Speckle statistics of electromagnetic waves scattered from perfectly conducting random rough surfaces

By means of the extinction-theorem method, previously reported by J. M. Soto-Crespo and M. Nieto-Vesperinas [J. Opt. Soc. Am. A 6, 367 (1989)], the intensity statistics of the s-polarized electromagnetic field scattered from randomly rough, perfectly conducting, one-dimensional surfaces are studied in the case of surface transverse correlation lengths larger than the wavelength. In particular, the speckle contrast, the intensity probabilitydensity function, and the mean scattered intensity are calculated for both moderately rough, single-scattering surfaces and very rough, multiple-scattering surfaces, for which the rms height is comparable with the transverse correlation length. Two different geometries for which non-Gaussian, fully developed speckle patterns may be produced are considered. On the one hand, we study the scattered field in the Fresnel region. We find that within this region multiple-scattering surfaces may lead to negative-exponential intensity statistics even at distances from the interface for which single-scattering surfaces produce remarkable non-Gaussian effects. On the other hand, non-Gaussian effects arising as a consequence of the reduction of the illuminated area on the interface are encountered in the far zone either for moderately rough, single-scattering surfaces or for very rough, multiple-scattering surfaces. In addition, with respect to multiple-scattering surfaces, it is shown that a minimum distance from the interface and a minimum incident-beam width are required for the backscattering peak to appear in the angular distribution of the averaged speckle intensity, as follows from simple arguments based on the coherent interference among multiple scattered paths.