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This paper investigates the relationship between the integral equation and Kirchhoff approximation in the diffraction theory of coherent radiance. The spectrum of the reflected wave is formed in the far field (Fraunhofer zone) and the solution is to Fourier transform of effective reflectance coefficient of a surface. In the paper, the analytical relationship between the method of solving an integral equation and the Kirchhoff approximation has been proven. It helps to define the structure of the field of diffracted waves in a Fraunhofer zone for coherent scattered light. The analytical equations for calculation of the average value of intensity scattering field and the mirror reflection coefficient of a rough surface have been obtained. Analysis of the components of the scattering coherent light coming from a metal surface has been improved. It helps to specify the data processing algorithms for evaluation of statistical characteristics of rough surfaces.
