Analytical inversion of the focusing of high-numerical-aperture aplanatic systems

J Opt Soc Am A Opt Image Sci Vis. 2019 Oct 1;36(10):1642-1647. doi: 10.1364/JOSAA.36.001642.

Abstract

We propose a method for an analytical inversion of the electric and magnetic fields at the focus of a high-NA aplanatic system to obtain incident light beam distribution. Our approach is based on an inverse Fourier transform of the Richards-Wolf formalism for targeted longitudinal fields along the radial or axial directions at the non-paraxial focus. Analytical solutions are discussed for both axial and radial focal fields for a radially polarized incident light beam, and a criterion is defined to access a physically valid solution. We also validate the method according to results found in the literature. Finally, we show how the method can be generalized to other incident field distributions.