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Theory Methods And Algorithms For Interferometric Inversion And Phase Retrieval With Applications In Wave Based Imaging
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Book Synopsis Theory, Methods, and Algorithms for Interferometric Inversion and Phase Retrieval with Applications in Wave-based Imaging by : Bariscan Yonel
Download or read book Theory, Methods, and Algorithms for Interferometric Inversion and Phase Retrieval with Applications in Wave-based Imaging written by Bariscan Yonel and published by . This book was released on 2022 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Phase Retrieval with Application to Intensity Correlation Interferometers by : Russell Edward Trahan
Download or read book Phase Retrieval with Application to Intensity Correlation Interferometers written by Russell Edward Trahan and published by . This book was released on 2013 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: As astronomers and astrophysicists seek to view ever-increasingly distant celestial objects, the desired angular resolution of telescopes is constantly being increased. Classical optics, however, has shown a proportional relationship between the size of an optical telescope and the possible angular resolution. Experience has also shown that prohibitive cost accompanies large optical systems. With these limitations on classical optical systems and with the drastic increase in computational power over the past decade, intensity correlation interferometry (ICI) has seen renewed interest since the 1950's and 60's when it was initially conceived by Hanbury Brown and Twiss. Intensity correlation interferometry has the advantage of less stringent equipment precision and less equipment cost when compared to most other forms of interferometry. ICI is thus attractive as a solution to the desire for high angular resolution imaging especially in space based imaging systems. Optical interferometry works by gathering information about the Fourier transform of the geometry of an optical source. An ICI system, however, can only detect the magnitude of the Fourier components. The phase of the Fourier components must be recovered through some computational means and typically some a priori knowledge of the optical source. This thesis gives the physics and mathematical basis of the intensity correlation interferometer. Since the ICI system cannot detect the phase of an optical source's Fourier transform, some known methods for recovering the phase information are discussed. The primary method of interest here is the error-reduction algorithm by Gerchberg-Saxton which was adapted by Fienup to phase retrieval. This algorithm works by using known qualities of the image as constraints; however, sometimes it can be difficult to know what these constraints are supposed to be. A method of adaptively discovering these constraints is presented, and its performance is evaluated in the presence of noise. Additionally, an algorithm is presented to adapt to the presence of noise in the Fourier modulus data. Finally, the effects of the initial condition of the error-reduction algorithm are shown and a method of mitigating its effect by averaging several independent solutions together is shown. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/148155
Book Synopsis Phase Estimation in Optical Interferometry by : Pramod Rastogi
Download or read book Phase Estimation in Optical Interferometry written by Pramod Rastogi and published by CRC Press. This book was released on 2014-11-21 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the essentials of phase-stepping algorithms used in interferometry and pseudointerferometric techniques. It presents the basic concepts and mathematics needed for understanding modern phase estimation methods. The book first focuses on phase retrieval from image transforms using a single frame. It then examines the local environment of a fringe pattern, the phase estimation approach based on local polynomial phase modeling, temporal high-resolution phase evaluation methods, and methods of phase unwrapping. It also discusses experimental imperfections liable to adversely influence the accuracy of phase measurements.
Book Synopsis Advanced theory of optical wave propagation and interferometric sensors for topography measurement by : Markus C. Schake
Download or read book Advanced theory of optical wave propagation and interferometric sensors for topography measurement written by Markus C. Schake and published by BoD – Books on Demand. This book was released on 2014-01-01 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: This manuscript provides a compendium for the application of the nonuniform wave model to standard problems of two beam interference and addresses common educational issues associated with wave propagation at attenuating interfaces. It also reports scientific advances in interferometric applications focusing on an interferometric point sensor with optical path length modulation and an areal measuring RGB-interferometer for fast topography measurements in the sub millisecond regime.
