Spherical scattering of superpositions of localized waves

Power, Des; Donnelly, R.; MacIsaac, Robert

doi:10.1103/physreve.48.1410

Cited by 16 publications

(7 citation statements)

References 13 publications

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“…This property renders them suitable for applications involving parameter characterization using backscattered signals from objects of varying sizes. Along this direction, Donnelly and Power 25 have shown that an acoustical LW pulse backscattered from compressible spheres immersed in water can accurately provide information about the materials as well as the sizes of the spheres.…”

Section: Introductionmentioning

confidence: 99%

Aperture synthesis of time-limited X waves and analysis of their propagation characteristics

Chatzipetros

Shaarawi

Besieris

et al. 1998

The Journal of the Acoustical Society of America

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The feasibility of exciting a localized X-wave pulse from a finite aperture is addressed. Also, the possibility of using a finite-time excitation of a dynamic aperture to generate a finite-energy approximation to an X-wave pulse is explored. The analysis is carried out by using a Gaussian time window to time limit the infinite X-wave initial excitation. Huygens' construction is used to calculate the amplitude of the radiated wave field away from the finite-time source. The decay rate of the peak of the X wave is compared to that of a quasi-monochromatic signal. It is shown that the finite-time X-wave propagates to much farther distances without significant decay. Furthermore, the decay pattern of the radiated X-wave pulse is derived for a source consisting of an array of concentric annular sections. The decay behavior of the radiated pulse is similar to that of an X-wave launched from a finite-time aperture. This confirms the fact that time windowing the infinite energy X-wave excitation is a viable scheme for constructing finite apertures. A discussion of the diffraction limit of the X-wave pulse is also provided.

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Section: Introductionmentioning

confidence: 99%

Aperture synthesis of time-limited X waves and analysis of their propagation characteristics

Chatzipetros

Shaarawi

Besieris

et al. 1998

The Journal of the Acoustical Society of America

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“…Studies of the generation of acoustical and optical localized waves ͑LW͒ [1][2][3][4][5][6][7] and their use in high-resolution imaging and target identification [8][9][10] have advanced considerably in the past few years. Because of their large focusing depths and their wideband spectra, LWs have a potential in detecting objects buried at different depths and identifying wide ranges of the parameters characterizing a detected target.…”

Section: Introductionmentioning

confidence: 99%

“…Because of their large focusing depths and their wideband spectra, LWs have a potential in detecting objects buried at different depths and identifying wide ranges of the parameters characterizing a detected target. 8 A large number of different LW solutions have appeared in literature; they can be divided into two distinct categories. One category consists of solutions based on Brittingham's focus wave modes ͑FWM͒, [11][12][13][14] while the other is based on the X-waves deduced by Lu and Greenleaf.…”

Section: Introductionmentioning

confidence: 99%

Acoustic X-wave reflection and transmission at a planar interface: Spectral analysis

Shaarawi

Besieris

Attiya

et al. 2000

The Journal of the Acoustical Society of America

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The spectral structure of a three-dimensional X-wave pulse incident on a planar surface of discontinuity is examined. Introducing a novel superposition of azimuthally dependent pulsed plane waves, it is shown for oblique incidence that the reflected pulse has a localized wave structure. On the other hand, the transmitted field maintains its localization up to a certain distance from the interface, beyond which it starts disintegrating. An estimate of the localization range of the transmitted pulse is established; also, the parameters affecting the localization range are identified. The reflected and transmitted fields are deduced for X-waves incident from either a slower medium or a faster one. For the former case the evanescent fields in the second medium are calculated and their explicit time dependence is deduced for a normally incident X-wave. Furthermore, at near-critical incidence the transmitted pulse exhibits significant pulse compression and focusing.

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“…Due to the importance of this method, it was noted as one of the predictions of the 21 st century medical ultrasonics in 2000 [83]. After the introduction of X waves in 1991 [41]- [43], these waves have been studied extensively by many investigators [56], [58]- [60], [84]- [118]. There are also some review papers on X waves and their applications [119]- [126].…”

Section: Introductionmentioning

confidence: 99%

Ultrasonic Imaging with Limited‐Diffraction Beams

2007

Localized Waves

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Limited-diffraction beams are a class of waves that may be localized in space and time. Theoretically, these beams are propagation invariant and can propagate to an infinite distance without spreading. In practice, when these beams are produced with wave sources of a finite aperture and energy, they have a very large depth of field, meaning that they can keep a small beam width over a large distance. Because of this property, limited-diffraction beams may have applications in various areas such as medical imaging and tissue characterization. In this paper, fundamentals of limiteddiffraction beams are reviewed and the studies of these beams are put into a unified theoretical framework. Theory of limited-diffraction beams is further developed. New limited-diffraction solutions to Klein-Gordon Equation and Schrodinger Equation, as well as limited-diffraction solutions to these equations in confined spaces are obtained. The relationship between the transformation that converts any solutions to an ( -1)-dimensional wave equation to limited-diffraction solutions of an -dimensional equation and the Lorentz transformation is clarified and extended. The transformation is also applied to the Klein-Gordon Equation. In addition, applications of limited-diffraction beams are summarized. N N

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Spherical scattering of superpositions of localized waves

Cited by 16 publications

References 13 publications

Aperture synthesis of time-limited X waves and analysis of their propagation characteristics

Aperture synthesis of time-limited X waves and analysis of their propagation characteristics

Acoustic X-wave reflection and transmission at a planar interface: Spectral analysis

Ultrasonic Imaging with Limited‐Diffraction Beams

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