Download or read book Inverse Source Problems in Optics written by H.P. Baltes and published by Springer. This book was released on 1978-11 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: With contributions by numerous experts

Download or read book Inverse Source Problems in Optics written by Heinrich P. Baltes and published by Springer. This book was released on 1978 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Inverse Scattering Problems in Optics written by H.P. Baltes and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: When, in the spring of 1979, H.P. Baltes presented me with the precursor of this vo 1 ume, the book on "Inverse Source Problems in Opti cs", I expressed my gratitude in a short note, 11hich in translation, reads: "Dear Dr. Ba ltes, the mere titl e of your unexpected gift evokes memori es of a period, which, in the terminology of your own contribution, would be described as the Stone Age of the Inverse Problem. Those were pleasant times. Walter Kohn and I lived in a cave by ourselves, drew pictures on the walls, and nobody seemed to care. Now, however, Inversion has become an Industry, which I contemplate with as much bewilderment as a surviving Tasmanian aborigine gazing at a modern oil refinery with its towers, its fl ares, and the confus i ng maze of its tubes." The present volume makes me feel even more aboriginal - impossible for me to fathom its content. What I can point out, however, is one of the forgotten origins of the Inverse Scattering Problem of Quantum Mechanics: Werner Heisenberg's "S-Matrix Theory" of 1943. This grandiose scheme had the purpose of eliminating the notion of the Hamiltonian in favour of the scattering operator. If Successful, it would have done away once and for all with any kind of inverse problem.

Download or read book Inverse Source Problems written by Victor Isakov and published by American Mathematical Soc.. This book was released on 1990 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: A careful exposition of a research field of current interest. This includes a brief survey of the subject and an introduction to recent developments and unsolved problems.

Download or read book Advances in Inverse Problems for Partial Differential Equations written by Dinh-Liem Nguyen and published by American Mathematical Society. This book was released on 2023-04-12 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of two AMS Special Sessions “Recent Developments on Analysis and Computation for Inverse Problems for PDEs,” virtually held on March 13–14, 2021, and “Recent Advances in Inverse Problems for Partial Differential Equations,” virtually held on October 23–24, 2021. The papers in this volume focus on new results on numerical methods for various inverse problems arising in electrical impedance tomography, inverse scattering in radar and optics problems, reconstruction of initial conditions, control of acoustic fields, and stock price forecasting. The authors studied iterative and non-iterative approaches such as optimization-based, globally convergent, sampling, and machine learning-based methods. The volume provides an interesting source on advances in computational inverse problems for partial differential equations.

Download or read book Variational Source Conditions Quadratic Inverse Problems Sparsity Promoting Regularization written by Jens Flemming and published by Springer. This book was released on 2018-09-08 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book collects and contributes new results on the theory and practice of ill-posed inverse problems. Different notions of ill-posedness in Banach spaces for linear and nonlinear inverse problems are discussed not only in standard settings but also in situations up to now not covered by the literature. Especially, ill-posedness of linear operators with uncomplemented null spaces is examined.Tools for convergence rate analysis of regularization methods are extended to a wider field of applicability. It is shown that the tool known as variational source condition always yields convergence rate results. A theory for nonlinear inverse problems with quadratic structure is developed as well as corresponding regularization methods. The new methods are applied to a difficult inverse problem from laser optics.Sparsity promoting regularization is examined in detail from a Banach space point of view. Extensive convergence analysis reveals new insights into the behavior of Tikhonov-type regularization with sparsity enforcing penalty.

Download or read book Inverse Problems in Optics written by and published by . This book was released on 1987 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Computational Methods for Inverse Problems written by Curtis R. Vogel and published by SIAM. This book was released on 2002-01-01 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems.

