Optical description and design method with annularly stitched aspheric surface

The relentless pressure for designs with new optical functions, small volume, and light weight has greatly increased the importance of aspheric surfaces. In this paper, we propose an annularly stitched aspheric surface (ASAS) description method to increase the freedom and flexibility of imaging system design. The rotationally symmetric ASAS consists of a circular central zone and one or more annular zones. Two neighboring zones are constrained to have the same derivatives on their joint curve, and this means the ASAS is C1 continuous. This finding is proved and verified by the mathematical deduction of the surface formulas. Two optimization strategies and two design methods with the C1 continuous constraints are also discussed. This surface can greatly facilitate the design and even achieve some previously impossible designs without increasing the fabrication difficulty. Two different systems with the proposed ASAS are optimized and the results are presented. The design results verified the practicability of the ASAS.