Spot diagram borders are always caustic curves and/or marginal rays III: segmented mirror in hexagons and trapezoids

Abstract

For annular (circular and elliptical) and hexagonal exit pupils with any optical path differences (described by Zernike Polynomials), it was proven [Appl. Opt. 61, 1876 (2022)APOPAI0003-693510.1364/AO.449270; Appl. Opt. 61, C20 (2022)APOPAI0003-693510.1364/AO.435850] that the border of any spot diagram is composed of the caustic surface and/or marginal rays. In this paper, the previous results are extended to segmented (by hexagons or trapezoids) exit pupils. Examples with exact spherical, coma, and astigmatism aberrations are included, while a mathematical demonstration is also included.