Modeling and model-aware signal processing methods for enhancement of optical systems
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Theoretical and numerical modeling of optical systems are increasingly being utilized in a wide range of areas in physics and engineering for characterizing and improving existing systems or developing new methods. This dissertation focuses on determining and improving the performance of imaging and non-imaging optical systems through modeling and developing model-aware enhancement methods. We evaluate the performance, demonstrate enhancements in terms of resolution and light collection efficiency, and improve the capabilities of the systems through changes to the system design and through post-processing techniques. We consider application areas in integrated circuit (IC) imaging for fault analysis and malicious circuitry detection, and free-form lens design for creating prescribed illumination patterns. The first part of this dissertation focuses on sub-surface imaging of ICs for fault analysis using a solid immersion lens (SIL) microscope. We first derive the Green's function of the microscope and use it to determine its resolution limits for bulk silicon and silicon-on-insulator (SOI) chips. We then propose an optimization framework for designing super-resolving apodization masks that utilizes the developed model and demonstrate the trade-offs in designing such masks. Finally, we derive the full electromagnetic model of the SIL microscope that models the image of an arbitrary sub-surface structure. With the rapidly shrinking dimensions of ICs, we are increasingly limited in resolving the features and identifying potential modifications despite the resolution improvements provided by the state-of-the-art microscopy techniques and enhancement methods described here. In the second part of this dissertation, we shift our focus away from improving the resolution and consider an optical framework that does not require high resolution imaging for detecting malicious circuitry. We develop a classification-based high-throughput gate identification method that utilizes the physical model of the optical system. We then propose a lower-throughput system to increase the detection accuracy, based on higher resolution imaging to supplement the former method. Finally, we consider the problem of free-form lens design for forming prescribed illumination patterns as a non-imaging application. Common methods that design free-form lenses for forming patterns consider the input light source to be a point source, however using extended light sources with such lenses lead to significant blurring in the resulting pattern. We propose a deconvolution-based framework that utilizes the lens geometry to model the blurring effects and eliminates this degradation, resulting in sharper patterns.