Analytical Aberration Theory for Plane-symmetric Optical Systems and its Application in the Analysis of Distortion in Freeform Spectrometers

TL;DR

This paper develops an analytical aberration theory for plane-symmetric optical systems, including freeform surfaces, and demonstrates its application in analyzing distortion in complex spectrometers, offering insights beyond traditional raytracing methods.

Contribution

The work generalizes paraxial optics and wavefront aberration expansion to include freeform surfaces and higher-order effects, providing a new analytical tool for distortion analysis in plane-symmetric systems.

Findings

Analytical aberration coefficients agree with raytracing results for certain systems.

The theory reveals the contribution of surface and induced aberrations to distortion.

Limitations identified in the theory when higher-order aberrations are significant.

Abstract

The recent history of optical design saw a progressive trend of also designing without rotational symmetry, especially spectrometers due to the use of reflective and diffractive elements in their designs. A freeform hyperspectral imager design in CubeSat format is presented in this work, which has large deviation from rotational symmetry. Based on a generalization of paraxial optics and wavefront aberration expansion applicable to plane-symmetric systems, in this dissertation we derived the aberration coefficients of aberration types in the third group for plane-symmetric systems that include the second order effects of the light beam footprint on optical surfaces. We also expanded the theory to include the contributions from freeform surfaces and induced aberrations. For the application to plane-symmetric spectrometers, the aberration coefficients related to distortion are of special interest. Comparisons between the distortion results predicted by the aberration coefficients and simulated from real raytracing show good consistency in example systems of a Dyson spectrometer and freeform spectrometers that share the three-mirror double-pass structure, which is similar to the spectrometer component of the hyperspectral imager we designed. In comparison to real raytracing, results of the theory applied to the spectrometer of the hyperspectral imager we designed show the limits of the theory that is limited to the third group of aberrations, while in this design, high-order groups also significantly contribute. In all cases, the analytical formulae of the aberration coefficients contain the information on surface contributions, induced aberrations, and the relation between the aberration behavior and system parameters, which provide valuable insights in the analysis of plane-symmetric systems.