32.6 Photometric Accuracies

• Time-dependent variations in FOS sensitivity.
• Target miscentering.
• FGW mechanism non-repeatability.
• Thermal breathing.
• Jitter and Guiding.
• Change in telescope focus.
• Thermal breathing.
• Location of spectra.
• GIM.
• Extended source calibration error.
• Calibration system offsets. After recalibration of your FOS data with AIS_CORR using the best reference files from the calibration close-out, these error sources will typically still affect the accuracy of your data. Table 32.4 summarizes the approximate levels of photometric inaccuracy introduced by these error sources, for both the pre- and post-COSTAR cases. In the subsections below we describe these error sources in great detail.

  Table 32.4: FOS Photometric Errors not Removed by AIS_CORR Calibration

  	Level of Error
  Source of Error	Pre-COSTAR	Post-COSTAR	Comment
  Miscentering target in aperture	~5% variable	~3% variable	Depends on target acquisition technique and aperture used. Error can be estimated.
  Y-base of spectra	3-10%	1-10%	Introduces spectrum shape (color) anomalies. Strongly affects extended objects
  FGW non-repeatability	3-10%	1-10%	Similar scale and effect to that of Y-base offset
  Thermal breathing	~4-7%	~1-3%	Aperture dependent
  Jitter	<3%	<1%	Aperture dependent
  GIM1	<5%	<1%	Introduces spectrum shape (color) anomalies. Strongly affects extended objects

  1 Pre-COSTAR GIM estimate refers to period before April 5, 1993.

  To summarize the principal impacts for different types of observations are:

• Y-base uncertainty-absolute and relative (color) effects.
• Target centering (target acquisition predominant contributor)-absolute and, for centering errors larger than 0.2", relative effects).
• Extended object-must be re-calibrated, if it partially fills the aperture there can be color effects. If your observations used a small aperture (0.5 and smaller), the primary source of flux calibration errors are:

• Target centering (target acquisition predominant contributor)-leads to absolute photometric errors; color OK.
• Jitter, guiding, and breathing-absolute photometry errors; color OK.
• Extended object-must be re-calibrated, color OK.

The FOS flux calibration was obtained from carefully centered (<=0.025" pointing accuracy in each coordinate) and flatfielded observations of spectrophotometric standard stars. Five standard stars, G191B2B, BD+28D4211, BD+33D2642, BD+74D325, and HZ44, were used for the pre-COSTAR calibration observations. For the post-COSTAR calibrations, this set and three additional white dwarf standards, GD71, GD153, and HZ43 were used. All pre-COSTAR observations were made with the 4.3 aperture and post-COSTAR observations were made with either the 4.3 or the 1.0 aperture. Typical formal S/N of binned spectral regions for these observations were 100 or often substantially greater.

Two methods of flux calibration have been used: FLX_CORR and AIS_CORR.

• FLX_CORR: Only spectropolarimetry data are reduced with the FLX_CORR method. One average set of sensitivity corrections was applied to all pre-COSTAR data regardless of when the data were taken or how far the telescope may have been from nominal focus. Similarly, only one epoch was used to set the post-COSTAR polarimetry flux calibration, but no time-dependent variables, such as focus or sensitivity changes existed for the post-COSTAR timeframe. FLX_CORR method photometry was substantially inferior to fluxes derived from the AIS_CORR method as several important sources of photometric error could not be removed in FLX_CORR processing. For example, pre-COSTAR FLX_CORR pipeline-calibrated fluxes may contain errors of up to 5% (FOS/RD) or up to 8% (FOS/BL) due to the pre-COSTAR sensitivity decline, of 5% due to telescope focus changes, and 3-15% (depending on spectral region) due to the offset between the IUE-based absolute flux system and the newer white dwarf model system (see See "Absolute Photometric Calibration System Offsets" on page 32-36.).

