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6.2. Flux Calibration

The surface brightness of an aperture-filling source is a function of the pipeline-calibrated spectrum, F(lambda) in ergs s-1 cm-2 Å-1, the detector solid angle, Omega, and the aperture correction, T(A-1) × D, which includes a term for flux lost at the A-1 science aperture (T(A - 1)) and at the detector (D):

Equation 2       (2)

The pipeline calibration (calibration of the spectrum as appropriate for a point source) depends on the stability of the instrument for relative flux calibration and on the accuracy of the fiducial standards for absolute flux calibration. The accuracy of the secondary standard star system does not dominate the FOS calibration uncertainty; it was already discussed briefly in Section 4.2.5 and is discussed further in Paper II.

The pipeline calibration converts DN sec-1 per diode to ergs sec-1 Å-1, as appropriate for point sources, achieving repeatability of 1-2% for point sources only if they are centered in the aperture to within ± 0.2 arcsec (Keyes 1995). This sensitivity to centering implies at least two serious complications for surface photometry. First, the transmission efficiency across the photocathode can vary by as much as 20% over surface areas corresponding to 10 diodes. Second, and more importantly, the PSF is not well contained within either the aperture, the detector, or both. An accurate aperture correction is therefore crucial to surface photometry.

The aperture dilution factor, T(ap) × D, given in the FOS Instrument Handbook is an estimate produced by modeling based on the OTA with post-COSTAR configuration. While no official Instrument Science Report exists, unofficial estimates for the monochromatic transmission of the A-1, post-COSTAR configuration at 6500Å range from 97% (R. Bohlin, private communication) to 95% (The Data Handbook V3.0). Because this factor is crucial to our result, we have recalculated it using data taken for this purpose as part of the FOS calibration program (Proposal 5262, Koratkar). These data were taken in ACQ/IMAGE mode, which uses no dispersing element, providing a two dimensional image in the diode plane. The stepping pattern used for the observations was kindly provided to us by E. Smith at STScI. Our reduction and analysis of these data are described in Bernstein (1998). We find that 98% of the flux from a point source is contained within the A-1 aperture at the focal plane, and 96.5% of that flux is then imaged onto the 1.29 arcsec spatial extent of the diode array: T(A - 1) = 0.98 and D = 0.965. Thus, we find

Equation 3       (3)

in which we have included a small (0.002) correction for conversion from the "white" light of the ACQ/IMAGE data to our central wavelength of 5500Å. The statistical error in this estimation is much less than 1%, but the systematic uncertainty may be as large as 2%.

The A-1 science aperture measures 3.63 × 3.71 arcsec2, with 1% errors in both dimensions. In the spatial direction the solid angle is determined by the diodes, which are 1.289 (± 1%) arcsec in the spatial direction. This values is based on a laboratory measurement made before launch (Instrument Science Report ISR CAL/FOS-019), and has been corrected for the measured change in the FOS plate scale before and after COSTAR was installed (ISR CAL/FOS-123,141). The effective solid angle through the A-1 aperture is then 3.63 × 1.29 arcsec2, or 4.68 arcsec2 with an uncertainty of ~ 2%.

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