Modeling and simulating the thermoelastic deformation of mirrors using transient multilayer models

We present a dynamic model with distributed parameters for the thermoelastic transfer behavior in multilayer structures, which are motivated by optically addressed deformable mirrors (OADMs). These are encountered in adaptive optics and utilized for correcting wavefront disturbances of high-power radiation. Our modeling approach is based on a continuum-mechanic multilayer model which distinguishes between an addressing heat load - the control input - and a boundary disturbance evoked by the high-power primary radiation. Thus, the model without control action can be used for passive mirrors as well. The relevant transient effects are investigated with physically motivated assumptions, the plate-like geometry, and parametric rheological analogue models. Furthermore, an efficient simulation scheme is established using Fourier methods in conjunction with model order reduction. The model's accuracy and the validity of all assumptions is demonstrated by means of an experimental setup. The parametric model is a first step towards feedback and feedforward control designs and disturbance compensation algorithms for OADMs.