Book Synopsis Iterative Phase Estimation Algorithms in Interferometric Systems by : Wesley E. Farriss
Download or read book Iterative Phase Estimation Algorithms in Interferometric Systems written by Wesley E. Farriss and published by . This book was released on 2021 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Coherent optical interferometry has a long history of enabling extremely precise measurements at length scales of less than the wavelength of light used in the interferometer. It is the ability of these systems to measure both the relative phase and amplitude information of the optical field that makes them so useful. As the name would imply, measuring phase and amplitude is accomplished by interfering two or more beams of light. Interferometric techniques have been adopted for use in both imaging/sensing technologies. For imaging systems under ideal conditions, the ability to measure both phase and amplitude information in one transverse plane allows for the calculation of that field's phase and amplitude distribution in any other transverse plane. However, the presence of atmospheric turbulence unpredictably alters the index of refraction in the propagation medium thereby adversely affecting the reliability of calculation of phase and amplitude in other transverse planes. To address this problem, we demonstrate iterative sharpness maximization (ISM) correction of anisoplanatic turbulence effects in simulated range-compressed holography (RCH) fields and their corresponding range images. Our turbulence correction estimated four phase screens placed along the path of optical propagation using nonlinear optimizations aided by the method of sieves technique. We conducted a study of range images created from simulated single speckle realization 3D RCH fields subjected to twenty different turbulence profiles at five different strengths of turbulence, D/r0 = 7, 14, 21, 28, and 36. Range images showed significant improvement for all strengths of turbulence. To assist in correction, we introduced a novel constraint limiting the spread of energy in the corrected pupil. Corrected range images were qualitatively very similar to unaberrated range images in all but the most severe turbulence case, D/r0 = 36. Additionally, our algorithm was tested for fields affected by shot noise. Mean target photons per speckle ranged from 10 -2 to 10 2 in these simulations. For an effective D/r0 = 36, range images corrected from fields with 102 mean photons per speckle had very similar RMSE when compared to corrected noiseless range images. On average, corrected range images created from fields with 1 mean target photon per speckle differed by less than 5% RMSE from noiseless corrected range images. We went on to construct a RCH system in a laboratory setting using a linear frequency modulated CW laser and a high frame rate camera which allowed us to create 3D images of laboratory targets. Data was collected both with and without the effects of turbulence. In the former, multiple Lexitek turbulence screens were used to aberrate the image fields of our lab target at two different effective strengths of anisoplanatic turbulence, D/r0 = 7 and D/r0 = 16, respectively. Both of these sets of real aberrated image fields showed profound improvement in quality after correction with our phase ISM turbulence mitigation algorithm. Novel interferometric systems are also being developed which enable modal analysis of an optical field. This generalized optical interferometry (GOI) treats coherent optical fields as a linear superposition of transverse modes and recovers the amplitudes of modal weighting coefficients. In order to maximize the utility of these systems, we used phase retrieval by nonlinear optimization to recover the phase of these modal weighting coefficients. Algorithms were developed both for use with an array detector and for use with a bucket detector. Information diversity increased the robustness of both algorithms by better constraining the solutions. In our array detection phase retrieval, the algorithm was able to recover nearly all coefficient phases for simulated fields consisting of up to 21 superpositioned Hermite Gaussian modes from simulated data and proved to be resilient to shot noise. Similarly, the algorithm we developed using data from a simulated bucket detector was able to consistently recover better than 95% of coefficient phases for simulated random fields consisting of up to 21 superpositioned Hermite Gaussian modes using between three and seven measurements per unknown phase coefficient. With shot noise, the algorithm achieved performance on par with noiseless simulations with 106 mean signal photons per measurement. The role played by number of measurements per unknown (mpu), photons per unknown per measurement (ppu), and order of superposition in the bucket detection algorithm's performance was also explored"--Pages xvi-xix
Book Synopsis Phase Retrieval Using an Imaging Sensor by : Charles V. Scull
Download or read book Phase Retrieval Using an Imaging Sensor written by Charles V. Scull and published by . This book was released on 1979 with total page 66 pages. Available in PDF, EPUB and Kindle. Book excerpt: This research study is concerned with spatial (relative) phase reconstruction using an imaging sensor. Specifically, work was completed which investigates the retrieval of the spatial phase of the aperture wavefront from sampled intensity data in the focal plane of an imaging sensor, where phase is not explicitly present. Techniques investigated are not interferometric methods, but are signal processing techniques that use the Fourier transform properties of a lens, analytics, and numerics to retrieve the spatial phase of the aperture field from intensity measurements in the focal plane of an imaging sensor. The techniques investigated include an analytic approach which is used to develop several numerical approaches, and the Gerchberg-Saxton Algorithm which is adapted to solve this specific phase retrieval problem. Finally, the results from simulations of these methods are compared yielding the Gerchberg-Saxton Algorithm as the most promising method to approximate the relative phase in the aperture plane. (Author).
