Recently Strohmayer and Kallman (2013, ApJ, 773, 103) explored in Monte Carlo simulations the number of X-ray interactions needed to achieve joint confidence limits of the amplitude of polarization of the X-ray beam and the direction of polarization. The following paper finds a simple analytic description of joint confidence areas of these variables.
"Statistics of X-Ray Polarization Measurements", Montgomery, C.G., & Swank, J.H. 2015, ApJ, 801, 21, astro-ph/1501.02222v2
The paper uses the calculations described in the following report: TechnicalReportStatisticsXRayPolarization.pdf
There is discussion additional to that in the paper and it includes the Fortran program used to generate the simulations for the figures. Selected figures are in color.
The Fortran program and its description are separately in: polsim1.txt
