Structural Topology Optimization of Reflective Mirror Based on Objective of Wavefront Aberration

Abstract

Due to the increasing requirements for the imaging quality of optical systems, the design method for optical–mechanical structures has become a research hotspot in recent decades. To improve the imaging performance of the reflective system, it is often necessary to increase the aperture of the mirror. To meet the imaging quality and lightweightedness requirements of the mirror, the topology optimization method aiming at the minimization of wavefront aberration is proposed. The optical–mechanical coupling relationship is established by ray tracing of the deformed mirror surface fitted by orthogonal bases. The topology optimization model is established by the solid isotropic material with penalization model (SIMP). Additionally, the adjoint method is used to analyze the sensitivity of the objective and the constraints. To illustrate the rationality and effectiveness of the method, the mirrors of the Cassegrain system have been optimized under the action of gravity with the objective of the weighted sum of squares of wavefront aberration coefficients under the constraints of the mass of the design domain, the rigid body displacement of the mirror surface, and the residual of deformation fitting. The results show that the proposed method can effectively improve imaging performance under the condition of satisfying the constraints. In addition, the optimization method with wavefront aberration as the objective is a concrete application of the idea of opto-mechanical integration, which can improve optical performance more directly and effectively.