Zernike-based matrix model of deformable mirrors: optimization of aperture size

The actuator influence functions of a typical deformable mirror are expanded in a Zernike polynomial decomposition. This expansion is then extended to a matrix formalism that describes the modal operation of the mirror. The size of the aperture over which the Zernikes are defined affects the accuracy of the expansion. The optimum size of this aperture is found by minimizing the variance of the wave-front error.