used during Cycle 1 were determined by a weighted average with Cycle 1 data weighted twice as much as OV/SV data (see Table 3). The differences in the optimal YBASE values between Cycle 1 and OV/SV for the redside ranged between -11 to -3 YBASE units, while the blueside ranged between -15 to 11 YBASE units. The optimal YBASE vales were updated in the PDB on Sept. 21, 1992. Cycle 2 Results: The inclusion of Cycle 2 results show that for all the blue detector gratings the data are linearly correlated and show a trend with time (see Figure 4). This is not the case for the redside detector and grating combinations (see Figure 4) except the G190H grating. The linear correlation coeffi- cients, and the spearman correlation coefficients for both detectors and grating combinations are given in Table 4. The probability that the data are correlated in time is also given in Table 4. The optimum YBASE values which represent the location of the spectra at the end of Cycle 2 were determined by computing the weighted average of all the Cycle 1 and Cycle 2 observations acquired so far for each disperser detector combination. The Cycle 2 data had twice the weight as Cycle 1 data. In the case of the redside detector, the optimum YBASE values determined for all the gratings, except the G190H and G270H, were within +/- 2 YBASE units of the values deter- mined for Cycle 1 and OV/SV. The G190H and G270H YBASE values differed from the Cycle 1 values by 14 and 4 YBASE units respectively. In the case of the blueside detector, the optimum YBASE values showed a trend in time and on an average the values for Cycle 1 differed from the optimum values for Cycle 2 by 20 YBASE units. The optimum YBASE values determined for each disperser detector combination has been used to update the PDB. The optimal YBASE val- ues were updated in the PDB on Aug 11, 1993 and are shown in Table 3. Shifts in YBASE as a function of Temperature: The YBASE measurements were also examined to investigate the effect of temperature of the FOS. Pre-flight investigations showed that the redside detector showed no systematic shift with temperature while the blue detector showed a shift of -61 microns (-78.08 YBASE units) between the cold (-30 C) and ambient calibration temperatures (20 C). The temperatures for onboard cali- bration observations have varied by only 10 C, and in this temperature range we see no systematic shift with temperature for both the blue and the red detectors. Although pre-flight investigations also showed that the location of the spectrum shifted with Digi- con voltage, shifts in YBASE as a function of Digicon voltage were not investigated since FOS observations are conducted at a fixed voltage for both the detectors. Photometric Consequences of Positioning Errors: Because any error in the location of the spectra is similar to miscentering in the aperture, there are associated photometric errors for each combination of detector, grating, and aperture. The effect of incorrect YBASE value is seen only in the 4.3" and the 0.25"X2.0" apertures, because the Y range of the apertures is determined by the projected positions of the edges of the diodes. To determine the extent of the errors, model point spread functions (generated using the TIM soft- ware; see details in CAL/FOS-10X) were convolved with the aperture size and the normalized shape of the spectrum in each disperser. The relative throughput was calculated for spectra dis- placed every 10 YBASE units from the optimal YBASE value. Figure 5 shows the relative throughput for each disperser in the two apertures as a function of wavelength and displacement of the spectrum from the optimal location (further details are being written in another CAL/FOS- 10X by Ian Evans). The solid line represents the throughput for the optimal location, the dashed line for spectra displaced in the positive direction and the dotted line for spectra displaced in the negative direction. The line marked 50 is for a displacement of 50 YBASE units the other lines are for 10, 20, 30 and 40 YBASE units. The error in the throughput has a different effect, depend- ing on the positive or negative nature of the positioning error, because the locus of the spectrum is not symmetric to the optimum YBASE location determined (see figure 2). There are photometric errors associated with most observations in Cycle2/early Cycle 3 because of the change in optimal YBASE value. The observations used he Cycle 1 values for the YBASE to obtain spectra. The typical photometric error due to this change in the optimal location of the spectra is <3% for the blueside and < 1% for the redside observations. The shape of the continuum is also affected by the positioning errors, since once again the locus of the spectrum is not symmetric with respect to the optimum YBASE location. The typical uncertainty in the shape of the spectrum is once again <3% on the blueside and <1% on the redside (for details see CAL/FOS-XXX by Ian Evans). ACKNOWLEDGEMENTS We would like to acknowledge B. Bhattacharya for reducing half of the Cycle 1 data, G. Hartig for accommodating us in his busy schedule, and I. Evans for the throughput simulations. REFERENCES G. Hartig, R. Bohlin, H. Ford and R. Harms, 1984, CAL/FOS-12: FOS Filter Grating Wheel Repeatability. G. Hartig, 1985, CAL/FOS-17: Improvements in Filter/Grating Wheel Repeatability. I.N. Evans, 1993, CAL/FOS-10X: Pre-Costar FOS Point Spread Functions and Line Spread Func- tions from Models. I.N. Evans, 1993, CAL/FOS-10X in preparation. FIGURE CAPTIONS FIG--1. Figures (a) and (b) are sample maps observed for the calibration analysis. Each line in this figure represents the relative counts above the noise level for each bin of 30 diodes. The dotted line is the box function used in the cross correlation and the + sign is the location of the maximum number of counts in each bin. FIG--2. Figures (a) and (b) are samples which show the location of spectra for two detector com- binations as a function of the diode number. The distortion in the shape of the spectrum is due to the imperfections in the magnetic field of the Digicons. The dotted line is the linear best fit to the spectrum. The slope of this dotted line is a measure of the orientation of the FOS spectrum on the photocathode. FIG--3. The average normalized shape of the spectrum on the photocathode for all dispersers and detector combinations is shown in this figure. The solid line represents the average shape of the spectrum, and the dotted lines represent the +/- 1 sigma deviations from the average. The disperser and detector combination is given in the title of each plot. The blueside is represented by the characters BSC and the redside by the characters ASC, followed by the grating. FIG--4. The optimal YBASE values as a function of time for the location of spectra for all grating detector combinations. The dashed lines are lines +/- 10 YBASE units from the best fit straight line to the data. These represent the possible range in the YBASE values to account for filter-grat- ing wheel non-repeatability. Most of the scatter in the data lies within the dashed lines indicating that the scatter is mostly due to filter-grating wheel non-repeatability. FIG--5. The relative throughputs for each disperser in the 4.3" and the 0.25"X2.0" apertures as a function of wavelength and displacement of the spectrum from the optimal location. The solid line represents the throughput for the optimal location, the dashed line for spectra displaced in the positive direction and the dotted line for spectra displaced in the negative direction. The line marked 50 is for a displacement of 50 YBASE units the other lines are for 10, 20, 30 and 40 YBASE units. Any error in the location of the spectrum not only leads to photometric errors, but also to errors in the shape of the continuum.