Analytic HG-mode propagation through circular apertures with Zernike phase offset

Abstract

Mode expansion methods (MEMs) have been used in both the scientific and commercial world to accurately propagate monochromatic light fields. Compared to classical methods for light propagation from scalar diffraction theory, it is often less costly and much more easily implemented into optical chains. We provide an analytic expression for the overlap between incoming and outgoing Hermite Gauss (HG) TEM modes over an aperture with potential wavefront error represented by Zernike terms for the purpose of propagating light through apertures. We show agreement between our results and those of prior studies of the topic, as well as an application of this method to an ongoing interferometry mission.