Optimization method using nodal aberration theory for coaxial imaging systems with radial basis functions based on surface slope

The radial basis functions based on the surface slope (RBF-Slope) freeform surfaces model has demonstrated stronger fitting ability and better optical performance than the conventional RBF model. However, the large number of basis functions and optimization variables of the RBF-Slope model may result in convergence problems during optimization for optical systems consisting of freeform surfaces characterized by RBF-Slope. To overcome these drawbacks, we use Zernike polynomials to link the RBF-Slope model to aberration correction and propose a new optimization method for coaxial imaging systems using the RBF-Slope model based on nodal aberration theory (NAT). The aberrations generated by the conic parameter and Zernike terms up to Z 17 / 18 of the Zernike freeform surface at the non-stop surface in the coaxial imaging system are analyzed, and the gradient descent is implemented to obtain the optimal coefficients of the Zernike surface, which is then fitted by the RBF-Slope surface for further optimization. The method is applied to the optimization of a secondary mirror using the RBF-Slope model in a two-mirror telescope and proved to have better results than traditional commonly used direct optimization. This research offers an important reference for optimization using NAT and provides valuable insight into the optimization method for RBF-Slope freeform surfaces.