Cumulant method for identifying spatial distributions of laser beam intensity

The article considers the identification of spatial distributions of laser beam intensity, which is of significant practical importance for laser developers when certifying radiation sources. As an identification parameter, a measure of similarity of the measured axisymmetric distributions of laser radiation intensity with a given Gaussian distribution is proposed and investigated. To determine this measure, it is not necessary to first find the beam width at the waist. A mathematical apparatus for identification based on the use of cumulants of spatial intensity distributions is developed. A feature of the method is a limited number of cumulants of the Gaussian distribution, which makes it attractive for practical application. A comparative analysis of a number of two-dimensional distributions with a Gaussian distribution is carried out and it is shown that even with a small number of measured cumulants, high sensitivity of the method to the shapes of intensity distributions is ensured. A similarity measure for continuous one- dimensional intensity distributions of arbitrary shape is presented. The asymmetry measure of two-dimensional spatial distributions of laser beam intensity based on the ratio of moments and cumulants of the fourth and second orders is considered. The proposed measure of similarity of the measured axisymmetric intensity distributions with the Gaussian distribution is an alternative to the well-known propagation coefficient M 2 and can be used together with this coefficient.