Research on mirror surface shape of space camera fitting based on SVD

Abstract

Large-aperture optics mirror is one of the high resolution space camera’s key components. The mirror surface shape accuracy which is subjected to external loadings can be obtained through fitting mirror surface shape. Zernike polynomials is widely used in fitting mirror surface shape due to the outstanding advantages, such as high precision and good convergence.Two methods of fitting mirror surface shape via Zernike polynomials are introdeced in this paper, namely, mirror surface deformation fitting and mirror surface shape fitting directly. Taking spherical mirror for example, the relation between the number of terms in Zernike polynomials and the fitting precision is investigated. During fitting mirror surface shape, the constructed normal equations are ill-conditioned. Reliable results cannot be obtained via the normal equation method. Singular value decomposition (SVD) method is presented to solve the abnormal equations in this paper. Through calculating the PV value and the RMS value between the fitting mirror surface and the standard spherical mirror surface, the influence of Zernike polynomials terms on the fitting precision is investigated. In the end, a design example is tested to show effectiveness of the proposed method. By fitting a deformed spherical mirror surface shape under the load condition of 1g gravity using 28-term Zernike polynomials, achieving the fitting residual, the PV value is 19.7nm and the RMS value is 3.97nm.