Numerical and analytical calculation of the influence functions of drives of a rectangular deformable mirror with free edges

We present a novel numerical and analytical method for calculating the influence functions of actuators of a rectangular deformable mirror with free edges in a model of concentrated loads. The deflection function of a mirror is found as a Fourier series in terms of transverse natural vibration modes of a thin homogenous rectangular plate with free edges. Vibration modes are numerically calculated using the finite element method. The obtained vibration modes are substituted into formulas for the coefficients of the used series (partial sum). The obtained solution is verified by comparison with the calculation of the influence functions purely by the finite element method in the ANSYS software. The result can be used to choose actuator patterns of rectangular and square deformable mirrors in problems of adaptive optics.