Microrough Surfaces: Influence of the Correlation Function on the Speckle Pattern

It is shown that the correlation function, which determines the properties of scattering from shallow microrough surfaces, no longer suffices to describe the speckle pattern as soon as the mean height of the irregularities exceeds one-tenth of the wavelength. With this aim, we numerically generate random microrough surfaces whose diffraction patterns are rigorously computed. Then, we show that surfaces having the same correlation function can diffract very different speckle patterns from a statistical point of view. In particular, it is shown that the transition between partially developed and fully developed speckle is very complicated and does not only depend on the mean groove height. These results are explained using a perturbation theory.