Shape achievement of optical membrane mirrors using coating/substrate intrinsic stresses

The U.S. Air Force, as well as many other organizations, has evinced considerable interest in developing large gossamer membrane radio antennas and optical quality telescopes. A concept is discussed of global shape maintenance of a reflective polymer membrane element after curing, coating, and release from a precision casting mold of the desired parabolic shape. The idea involves manipulation of intrinsic stresses in the coating and its membrane substrate. Results from an axisymmetric, geometrically linear, shallow-shell theory are presented as closed-form solutions for the displacement fields. A unique condition emerges from these solutions, suggesting that zero deformations can occur in a 0-g environment. Results of a finite element analysis are presented, showing that if a coated membrane satisfying this condition is subjected to a 1-g loading, rms errors of 9.3 mum and 2.8 mm can be expected for 1- and 20-m-diam mirrors, respectively. However, in the case of a 1-g load, another condition follows from the theory, which, if met, predicts zero deformation in the 1-g environment. Additional results of the finite element analysis are presented that lend support to these conclusions.