Towards diagnostics of random polarization: how Stokes correlations provide information content of stochastic optical fields

In this paper, we reviewed our recent work on the correlations of the Stokes parameters and their applications to diagnose random polarization in stochastic optical fields. With the aid of the ensemble-average van Cittert-Zernike theorem for the propagation of polar-coherence, we investigated the autocorrelation functions and power spectra of the Stokes parameters to expose the dependence of the polarization-related scale-size distributions. A generalized concept of the Stokes ensemble average coherence areas has been introduced to deal with the polarization-related average areas associated with polarization speckle. Noting the fact that the Stokes parameters cannot be measured at an ideal point, we also made investigation of the means and variances of the integrated Stokes parameters in polarization speckle after introduction of four parameters, i.e., the numbers of degrees of freedom for the Stokes detection. Furthermore, a new scheme of interferometry referred to as the Stokes Vector Interferometry has been proposed as an extension of intensity interferometry by taking the vector nature of electromagnetic field into account. Through the cross-covariance computations for the fluctuating Stokes parameters, the squared moduli of the generalized Stokes parameters are reconstructed for the first time.