  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.
