Stigmatic singlet with a user-defined apodization pupil function.

Here we present a method to design a stigmatic lens with a user-defined apodization pupil function. The motive is that the apodization pupil function is required by Richards-Wolf diffraction integrals to compute non-paraxial diffraction patterns. Then, the user-defined apodization pupil function can be chosen such that the focus spot obtained by the stigmatic lens is smaller. The mentioned method is based on numerically solving a non-linear differential equation.