Cumulant method for identifying spatial distributions of laser beam intensity

The article considers the identification of spatial intensity distributions of laser beams, which is of considerable practical importance for laser designers in the certification of radiation sources. As an identification parameter, the author proposes and studies a measure of similarity between measured axisymmetric laser intensity distributions and a given Gaussian distribution. To determine this measure, it is not necessary to find the beam width at the waist in advance. A mathematical apparatus for performing identification was developed using the cumulants of spatial intensity distributions. A special feature of the method consists in the limited number of cumulants of the Gaussian distribution, which makes it attractive for practical applications. A series of bivariate distributions and the Gaussian distribution are comparatively analyzed; it is shown that even with a small number of measured cumulants, a high sensitivity of the method to the shapes of intensity distributions is ensured. A similarity measure for continuous univariate intensity distributions of arbitrary shape is presented. The author considers an asymmetry measure for the bivariate spatial intensity distributions of laser beams that is based on the ratio of moments and cumulants of the fourth and second orders. The proposed measure of similarity between measured axisymmetric intensity distributions and the Gaussian distribution is an alternative to the known propagation ratio M² and can be used together with this ratio.