An analytical method for the calculation of the aberrations of optical systems

Based on the exact expression for the angular eikonal of a second-order surface, an analytical method for the analysis of the aberrations of an optical system is constructed and the principles for the optimization of such a system are formulated. Examples of the analysis and optimization of a single surface are given. The theoretical method developed is supported by the results of modeling of the caustic and the focal set in the image space of a point of a spherical refracting surface. The method constructed is exact and does not require using programs for tracing rays through the system.