Zernike polynomial based Rayleigh-Ritz model of a piezoelectric unimorph deformable mirror

Piezoelectric bimorph- or unimorph-type deformable mirrors are commonly used in adaptive optics to correct for time-dependent phase aberrations. In the optics community, the surface deformations that deformable mirrors are required to achieve, are routinely and conveniently described using Zernike polynomials. A Rayleigh-Ritz structural model, which uses Zernike polynomials directly to describe the displacements, is proposed in this paper. The proposed formulation produces a numerically inexpensive model that predicts deformations with remarkable accuracy. Since design variables, such as electrode layout, material properties, and mirror dimensions, are represented analytically, the model is well suited to optimization or sensitivity analysis applications. Furthermore, since the numerical implementation is very efficient, it could be employed in closed-loop control applications. Results achieved with the proposed model compare well with results from a traditional finite element analysis as well as experimental results of a representative design.