Spatial statistics of superposition of two uncorrelated speckle patterns with polarization diversity

A detailed theoretical and experimental study on the effect of the superposition of uncorrelated speckle patterns with polarization diversity on the spatial statistics of the superposed speckle pattern is presented. It is shown that depending on the mutual orientation of the polarization vectors of the constituent speckle patterns, the maximum degree of coherence (DoC) and degree of polarization (DoP) of the superposed speckle pattern changes between a maximum and minimum value in a sinusoidal fashion. Moreover, the average intensity ratio of the constituent speckle patterns is also found to be affecting these variations. A study of the change in the visibility of the two-point intensity correlation function also reveals a sinusoidal nature of the variation and its dependence on the ratio of the average intensity, which are found to be similar to the variations of the maximum DoC and DoP. A detailed study on the changes in the normalized probability density function is also performed for better understanding of the effect on the spatial statistics.