Book Synopsis Journal of the Optical Society of America by :
Download or read book Journal of the Optical Society of America written by and published by . This book was released on 1993 with total page 936 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis PHASE RETRIEVAL FROM TWO DEFOCUSED IMAGES BY THE TRANSPORT OF INTENSITY EQUATION FORMALISM WITH FAST FOURIER TRANSFORM. by :
Download or read book PHASE RETRIEVAL FROM TWO DEFOCUSED IMAGES BY THE TRANSPORT OF INTENSITY EQUATION FORMALISM WITH FAST FOURIER TRANSFORM. written by and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of phase retrieval from intensity measurements plays an important role in many fields of physical research, e.g. optics, electron and x-ray microscopy, crystallography, diffraction tomography and others. In practice the recorded images contain information only on the intensity distribution I(x, y)=[Psi]*[Psi]=[vert-bar]A[vert-bar][sup 2] of the imaging wave function[Psi]= A*exp( -i[var-phi]) and the phase information[var-phi](x, y) is usually lost. In general, the phase problem can be solved either by special holographic/interferometric methods, or by non-interferometric approaches based on intensity measurements in far Fraunhofer zone or in the Fresnel zone at two adjacent planes orthogonal to the optical axis. The latter approach uses the transport-of-intensity equation (TIE) formalism, introduced originally by Teague[1] and developed later in[2]. Applications of TIE to nonmagnetic materials and magnetic inductance mapping were successfully made in[3,4]. However, this approach still needs further improvement both in mathematics and in practical solutions, since the result is very sensitive to many experimental parameters.
Book Synopsis Interferometry in Speckle Light by : Pierre Jacquot
Download or read book Interferometry in Speckle Light written by Pierre Jacquot and published by Springer Science & Business Media. This book was released on 2000 with total page 684 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Proceedings contain state-of-the-art reviews and original materials related to up-to-date developments in a wide range of optical control methods. They are devoted in particular to shape, displacement and deformation measurement, strain analysis, mechanical behavior evaluation, inspection and non-destructive testing. Three principal classes of methods are under consideration: speckle photography, holographic interferometry and speckle interferometry. Both the state-of-the-art practices and the actual leading-edge techniques are discussed within a single volume, with reference to theoretical backgrounds common to all methods. Usually, similar information is distributed over many specialised works. The book presents both conceptual and practical aspects: theoretical considerations are fully analysed and applications illustrate the emphasis on many experimental aspects.
Book Synopsis Very Long Baseline Interferometry by : Marcello Felli
Download or read book Very Long Baseline Interferometry written by Marcello Felli and published by Springer Science & Business Media. This book was released on 1989-07-31 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: The quest for high resolution has preoccupied radio astronomers ever since radio waves were first detected from space fifty years ago. This venture was par ticularly stimulated by the discovery of quasars, and led to the development of interferometer techniques using baselines of transglobal dimensions. These meth ods have become known as Very Long Baseline Interferometry (VLBI). Arrays of radio telescopes situated all over the Earth (or even in space) are regularly used for researches in radio astronomy, reaching resolutions as small as a fraction of a milli arcsecond. The technique also allows the measurement of the positions of the radio telescopes to a few millimeters and so VLBI has become a major tool in geodesy and the study of the rotation of the Earth. VLBI has now passed the pioneer stage and is becoming a standard facility available to astronomers and geodesists, requiring the coordination of the operations of indpendently owned radio telescopes around the world. In Europe observatories from England, Federal Republic of Germany, France, Italy, Poland, Sweden and The Netherlands are coordinated in their VLBI activity by the European VLBI Network Consortium (EVN). The Programme Committee of the EVN allocates time to scientific projects on a routine basis three times a year. The Unites States has a similar arrangement of a network of independent radio observatories, and joint experiments using 'Global Network' are often made.
