Statistical properties of polarization speckle

The speckle phenomenon is ubiquitous, occurring whenever radiation is passed through a diffusing surface or is reflected from a surface that is rough on the scale of wavelength. In most studies on speckle phenomenon, the light in the speckle pattern is assumed to be perfectly polarized and the random optical field has been treated as a scalar optical field with the main interest being in the statistical properties and applications of the intensity distribution of the speckle pattern. In many practical applications, the light scattered by the rough object may be partially or totally depolarized. Just as the intensity of light varies across the speckle pattern, so too the state of polarization may vary. This random fluctuation of polarization has become known as polarization speckle.

Since polarization speckle plays an important role in many optical phenomena, it is essential to fully understand its statistical properties. With the aid of Gaussian random process for electric field and the concept of ensemble-average polarization and coherence, we derive the first-order statistics of the Stokes parameters and provide some higher-order statistics of polarization speckle including the Stokes autocorrelation functions and their power spectral densities, second-order joint probability density function and statistics of the derivatives of the Stokes parameters. Since the recorded polarization speckle patterns may be spatially/temporally integrated, consideration is given to the statistics of the integrated Stokes parameters. Finally, the relationship between detailed surface structure of a birefringent polarization scrambler and the resulting polarization speckle is explored to understand its development and evolution.