Dependence of speckle contrast on the light spectral broadening and the roughness root mean square

From an Interferometric point of view, the spatial random intensity distribution of speckle patterns photography is analytically derived. The surface roughness is assumed to be of scattering grains of random spatial and heights distributions. Two probability density functions, Gaussian and Lorentzian, for the roughness heights distribution are considered. Also, two spectral broadenings for the light beam, Gaussian and Lorentzian, are taken into consideration. The dependence of the speckle contrast on the roughness root mean square, the number of the interfering beams and the spectral light broadening is analytically derived and presented through computations.