Cascaded Fresnel diffraction theorem and its application

Abstract

The goal of the paper is to simplify a simulation of cascaded Fresnel diffraction (CFD) by reducing the number of integrals and giving a solution for arbitrary plane. The simplification becomes possible with a use of CFD theorem. CFD theorem is formulated and proved. CFD theorem for simplification of one-lens model and two-lens model is demonstrated, and their mathematical models are obtained. As a result, the number of integrals describing diffraction and light propagation in lens models is decreased multiple times. We consider the optical field in any plane, making our approach more universal by assuming ideal point spread function. This approach may be applicable to numerical simulations as well as analytical investigations, optimizations, and designs. Our work benefits Fresnel diffraction method for modeling complex optical systems. © 2018 Society of Photo-Optical Instrumentation Engineers (SPIE).