Global optical system optimization based on the network structure of the set of local minima (DWI.6817)

Research
In the design of high-quality optical systems and in many other engineering problems where multiple local minima can be found during optimization, finding the best of the local minima is an important practical challenge. We have recently shown that in the global optimization searches of a certain class of problems, the local minima form a network in which they are all connected via links that contain a special type of saddle point. Based on this property, we have proposed and implemented in a computer program a new approach to global optimization. For optical system optimization problems in which the dimensionality is not too large, the results are already promising and the proposed method compares favourably with the known methods. Our new method has a lower risk to miss difficult local minima and also produces additional information that can lead to new insight into the design possibilities. Also, our recent research shows that in optical system design the networks of local minima do have properties that can be used to reduce the computational time significantly. The understanding of these properties enables us to obtain multiple local minima efficiently in optimization problems with a large number of variables. Whereas in our past research the focus was on non-specific network detection methods, the goal of this project is the development of methods that use a-priori knowledge of the specific properties of the network for the physical problem under investigation. For this purpose, the properties of the detected networks will also be investigated in detail. We expect that the new method and software we plan to develop will be able to handle optical optimization problems having an arbitrary complexity, including problems with a large number of variables (e.g. the optimization of lithographic objectives for the semiconductor industry).

Utilisation
In the beginning, we plan to use our method mainly in the design of lens systems. However, we will examine other applications in optics, such as thin-film optimization and the optimization of optical position sensors, as well. With the presently known design methods, there is always a danger that, for highly complex designs (e.g. lithographic objectives), potentially interesting configurations (i.e. local minima in a global search) are missed in the design process. Thus, our systematic global search method could lead to improvements of complex designs, to substantial cost savings and to an improved reliability of the manufactured optical systems. Our new scientific knowledge will be implemented in the macro language of commercially available programs. During the envisaged four years of the proposed project, the main target users will be ASML, Philips Research and TPD - TNO Institute of Applied Physics. Philips Research will participate actively to the project, by developing part of the software. In the long term, companies that develop optical design software or even more general optimization software could implement our method in their codes.