86,515 research outputs found
Why are there so many system shapes in lens design?
Full text linkThe presence of many local minima in the merit function landscape is perhaps the most difficult challenge in lens design. We present a simplified mathematical model that illustrates why the number of local minima increases rapidly with each additional lens added to the imaging system. Comparisons with results obtained with lens design software are made for the design landscape of triplets with variable curvatures, a problem that is nontrivial, but still simple enough to be analyzed in detail. The mathematical model predicts how many types of local minima can exist in the landscape of the global optimization problem and what are, roughly, their curvatures. This model is mathematically quite general and might perhaps be useful as an analogy for understanding other global optimization problems as well, there where the number of local minima increases rapidly when more components of the same kind are added in the model of the problem.Optics Research GroepApplied Science
A systematic analysis of the optical merit function landscape: Towards improved optimization methods in optical design
No full textA major problem in optical system design is that the optical merit function landscape is usually very complicated, especially for complex design problems where many minima are present. Finding good new local minima is then a difficult task. We show however that a certain degree of order is present in the optical design space, which is best observed when we consider not only local minima, but saddle points as well. With a special method, which we call Saddle-Point Construction (SPC), saddle points can be constructed in a simple way. Via saddle points, new local minima can be obtained very rapidly. When using a local optimization method, the final design after optimization highly depends on the starting configuration. We can group the initial configurations that lead to a given local minimum after local optimization into a graphical region, which shape depends on the optimization method used. However, saddle points are critical points in the merit function landscape that always remain on the boundaries, independent of the used optimization method. When the local optimization process is not chaotic, the geometric decomposition of the space of initial configurations into discrete regions has boundaries given by simple curves. But when the optimization is chaotic, the curves separating the different regions are very complicated objects termed fractals. In such cases, starting configurations, which are very close to each other, lead to different local minima after optimization. A better understanding of these instabilities can be obtained by using low damping values in a damped least-squares method.Applied Science
The network structure of the merit function space of EUV mirror systems
No full textThe merit function space of mirror systems for EUV lithography is studied. Local minima situated in a multidimensional merit function space are connected via links that contain saddle points and form a network. In this work we present the first networks for EUV lithographic objectives and discuss how these networks change when control parameters, such as aperture and field are varied and constraints are used to limit the variation domain of the variables. A good solution in a network obtained with a limited number of variables has been locally optimized with all variables to meet practical requirements.Optics Research GroepApplied Science
Networks of local minima for extreme ultraviolet lithographic objectives
No full textPoster presentation Optics Research Group TU Delft in cooperation with ASM Lithograpy and TNOOptics Research GroupApplied Science
Reducible complexity in lens design
No full textA major challenge in lens design is the presence of many local minima in the optimization landscape. However, unlike other global optimization problems, the lens design landscape has an additional structure, that can facilitate the design process: many local minima are closely related to minima of simpler problems. For discussing this property, in addition to local minima other critical points in the landscape must also be considered. Usually, in a global optimization problem with M variables one has to perform M-dimensional searches in order to find minima that are different from the known ones. We discuss here simple examples where, due to the special structure that is present, all types of local minima found by other methods can be obtained by a succession of one-dimensional searches. Replacing M-dimensional searches by a set of one-dimensional ones has very significant practical advantages. If the ability to reach solutions by decomposing the search in simple steps will survive generalization to more complex systems, new design tools using this property could have a significant impact on lens design. © (2015) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.ImPhys/Imaging PhysicsApplied Science
Network search method in the design of extreme ultraviolet lithographic objectives
Full text linkThe merit function space of mirror system for extreme ultraviolet (EUV) lithography is studied. Local minima situated in the multidimensional optical merit function space are connected via links that contain saddle points and form a network. We present networks for EUV lithographic objective designs and discuss how these networks change when control parameters, such as aperture and field, are varied, and constraints are used to limit the variation domain of the variables. A good solution in a network, obtained with a limited number of variables, has been locally optimized with all variables to meet practical requirements.Imaging Science and TechnologyApplied Science
Saddle points in the merit function landscape of lithographic objectives
No full textThe multidimensional merit function space of complex optical systems contains a large number of local minima that are connected via links that contain saddle points. In this work, we illustrate a method to construct such saddle points with examples of deep UV objectives and extreme UV mirror systems for lithography. The central idea of our method is that, at certain positions in a system with N surfaces that is a local minimum, a thin meniscus lens or two mirror surfaces can be introduced to construct a system with N+2 surfaces that is a saddle point. When the optimization goes down on the two sides of the saddle point, two minima are obtained. We show that often one of these two minima can be reached from several other saddle points constructed in the same way. The practical advantage of saddle-point construction is that we can produce new designs from the existing ones in a simple, efficient and systematic manner.Optics Research GroepApplied Science
Saddle-point construction in the design of lithographic objectives, part 2: Application
No full textOptics Research GroupApplied Science
Saddle-point construction in the design of lithographic objectives, part 1: Method
No full textOptics Research GroupApplied Science
Optimization of extreme ultraviolet mirror systems comprising high-order aspheric surfaces
No full textOptics Research GroupApplied Science
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