Optimized tailoring for lens design

To this day the standard method of imaging design is optimization. Recently we have introduced tailoring as a radically different paradigm of optical design. Tailoring determines the shape of optical surface, a priory free, by solving one or more differential equations. This method has proved successful in illumination design where a high level of detail needs to be accommodated and indeed a perfect solution is possible often with only one optical surface. The weakness of tailoring is first that it cannot adequately deal with weak requirement which need to be optimized, because they can not be precisely met or at least not met simultaneously. Examples range from manufacturability, to size, sensitivity to tolerances, but also includes imaging errors. Wassermann and Wolf showed in a classical paper how tailoring can be used in an imaging system in order to achieve aplanatism with the addition of two aspheres. In our contribution we present a synthesis which combines the virtues of optimization with those of tailoring for imaging design. It encompasses freeform surfaces and thus a huge number of effective parameters, however, only a few of these are subject to optimization. On the other hand our method can adequately use optimality criteria such as conflicting features in a figure of merit, which need to be compromised upon. Finally the result is a mathematically rigorous optimum with respect to whatever figure of merit is specified.