Freeform illumination design in optical systems with partial differential equations

Zahlreiche Anwendungen in der Beleuchtung und Messtechnik erfordern das Design kompakter, energieeffizienter, nicht-abbildender optischer Systeme zur Generierung nichttrivialer Zielintensitätsverteilungen. Eine moderne Möglichkeit dieses Anforderungsprofil zu erfüllen bieten refraktive oder reflektive optische Flächen ohne jegliche Symmetrien, sogenannte Freiformflächen. Im Gegensatz zu klassischen Projektionsmethoden wie zum Beispiel der Durchlichtprojektion bieten Freiformen durch die geeignete Wahl ihrer lokalen Oberflächenkrümmung theoretisch die Möglichkeit beliebige Beleuchtungsmuster nahezu verlustfrei zu erzeugen. Für eine gegebene Lichtquelle und ein gewünschtes Muster besteht die Hauptschwierigkeit hierbei in der Berechnung der entsprechenden Freiformflächen, welche die Energieumverteilung realisieren. Dieses sogenannte inverse Problem der nicht-abbildenden Optik erfordert zum einen dessen mathematische Modellierung und zum anderen die numerische Lösung des Models. Das Ziel dieser Arbeit ist demzufolge die Entwicklung einer allgemeinen mathematischen Beschreibung des inversen Problems und dessen numerischer Lösung, sowie die Entwicklung anwendungsorientierter Freiformbeleuchtungskonzepte.Numerous applications in illumination and metrology require the design of compact, energy-efficient nonimaging optical systems for nontrivial irradiance or intensity distributions. A modern way to fulfill the profile of requirements are freeform surfaces, meaning refractive or reflective surfaces without any symmetries.In contrast to classical projection methods, for instance transmitted-light illuminators, freeform surfaces offer the possiblity to generate nearly arbitrary target distributions by an appropriate choice of the local surface curvature. For a given light source and a desired target distribution the main difficulty is thereby the computation of the freeform surfaces, which realize the required energy redistribution. This so-called inverse problem of nonimaging optics necessitates on the one hand a mathematical description and on the other hand the numerical solving of the corresponding model. Therefore, the goal of this thesis is to develop a general mathematical description of the inverse problem, the numerical solving of the corresponding model as well as the development of application oriented freeform illumination design concepts

Lensfree computational microscopy tools for cell and tissue imaging at the point-of-care and in low-resource settings.

The recent revolution in digital technologies and information processing methods present important opportunities to transform the way optical imaging is performed, particularly toward improving the throughput of microscopes while at the same time reducing their relative cost and complexity. Lensfree computational microscopy is rapidly emerging toward this end, and by discarding lenses and other bulky optical components of conventional imaging systems, and relying on digital computation instead, it can achieve both reflection and transmission mode microscopy over a large field-of-view within compact, cost-effective and mechanically robust architectures. Such high throughput and miniaturized imaging devices can provide a complementary toolset for telemedicine applications and point-of-care diagnostics by facilitating complex and critical tasks such as cytometry and microscopic analysis of e.g., blood smears, Pap tests and tissue samples. In this article, the basics of these lensfree microscopy modalities will be reviewed, and their clinically relevant applications will be discussed

Robust level-set-based inverse lithography

Level-set based inverse lithography technology (ILT) treats photomask design for microlithography as an inverse mathematical problem, interpreted with a time-dependent model, and then solved as a partial differential equation with finite difference schemes. This paper focuses on developing level-set based ILT for partially coherent systems, and upon that an expectation-orient optimization framework weighting the cost function by random process condition variables. These include defocus and aberration to enhance robustness of layout patterns against process variations. Results demonstrating the benefits of defocus-aberration-aware level-set based ILT are presented. © 2011 Optical Society of America.published_or_final_versio

Coordinate-based neural representations for computational adaptive optics in widefield microscopy

