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28.3 Polarimetry

WFPC2 has a polarizer filter which can be used for wide-field polarimetric imaging from about 200 through 700 nm. This filter is a quad, meaning that it consists of four panes, each with the polarization angle oriented in a different direction, in steps of 45o. The panes are aligned with the edges of the pyramid, thus each pane corresponds to a chip. However, because the filters are at some distance from the focal plane, there is significant vignetting and cross-talk at the edges of each chip. The area free from vignetting and cross-talk is about 60" square in each WF chip, and 15" square in the PC. It is also possible to use the polarizer in a partially rotated configuration, which gives additional polarization angles at the expense of more severe vignetting.

Each polarimetry observation consists of several images of the same object with different orientations of the polarizer angle. A minimum of three observations is required to obtain full polarimetry information. This can be achieved by observing the target in different chips, by rotating the filter wheel (partial rotation), or by changing the orientation of the HST field of view in the sky, using a different roll angle. In the latter case, observations must frequently occur at different times, as the solar array constraints on HST allow only a limited range of roll angles at any given time.

Accurate calibration of WFPC2 polarimetric data is rather complex, due to the design of both the polarizer filter and the instrument itself. WFPC2 has an aluminized pick-off mirror with a 47° angle of incidence, which rotates the polarization angle of the incoming light, as well as introducing a spurious polarization of up to 5%. Thus, both the HST roll angle and the polarization angle must be taken into acccount. In addition, the polarizer coating on the filter has significant transmission of the perpendicular component, with a strong wavelength dependence (see Figure 28.1).

Figure 28.1: Parallel and Perpendicular Transmission of the WFPC2 Polarizer

Biretta and McMaster (WFPC2 ISR 97-11) recently achieved a calibration accuracy of about 2% rms for well-exposed WFPC2 polarimetry data. Their method uses a Mueller matrix approach to account for the orientation of both telescope and polarizer, the effect of the pick-off mirror, and the significant perpendicular transmission of the polarizer itself. A full description of the motivation behind this approach, the implementation details, and the necessary caveats are given in this document. A web-based tool to aid in the calibration of polarization data has also been developed. With the aid of this tool, polarization properties can be derived for point sources and extended sources from an arbitrary combination of polarized images. The tool is available at:

http://www.stsci.edu/ftp/instrument_news/WFPC2/Wfpc2_pol/

wfpc2-pol2.html

The procedure to obtain polarization information begins with the calibrated images, as they come out of the pipeline (plus cosmic ray and warm pixel rejection, if appropriate). The characteristics of the polarized images and the fluxes in each image are entered in the Web tool, and the calculation started. The tool then reports the values of the Stokes parameters I, Q, and U, as well as fractional polarization and position angle. The optional synphot values in the first part of the tool can be used to fine-tune the results to a specific spectral energy distribution, but are in most cases not necessary.

The tool also reports expressions for I, Q, and U as a function of fluxes in the three images. These can be used to test the sensitivity of the results to errors in the individual fluxes, or to combine images in order to obtain pixel-by-pixel values of the Stokes parameters for extended objects, resulting in I, Q, and U images.

More details will be provided in a future ISR, as well as in the extensive help available in the web tool itself.

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