• AIS_CORR: All other flux-calibrated modes use this method of flux calibration, which includes corrections for time-dependent sensitivity variations, as needed, and for the actual focus history of the telescope. In the post-COSTAR era the effect of OTA focus changes is non-existent and that of time-dependent sensitivity variation is much less severe than for the pre-COSTAR period. All AIS_CORR corrections and aperture throughputs, with the exception of those for the 0.1-PAIR and the two barred apertures are based on actual observations. The barred aperture sensitivity has been defined as identical to that of the 4.3 aperture, and 0.1-PAIR throughputs defined as 20% of the 4.3 for pre-COSTAR and 40% post-COSTAR.

From early 1991 through mid-1992 the FOS experienced a systematic decline in sensitivity for all gratings and detector combinations. The systematic FOS/BL degradation in sensitivity by early 1992 amounted to approximately 10% for all gratings, and approximately 5% per year for FOS/RD (except for the G190H grating). The degradation in the FOS/RD G190H and G270H regions occurred at a rate of ~10% per year and was quite wavelength dependent.¹ All pre-COSTAR degradation leveled off between mid-1992 and the end of 1993. In Figure 32.5 we show the time dependence of the pre-COSTAR sensitivity for FOS/BL G130H which was typical for that detector. Pre-COSTAR sensitivity changes for FOS/RD G400H, which were typical of most spectral regions for that detector, are shown in Figure 32.6 and for the FOS/RD G190H in Figure 32.9.

Post-COSTAR sensitivity shows a dip relative to the pre-COSTAR values between approximately 1500 and 2500 Å. Except for FOS/RD G190H and G160L post-COSTAR sensitivity has shown no believable systematic temporal variation (see Figures 32.7 through 32.11). From February, 1994 through July, 1994 FOS/RD G190H sensitivity dropped by approximately 2% and then increased from 3 to 15% between July, 1994 and September, 1996. These changes are contemporaneous with substantial flatfield changes in portions of this grating. FOS/RD G160L showed similar changes shortward of 2200 Å. Figures 32.8 and 32.10 show the time dependence of post-COSTAR FOS sensitivity for the FOS/RD G190H grating.

The thick lines in Figure 32.8 indicate the average time-dependent sensitivity correction applied by the TIM-CORR calibration step (as contained in the .cyc reference file).

Overall Flux Calibration Accuracy Summary

The overall accuracy of the FOS photometric calibration for well-centered sources in the larger apertures, following recalibration with the appropriate updated reference files, is currently estimated to be 3% (1 ) for all grating modes except for FOS/RD G160L, FOS/RD PRISM and G780H longward of 7500 Å; for those specific settings the accuracy is 4% (1 ). In addition, there may have been systematic changes in the sensitivities at the 2% level which were not accurately tracked in the calibrations over some periods of times (see Figures

The relative photometry within a given standard spectrum is estimated to show roughly ± 2% curvature about the mean over correlation lengths of approximately 250 Å (see for example the relative spectra in Figure 32.14 and Figure 32.15, which show limiting examples of this effect that occurred occasionally in standard star spectra). Excursions to ± 4% are seen in some extreme cases.

The principal factors which contribute to this overal calibration accuracy include the following.

• The white dwarf models empirically reproduce the G191B2B and other standard star stellar flux distributions to roughly 1% in the visible region (using Landolt visible region normalizing photometry) and 2% in the ultraviolet. The reference system slope uncertainty over the 1200-5500 Å range is +/- 2%.
• The FOS exhibits ~2% or better repeatability for observations taken near in time in a given mode for all modes except FOS/RD PRISM and G160L and the long-wavelength region of G780H (at > 7500 Å), where repeatability is good to ~3%. See FOS ISR 144 for plots of accuracies for each mode as a function of wavelength. The sensitivity calibration files are computed as the mean of independent standard star observations over some time period, with any variations from observation to observation within that time period attributed to non-reproducibility in the FOS, and not to variations in the sensitivity (except for FOS/RD G190H and G160L). For any time periods and wavelength regions where true time variations have not been removed, there can be systematic effects in the absolute calibration scale at the 2-4% level (see Figure 32.7 for example-and consult FOS ISR 144 and the final closeout sensitivity ISR (158, in preparation) if you are concerned about effects at this level.)