Book Synopsis Phase Retrieval from Continuous and Discrete Ptychographic Measurements by : Sami Eid Merhi
Download or read book Phase Retrieval from Continuous and Discrete Ptychographic Measurements written by Sami Eid Merhi and published by . This book was released on 2019 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation, we present and study two novel approaches to phase retrieval -- an inverse problem in which one attempts to reconstruct a complex-valued function (or vector) from phaseless (or magnitude-only) measurements. Phase retrieval arises in several scientific areas including bio-chemistry, optics, astronomy, quantum mechanics, and speech signal processing. Early solutions to phase retrieval, although practical, lacked robustness guarantees. To this day, practitioners in scientific imaging are still seeking demonstrably stable and robust recovery algorithms. Ptychography is a form of coherent diffractive imaging where diffraction patterns are processed by algorithms to recover an image of a specimen. More specifically, small regions of a specimen are illuminated one-at-a-time, and a detector captures the intensities of the resulting diffraction patterns. As such, the measurements are local and phaseless. In this work, we present two algorithms to recover signals from ptychographic measurements. The first algorithm aims to recover a discrete one-dimensional signal from discrete spectrogram measurements via a modified Wigner distribution deconvolution (WDD) method. While the method is known to practitioners of scientific imaging, robustness and recovery guarantees are lacking, if not absent; our contribution is to supply such guarantees. The second algorithm aims to approximately recover a compactly supported function from continuous spectrogram measurements via lifting and angular synchronization. This setup can be interpreted as the infinite-dimensional equivalent of discrete ptychographic imaging. Our contribution is a model which assumes infinite-dimensional signals and measurements ab initio, as opposed to most recent algorithms in which discrete models are a necessity. Finally, we consider the worst-case noise robustness of any phase retrieval algorithm which aims to reconstruct all nonvanishing vectors from the magnitudes of an arbitrary collection of local correlation measurements. The robustness results provided therein apply to a wide range of ptychographic imaging scenarios. In particular, our contribution is to show that stable recovery of high-resolution images of extremely large samples is likely to require a vast number of measurements, independent of the recovery algorithm employed. The first chapter introduces the phase retrieval problem and presents historical context, as well as applications in which phase retrieval manifests. In addition, we introduce ptychography, discuss existing WDD formulations, and compare these to our contribution in the discrete setting. Chapter 2 provides recovery guarantees for using aliased WDD methods to solve the phase retrieval problem in a discrete setting with sub-sampled measurements. In Chapter 3 we provide lower Lipschitz bounds for generic phase retrieval algorithms from locally supported measurements. Finally, Chapter 4 presents a numerical method to recover compactly supported functions from local measurements via lifting and angular synchronization.
Book Synopsis Two-Dimensional Phase Unwrapping by : Dennis C. Ghiglia
Download or read book Two-Dimensional Phase Unwrapping written by Dennis C. Ghiglia and published by Wiley-Interscience. This book was released on 1998-04-28 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: A resource like no other-the first comprehensive guide to phase unwrapping Phase unwrapping is a mathematical problem-solving technique increasingly used in synthetic aperture radar (SAR) interferometry, optical interferometry, adaptive optics, and medical imaging. In Two-Dimensional Phase Unwrapping, two internationally recognized experts sort through the multitude of ideas and algorithms cluttering current research, explain clearly how to solve phase unwrapping problems, and provide practicable algorithms that can be applied to problems encountered in diverse disciplines. Complete with case studies and examples as well as hundreds of images and figures illustrating the concepts, this book features: A thorough introduction to the theory of phase unwrapping Eight algorithms that constitute the state of the art in phase unwrapping Detailed description and analysis of each algorithm and its performance in a number of phase unwrapping problems C language software that provides a complete implementation of each algorithm Comparative analysis of the algorithms and techniques for evaluating results A discussion of future trends in phase unwrapping research Foreword by former NASA scientist Dr. John C. Curlander Two-Dimensional Phase Unwrapping skillfully integrates concepts, algorithms, software, and examples into a powerful benchmark against which new ideas and algorithms for phase unwrapping can be tested. This unique introduction to a dynamic, rapidly evolving field is essential for professionals and graduate students in SAR interferometry, optical interferometry, adaptive optics, and magnetic resonance imaging (MRI).
Book Synopsis Interferogram Analysis, Digital Fringe Pattern Measurement Techniques by : David W. Robinson
Download or read book Interferogram Analysis, Digital Fringe Pattern Measurement Techniques written by David W. Robinson and published by CRC Press. This book was released on 1993 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: Very Good,No Highlights or Markup,all pages are intact.
