On the diffraction of a high-NA aplanatic and stigmatic singlet

Abstract

We present a study of the diffraction pattern according to Richards–Wolf for an aplanatic and stigmatic singlet based on an exact analytical equation. We are able to put emphasis on the maximum diameter and illumination pattern, which are the two parameters that influence the diffraction pattern and how to compute it. Designs of low- and high-NA aplanatic and stigmatic lenses are implemented to display these effects.

Focusing of an aberrated radially polarized beam by microscope objectives

“…This treatment, beyond the scalar approximation, is necessary in several areas of science, including high-resolution microscopy, [6][7][8][9] optical trapping, 10 electron acceleration, 11 optical vortex knots, 12,13 beam shaping, etc. [14][15][16][17][18][19][20][21] Nevertheless, the Richards-Wolf integral only considers perfect spherical wavefronts 4,5 and real optical systems do not generate perfect spherical wavefronts at the exit pupil, but aberrated wavefronts. A new diffraction integral has been published in Refs.…”

“…This treatment, beyond the scalar approximation, is necessary in several areas of science, including high-resolution microscopy, 6 – 9 optical trapping, 10 electron acceleration, 11 optical vortex knots, 12 , 13 beam shaping, etc 14 – 21 …”

General diffraction integral for converging freeform vectorial fields

“…The models of Stratton and Chu and Richards and Wolf had been widely used to study tight focusing [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. In particular the model of Richards and Wolf it is limited only to stigmatic systems and non-aberrated systems [25].…”