Statistical analysis for beam smoothing and some applications

We develop statistical tools for beam smoothing analysis. As applications we study the respective performances of two-dimensional smoothing by spectral dispersion and of smoothing by optical fiber. The calculations are valid in the asymptotic framework of a large number of elements of the random-phase plate and of excited optical modes of the fiber. Theoretical results and closed-form expressions for the contrast and the spatial spectrum of the integrated intensity of the speckle pattern are derived so as to produce evidence of performance differences between these methods, which are essentially based on the longer time delay induced by the multimode fiber with respect to that induced by the gratings and on the nature of the spectral broadening.