Statistics of dynamic polarization speckle generated from a moving rough-surfaced retardation plate

Laser speckle has received extensive studies in its basic properties and wide applications. In the majority of research on speckle phenomena, these random optical fields have been treated as scalar optical fields, and the main interest has been in the statistical properties together with applications of the intensity distribution of the speckle patterns. In recent years, increasing attention has been paid to the statistical properties of random electric vector fields referred to as polarization speckle with spatially varying polarization state. Statistical phenomena of random electric vector fields with their close relevance to the theories of speckles, polarization and coherence theory have come to attract emerging interest due to their importance in a variety of areas for practical applications such as biomedical optics, remote sensing, astronomical observation and optical metrology. In this paper, we investigate the dynamic polarization speckle generated by a moving rough-surfaced retardation plate and present an exact analytical expression for the space-time lagged correlation for the stochastic fields within the framework of ABCD matrix theory (Canonical Transforms). General expressions are derived for the spot size, the mean polarization speckle size, the temporal coherence length, and the peak shift of the temporal correlation. Some interesting phenomena associated with dynamic polarization speckle have been predicted including polarization speckle boiling and polarization speckle translation. A general description of these phenomena has been given for arbitrary complex-valued ABCD optical systems.