Membrane Reflector Surface Reconstruction Using Zernike Polynomials and Two-stage Algorithm

The membrane reflector is an important component in space optical systems. In a membrane reflector forming process, the surface reconstructed by discrete sampling points is used as a feedback signal for the forming control. Precise and efficient surface reconstruction directly affects the controller design and the control performance. As the most popular tool for optical surface reconstruction, the Zernike polynomials encounter the contradictory requirements between performance and model complexity. The reconstruction error may become no-convergent due to ill-conditioned matrix with highdegree polynomials. Therefore, the Zernike polynomial term selection becomes a key and hot topic. This paper proposes to construct the Zernike polynomials based model using a two-stage algorithm. The experimental results confirm the effectiveness of the proposed technique.