General diffraction integral for converging freeform vectorial fields

Abstract

Herein it is presented a new vector diffraction integral capable to compute the diffraction patterns for aspheric and freeform wavefronts, with different pupil shapes, and different polarization states. The aforementioned vector diffraction integral is based on the energy conservation theorem, the far field approximation, and the angular spectrum representation of optical fields. The integral is validated through illustrative examples whose results are as expected and coincide with the related works.

Focusing of an aberrated radially polarized beam by microscope objectives

“…23 differs from the models presented in Refs. 15, 24, and 25 that the aberrations are taken directly from the wavefront using the Malus-Dupin theorem, 23 instead of considering the aberration function as an additional phase in over a spherical wavefront. 15,24,25 This manuscript aims to present a rigorous method to compute the vector diffraction pattern of microscope objectives considering on-axis aberrated and radially polarized wavefronts.…”

“…The work in Ref. 23 differs from the models presented in Refs. 15, 24, and 25 that the aberrations are taken directly from the wavefront using the Malus-Dupin theorem, 23 instead of considering the aberration function as an additional phase in over a spherical wavefront.…”

“…Ref. 23 presents a new vector diffraction integral capable of computing the diffraction patterns for aspheric and freeform wavefronts, with any polarization. This paper does not consider an arbitrary polarization state since working with arbitrary polarization states is not straightforward, and it highly increases the complexity of the problem.…”

“…Like the Richards-Wolf integral, the integral presented in Ref. 23 is formulated by the assumption that the diffraction pattern is computed by the superposition of plane waves, and the contribution of evanescent waves is ignored. This integral is given as E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 1 ; 1…”

“…Here, the model presented in Ref. 23 is used to compute the diffraction pattern of several microscope objectives considering the polarization of the wavefront and its aberrations. The work in Ref.…”