Modelling Thermoelastic Distortion of Optics Using Elastodynamic Reciprocity

TL;DR

This paper introduces a method based on elastodynamic reciprocity to efficiently model thermoelastic distortions in optical components, improving prediction speed for adaptive thermal compensation in high-power laser systems.

Contribution

It applies the Betti-Maxwell elastodynamic reciprocity theorem to accurately predict thermoelastic distortions with reduced computational effort compared to finite-element analysis.

Findings

The method provides accurate results for optical distortions.

It significantly reduces computational time.

Applicable to complex heating distributions.

Abstract

Thermoelastic distortion resulting from optical absorption by transmissive and reflective optics can cause unacceptable changes in optical systems that employ high power beams. In advanced-generation laser-interferometric gravitational wave detectors for example, optical absorption is expected to result in wavefront distortions that would compromise the sensitivity of the detector; thus necessitating the use of adaptive thermal compensation. Unfortunately, these systems have long thermal time constants and so predictive feed-forward control systems could be required - but the finite-element analysis is computationally expensive. We describe here the use of the Betti-Maxwell elastodynamic reciprocity theorem to calculate the response of linear elastic bodies (optics) to heating that has arbitrary spatial distribution. We demonstrate using a simple example, that it can yield accurate results in computational times that are significantly less than those required for finite-element analyses.