Non-circular gaussian speckle contrast in the exact theory of multiple scattering of waves from random rough surfaces

In this paper the expression for the speckle contrast, under the assumption of non-circular gaussian statistics of the scattered field, is derived by using the exact scattering theory of waves by random rough surfaces previously established by the authors. This implies to find the second order moment 〈A²〈 of the scattering amplitude. It is shown that this zero outside the specular direction for large correlation distances of the random heights of the surface. as such, it coincides with the value obtained from the Kirchhoff approximation of Beckmann's theory and contributes to support the use of Beckmann's theory for measurements of speckle contrast in the specular direction, even when multiple scattering takes place.