Abstract

The local control of B-spline surfaces has the potential to provide better surface representation for free-form imaging optics; however, it also makes B-spline surface optimization more challenging. To solve this problem, we, for the first time to the best of our knowledge, present an algorithm to design free-form imaging optics with nonrational B-spline surfaces. In this method, the local z-coordinates of a set of data points on B-spline surfaces are defined as independent variables, and the location of each ray point in the image plane is considered as a nonlinear function of these independent variables. By this mathematical consideration, a prescribed imaging system design with B-spline surfaces can be converted into an overdetermined system of nonlinear equations, and the least-squares solution to this nonlinear problem is found by using the Gauss–Newton method based on a ray-tracing technique. An off-axis two-mirror system is presented to demonstrate the elegance of this method in imaging system design with B-spline surfaces.

© 2017 Optical Society of America

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