Optimal thickness variation of an inflatable circular membrane mirror

Abstract

This study focuses on the optimal thickness variation of a large inflatable parabolic mirror. The inflatable mirror consists of two circular membranes joined at their edges. One membrane serves as an optical window while the other serves as an optical reflector. The. membranes are shaped by pressurizing the inner space bounded by the two membranes. In this study, the thickness of the optical membrane is optimized by minimizing the root-mean-square (RMS) surface profile deviation from an ideal parabola. This study optimizes the membrane mirror by using a finite-element analysis of the membranes, in contrast to the previous membrane optimization, which utilized the mathematical theory of membrane mirrors. This study finds that a simple thickness variation does not improve the surface shapes up to the conventional requirements for visible wavelengths (RMS 1/20). However, the study demonstrates that the RMS surface,error of the inflatable mirror can be reduced to 1 wave in visible passbands by limiting the effective optical surface area, thus demonstrating that this mirror can be used as a primary mirror in infrared, bands.