  Actual FOS observations could have more uncertainty than this global 3% limiting accuracy, especially if the pointing uncertainty exceeded 0.1-0.2" as it often did, particularly in the pre-COSTAR era.

  Indeed, for any individual observation, the overall calibration accuracy is limited by a series of factors that, for the most part, can not be removed in calibration processing. These are described in the remainder of this section.

For example, with the 0.3 (B-2) aperture a target miscentering of 0.12" (the centering accuracy routinely achieved with ACQ/BINARY acquisition mode) led to a flux loss of about 60% with respect to perfect centering. The expected flux loss for a pointing accuracy of 0.03" (typically reached with a high precision multi-stage peak-up sequence) led to flux losses of less than 4% in the 0.3 aperture. Observing with the 1.0 aperture, the same pointing accuracy of 0.03" led to no measurable flux losses. For this aperture, the pointing accuracy of the binary target acquisition technique was sufficient. It resulted in flux losses of less than 3%

Determine your pointing accuracy from the FOS paper products for ACQ/PEAK acquisitions or assume one values from Table 32.5 for ACQ/BINARY. Use Figures 32.12 and 32.13 to estimate light loss for this degree of miscentering.

• For the 4.3 aperture, large y miscenterings have observable results that mimic the effect of poor Y-bases. Color anomalies and, especially, grating overlap region flux mismatches are a common consequence of poor large aperture centering. Many pre-COSTAR observations used only very approximate target acquisition strategies for 4.3 aperture observation, often under the mistaken impression that because of the large PSF one did not have to center accurately. Typically, any large aperture miscentering of more than 0.2" (40 Y-bases) in y will yield clearly discernible spectrum shape anomalies. Small aperture observation spectrum shapes are not affected by miscentering, although photometric accuracy is, of course.
• Highest precision absolute spectrophotometry required precise centering of <0.06", preferably 0.025" in each coordinate.
• Highest precision relative spectrophotometry with apertures larger than 0.5 required precise centering of <0.06", preferably 0.025" in y.

The effect of jitter and guiding errors is aperture dependent. The duration of jitter events is typically short and the size of guiding errors is typically small (1 =0.007") so that large aperture observations are not affected unless the target was poorly centered by the target acquisition. Smaller aperture observations can be affected. Typical random jitter produced <3% light loss for 0.3 pre-COSTAR and <1% post-COSTAR.

The primary photometric effect of any x-component of FGW non-repeatability was to introduce some uncertainty as to the exact correspondence between the portion of the photocathode granularity sampled by an arbitrary observation and that sampled by STScI calibration observations. The net effect, for most gratings, was to introduce a small amount of random additional noise, typically on the order of <1%, into the flatfielded spectrum (See "Flatfield Calibration" on page 32-38.).

32.6.4 Image Centering (Image Location) Factors

Look for broad features similar to the residuals seen in Figures 32.14 and 32.15. The shape of the features can be anticipated by considering the effect of shifting the s-curves in Figures 32.3 and 32.4 toward the top and bottom of the diode array. Reference to Figures 32.1 and 32.2 provides an idea of how close the installed Y-bases were to the continuing trend. Remember that the typical scale of Y-base uncertainty was up to 25 Y-bases, which could be exacerbated by similar amounts of FGW positioning offsets.

Breathing

Examine the paper products group plot for any series of readouts lasting more than 1000 seconds. Figure 32.16 shows an example of an approximate 3% thermal breathing effect for a precisely centered, low jitter (peak-to-peak excursions = 0.01") photometric target observed through the 0.3 aperture in a RAPID mode time-series of nearly eighty 30-second integrations all in one visibility.

