Philipp Jester

B-spline representation of optical surfaces and its accuracy in a ray trace algorithm

We introduce a representation of aspheric surfaces that is based on a B-spline quasi-interpolation scheme. The scheme is implemented in a ray trace algorithm, and bounds on the approximation error are established. Examples for the reproduction of aspheric surfaces in polynomial description and the ray tracing accuracy are presented. The proposed approach allows the specification of local and global structures and the efficient treatment of measured surface data. The representation gives access to a wavelet analysis, offering extended possibilities for the tolerance analysis of optical systems containing aspheric elements.

Wavelet Methods for the Representation, Analysis and Simulation of Optical Surfaces

Wavelets are well adapted to describe local perturbations as well as global structures and so lead to an alternative representation of optical surfaces that combines a high approximation accuracy with a fast evaluation. We show that such a representation is usable in a ray trace algorithm to describe aspherical or free-form surfaces and give results for the achieved accuracy. Moreover the representation can be used for wavelet analysis of manufactured surfaces. We present numerical experiments for the detection of local errors, the separation of low and mid spatial frequency errors and the localization of regions with varying quality. A broad field of applications in optics, especially in tolerancing and manufacturing, is expected.