Optimum design of a lightweight mirror using aluminum foam or honeycomb sandwich construction: a case study for the GLAS telescope

Abstract

A simple closed form solution was derived for the optimum weight design of a cylindrical sandwich mirror for a given self-weight deflection and mirror radius. This optimum solution is based on the generalized deflection equation for an axisymmetrically supported thick circular plate. This two parameter equation of deflection captures the deflection of the plate caused by bending and transverse shear. The solution yields the optimum facesheet thickness, core thickness, and core density. The derived optimum solution was used in a case stud for the GLAS (Geoscience Laser Altimeter System) primary mirror. This Beryllium mirror is manufactured with an open back isogrid pattern. The objective of this study is to determine a lightweight mirror design using Aluminum sandwich construction that can meet the performances of the current mirror and reduce fabrication costs. With the optimum solution several first order approximations using Aluminum honeycomb or foam core were determined. The performance, 1 g deflection, and wave front error of these designs was determined from Finite Element Analysis. The results conclude that sandwich construction outperforms the isogrid design by significant margins on both weight and distortion if the same material is used. Because of its superior specific stiffness the Beryllium isogrid design still marginally outperforms the optimum Aluminum sandwich design. However, the Aluminum sandwich design should provide significant advantages on cost and ease of fabrication over Beryllium isogrid designs.