Optomechanical topology optimization for mirrors with wavefront aberration control: an efficient decoupled approach with application to a Cassegrain telescope

We present an efficient optomechanical topology optimization framework for lightweight, high-precision mirrors with explicit control of wavefront aberration. To reduce the dimensionality of the optomechanical interface, the mirror surface deformation is represented by a filtering basis of orthogonal surface eigenmodes. Sensitivities are decoupled through a hybrid strategy: structural sensitivities are obtained by an adjoint method, while the Jacobian from modal coefficients to Zernike aberrations is evaluated via finite differences at the current deformed configuration and periodically refreshed every 20 iterations, reducing the per-iteration optical evaluation to a single constraint call, with ray-tracing invoked only periodically to refresh the Jacobian rather than at every gradient evaluation. Reusing the factorized stiffness matrix for multiple adjoint right-hand sides further reduces computational cost. A Cassegrain primary-mirror example demonstrates effective suppression of selected Zernike terms with only a modest overhead over compliance minimization, while also revealing that simultaneous suppression of all aberration modes under multi-load conditions is physically constrained by conflicting deformation patterns.