Application of NURBS free-form surface in optomechanical design and analysis

Knowing that optical surface should have strong surface description and fitting ability and that ray-tracing speed of the surface should be fast, the fitting method and ray tracing algorithm of NURBS free-form surface were studied. Fitting mild slope asphere, deep slope asphere and peaks surface respectively to NURBS surface using Multilevel B-splines approximation(MBA), all of the fitting residual errors were less than 10 nm, and it proved the NURBS surface is qualified for various free-form surface. Several high-precision and fast methods for inversion of NURBS surface were studied, and the ray tracing algorithm's speed was 3 times faster than traditional derivative algorithm. Given an appropriate iterative initial value, the time for calculating each point could be minimized to 0.3 ms. Examples of successfully using NURBS surface in optomechanical analysis of free-form surface prism system and in CODEV user-defined surface, show that the NURBS surface is fully adequate in optomechanical design, analysis and fabrication.