Optomechanical topology optimization of a primary mirror using adjoint sensitivity analysis

To address the issues of conventional optomechanical sensitivity methods, which consume substantial resources at each iteration due to their direct approach, we introduce an adjoint sensitivity strategy. In this strategy, the sensitivity of orthogonal Zernike polynomial coefficients to nodal displacements is first derived, establishing a clear relationship between optical performance and structural deformation. The adjoint variables obtained from the optical performance adjoint equations are then used to compute the sensitivity of Zernike coefficients with respect to element densities. The efficacy of the proposed method is demonstrated by designing a primary mirror with 1.7 million design variables under multiple loading conditions. The material distribution in the final iteration is sufficiently clear to extract detailed structural features, achieving a lightweight design with a mass of 4.165 kg (area-to-mass ratio of 20.39kg/m²) while constraining the surface figure error (SFE). The proposed approach achieves accurate optical performance, provides sensitivities with respect to design variables, and enables rapid and stable convergence of the optimization process.