Topology Optimization Design of an Active Deformable Mirror Based on Discrete Orthogonal Zernike Polynomials

Abstract

In order to design an active deformation mirror for projection objective aberration imaging quality control, a topology optimization design method of active deformation mirrors based on discrete orthogonal Zernike polynomials is proposed in this paper. Firstly, in order to solve the problem that continuous Zernike polynomials do not have orthogonality on the discrete coordinates inside the unit circle, which causes the instability of topology optimization results, discrete orthogonal Zernike polynomials are used to characterize the active deformation mirror wave aberrations. Then, the optical and structural deformations are combined to establish an optical-mechanical coupling topology optimization model with the help of the variable density method to derive the sensitivity of the mathematical model. Finally, a wave aberration corrected deformation mirror in an optical machine system is used as an arithmetic example for topology optimization, and the results show that the absolute value of the Zernike coefficient Z4 after optimization is improved by nearly one order of magnitude compared with the value before optimization, and the vibration characteristics of the optimized structure meet the design requirements. The optimization effect is significant, which improves the optical performance of the deformed mirror and provides a new scheme for the design of the deformed mirror structure which has a certain practical value for engineering.

Keywords

• topology optimization
• Zernike polynomials
• active deformation mirror
• wave aberration
• extreme ultraviolet lithography