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linear sampling and magnification technique based on phase modulators and dispersive elements: The temporal lenticular lens

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OPTICAL FIBER TECHNOLOGY 2017年 36卷 125-129页

作者： Nuno, Javier Finot, Christophe Fatome, Julien Univ Bourgogne Franche Comte CNRS Lab Interdisciplinaire Carnot Bourgogne UMR 6303 9 Av A Savary F-21078 Dijon France

In this work, we exploit the space/time duality in optics to implement a temporal lenticular lens allowing to simultaneously sample and magnify an arbitrary-shaped optical signal. More specifically, by applying a sinusoidal phase-modulation, the signal under test is propagated through a discrete dispersive element that samples and magnifies its initial waveform. Thanks to this temporal lenticular lens, optical sampling associated to an intensity magnification factor of 3.6 is experimentally demonstrated at a repetition rate of 10 GHz. (C) 2017 Elsevier Inc. All rights reserved.

关键词： All-optical signal processing Fiber devices linear sampling Phase modulation Dispersion

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The Time Domain linear sampling Method for Determining the Shape of Multiple Scatterers Using Electromagnetic Waves

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COMPUTATIONAL METHODS IN APPLIED MATHEMATICS 2022年第4期22卷 889-913页

作者： Lahivaara, Timo Monk, Peter Selgas, Virginia Univ Oviedo Dept Matemat EPIG C Luis Ortiz Berrocal S-N Gijon 33203 Spain Univ Eastern Finland Dept Appl Phys Kuopio 70211 Finland Univ Delaware Dept Math Sci Newark DE 19716 USA

The time domain linear sampling method (TD-LSM) solves inverse scattering problems using time domain data by creating an indicator function for the support of the unknown scatterer. It involves only solving a linear integral equation called the near-field equation using different data from sampling points that probe the domain where the scatterer is located. To date, the method has been used for the acoustic wave equation and has been tested for several different types of scatterers, i.e. sound hard, impedance, and penetrable, and for waveguides. In this paper, we extend the TD-LSM to the time dependent Maxwell's system with impedance boundary conditions - a similar analysis handles the case of a perfect electric conductor (PEC). We provide an analysis that supports the use of the TD-LSM for this problem, and preliminary numerical tests of the algorithm. Our analysis relies on the Laplace transform approach previously used for the acoustic wave equation. This is the first application of the TD-LSM in electromagnetism.

关键词： Wave Based Imaging Electromagnetism Impedance linear sampling Time Domain

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A linear sampling method for near-field inverse problems in elastodynamics

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INVERSE PROBLEMS 2004年第3期20卷 713-736页

作者： Fata, SN Guzina, BB Univ Minnesota Dept Civil Engn Minneapolis MN 55455 USA

yThe problem of reconstructing underground obstacles from near-field, surface seismic measurements is investigated within the framework of a linear sampling method. Although the latter approach has been the subject of mounting attention in inverse acoustics dealing with far-field wave patterns in infinite domains, there have apparently not been any attempts to apply this new method to the interpretation of near-field elastic wave forms such as those relevant to the detection of subterranean objects. Aimed at closing this gap, a three-dimensional inverse analysis of elastic waves scattered by an obstacle (or a system thereof), manifest in the surface ground motion patterns, is formulated as a linear integral equation of the first kind whose solution becomes unbounded in the exterior of the hidden scatterer. To provide a comprehensive theoretical foundation for this class of imaging solutions, generalization of the linear sampling method to near-field elastodynamics and semi-infinite domains is highlighted in terms of its key aspects. A set of numerical examples is included to illustrate the performance of the method. On replacing the featured elastodynamic half-space Green function by its free-space counterpart, the proposed study is directly applicable to infinite media as well.

关键词： .far field Elastic waves half-space scattered semi-in OBSTACLES dealing ELASTODYNAMICS first kind linear sampling linear integral becomes unbounded scatterer field inverse field elastic

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The linear sampling method for sparse small aperture data

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APPLICABLE ANALYSIS 2016年第8期95卷 1599-1615页

作者： Guo, Y. Monk, P. Colton, D. Harbin Inst Technol Dept Math Harbin 150006 Peoples R China Univ Delaware Dept Math Sci Newark DE 19716 USA

In an effort to improve the performance of the linear sampling method in situations involving sparse data-sets, this method in inverse scattering has recently been extended from the frequency domain to the time domain. In this paper, we consider the relative merits of the time and multifrequency linear sampling methods for sparse, limited aperture, and data-sets. Among our conclusions are that, for limited aperture measurements single-frequency data can fail to reconstruct the scatterer, whereas both time and multifrequency domain data perform satisfactorily. On the other hand, if the aperture is too small all the sampling methods fail and increasing the number of measurements in a fixed size aperture is of no help.

关键词： linear sampling inverse scattering multifrequency time domain 34L25 65L09

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The linear sampling method in inverse electromagnetic scattering /

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2011年

作者： Cakoni Fioralba.