Download or read book Methods of Inverse Problems in Physics written by Dilip N. Ghosh Roy and published by CRC Press. This book was released on 1991-03-14 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: This interesting volume focuses on the second of the two broad categories into which problems of physical sciences fall-direct (or forward) and inverse (or backward) problems. It emphasizes one-dimensional problems because of their mathematical clarity. The unique feature of the monograph is its rigorous presentation of inverse problems (from quantum scattering to vibrational systems), transmission lines, and imaging sciences in a single volume. It includes exhaustive discussions on spectral function, inverse scattering integral equations of Gel'fand-Levitan and Marcenko, Povzner-Levitan and Levin transforms, Møller wave operators and Krein's functionals, S-matrix and scattering data, and inverse scattering transform for solving nonlinear evolution equations via inverse solving of a linear, isospectral Schrodinger equation and multisoliton solutions of the K-dV equation, which are of special interest to quantum physicists and mathematicians. The book also gives an exhaustive account of inverse problems in discrete systems, including inverting a Jacobi and a Toeplitz matrix, which can be applied to geophysics, electrical engineering, applied mechanics, and mathematics. A rigorous inverse problem for a continuous transmission line developed by Brown and Wilcox is included. The book concludes with inverse problems in integral geometry, specifically Radon's transform and its inversion, which is of particular interest to imaging scientists. This fascinating volume will interest anyone involved with quantum scattering, theoretical physics, linear and nonlinear optics, geosciences, mechanical, biomedical, and electrical engineering, and imaging research.

Download or read book Inverse Problems in Scattering and Imaging written by Society of Photo-optical Instrumentation Engineers and published by SPIE-International Society for Optical Engineering. This book was released on 1992 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Nonlinear Inverse Problems in Imaging written by Jin Keun Seo and published by John Wiley & Sons. This book was released on 2012-11-16 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides researchers and engineers in the imaging field with the skills they need to effectively deal with nonlinear inverse problems associated with different imaging modalities, including impedance imaging, optical tomography, elastography, and electrical source imaging. Focusing on numerically implementable methods, the book bridges the gap between theory and applications, helping readers tackle problems in applied mathematics and engineering. Complete, self-contained coverage includes basic concepts, models, computational methods, numerical simulations, examples, and case studies. Provides a step-by-step progressive treatment of topics for ease of understanding. Discusses the underlying physical phenomena as well as implementation details of image reconstruction algorithms as prerequisites for finding solutions to non linear inverse problems with practical significance and value. Includes end of chapter problems, case studies and examples with solutions throughout the book. Companion website will provide further examples and solutions, experimental data sets, open problems, teaching material such as PowerPoint slides and software including MATLAB m files. Essential reading for Graduate students and researchers in imaging science working across the areas of applied mathematics, biomedical engineering, and electrical engineering and specifically those involved in nonlinear imaging techniques, impedance imaging, optical tomography, elastography, and electrical source imaging

Download or read book Linear and Nonlinear Inverse Problems with Practical Applications written by Jennifer L. Mueller and published by SIAM. This book was released on 2012-11-30 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse problems arise in practical applications whenever there is a need to interpret indirect measurements. This book explains how to identify ill-posed inverse problems arising in practice and gives a hands-on guide to designing computational solution methods for them, with related codes on an accompanying website. The guiding linear inversion examples are the problem of image deblurring, x-ray tomography, and backward parabolic problems, including heat transfer. A thorough treatment of electrical impedance tomography is used as the guiding nonlinear inversion example which combines the analytic-geometric research tradition and the regularization-based school of thought in a fruitful manner. This book is complete with exercises and project topics, making it ideal as a classroom textbook or self-study guide for graduate and advanced undergraduate students in mathematics, engineering or physics who wish to learn about computational inversion. It also acts as a useful guide for researchers who develop inversion techniques in high-tech industry.

Download or read book Inverse Problems in Optics written by Edward Roy Pike and published by . This book was released on 1987 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Progress in Optics written by and published by Elsevier. This book was released on 2003-07-01 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: A volume in the Progress in Optics series, the papers in this book cover a range of topics, including: anamorphic beam shaping for laser and diffuse light; ultra-fast all-optical switching in optical networks; generation of dark hollow beams and their application; and two-photon lasers.

