Optical description and design method of smoothly stitched polynomial freeform surfaces

Freeform surfaces provide more design degrees of freedom (DOFs) to optical systems, making it possible to achieve higher performance and more powerful capability, and even realize advanced systems, which are not possible using conventional optical surfaces. Mathematical description methods for freeform surfaces significantly affect the optimization result, fabrication, testing, and alignment process. In this study, we propose a novel smoothly stitched polynomial (SSP) freeform surface with more DOFs and flexibility. The SSP freeform surface comprises two subsections, and each is expressed by a polynomial, thus providing several additional design variables. Two sections of the SSP are physically contacted, and the intersection zone is controlled to satisfy C1 continuity, thereby avoiding the sharp shape change in adjacent areas of the two sections. Two off-axis reflective systems are designed with the SSP surface, and compared with the traditional XY polynomial (XYP) surface designs. The design results reveal that the imaging performances, including the wavefront error and MTF of the systems are significantly improved.