Investigation of surface imperfection in freeform optics with high-order XY polynomial design

Freeform surfaces find potential applications in optics but pose new challenges for manufacturing and functional testing. A basic description of such surfaces is observed in terms of surface spatial frequencies which have been altered as a result of evolution in the fabrication of optics. While mid-spatial-frequency (MSF) errors arising from manufacturing and metrology processes are well documented, our investigation reveals that such errors originate not only during these stages but also during the surface construction at the design phase, particularly for high-order XY polynomial optical surfaces. The presence of MSF errors can significantly affect the performance of high-performance optical systems across various applications. The study discussed in this paper focuses on the relationship between the resolution of the design dataset of freeform surfaces with high-order polynomials and the subsequent surface imperfections in the production of precision optics. The main contributions of this investigation are the identification of MSF errors at surface construction of the design phase and the control over the MSF errors in design dataset using the 2nd-order Gaussian filtration which will bridge the gap between freeform optics design and ultra-precision manufacturing.