Geometric layout optimization of a large aperture thin elliptical mirror's axial and lateral support

For passive support of large aperture telescopes, geometric layout optimization of the support structure is one of the most critical tasks because it determines the deformation of the mirror under gravity, which affects the wavefront aberration and image quality of the system. Due to a lack of symmetry, the optimization of an elliptical mirror support can be much more complex compared with circular mirrors. We optimize the geometric layout of axial and lateral support for the tertiary mirror of the Thirty Meter Telescope (TMT). Based on a theoretical analysis of the whiffletree principle, a parametric model of axial support is established based on the multi-point constraint equation. The mirror deformation SlopeRMS of the tertiary mirror under vertical gravity is used as the optimization target of the support points. The axial support point position is optimized by means of a simulated annealing algorithm and a mirror-deformed post-processing script written in Python. The TMT tertiary mirror lateral support also uses the whiffletree structure, and its in-plane layout affects the system's resonant modal frequency and the maximum load at each point. According to the dynamic equation and the static principle, the lateral support optimization model is established. The first-order resonant frequency and maximum load of the support point are the objective function. Through optimization of the axial and lateral support, the overall mirror distortion of the system is improved.