An Entropy Measure for Partially Polarized Radiation and its Application to Estimating Radio Sky Polarization Distributions from Incomplete 'Aperture Synthesis' Data by the Maximum Entropy Method

To apply the maximum entropy method to the task of mapping a radio sky polarization distribution from incomplete ‘aperture synthesis’ data, it is necessary to have a measure of the relative entropy in a polarization map. Such a measure is derived. It allows the change in entropy measure due to a variation in intensity to be compared with that due to a change in the degree of polarization. Using the new measure the variational problem for choosing the maximum entropy estimate of a polarized sky distribution is set up, and some progress is made towards its solution. A field of given mean intensity is found to have maximum entropy measure when it is unpolarized and of uniform brightness.