Figure 32.8: Post-COSTAR Sensitivity Time Dependence: FOS/RD G190H

Figure 32.9: Pre-COSTAR Time -Dependence in FOS/RD G190H Grating

Figure 32.11: Post-COSTAR Sensitivity Time Dependence: FOS/RD

Figure 32.12: Post-COSTAR Transmitted Flux Versus Pointing Error: FOS/RD

Figure 32.15: FOS Standard Stars Compared with Models: FOS/RD

Figure 32.16: Example of Breathing Effect on Well-Centered 0.3 Observation

32.6.6 Extended Source Aperture Dilution Correction

Flux calibrations are determined from observations of standard stars and compensate automatically only for any light in the PSF that falls outside the aperture. For observations of extended sources, a correction needs to be applied to the final flux calibrated spectrum to correct for the non-pointlike illumination pattern. The correction is given by:

where:

• I = Specific surface intensity of a diffuse source in
  ergs s^-1 cm^-2 Å^-1 arcsec^-2.
• F = Flux in the calibrated spectrum.
• A(ap) = Relative point source transmission through the aperture area when A(4.3) = 1. These are given in Tables 32.6 and 32.7.
• = Solid angle of the aperture or object, whichever is smaller, in square arcseconds, e.g., 4.3" x 1.43" (pre-COSTAR) and 3.66" x 1.29" (post-COSTAR) for the 4.3 aperture.
• T_4.3 = Absolute transmission for a point source at zero focus of the 4.3 aperture. This number is estimated to be ~0.73+/-0.03 (pre-COSTAR) and 0.95+/-0.02 (post-COSTAR).² Pre-COSTAR aperture throughputs are given in Table 32.6 below. Substantial wavelength-dependent differences do not exist for the pre-COSTAR instrument, but detector differences are seen for equivalently sized apertures.

  The deployment of COSTAR produced a narrower PSF, which led to considerably higher aperture throughputs. For the large apertures (1.0 and larger) post-COSTAR there is no measurable difference in aperture throughput between FOS/RD and FOS/BL. Therefore, we list both detectors separately only for the 0.3 aperture and the slit in Table 32.7. Throughputs do change as a function of wavelength (or grating). Therefore, we list ratios for the different dispersers separately. The numbers are from FOS ISR 136.

  Recommended Pre-COSTAR Aperture Corrections and Uncertainties at -Nominal OTA Focus (4.3 aperture = 1.0)

  Grating	BLUE	RED	UNC1	BLUE	RED	UNC	BLUE	RED	UNC	BLUE	RED	UNC
  Mode	B-3 (1")			B-1 (0.5")			B-2 (0.3")			C2-SLIT
  HIGH	0.58	0.60	.02	0.41	0.44	.02	0.27	0.31	.03	0.39	0.41	.02
  LOW	0.65	0.67	.06	0.46	0.50	.04	0.31	0.35	.03	0.43	0.45	.03
  PRISM	0.53	0.54	.06	0.37	0.39	.04	0.26	0.30	.03	0.37	0.39	.03

  1 The uncertainties (UNC) do not include the possible contributions of pointing errors, OTA breathing, -jitter, or Y-base errors in an arbitrary science observation.

  Bar aperture throughputs are assumed to equal unity for all cases.

32.6.7 Absolute Photometric Calibration System Offsets

FLX_CORR and AIS_CORR Calibration System Differences

Wavelength	% Uncertainty
Far UV	~10%
Near UV	~5%
Visible	~3%

Figure 32.18: FLX_CORR to AIS White Dwarf Flux System Ratio

There can be some wavelength calibration uncertainty in certain overlap regions, but this does not exceed more than 0.5 diodes. This uncertainty is due to the lack of arc comparison lines in the overlap region of the gratings, so the wavelength solution must be an extrapolation. For the affected FOS overlap regions, this error in the wavelength calibration introduces a negligible (<<1%) error in the flux calibrations.

² See FOS ISRs 106 and 107.

³ FOS ISR 144.