Overview of Surface Representations for Freeform Surfaces

Freeform surfaces are a new and exciting opportunity in lens design. The technological boundary conditions for manufacturing surfaces with reduced symmetry are complicated. Recently the progress in understanding and controlling this kind of components is ready for use in commercial products. Nearly all procedures of classical design development are changing, if freeform surfaces are used. The mathematical description of the surfaces, the optimization algorithms in lens design and their convergence, the initial design approaches, the evaluation of performance over the field of view, the data transfer in the mechanical design software and in the manufacturing machines, the metrology for characterization of real surfaces and the return of the real surfaces into the simulation are affected. In this contribution, in particular an overview on possible mathematical formulations of the surfaces is given. One of the requirements on the descriptions is a good performance to correct optical aberrations. After fabrication of real surfaces, there are typical deviations seen in the shape. First more localized deformations are observed, which are only poorly described by mode expansions. Therefore a need in describing the surface with localized finite support exists. Secondly the classical diamond turning grinding process typically shows a regular ripple structure. These midfrequency errors are best described by special approaches. For all these cases it would be the best to have simple, robust solutions, that allow for fast calculation in fitting measured surfaces and in raytrace.