Download or read book Inverse Problems in Differential Equations written by G. Anger and published by Springer Science & Business Media. This book was released on 1990-06-30 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elucidates the fundamental mathematical structures of inverse problems, analyzing both the information content and the solution of some inverse problems in which the information content of the coefficients and the source term of a given differential equation is not too large. In order to be accessib

Download or read book Inverse Techniques written by Laura C. Thomson and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, two, seemingly different, classes of problems are discussed: locating gas sources from downwind gas concentration measurements and designing diffractive optics (i.e. computer generated holograms), which on illumination will produce a desired light beam in the far field. The similarity between these problems is that they are both?inverse problems? and we discuss the use of inverse techniques to solve them. In many instances within science, it is possible to calculate accurately a set of consequences which result from defined events. In most cases, however, it is math- ematically impossible to analytically calculate the unique set of events which led to the observed consequences. Such problems are termed?inverse problems?. Taking the example of gas dispersion, one sees that a known source leads to a calculable set of downwind concentrations. However, given a single concentration measurement it is impossible to distinguish a specific source and location from a larger, more distant source that would have given the same measured concentration. This is an example of the same consequence resulting from two, or more, different events. Key to solving inverse problems are iterative algorithms which randomly trial different possible events to find those which best describe the observed consequences. Such algorithms use a search method to postulate possible events, apply a forward model to calculate the anticipated consequences and then use a cost function to compare the postulated with the known consequences. The process is iterated until the optimum value of the cost function is found, at which point the current set of postulated events are taken to be the best estimate of the real events. In this thesis I apply similar iterative algorithms to solve the two classes of problem. The current demand on the world?s oil resources have encouraged the development of new prospecting techniques. LightTouch is one such solution which is discussed in this thesis and was developed with Shell Global Solutions. LightTouch uses the fact that oil reserves, through microseepages, leak hydrocarbons to their surface. Detection of these hydrocarbons can indicate the presence of oil reserves. LightTouch measures Ethane to sub-part-per-billion sensitivity at multiple positions across a survey area. Locating the source of the Ethane from the sparse downwind concentration measurements is an inverse problem and we deploy algorithms of the type discussed above to locate the Ethane sources. The algorithm is written in LabView and the software, Recon, is currently used by Shell Global Solutions to solve this problem. In appendix B the Recon user interface is shown. We investigate both the impact of choice of cost function (chapter 3) and forward model (chapter 4), which in this inverse problem is a gas dispersion model, on the algorithm?s ability to locate the gas sources. We find that the choice of cost function is more important to the success of the algorithm than the choice of forward model. Optical tweezers trap and manipulate particles with light beams. In order to manipulate the particles in a desired way it is necessary for the shape and position of the light beam to be controlled. One way of achieving a desired light beam is to use a spatial light modulator (SLM) which displays a phase pattern (referred to as a computer generated hologram), off which the light is diffracted. Calculating the phase pattern which will result in the desired light beam is an inverse problem and is referred to as holographic light shaping. The forward model in this case is a Fourier transform. In this thesis we use an algorithm similar to that used to solve the gas location problem and the Gerchberg-Saxton algorithm to calculate phase patterns with applications in optical tweezers. Within an optical tweezers system the highest trap resolution (the smallest distance between neighboring traps) that can be achieved is conventionally dictated by the diffraction limit. In this thesis we investigate two possible ways of beating the diffraction limit: superresolution and evanescent waves. In chapter 5 we investigate the application of inverse techniques to calculating phase patterns which produce superresolution optical traps. We calculate theoreti- cally the improvements to both relative trap stiffness and trap resolution using the superresolution optical traps. Although both are improved it comes at a cost to trap strength. In chapter 7 we simulate evanescent wave fields and demonstrate shaping three dimensional evanescent optical traps. Similar light shaping techniques are used in chapter 6 to shape light beams which after being disturbed will self-reconstruct.

Download or read book Variational Source Conditions and Conditional Stability Estimates for Inverse Problems in PDEs written by Frederic Weidling and published by Göttingen University Press. This book was released on 2019 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: In inverse problems one wants to find some parameter of interest which is not directly observable by indirect measurement. These measurements are usually noisy while the mapping of measurement to parameter is typically illposed (that is unstable). Therefore one applies regularization techniques that balance these two factors to find a stable approximation of the sought for parameter. However, in order to bound the reconstruction error, one needs additional information on the true parameter, which is nowadays typically formulated in terms of variational source conditions. In this thesis, we develop a general strategy to verify these conditions based on smoothness of the true parameter and the illposedness of the problem; the latter will be characterized by exploiting structural similarities to stability estimates. Following this, we apply our strategy to verify variational source conditions for parameter identification problems, inverse scattering and electrical impedance tomography.