Methods of defining circular off-axis aspheric mirrors

Abstract

We investigated the definition for circular off-axis aspheric mirrors (COAMs). The clear opening of the COAM obtained by projecting a circular aperture on the aspheric surface does not form a plane but a curved surface. To solve this problem, we propose to use a plane to cut the aspheric surface to obtain a COAM. The COAM has three characteristics: (i) an elliptical opening; (ii) the major axis of the opening lies on the meridional plane containing the original optical axis of the aspheric surface and the minor axis lies on the sagittal plane perpendicular to the meridian plane; and (iii) it is not deepest at the center of the ellipse. The third characteristic suggests two methods for defining the COAM using a plane: (i) with the center of the elliptical opening as a reference and (ii) with the deepest point of the mirror as a reference. All the formulas required to obtain the desired COAM using the two methods are presented. © The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

Parametric geometry analysis for circular-aperture off-axis parabolic mirror segment

“…This indicates that it is possible to set the distance from the ROA to the OAP, regardless of whether it refers to the elliptical aperture center of the OAP or to the deepest point of the OAP mirror. Unlike off-axis aspheric surface segment mirrors, 14 the two choices result in the same OAP, and we can propose that the center of the elliptical aperture of the OAP is more intuitive and a clearer definition. The fact that both definitions result in the same OAP can be extended to another interesting property, the y component of the major diameter of the OAP, which can be expressed as follows:…”

“…As a side note, this interesting result applies only to the OAP, not to off-axis aspheric mirrors in general. 14…”