Application of the Pattern Equation Method to the Problem of Diffraction by a Group of Randomly Located Small Scatterers

A technique of calculating the averaged scattering pattern of a group of identical infinite perfectly reflecting cylinders is suggested on the basis of the pattern equation method and the method of small perturbations. The cylinders have random coordinates and random orientations. The problem is solved under the supposition that dimensions of the scatterers’ sections are small as compared with the wavelength and the average distance between the bodies. It is supposed also that the root-mean-square deviation of the scatterers’ coordinates is small as compared with the wavelength. The method is tested for a small number of bodies by comparing the calculation results obtained with the help of the method of small perturbations with the results obtained with the help of direct averaging of the scattering pattern.