The flight data is reduced using a reduction and analysis program (REDUCE) already in use with the visible-wavelength spectropolarimeter at the University of Wisconsin Pine Bluff Observatory. Steps include (Data Reduction Flowchart (ps file)) :
Several components of the background must be removed. First, cosmic ray events in the detector are seen as large spikes in single frames. Second, a timing problem in the telemetry electronics resulted in occasional single-pixel digital errors which were recognizable by their bit pattern and by comparison of redundant telemetry streams. Both are removed by replacement with the average of unaffected frames through the same analyzer filter. Third, thermal background in the photodiodes, which has a smooth dependence on pixel, was removed using background integrations obtained before and after the science observation, normalized to the signal at very low wavelengths where the response to light is negligible. Fourth, thermal photon events from the photocathode were evaluated from several long observations of background (e.g. undetectable targets of the other instruments) during orbital night. Finally, background from the "sky" was dominated by solar scattered light in the daytime. This could be evaluated using three analog bright object sensors (phototransistors) mounted within the sunshade at the aperture door. Several observations obtained at solar angles less than 90 degrees were contaminated in the longer wavelengths by this source. Orbital nighttime sky sources (zodiacal light, NO residual airglow) were not detected, as predicted prelaunch.
Removal of the residual effects of image motion proved to be problematic due to poor performances by the Spacelab Instrument Pointing System (IPS) . For most of the mission, the IPS did not attain a closed-loop "optical hold" and the observations were hand-guided by the crew using video images of the star-field and a hand paddle. This resulted in image motion an order of magnitude greater than specification, which was in most cases beyond the operational capability of the Image Motion Compensation System (IMCS). The result was a degradation in spectral purity and, most seriously, a time- dependent pixel response which compromised the precision of the polarimetry. However, some of these effects could be removed by a frame-by-frame pointing correction procedure: The target image in the zero-order camera and data from the IMCS could be used to establish the image position for a given frame. Parallel to the dispersion, a simple shift restored some of the spectral purity; perpendicular to the dispersion, a table of pixel response variation was developed using the brightest stars, and was applied to each frame, so that each frame was referenced to the detector gain at a single standard point on the detector. These procedures resulted in an ultimate spectral purity of 2.5 nm and a signal/noise ratio which approached input photon limited.
For halfwave mode data, three normalized "filter-pair" differences were formed pixel-by-pixel from the response of the two split spectra "A" and "B" through two halfwave filters with optic axes 45 degrees apart. These filter pairs correspond to orthogonal rotations of the input linear polarization. For instance, a difference spectrum d(0) is formed from A and B spectra through the halfwave filters at angles 0 degrees and 45 degrees as follows:
d(0) = (A(0) - A(45))/(A(0) + A(45)) - (B(0) - B(45))/(B(0) + B(45))
and similarly for d(15) and d(30) using angle pairs (15, 60) and (30,75) degrees. From the waveplate model one knows the (roughly sinusoidal) dependence of d(phi) on phi, given input Stokes parameters Q(lambda) & U(lambda),
d(phi) = dQ(lambda) Q/I + dU(lambda) U/I
A weighted linear least squares fit of the three d(phi) then yields Q(lambda)/I, U(lambda)/I, and Error(lambda), where Error is an estimate of the mean error in Q/I and U/I. In practice, the data is divided into many independent sets, and the error-weighted mean of the independent data sets yields the final Q,U,Error spectrum. This formulation has been found to be insensitive to changes in total received flux due to pointing errors, gain changes in the detector, and noise events in the image tube.
The above polarimetric analysis does not depend on the absolute response of the system. In order to obtain an absolute flux spectrum, additional standard flux reduction techniques were applied to the sum of the two polarimetric channels A and B. The spectrum of a hot white dwarf (G191B2B) was used to derive a "flat-field" spectrum which gives the relative pixel-to-pixel response variations at the reference detector point. The raw flux spectra were divided by this flat-field and multiplied by a smooth flux response curve derived from ultraviolet flux standards.
The above figure illustrates the standard data product of the reduction: a three-part spectrum showing the flux spectrum, linear polarization spectrum, and linear position angle theta = 0.5 tan-1(U/Q). The polarization is usually "binned" (neighboring pixels averaged) until a constant mean error is achieved, to further improve the signal-to-noise. Finally, a standard set of spectropolarimetric analysis tools (vector arithmetic, Q-U vector plots, wavelength dependence fitting) is used for scientific interpretation.
-taken from Nordsieck et al., 1994, SPIE, Vol. 2010, p.2.