Analysis of Lens Surface Shape Based on Theory of Plates and Shells

Abstract

The purpose of this article is to improve the accuracy and expand the force analysis of the lens by using the theory of plates and shells and reciprocal theorem. The first one concerns the deflection expression of a circular lens of equal thickness supported at several uniform points. The second calculates the deflection of the lens under its own weight, and then starting from known Zernike coefficient, PV value and RMS value in optics, the first 37 Zernike coefficients are obtained. The third compares the Zernike coefficients and lens center deflections of partic-ular cases. The derivation process based on plates and shells theory and reciprocal theorem is given in details. As validation, the lens deflec-tion expression is applied to calculate 4 points support, the predicted re-sults illustrate great agreements with the finite element simulation solution. Finally, the proposed method has shown great potential for engi-neering analysis and may also bring inspirations for optical field, as well as other plate and shell theory system.