Widefield microscopy is widely used for non-invasive imaging of biological structures at subcellular resolution. When applied to complex specimen, its image quality is degraded by sample-induced optical aberration. Adaptive optics can correct wavefront distortion and restore diffraction-limited resolution but require wavefront sensing and corrective devices, increasing system complexity and cost. Here, we describe a self-supervised machine learning algorithm, CoCoA, that performs joint wavefront estimation and three-dimensional structural information extraction from a single input 3D image stack without the need for external training dataset. We implemented CoCoA for widefield imaging of mouse brain tissues and validated its performance with direct-wavefront-sensing-based adaptive optics. Importantly, we systematically explored and quantitatively characterized the limiting factors of CoCoA's performance. Using CoCoA, we demonstrated the first in vivo widefield mouse brain imaging using machine-learning-based adaptive optics. Incorporating coordinate-based neural representations and a forward physics model, the self-supervised scheme of CoCoA should be applicable to microscopy modalities in general.Comment: 33 pages, 5 figure

Investigating block mask lithography variation using finite-difference time-domain simulation

Simulation work has long been realized as a method for analyzing semiconductor processing expediently and cost-effectively. As technology advancements strive to meet increasingly stringent parameter constraints, difficult issues arise. In this paper, challenges in block mask lithography will be discussed with the aid of using simulation packages developed by Panoramic Technology®. Halo formation utilizes a 20-30° tilt-angle implantation [1]. The block mask defines the geometries of the resist opening to allow implantation of atoms to extend into the channel region. Due to designed resolution scaling and tolerance in conjunction with substrate topography, there can be undesired influence on the electrical device characteristics due to block variations. Although the block mask pattern definition is relatively simple, additional investigation is required to understand the sensitivities that drive the implant resist CD variation. In this study, block mask measurements processed using 248 nm and 193 nm illumination sources were used to calibrate the simulation work. Addition of optical proximity correction (OPC) and wafer topography geometry parameters have been shown to improve modeling capabilities. The modeling work was also able to show the benefits of a developable bottom anti-reflection coating (dBARC) process over a single layer resist (SLR) process in the resist intensity profiles as gate pitch is decreased. The goal of this work was to develop an accurate simulation model that characterizes the lithographic performance needed to support the transition into future technology nodes

Measuring aberrations in lithographic projection systems with phase wheel targets

A significant factor in the degradation of nanolithographic image fidelity is optical wavefront aberration. Aerial image sensitivity to aberrations is currently much greater than in earlier lithographic technologies, a consequence of increased resolution requirements. Optical wavefront tolerances are dictated by the dimensional tolerances of features printed, which require lens designs with a high degree of aberration correction. In order to increase lithographic resolution, lens numerical aperture (NA) must continue to increase and imaging wavelength must decrease. Not only do aberration magnitudes scale inversely with wavelength, but high-order aberrations increase at a rate proportional to NA2 or greater, as do aberrations across the image field. Achieving lithographic-quality diffraction limited performance from an optical system, where the relatively low image contrast is further reduced by aberrations, requires the development of highly accurate in situ aberration measurement. In this work, phase wheel targets are used to generate an optical image, which can then be used to both describe and monitor aberrations in lithographic projection systems. The use of lithographic images is critical in this approach, since it ensures that optical system measurements are obtained during the system\u27s standard operation. A mathematical framework is developed that translates image errors into the Zernike polynomial representation, commonly used in the description of optical aberrations. The wavefront is decomposed into a set of orthogonal basis functions, and coefficients for the set are estimated from image-based measurements. A solution is deduced from multiple image measurements by using a combination of different image sets. Correlations between aberrations and phase wheel image characteristics are modeled based on physical simulation and statistical analysis. The approach uses a well-developed rigorous simulation tool to model significant aspects of lithography processes to assess how aberrations affect the final image. The aberration impact on resulting image shapes is then examined and approximations identified so the aberration computation can be made into a fast compact model form. Wavefront reconstruction examples are presented together with corresponding numerical results. The detailed analysis is given along with empirical measurements and a discussion of measurement capabilities. Finally, the impact of systematic errors in exposure tool parameters is measureable from empirical data and can be removed in the calibration stage of wavefront analysis