Electrostatic membrane mirrors are potentially useful as aberration generators. To realize this capability, it is necessary to know the influence functions (each giving mirror response to a single electrode) and then to use a fitting procedure to determine the optimal voltage settings for reproducing a desired surface shape. We show that an approximate analytical solution of Poisson’s equation exists that can generate the influence functions for a circular electrostatic mirror. We also show, by demonstration, that it is computationally feasible to calculate these influence functions and to use them with a fitting procedure to fit the surface of a 109-electrode mirror to a desired shape. Our methods allow one to test the theoretical performance of the 109-electrode mirror; we find that good fits are obtainable for Zernike polynomials of up to degree 6.
© 1986 Optical Society of America
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