Characterization of subwavelength elastic cylinders with the decomposition of the time-reversal operator: Theory and experiment

Minonzio, Jean‐Gabriel; Prada, Claire; Chambers, David H.; Clorennec, Dominique; Fink, Mathias

doi:10.1121/1.1811471

Cited by 24 publications

(38 citation statements)

References 16 publications

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“…[4][5][6][7]15 The derivations in this paper assumed a rigid scatterer. For elastic scatterer, it has been shown, 30,31 in the case of pointlike objects, that additional singular vectors arises, corresponding to dipolar Green's functions. This is probably the case for extended objects as well.…”

Section: Discussionmentioning

confidence: 98%

The prolate spheroidal wave functions as invariants of the time reversal operator for an extended scatterer in the Fraunhofer approximation

Robert

Fink

2009

The Journal of the Acoustical Society of America

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The decomposition of the time reversal operator, known by the French acronym DORT, is widely used to detect, locate, and focus on scatterers in various domains such as underwater acoustics, medical ultrasound, and nondestructive evaluation. In the case of point-scatterers, the theory is well understood: The number of nonzero eigenvalues is equal to the number of scatterers, and the eigenvectors correspond to the scatterers Green's function. In the case of extended objects, however, the formalism is not as simple. It is shown here that, in the Fraunhofer approximation, analytical solutions can be found and that the solutions are functions called prolate spheroidal wave-functions. These functions have been studied in information theory as a basis of band-limited and time-limited signals. They also arise in optics. The theoretical solutions are compared to simulation results. Most importantly, the intuition that for an extended objects, the number of nonzero eigenvalues is proportional to the number of resolution cell in the object is justified. The case of three-dimensional objects imaged by a two-dimensional array is also dealt with. Comparison with previous solutions is made, and an application to super-resolution of scatterers is presented.

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Section: Discussionmentioning

confidence: 98%

The prolate spheroidal wave functions as invariants of the time reversal operator for an extended scatterer in the Fraunhofer approximation

Robert

Fink

2009

The Journal of the Acoustical Society of America

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“…For higher frequencies (or larger targets), additional multipole moments will contribute to the scattered field, increasing the rank of the multistatic response matrix. A similar analysis for the acoustic (scalar) case can be found in references [21,22,28].…”

Section: Decomposition Of the Time-reversal Operatormentioning

confidence: 75%

“…The presence of multiple singular values for point-like targets has been detected experimentally by Minonzio et al [22], and used by Prada and Thomas [23] to resolve closely spaced targets. Chambers and Gautesen [21] showed how the actual number of singular values associated with a small sphere in acoustics depends on the array geometry and the material composition.…”

Section: Introductionmentioning

confidence: 99%

Target characterization using decomposition of the time-reversal operator: electromagnetic scattering from small ellipsoids

Chambers

Berryman

2006

Inverse Problems

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Decomposition of the time-reversal operator for an array, or equivalently the singular value decomposition of the multistatic response matrix, has been used to improve imaging and localization of targets in complicated media. Typically, each singular value is associated with one scatterer even though it has been shown in several cases that a single scatterer can generate several singular values. In earlier papers Chambers and Berryman [1,2] showed that a small spherical scatterer can generate up to six singular values depending on the array geometry and sphere composition.It was shown that the existence and characteristics of multiple singular values for each scatterer can, in principle, be used to determine certain properties of the scatterers, e.g. conducting or non-conducting material. In this paper, we extend this analysis to non-spherical targets and show how orientation information about the target may be obtained from the spectrum of singular values. The general properties of the decomposition for small non-spherical dielectric (and possibly conductive) targets in an electromagnetic field are derived and detailed results are obtained for the specific cases of non-magnetic and perfectly conducting needles and disks. It is shown that scatterer orientation can be estimated by tracking the singular values of a linear array as it is rotated around its midpoint.

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“…The echo spectrum from the sphere was then used to convert recorded echo spectra to target strength. This process was repeated with the nylon monofilament using the scattering model described by Minonzio et al ͑2005͒. To check consistency of the calibration, echo spectra-converted to target strength using each calibration method-were compared and found to be within 3 dB.…”

Section: System Alignment and Calibrationmentioning

confidence: 99%

Classification of live, untethered zooplankton from observations of multiple-angle acoustic scatter

Roberts

Jaffe

2008

The Journal of the Acoustical Society of America

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A broadband, multiple-angle acoustic array was used to classify millimeter to centimeter sized live zooplankton in a laboratory tank. Reflections in the frequency range from 1.5 to 2.5 MHz were recorded from untethered 1-4 mm calanoid copepods and 8-12 mm mysids over an angular range of 0 degrees -47 degrees . A synchronized, coregistered video system recorded animal location and orientation. To highlight differences between animals, a frequency correlation matrix was computed from the observed wide-band power spectra of the scattered sound. Significant differences in the slopes and shapes of the eigenvalue spectra of this matrix were found for mysids versus copepods. These results support the idea that broadband, multiple-angle scatter can be used to classify organisms of different sizes and shapes.

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Characterization of subwavelength elastic cylinders with the decomposition of the time-reversal operator: Theory and experiment

Cited by 24 publications

References 16 publications

The prolate spheroidal wave functions as invariants of the time reversal operator for an extended scatterer in the Fraunhofer approximation

The prolate spheroidal wave functions as invariants of the time reversal operator for an extended scatterer in the Fraunhofer approximation

Target characterization using decomposition of the time-reversal operator: electromagnetic scattering from small ellipsoids

Classification of live, untethered zooplankton from observations of multiple-angle acoustic scatter

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