Hybrid asymptotic method for analyzing caustics of optical elements in the axially symmetric case

In this work we propose a new approach to calculating the distribution of light fields in the framework of geometrical optics. A new integral operator for computing the intensity distribution in the geometrical optics approximation is suggested. Using the proposed method, we derive the intensity distributions of previously studied wavefronts. Singular points of these distributions are found and the intensity distributions near the caustics are calculated. The developed method is used to calculate the formation of caustics by harmonic diffractive optical elements in the axially symmetric case.