Formation of Circular Optical Membranes under Free‐Form Yielding

Abstract

High‐quality optical reflector surfaces are attainable with the use of pressure‐formed membranes. The formation technique involves gradual application of fluid pressure on initially flat, simply supported circular membranes until a desirable center deflection is reached. After the fluid is removed, a uniform pressure is subsequently applied to offset the surface slope error. Empirical testing of membrane‐forming technique was conducted at two scales to define the critical process variables that controlled material yielding. Aluminum membranes with 54‐in. (1.4‐m) diameter were constructed for the smaller scale and with 144‐in. (3.7‐m) diameter for the larger scale. The experiments were carried out with the intent of forming a paraboloid with a focal length‐to‐diameter ratio of 0.6. Water or sand was used as the loading medium. Membrane surfaces with slope error less than four millirads relative to parabolic profile were achieved. The test results can be used to validate an analytical model developed to simulate the inelastic membrane deformation mechanism during free‐form yielding. With a validated model, the membrane forming process can be optimized by controlling the essential process variables identified in this study.