Classical imaging optics have a long tradition and there is widely developed expertise in this field. In contrary advances in manufacturability allow the optical design to head for the novel region of freeform optics. What was the establishment of the aspherics some years ago, is now the investigation on how to utilize the many degrees of freedom that come along with freeform optics.
Freeform surfaces can be used for imaging and in illumination systems. In both cases, the traditional theories, approaches, methods and realization procedures must be extended and generalized to systems without symmetry.
Lack of experience and the huge number of degrees of freedom causes several problems in the optimization of freeforms surfaces in practice. There are several exact mathematical approaches to solve the problems under simplified conditions. These are the SMS method of Minano and Benitez, tailoring method of Ries, cartesian oval method of Michaelis (IOF), Monge-Ampere PDE solution of Oliker. They can serve as initial systems for numerical optimization on more realistic systems models.

Schiefspiegler mirror system with freeform surfaces
Schieferspiegler mirror system with freeform surfaces

Within the project 1, the subproject TP 4 is related to the treatment of specific topics in basic research as well as training of specifically qualified employees. The Institute of Applied Physics (IAP) brings its strengths into the Alliance, whereby a close interconnection between the university and local companies is institutionalized and the qualification of the employees can be integrated directly with their expertise in the company without a long learning curve. Therefore, TP 4 is leading in Alliance in the areas of optical design and micro-structuring, which is reflected in responsible roles in the fields of competence KTP 1 (development of optical and mechanical design tools and rules for free-form systems) and KTP 5 (high-end micro-and nanostructure technology for new optical functionalities on freeforms). These two technical aspects of the development and design of freeform systems represent basic essentials for the joint project.

Subproject TP 4 is basically divided into two parts. On the one hand, the development of models, algorithms and tools for optical design and simulation of freeform surface systems will be elaborated in the research group "Optical System Design" (Head Prof. Gross). On the other hand, the group "Microstructure Technology" (Head Dr. Kley) investigates fundamentally and provides processing technology of micro-structured surfaces for freeform surfaces. These two areas are substantially dependent, since the conception of micro-structured freeform surfaces requires a close cooperation in their calculation at component and system level as well as their tolerance.

In the theoretical part of this project, the basic work for models and algorithms in terms of tool development for simulation and design will be carried out. As a result, a platform will be developed that gather mathematical description of freeform surfaces, their efficient and robust optimization in systems, a toleration of production-related deviations, a feedback of measured surface data into the simulation and the calculation of adjustment and assembly tolerances in the system. Compared to the so far available tools and algorithms, a model description is targeted, which covers 90% of the practically relevant cases and to improve their algorithms convergence speed of optimization by a factor of 5. Hence, an essential basis for the theoretical understanding of freeform systems will be set. In addition and if it is desired, practical experience can be reproduced methodically via appropriate simulations in order to derive design rules for this type of system. However, the system aspect is observed and not the simple consideration of individual components. By means of the creation of realistic evaluation criteria and pragmatic design rules and assembly concepts for freeform surface systems a shortening of the development time of freeform optical systems by a factor of three for is aimed.

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