Scaling limits for wave pulse transmission and reflection operators

Garnier, Josselin; Sølna, Knut

doi:10.1016/j.wavemoti.2008.10.002

Cited by 17 publications

(21 citation statements)

References 15 publications

(37 reference statements)

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“…These are classical results (see [20,Chapter 20] and [15]) once the paraxial and white-noise approximations have been proved to be correct, as is the case here. The result on the first-order moment shows that any coherent wave imaging method based on the mean field cannot give good images if the propagation distance is larger than the scattering mean free path…”

Section: The Fundamental Solutionsupporting

confidence: 75%

Imaging through a scattering medium by speckle intensity correlations

Garnier

Sølna

2018

Inverse Problems

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In this paper we analyze an imaging technique based on intensity speckle correlations over incident field position proposed in [J. A. Newmann and K. J. Webb, Phys. Rev. Lett. 113, 263903 (2014)]. Its purpose is to reconstruct a field incident on a strongly scattering random medium. The thickness of the complex medium is much larger than the scattering mean free path so that the wave emerging from the random section forms an incoherent speckle pattern. Our analysis clarifies the conditions under which the method can give a good reconstruction and characterizes its performance. The analysis is carried out in the white-noise paraxial regime, which is relevant for the applications in optics that motivated the original paper.Keywords: Waves in random media, speckle imaging, multiscale analysis. Imaging by speckle intensity correlationsReceived xxxx 20xx; revised xxxx 20xx.

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Section: The Fundamental Solutionsupporting

confidence: 75%

Imaging through a scattering medium by speckle intensity correlations

Garnier

Sølna

2018

Inverse Problems

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“…This model is a simplification of the Helmholtz equation with random index of refraction, it gives the correct statistical structure of the wave field when the propagation distance is larger than the correlation length of the medium which is itself larger than the wavelength and when the typical amplitude of the medium fluctuations is small. The Itô-Schrödinger model can be derived rigorously from the Helmholtz equation by a separation of scales technique in the high-frequency regime [8,9,10]. It is physically relevant and it models many situations, for instance laser beam propagation [1,21], time reversal in random media [2,18], or underwater acoustics [22].…”

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confidence: 99%

Focusing Waves Through a Randomly Scattering Medium in the White-Noise Paraxial Regime

Garnier¹,

Sølna²

2017

SIAM J. Appl. Math.

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When waves propagate through a complex or heterogeneous medium the wave field is corrupted by the heterogeneities. Such corruption limits the performance of imaging or communication schemes. One may then ask the question, Is there an optimal way of encoding a signal so as to counteract the corruption by the medium? In the ideal situation the answer is given by time reversal: for a given target or focusing point, in a first step let the target emit a signal and then record the signal transmitted to the source antenna, time reverse this, and use it as the source trace at the source antenna in a second step. This source will give a sharply focused wave at the target location if the source aperture is large enough. Here we address this scheme in the more practical situation with a limited aperture, time-harmonic signal, and finite-sized elements in the source array. Central questions are then the focusing resolution and signal-to-noise ratio at the target, their dependence on the physical parameters, and the capacity to focus selectively in the neighborhood of the target point and therefore to transmit images. Sharp results are presented for these questions.

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“…However, the framework can be used to analyze also the wave field reflected by a strong interface or the relatively weak reflections generated by the medium heterogeneities. In the context of acoustic waves this is discussed in [26,29,30]. Appendix B.…”

Section: Discussionmentioning

confidence: 99%

“…The second-order moment exhibits a very interesting multiscale behavior and we refer to [30] for a detailed discussion. This second-order moment along with the fourthorder moment play an important role in applications to time reversal and imaging.…”

Section: Statistics Of the Wave In The White-noise Paraxial Approximamentioning

confidence: 99%

White-Noise Paraxial Approximation for a General Random Hyperbolic System

Garnier¹,

Sølna²

2015

Multiscale Model. Simul.

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In this paper we consider a general hyperbolic system subjected to random perturbations which models wave propagation in random media. We consider the paraxial white-noise regime, which is the regime in which the propagation distance is much larger than the diameter of the input beam or source, which is itself much larger than the typical wavelength, and in which the correlation length of the medium is of the same order as the diameter of the input beam or source. We introduce a general framework that allows to consider the general random hyperbolic system. Using invariant imbedding and asymptotic analysis we show how to derive the system of Itô-Schrödinger equations driven by Brownian fields that govern the wave propagation. The form of the diffraction operator and the covariance matrix of the Brownian fields are computed from the eigenvalues and eigenvectors of the unperturbed system and from the two-point statistics of the random fluctuations of the medium. Applications are given for acoustic, elastic, and electromagnetic waves.

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Scaling limits for wave pulse transmission and reflection operators

Cited by 17 publications

References 15 publications

Imaging through a scattering medium by speckle intensity correlations

Imaging through a scattering medium by speckle intensity correlations

Focusing Waves Through a Randomly Scattering Medium in the White-Noise Paraxial Regime

White-Noise Paraxial Approximation for a General Random Hyperbolic System

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