Numerical Diffraction Using the Collins Formula

doi:10.1117/3.2652240.ap1

Book: Computational Optical Coherence and Statistical Optics

Author(s): Milo W. Hyde IV

Published: 2023

https://doi.org/10.1117/3.2652240.ap1

Author Affiliations +

Abstract

For diffraction in general paraxial systems, G is given by the Collins formula. Like the Fresnel diffraction integral, the Collins formula (for optical systems with certain symmetries) can be expressed as either a convolution integral or a spatial Fourier transform. The purpose of this appendix is to derive the sampling criteria for both forms of the Collins formula. We start with a general overview of the Collins diffraction integral and specialize it to an x-y separable (fourfold rotationally symmetric) optical system. Using this form of the integral, we derive the convolution and Fourier transform versions of the Collins formula. We then analyze each in turn, deriving inequalities for the source-plane grid spacing Δ_src and number of grid points N. Lastly, we present an example where we use both forms of the Collins formula to simulate wave propagation through an astigmatic optical system.