The net result of using this approach is that the DQE appears to be lower than the values presented in older versions of the FOC Instrument Handbook (Versions 1.0-4.0), particularly at ultraviolet wavelengths. There are three reasons for this. Firstly, a larger fraction of flux is scattered into the region between 1.0" < r < 3.5" and is not counted towards the absolute sensitivity. This amounts to approximately 6% of the total flux for the F140M filter. Secondly, when the background is determined at a radius of 1.0 arcseconds, one is effectively subtracting more background than would make the encircled energy curve flatten asymptotically at larger radii. This effect amounts to about 7% of the total flux for this filter. Lastly, the COSTAR reflectivities that had been used to predict the DQE in the previous version of the Handbook were based on those measured just after the COSTAR mirrors had been coated; in the year between coating and launch the reflectivity had degraded by a few percent due to small amounts of molecular contaminants and some dust covering introduced in the COSTAR vibration testing. The apparent "loss" compared to the previous Handbook is offset by a corresponding increase in encircled energy at all radii, since the total flux is made smaller. All of this sounds like a long-winded discussion, but it is merely to explain why the DQE measurements presented here are significantly different from those in the older versions of this Handbook (Versions 1.0-4.0). A more thorough discussion is given in FOC Instrument Science Report FOC-085.
The fluxes of the spectrophotometric standards within 1" were compared with SYNPHOT predictions. The spectrophotometric standards had been recalibrated using the best model of the white dwarf star G191B2B to redetermine the IUE sensitivity calibration (a correction of several percent in the 1200-2000 Å wavelength range). It was found that the observed/expected flux values depended on wavelength linearly for the reasons outlined in the previous paragraph, so the DQE curve was transformed by this linear function to derive the new DQE curve.
The overall (OTA + COSTAR + FOC) central absolute quantum efficiency Q(l) in counts photon-1 with no filters in the beam is plotted and tabulated as a function of wavelength in Figure Table 6.3: Overall (OTA+FOC+COSTAR) Absolute Quantum Efficiency Q(l) in 10-3 Counts Photon-1
The encircled energy and detector quantum efficiency are somewhat coupled since the PSF does not have a well-defined edge; instead the flux drops steadily with distance from the star center until it gets lost in the background noise. The flux in the wings is due to scattering by dust and small imperfections in the OTA+COSTAR+FOC optical train, and is more pronounced at shorter wavelengths. When constructing an encircled energy curve, which is the curve of the fraction of light enclosed within a circular aperture of a given radius as a function of radius, one naturally has to define how one measures the total flux. In the past, this was done by choosing an aperture size that was large enough to include the spherically aberrated PSF, or about 3.5 arcseconds radius. This aperture size could comfortably fit inside the workhorse 512 x 512 imaging format before COSTAR was installed.
Figure 6.7: Baseline Overall (OTA+COSTAR+FOC) Absolute Quantum Efficiency in Counts Photon-1 as a Function of Wavelength for the Three Imaging Modes and the Four Long Slit Spectrograph Orders, Including the Obscurration of the OTA.
With COSTAR, the magnified plate scale means that such a large aperture size cannot be used for DQE measurements, particularly since most of the measurements of spectrophotometric standards were made using the 256 x 256 imaging format to improve the linearity performance. For this reason, it was decided to define the encircled energy to be 1.0 at a radius of 1.0 arcsecond (70 pixels) and to define the background as that value which minimizes the scatter of the points in the encircled energy curve with 0.9" < r < 1.1". In practice, this is equivalent to setting the background to the value measured at approximately 1.0" radius, and it does give encircled energy curves that are qualitatively in agreement with what such a curve would look like: the encircled energy asymptotically approaches a constant value at the last measured points. Users should be aware that there is some flux outside 1 arcsecond radius, especially in the ultraviolet, but this flux is not considered "useful" and its contribution to the total DQE is not included. 
The spectrograph efficiency is shown for the four orders of the grating (I, II, III and IV) with no order sorting filters in the beam. These measurements were made before launch; no on-orbit calibration of the spectrograph sensitivity has been attempted, although the observations that have been made show that the ground-based calibrations are consistent at the 50% level.
For the F/96 relay, uncertainties in the DQE curve are approximately xb1 10% (1s), while for F/48 errors in the 2000-6500Å range for the imaging modes should not exceed xb1 20% and for wavelengths below 2000Å they are expected to be of the order xb1 50%. This latter uncertainty should be applied to all the spectrograph data especially in the orders III and IV.
Format-dependent Effects
It has been found that the DQE is a function of detector format (see Instrument Science Report FOC-075). The cause of this is not known. The relative sensitivities for each format are given in Table 6.4, where the 512 x 512 format is set to 1.0 by definition. The DQE values given in Table 6.3 and Figure 6.7 refer to the 512 x 512 format. Typical uncertainties in these numbers are approximately 5%
Table 6.4: Format-Dependent Sensitivity Ratios.
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