Uniform Pressure Formation of Optical Membranes

Abstract

High‐quality optical reflector surfaces are attainable with the i use of pressure‐formed membranes. Those reflector surfaces offer the prospect of very light weight and low cost. The formation of those surfaces, using initially flat circular membranes with uniform pressure loading, is studied in this paper. Finite axisymmetric deformations, along with both linear and nonlinear material responses are considered. A wide range of focal‐length‐to‐diameter ratios are addressed, and the structural/optical response mechanisms that lead to optical distortions relative to ideal parabolic reflector shapes are also considered. Results show that elastic material response can often lead to a significantly larger deviation from the ideal shape than inelastic material response. This results primarily from the ability to limit stress nonuniformities when inelastic material response is operative. When under pressure loading, the membrane focal length decreases monotonically with increasing radius for both linear and nonlinear material responses. Further, the predicted focal‐length variation is increasingly nonlinear near the membrane support.