Download or read book Optics Letters written by and published by . This book was released on 2008 with total page 760 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Waves and Imaging through Complex Media by : P. Sebbah
Download or read book Waves and Imaging through Complex Media written by P. Sebbah and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent advances in wave propagation in random media are certainly consequences of new approaches to fundamental issues, as well as of a strong interest in potential applications. A collective effort has been made to present in this book the state of the art in fundamental concepts, as well as in biomedical imaging techniques. As an example, the recent introduction of wave chaos, and more specifically random matrix theory - an old tool from nuclear physics - to the study of multiple scattering, has pointed the way to a deeper understanding of wave coherence in complex media. At the same time, efficient new approaches for retrieving information from random media promise to allow wave imaging of small tumors in opaque tissues. Review chapters are written by experts in the field, with the aim of making the book accessible to the widest possible scientific audience: graduate students and research scientists in theoretical and applied physics, optics, acoustics, and biomedical physics.
Book Synopsis Phase Retrieval Using Power Measurements by : Jamal Arif
Download or read book Phase Retrieval Using Power Measurements written by Jamal Arif and published by . This book was released on 2013 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Optical signals have two basic components that are power and phase, which can be demonstrated in both time and frequency domains. The common diagnostics which are available in the market only measure power component in time or frequency domain. However in certain areas phase measurements are also required. The phase retrieval techniques are used to calculate phase measurements from different methods. There are a number of applications where phase measurements are required like astronomy, wavefront sensing technique (James Webb space telescope), x-ray crystallography, fiber optic telecommunications etc. Various phase retrieval algorithms have been used in retrieving phase measurements in temporal and frequency domains. Gerchberg Saxton Algorithm technique is an iterative phase retrieval technique which has been used in phase retrieval methods. This iterative process involves iterative Fourier transformation back and forth between the object and Fourier domains with applications of the measured data or known constraints in each domain. We worked on developing an iterative phase retrieval technique keeping Gerchberg Saxton Algorithm as the basis of it and were able to successfully demonstrate phase retrieval in both temporal and spectral forms for a) Gaussian pulses having a wide range of initial educated guess phase; b) Chirped Gaussian pulses having various amounts of chirp; c) Chirped Super Gaussian pulses having various amounts of chirp. A metrics system was denied on which phase retrieval technique's success was based showing minimization of power, phase and instantaneous frequency metrics. During the study we found that chirped super Gaussian pulses of order 4 converge better than the chirped Gaussian pulses and also explored a way to choose a good educational phase without knowledge of the actual phase. Thus, this research provided a new foundation for further research on phase retrieval techniques of Gaussian and chirped Gaussian pulses."--Abstract.
Book Synopsis Algorithms and Array Design Criteria for Robust Imaging in Interferometry by : Binoy George Kurien
Download or read book Algorithms and Array Design Criteria for Robust Imaging in Interferometry written by Binoy George Kurien and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Optical interferometry is a technique for obtaining high-resolution imagery of a distant target by interfering light from multiple telescopes. Image restoration from interferometric measurements poses a unique set of challenges. The first challenge is that the measurement set provides only a sparse-sampling of the object's Fourier Transform and hence image formation from these measurements is an inherently ill-posed inverse problem. Secondly, atmospheric turbulence causes severe distortion of the phase of the Fourier samples. We develop array design conditions for unique Fourier phase recovery, as well as a comprehensive algorithmic framework based on the notion of redundant-spaced-calibration (RSC), which together achieve reliable image reconstruction in spite of these challenges. Within this framework, we see that classical interferometric observables such as the bispectrum and closure phase can limit sensitivity, and that generalized notions of these observables can improve both theoretical and empirical performance. Our framework leverages techniques from lattice theory to resolve integer phase ambiguities in the interferometric phase measurements, and from graph theory, to select a reliable set of generalized observables. We analyze the expected shot-noise-limited performance of our algorithm for both pairwise and Fizeau interferometric architectures and corroborate this analysis with simulation results. We apply techniques from the field of compressed sensing to perform image reconstruction from the estimates of the object's Fourier coefficients. The end result is a comprehensive strategy to achieve well-posed and easily-predictable reconstruction performance in optical interferometry.
