Discrete freeform optical design based on collaborative optimization of point cloud and local normals

This paper proposes a freeform optical design method based on collaborative optimization of point clouds and normals. The method represents the freeform surface as a discrete point cloud with local normal information, and realizes collaborative optimization of point position updating and normal reconstruction under the guidance of system image quality evaluation. This method avoids dependence on a preset analytical form of the target freeform surface, as well as repeated complex ray intersection calculations with the analytical target freeform surface during optimization. To ensure the stability of the optimization process, the sensitivity of local normal reconstruction parameters and sampled ray density is further analyzed. The method is then applied to the design of an off-axis three mirror telescope with a wide field of view of 30^∘×5^∘, in which the third mirror is selected as the freeform surface to be optimized. After optimization, the system merit function decreases significantly from 0.3923 to 0.002789. The final design achieves an average RMS spot radius of 5.939µm, and the full field MTF remains above 0.6 at 56 lp/mm. The results show that the proposed method can effectively obtain a discrete freeform surface solution that satisfies the imaging quality requirements of the system.