Abstract
Based on Karman's equation for symmetrical circular membrane and Qian's theory of circular membrane under the action of uniformly distributed loads in its central portion, the relationship between the curvature of the center cross section of a membrane mirror on a substrate of polyethylene terephthalate (PET) film and the external pressure, and the deviation between the surface shape of the membrane mirror and that of a paraboloid mirror with the same diameter and F/number have been calculated in this paper. The changes of the surface shape of the mirror under various initial boundary conditions and various external pressures applied on it have been analyzed theoretically. An experimental setup for the figuration of a membrane mirror in a diameter of 100mm has been designed and established. The pre-shape of the membrane, the negative air-pressured deformation and the electrostatic deformation were combined to shape a membrane mirror with a relative small curvature radius. The focal lengths of the mirror under different initial boundary condition and different external pressures have been measured and analyzed comparing to that of the theoretical one. The experimental results show the possibility of the method for the figuration of membrane mirrors.
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