Evolution of a complex-source-point spherical wave through a symmetric optical system with spherical aberration

We discuss the evolution of a complex-source-point spherical wave (CSPSW) along the axis of a symmetric optical system with spherical aberration. The CSPSW is equivalent to the sum of all the higher order corrections to a paraxial Gaussian beam. First we formulate the diffracted CSPSW through spherical boundaries, where the terms of up to fourth order in aperture variables are taken into account. We then find a ray-optical solution for the diffracted beam that can be represented in terms of the coefficient of spherical aberration. Next we formulate the beam spot size, the far-field divergence angle, and the beam quality factor which are characteristic of the aberrated beam. For the case of a thick lens, we examine the effect of lens aberration on the beam parameters. The derived formulas can be used to determine the parameters of the Gaussian beam degraded by an arbitrary symmetric optical system with spherical aberration.