A study of the statistics of the polarization properties of one-dimensional randomly rough surfaces is presented. Based on the assumption that the s and p components of the electric-field vector constitute correlated circular complex Gaussian processes, some first-order statistical properties of the polarization of scattered fields are first established. In particular, results are presented for the probability density function of the Stokes parameters and their correlations. For each realization of the surface the random Mueller matrix elements associated with the surface may be determined from measurements of the Stokes parameters of the scattered light. Choosing a +45° linear polarization for the incident field, one is then able to study the statistics of the Mueller matrix elements. Numerical and experimental data on the statistics of the Mueller matrix elements are presented and compared with theoretical results. Finally, the usefulness and the significance of the results are illustrated with some examples.
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