The f/96 camera of the FOC contains three linearly polarizing prisms with names POL0, POL60, and POL120. The E-vector pass directions of these prisms are 0 degrees, 60 degrees, and 120 degrees respectively, counterclockwise from the image x axis (-S direction), as projected onto the sky. The prisms are birefringent beam splitters that transmit one mode of polarization straight through, while deflecting the orthogonal mode so that it misses the central 512 x 512 region of the photocathode.
The pipeline calibration for polarization observations is no different than for other images. That is, no special correction for polarization is applied, and the images are not combined to form Stokes parameter images.
A polarimeter based on three separate polarizers cannot be expected to yield extremely accurate results. One difficulty is that the throughputs of the three polarizers are not identical, and these differences in throughput depend on wavelength. While the filter transmissions have been measured on the ground, filters do change with time, and color variations in the source will result in small differences in the observed throughput. Variations of order one percent exist throughout the visual wavelength range, but the major difference is that the short-wavelength cutoff of POL60 occurs about 500 Å longward of the cutoff of POL0 and POL120. This divergence begins at about 3000 Å. Tasks in the SYNPHOT package can be used to determine the expected throughputs of each of the polarizers together with other filters used for your observations. You can then divide each of the three images by the expected throughput to correct for this difference.
Another limitation of FOC polarimetry is that the incoming light reflects off several mirrors at oblique angles, ranging from a few degrees up to about 11.5 degrees. An oblique reflection at 11.5 off aluminum induces a linear polarization of about 0.2% in incident unpolarized light, and it also results in a phase shift of about one degree. Such a phase shift is insignificant for incident linearly polarized light. If the incident light were 100% circularly polarized, however, a one-degree phase shift would induce a spurious linear polarization of nearly two percent, which would be significant.
Introducing a polarizer into the beam shifts the image by several pixels. The amount of this shift must be known in order to determine the Stokes parameters from the three images. The shifts at various wavelengths are shown in Table 8.1. These values were based primarily on observations with the F346M filter and an objective prism, but observations with F220W and F140W were also used. The wavelength dependence is then derived from the dispersion curve of the far-UV objective prism (FUVOP). With POL0 or POL120 these values are believed to be good to 0.1 or 0.2 pixel, but with POL60 the uncertainty is more like half a pixel because the observations were of lower quality.
The image quality of the FOC suffers somewhat when a polarizing prism is used. While POL0 and POL120 are not bad, and POL60 seems to be good in the visual and blue range, the optical quality of POL60 deteriorates substantially at the shortest wavelengths that the polarizer passes, around 2200 Å. However, polarization observations at wavelengths shortward of about 3000 Å will be very difficult anyway because of the UV transmission cutoff of POL60.
After correcting for these unequal throughputs and shifting the images to register them, you can compute the Stokes parameters (I, Q, U) by simple arithmetic using the imcalc task. Using the imcalc notation im1, im2, and im3 to represent the images taken through the polarizers POL0, POL60, and POL120 respectively, the Stokes parameters are as follows: 
These values can be converted to the degree of polarization P and the polarization angle θ, measured counterclockwise from the x axis as follows:
The polarization errors arising from Poisson noise when N counts have been gathered in the three polarization image are given by:
Even for very large N (i.e. very good signal-to-noise), polarizations of point sources as low as 1-2% are very difficult to detect reliably because the limiting photometric accuracy of the FOC itself is close to this level. Uncertainties in flatfielding, filter transmission uncertainties, PSF differences between polarizers and other effects will conspire to thwart any attempts to measure polarizations to very high accuracy unless great care is taken to try and minimize the instrumental effects (e.g. by dithering the images, dividing into shorter exposures to investigate PSF changes and differences). Flatfield uncertainties and PSF dependences are less of a factor when analyzing extended sources (with sizes larger than 15 pixels or so), so polarization accuracies of 1% or so are probably achievable for extended sources.
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Last updated: 11/13/97 16:46:45