Statistical properties of the integrated Stokes parameters of polarization speckle or partially polarized thermal light

The Stokes parameters, observables in physics, cannot be measured at an ideal point or at an instant in time. This paper is devoted to investigating the statistical properties of the integrated Stokes parameters in polarization speckle or partially polarized thermal light. As an extension to previous study on integrated intensity, spatially integrated and temporally integrated Stokes parameters have been applied to study integrated and blurred polarization speckle and partially polarized thermal light. A general concept referred to as the numbers of degrees of freedom for the Stokes detection has been introduced to investigate the means and variances of the integrated Stokes parameters. The approximate forms of the probability densities functions of the integrated Stokes parameters are also derived to provide the entire first-order statistics of integrated and blurred stochastic phenomena in optics.