Panoramic polarimetry data analysis

Derivation of accurate polarization information about an astronomical target is a vital tool for investigation of astrophysical processes. Use of large area detectors for imaging and spectroscopy has become commonplace, and frequently such instruments offer a polarization capability. Processing of polarimetric data, however, is nontrivial, especially when the polarimeter is far from ideal. Here we present an overview of the analysis procedures needed to properly process polarimetry data that comprise a series of images of an object taken through a given set of polarizers, such as the imaging instruments on the Hubble Space Telescope (HST). The analysis can also be used for other types of polarization data, such as spectra. We consider only linear polarization, not circular. The polarizers do not need to be perfect polarizers, although it is important that their characteristics be well established. From an input data set of n intensities (or, equivalently, fluxes) and their errors, assumed independent between observations, corresponding to a set of observations through n polarizers (not necessarily identical or perfect), we show how to derive the Stokes parameters and their covariance matrix both for the special case of n =3 and for general n, We then discuss how to derive higher level parameters such as polarization degree and position angle and their associated uncertainties and indicate ways to "debias" the positive definite polarization degree. We present tests of our analysis using Monte Carlo simulations. Finally, we show the achievable accuracy for various levels of polarization and signal-to-noise ratio for typical cases, which should be useful for observation design. The techniques allow accurate recovery of polarization information from several of the instruments an board the HST as well as estimates of the uncertainties in the results.