An optimization method for radial NURBS surfaces

Freeform optical surfaces provide additional degrees of freedom for the design of imaging systems. This enables systems with fewer optical elements and leads to more compact and lightweight systems, while at the same time the image quality is improved. Commonly used representations for freeform surfaces are x-y-polynomials and Zernike polynomials. Initially developed for the (computer aided) design of freeform surfaces such as car bodies, NURBS now also have found some applications in optical design. We present an optimization method for rotationally symmetric NURBS surfaces that requires less computation time than conventional methods and that in some cases converges where conventional methods do not. This new method is applied to an off-axis system and compared to conventional optimization of NURBS surfaces and aspheric surfaces.