Research on neutral surface of lightweight, horizontally supported mirror

Abstract

The surface distortion due to gravity can be minimized when the flexure is located at the mirror’s neutral surface. When the mirror has relatively small surface curvature and simple lightweight structure, the location of neutral surface can be calculated by empirical formula or can approximately coincide with the mirror’s center of gravity. Otherwise, it is insufficient to determine the exact location of neutral surface. In addition, when the torque stiffness of flexure cannot be neglected, the optimum mount location may deviate from neutral surface and should be determined by more sophisticated analysis. The RMS surface distortions will degenerate significantly when the flexure has deviations from the optimum axial mount location due to fabrication and assembly errors. The distortion sensitivity to support axial location is critical to achieving low surface distortions in practice. We demonstrate a method of calculating the exact location of neutral surface and optimum mount location. The sensitivity of surface distortion to support axial location is theoretically calculated and compared with the results obtained from finite element analysis.