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Elastic scatterer reconstruction via the adjoint sampling method

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SIAM JOURNAL ON APPLIED MATHEMATICS 2007年第5期67卷 1330-1352页

作者： Fata, S. Nintcheu Guzina, B. B. Univ Minnesota Dept Civil Engn Minneapolis MN 55455 USA Oak Ridge Natl Lab Comp Sci & Math Div Oak Ridge TN USA

An inverse problem dealing with the reconstruction of voids in a uniform semi-infinite solid from near-field elastodynamic waveforms is investigated via the linear sampling method. To cater to active imaging applications that are characterized by a limited density of illuminating sources, existing formulation of the linear sampling method is advanced in terms of its adjoint statement that features integration over the receiver surface rather than its source counterpart. To deal with an ill-posedness of the integral equation that is used to reconstruct the obstacle, the problem is solved by alternative means of Tikhonov regularization and a preconditioned conjugate gradient method. Through a set of numerical examples, it is shown (i) that the adjoint statement elevates the performance of the linear sampling method when dealing with scarce illuminating sources, and (ii) that a combined use of the existing formulation together with its adjoint counterpart represents an effective tool for exposing an undersampling of the experimental input, e. g., in terms of the density of source points used to illuminate the obstacle.

关键词： inverse scattering elastic waves near-field waveforms linear sampling

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Identifying scattering obstacles by the construction of nonscattering waves

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SIAM JOURNAL ON APPLIED MATHEMATICS 2007年第1期68卷 271-291页

作者： Luke, D. Russell Devaney, Anthony J. Univ Delaware Dept Math Sci Newark DE 19716 USA Northeastern Univ Dept Elect & Comp Engn Boston MA 02115 USA

There are many methods for identifying the shape and location of scatterers from far field data. We take the view that the connections between algorithms are more illuminating than their differences, particularly with regard to the linear sampling method [D. Colton and A. Kirsch, Inverse Problems, 12 (1996), pp. 383-393], the point source method [R. Potthast, Point Sources and Multipoles in Inverse Scattering Theory, Chapman & Hall, London, UK, 2001], and the MUSIC algorithm [A. J. Devaney, IEEE Trans. Antennas and Propagation, 53 (2005), pp. 1600-1610]. Using the first two techniques we show that, for a scatterer with Dirichlet boundary conditions, there is a nontrivial incident field that does not generate a scattered field. This incident. field, written as an expansion of eigenfunctions of the far field operator, is used in the MUSIC algorithm to image the shape and location of the obstacle as those points z where the incident field is orthogonal to the far field pattern due to a point source located at z. This has two intriguing applications, one for inverse scattering and the other for signal design. Numerical examples demonstrate these ideas.

关键词： inverse scattering MUSIC linear sampling point source method

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Reconstruction of a grounded object in an electrostatic halfspace with an indicator function

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INVERSE PROBLEMS IN SCIENCE AND ENGINEERING 2007年第6期15卷 585-600页

作者： van Berkel, C. Lionheart, W. R. B. Philips Res Labs Redhill RH1 5HA Surrey England Univ Manchester Sch Math Manchester M60 1QD Lancs England

This article explores the use of capacitance measurements made between electrodes embedded in or around a display surface, to detect the position, orientation and shape of hands and fingers. This is of interest for unobtrusive 3D gesture input for interactive displays, so called touch- less interaction. The hand is assumed to be grounded and formally the problem is a Cauchy problem for the Laplace equation in which Cauchy data on the boundary partial derivative H (the display surface) is used to reconstruct the zero potential contour of the unknown object D (the hand). The problem is solved with the so-called factorisation method developed for acoustic scattering and electrostatic problems. In the factorisation method, a test function g(z) is used to characterise points z is an element of D double left right arrow g(z) is an element of Rd(Lambda(1/2)(D)), in which Lambda(D): L-2 (partial derivative H) -> L-2 (partial derivative H) is the Dirichlet to Neumann map on the display surface. We demonstrate a suitable test function g(z) appropriate to the boundary conditions present here. In the application, Lambda(D) is obtained from measurements at finite precision as a finite matrix and the calculation of parallel to Lambda(-1/2)(D) g(z) parallel to(2) is implicitly regularised. The resulting level set P(z) is finite and differentiable everywhere. The level representing the object partial derivative D is found through minimising the cost function. Numerical simulations demonstrate that for realistic electrode layouts and noise levels the method provides good reconstruction. The application of explicit regularisation filters can be beneficial and allows a trade-off between resolution and stability.

关键词： Laplace equation inverse boundary factorisation method linear sampling capacitance measurements interactive displays

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A Low-Power Capacitive Charge Pump Based Pipelined ADC

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IEEE JOURNAL OF SOLID-STATE CIRCUITS 2010年第5期45卷 1016-1027页

作者： Ahmed, Imran Mulder, Jan Johns, David A. Univ Toronto Dept Elect & Comp Engn Toronto ON M5S 3G4 Canada Broadcom Netherlands Bunnik Netherlands

A low-power pipelined ADC topology is presented which uses capacitive charge pumps, source-followers, and digital calibration to eliminate the need for power-hungry opamps to achieve good linearity in a pipelined ADC. The differential charge pump technique achieves 10-bit linearity, and does not require an explicit common-mode-feedback circuit. The ADC was designed to operate at 50 MS/s in a 1.8 V, 0.18 mu m CMOS process, where measured results show the peak SNDR and SFDR of the ADC to be 58.2 dB (9.4 ENOB), and 66 dB respectively. The ADC consumes 3.9 mW for all active circuitry and 6 mW for all clocking and digital circuits.

关键词： ADC charge pump CMOS common-mode-feedback foreground calibration linear sampling low-power opampless pipelined

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Peter Monk and inverse scattering theory

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2017年第11期74卷 2640-2644页

作者： Colton, David Univ Delaware Dept Math Sci Newark DE 19716 USA

Peter Monk has made numerous significant contributions to the field of inverse scattering theory. In the following I try to highlight Peter's most significant achievements in this area with emphasis on the renaissance that took place in the mathematical and numerical treatment of inverse scattering problems that began in the mid 1980s. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Inverse scattering linear sampling

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