A Monte Carlo analysis of uncertainty in supporting assembly of large-aperture optical lenses

Large-aperture lenses are widely used to improve optical resolution and enlarge field of view of a precision optical system, and reasonable mounting can result in higher optical performance. Flexure mounts are usually utilized to minimize distortion of the lens under its own weight and must be accurately assembled so as to provide uniform support loads for the lens. The supporting loads produced by flexure mounts are difficult to be identical because of various uncertainties during assembly process, such as human operation and tool resolution. These nonuniform supporting loads may generate asymmetric deformation of the lens and deteriorate its performance. It is essential to explore the influence of uncertainty supporting loads on the optical performance. A Monte Carlo analysis method is proposed to investigate the optical performance of a lens under uncertainty supporting loads at different load levels. Patran Command Language is used for repetitive calculation of finite element model with random sample of supporting loads. The optical performance responses, such as the surface peak-to-valley and root-mean-square errors and Zernike coefficients, are calculated by fitting the surface deformation data, and their stochastic properties are researched by statistical testing. Consequently, the critical variation range of uncertainty supporting loads considering assembly process can be determined based on Three Sigma theorem with specific optical performance requirement. The results can be used to assign appropriate tolerance of flexure mounts during assembly and to optimize the supporting system of a high-precision optical system.