Mathematical model of a variable-curvature thin-film mirror

A solution of the equations describing the deformation of an elastic mirror under the action of a transverse pressure and a longitudinal tensile force is obtained in the form of dependences of the deflection and the longitudi nal force on the radius, external loads, and geometric and physical paramet ers of the film. It is shown that the cross section of the mirror tends to a parabolic shape as the initial stretching is increased. The degree of str etching is restricted by the yield stress, precluding the achievement of a high optical quality for the mirror. The results of the numerical calculati ons presented illustrate this fact. (C) 2000 The Optical Society of America .