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Analysis Of The Diffraction Spectrum Of A Population Of Particles

We study the diffraction spectrum of a population of circular objects randomly distributed. We present a rigorous study of the deconvolution of the intensity of a diffracted spectrum, permitting us to obtain the complete histogram of the distribution of sizes. (The method is applied notably to multi-modal histo-grams). The granularity term corresponding to the random positionings of diffracting objects was studied by means of a statistical model based on the independence of the positionings of the objects. We find that the size of the speckle wo is proportional to the inverse of the width of the object field studied. In the field of frequencies greater than wo we find the conventional properties of the speckle, which permits us to verify the approximations made in the complete expression of the spectral intensity recorded.