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Statistics of specular points at a randomly rough surface.

Statistical parameters are obtained for an ensemble of specular points at a randomly rough Gaussian statistically isotropic surface at normal incidence. The joint probability density functions (PDFs) of specular point heights and total curvatures are derived separately for maxima, minima, and saddle points. The joint PDFs of brightness and surface elevations of specular points of different types are obtained analytically in an explicit form.