Computational Methods And Applications In Optical Imaging And Spectroscopy

This dissertation presents my work in application of computational techniques and the resulting enhancements to several non-linear and ultrafast optical imaging and spectroscopy modalities. The importance of novel computational optical imaging schemes which aim to overcome the limitations of conventional imaging techniques by leveraging the availability of computational resources and the vast body of literature in computational signal processing is emphasized. In particular the computational techniques of compressive sensing and two dimensional phase retrieval are introduced in the broad context as inversion techniques suitable for optical applications including coherent anti-Stokes Raman holography, non-linear spectroscopy, and ultrashort pulse characterization. It is shown that both computational techniques seek to improve key signal metrics such as higher signal to noise ratio (SNR) and better resolution than can be obtained traditionally within the specific imaging modality.Coherent anti-Stokes Raman scattering (CARS) holography is a novel imaging modality which combines the principles of coherent anti-Stokes Raman scattering and holography to provide label-free, chemical selective, scanning-free, and single shot 3D imaging modality. Compressive CARS holography is introduced as a sparsity constrained holographic image reconstruction technique to enhance the optical sectioning capability of CARS holography by suppressing out-of-focus background noise inherent in 3D images processed from a typical single 2D hologram. The advantages of compressive sensing guided signal acquisition strategy in optical spectroscopy is presented by proposing compressive multi-heterodyne optical spectroscopy as a novel technique for ultra-high resolution frequency comb spectroscopy. Using numerical simulations, our proposed compressive frequency comb spectroscopy technique is shown to be well-suited for recording narrow line spectra at ultra-high sampling over broad spectral range by leveraging sparsity inherent in such spectra.We next present applications of phase retrieval in optical imaging and spectroscopy. In particular we use 2D phase retrieval technique to enhance the resolution of sum frequency generation vibrational spectroscopy (SFG-VS) whose unique surface selectivity enables qualitative and quantitative study of chemical species at surfaces/interfaces. Specifically, our key contribution is that we show that our 2D phase retrieval based inversion algorithm enables measurement of characteristic molecular vibrational spectra of air/dimethyl sulfoxide interface at resolutions significantly better than that achievable in conventional SFG-VS acquisition system. Lastly, we address the limitation of the commonly used pulse characterization technique: frequency resolved optical gating (FROG) to spatio-temporally characterize the ultrafast pulse. Using a simple spectral holographic recording technique, we present a modified 2D phase retrieval based algorithm to measure the spectral phase at every spatial location in the vicinity of focus of an objective and thereby track the spatio-temporal evolution of the pulse along its optical axis.

Computational Optical Biomedical Spectroscopy and Imaging covers recent discoveries and research in the field by some of the best inventors and researchers in the world. It also presents useful computational methods and applications used in optical biomedical spectroscopy and imaging. Topics covered include:New trends in immunohistochemical, genome

This multi-author contributed volume gives a comprehensive overview of recent progress in various vibrational spectroscopic techniques and chemometric methods and their applications in chemistry, biology and medicine. In order to meet the needs of readers, the book focuses on recent advances in technical development and potential exploitations of the theory, as well as the new applications of vibrational methods to problems of recent general interest that were difficult or even impossible to achieve in the not so distant past. Integrating vibrational spectroscopy and computational approaches serves as a handbook for people performing vibrational spectroscopy followed by chemometric analysis hence both experimental methods as well as procedures of recommended analysis are described. This volume is written for individuals who develop new methodologies and extend these applications to new realms of chemical and medicinal interest.

An essential reference for optical sensor system design This is the first text to present an integrated view of the optical and mathematical analysis tools necessary to understand computational optical system design. It presents the foundations of computational optical sensor design with a focus entirely on digital imaging and spectroscopy. It systematically covers: Coded aperture and tomographic imaging Sampling and transformations in optical systems, including wavelets and generalized sampling techniques essential to digital system analysis Geometric, wave, and statistical models of optical fields The basic function of modern optical detectors and focal plane arrays Practical strategies for coherence measurement in imaging system design The sampling theory of digital imaging and spectroscopy for both conventional and emerging compressive and generalized measurement strategies Measurement code design Linear and nonlinear signal estimation The book concludes with a review of numerous design strategies in spectroscopy and imaging and clearly outlines the benefits and limits of each approach, including coded aperture and imaging spectroscopy, resonant and filter-based systems, and integrated design strategies to improve image resolution, depth of field, and field of view. Optical Imaging and Spectroscopy is an indispensable textbook for advanced undergraduate and graduate courses in optical sensor design. In addition to its direct applicability to optical system design, unique perspectives on computational sensor design presented in the text will be of interest for sensor designers in radio and millimeter wave, X-ray, and acoustic systems.

Going beyond standard introductory texts, Mathematical Optics: Classical, Quantum, and Computational Methods brings together many new mathematical techniques from optical science and engineering research. Profusely illustrated, the book makes the material accessible to students and newcomers to the field. Divided into six parts, the text presents state-of-the-art mathematical methods and applications in classical optics, quantum optics, and image processing. Part I describes the use of phase space concepts to characterize optical beams and the application of dynamic programming in optical waveguides. Part II explores solutions to paraxial, linear, and nonlinear wave equations. Part III discusses cutting-edge areas in transformation optics (such as invisibility cloaks) and computational plasmonics. Part IV uses Lorentz groups, dihedral group symmetry, Lie algebras, and Liouville space to analyze problems in polarization, ray optics, visual optics, and quantum optics. Part V examines the role of coherence functions in modern laser physics and explains how to apply quantum memory channel models in quantum computers. Part VI introduces super-resolution imaging and differential geometric methods in image processing. As numerical/symbolic computation is an important tool for solving numerous real-life problems in optical science, many chapters include Mathematica® code in their appendices. The software codes and notebooks as well as color versions of the book’s figures are available at www.crcpress.com.

This text examines a variety of spectral computational techniques— including k-space theory, Floquet theory and beam propagation— that are used to analyze electromagnetic and optical problems. The authors tie together different applications in EM and optics in which the state variable method is used. Emphasizing the analysis of planar diffraction gratings using rigorous coupled wave analysis, the book presents many cases that are analyzed using a full-field vector approach to solve Maxwell’s equations in anisotropic media where a standard wave equation approach is intractable.

In this book, computational optical phase imaging techniques are presented along with Matlab codes that allow the reader to run their own simulations and gain a thorough understanding of the current state-of-the-art. The book focuses on modern applications of computational optical phase imaging in engineering measurements and biomedical imaging. Additionally, it discusses the future of computational optical phase imaging, especially in terms of system miniaturization and deep learning-based phase retrieval.

This book covers both the mathematics of inverse problems and optical systems design, and includes a review of the mathematical methods and Fourier optics. The first part of the book deals with the mathematical tools in detail with minimal assumption about prior knowledge on the part of the reader. The second part of the book discusses concepts in optics, particularly propagation of optical waves and coherence properties of optical fields that form the basis of the computational models used for image recovery. The third part provides a discussion of specific imaging systems that illustrate the power of the hybrid computational imaging model in enhancing imaging performance. A number of exercises are provided for readers to develop further understanding of computational imaging. While the focus of the book is largely on optical imaging systems, the key concepts are discussed in a fairly general manner so as to provide useful background for understanding the mechanisms of a diverse range of imaging modalities.