Theoretical compensation of static deformations of freeform multi mirror substrates

TL;DR

This paper develops a theoretical method to compensate for static deformations in freeform multi-mirror substrates caused by temperature variations, using perturbation theory and finite element analysis.

Contribution

It introduces a general theoretical compensation approach for static shape errors in freeform mirrors due to thermal effects, verified by finite element analysis.

Findings

The approach effectively predicts shape errors under temperature changes.

Finite element analysis confirms the validity of the compensation method.

Remaining errors can be corrected with standard manufacturing techniques.

Abstract

Varying temperatures influence the figure errors of freeform metal mirrors by thermal expansion. Furthermore, different materials lead to thermo-elastic bending effects. The article presents a derivation of a compensation approach for general static loads. Utilizing perturbation theory this approach works for shape compensation of substrates which operate in various temperature environments. Verification is made using a finite element analysis which is further used to produce manufacturable CAD models. The remaining low spatial frequency errors are deterministically correctable using diamond turning or polishing techniques.