Spot size and radial intensity distribution of focused Gaussian beams in spherical and non-spherical aberration lenses

We discussed the radial intensity distribution in the presence of spherical aberrations (SA) for cases in which the incident field is a focused Gaussian spot. A numerical solution of a two dimensional integral diffraction (paraxial ray) equation for a relatively large SA is developed by using the well-known trapezoidal rule for integration. The mesh size was chosen so that convergence of the integration is insured to one part in 10⁻⁸ at successive steps. The spot size and the radial intensity distribution in both SA free lens and lens exhibiting SA are calculated. A relation that determines the spot size at the geometrical focus in aberrated case is developed.