Cross-spectral purity of Stokes parameters, purity of partial polarization and statistical similarity

In this paper, we discuss the concept of cross-spectral purity of Stokes parameters, purity of general partial polarization and implications of statistical similarity of an optical field. The conditions of cross-spectral purity of Stokes parameters and purity of partial polarization are obtained. Then, by utilizing statistical similarity, the relationships between the two purity and spatial coherence are explored. At last, a special situation that gives a relation of these two kinds of purity is briefly discussed.