Wigner distribution of a transducer beam pattern within a multiple scattering formalism for heterogeneous solids

Journal of the Acoustical Society of America

Volumn 122, Issue 4, 2007, Pages 2009-2021

  Ghoshal, Goutam ^a   Turner, Joseph A ^a   Weaver, Richard L ^b  

^a UNIVERSITY OF NEBRASKA LINCOLN   (United States)

^b United States of America   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACOUSTIC WAVE SCATTERING; MATHEMATICAL MODELS; MICROSTRUCTURE; POLYCRYSTALLINE MATERIALS; WAVE EQUATIONS;

SCATTERING MODELS; SPECTRAL ENERGY DENSITY; TRANSDUCER BEAM PATTERN; WIGNER DISTRIBUTION;

ULTRASONIC MEASUREMENT;

CRYSTALLIN;

ACCURACY; ARTICLE; ENERGY; MATHEMATICAL COMPUTING; MEASUREMENT; NORMAL DISTRIBUTION; PRIORITY JOURNAL; QUANTITATIVE ANALYSIS; SOLID; STOCHASTIC MODEL; STRUCTURE ANALYSIS; TRANSDUCER; ULTRASOUND;

EID: 34848853831     PISSN: 00014966     EISSN: None     Source Type: Journal    
DOI: 10.1121/1.2773989     Document Type: Article

References (61)

1. A. K. Holmes, R. E. Challis, and D. J. Wedlock, " A wide bandwidth study of ultrasound velocity and attenuation in suspensions: Comparison of theory with experimental measurements., " J. Colloid Interface Sci. 156, 261-268 (1993).
2. M. S. Greenwood, J. L. Mai, and M. S. Good, " Attenuation measurements of ultrasound in a Kaolin-Water slurry: A linear dependence on frequency., " J. Acoust. Soc. Am. 94, 908-916 (1993).
3. J. M. Hovem and G. D. Ingram, " Viscous attenuation of sound in saturated sand., " J. Acoust. Soc. Am. 66, 1807-1812 (1979).
4. C. M. Sayers and R. L. Grenfell, " Ultrasonic propagation through hydrating cements., " Ultrasonics 31, 147-153 (1993).
5. M. Biot, " Theory of propagation of elastic waves in a fluid saturated porous solid I., " J. Acoust. Soc. Am. 0001-4966 10.1121/1.1908239 28, 168-178 (1956); M. Biot, " Theory of propagation of elastic waves in a fluid saturated porous solid II., " J. Acoust. Soc. Am. 28, 179-191 (1956).
6. M. Biot, " Theory of propagation of elastic waves in a fluid saturated porous solid I., " J. Acoust. Soc. Am. 0001-4966 10.1121/1.1908239 28, 168-178 (1956); M. Biot, " Theory of propagation of elastic waves in a fluid saturated porous solid II., " J. Acoust. Soc. Am. 28, 179-191 (1956).
7. D. Wu, Z. W. Qian, and D. Shao, " Sound attenuation in a coarse granular medium., " J. Sound Vib. 162, 529-535 (1993).
8. R. C. Courtney and L. Mayer, " Acoustic properties of fine grained sediments., " J. Acoust. Soc. Am. 93, 3193-3200 (1993).
9. L. Schwartz and T. J. Plona, " Ultrasonic propagation in close packed disordered suspensions., " J. Appl. Phys. 55, 3971-3977 (1984).
10. H. Tavossi and F. Cohen-Tenoudji, " Ultrasonic investigation of contact surfaces between grains in random granular media. Effects of variable compression., " Proceedings of Ultrasonics International Conference, Vienna,, 1993, pp. 347-350.
11. L. Tsang, J. A. Kong, and T. Habashy, " Multiple scattering of acoustic waves by random distributions of discrete spherical scatterers., " J. Acoust. Soc. Am. 71, 552-558 (1982).
12. J. Liu, L. Ye, D. Weitz, and P. Sheng, " Novel acoustic excitations in suspensions of hard sphere colloids., " Phys. Rev. Lett. 65, 2602-2605 (1990).
13. R. L. Weaver, " Diffuse field decay for materials characterization., " in Solid Mechanics Research for Quantitative Non-Destructive Evaluation, edited by, J. D. Achenbach, and, Y. Rajapakse, (Martinus Nijhoff, The Hague, 1987), pp. 425-434.
14. C. B. Guo, P. Holler, and K. Goebbels, " Scattering of ultrasonic waves in anisotropic polycrystalline metals., " Acustica 59, 112-120 (1985).
15. R. L. Weaver, W. Sachse, K. Green, and Y. Zhang, " Diffuse ultrasound in polycrystalline solids., " in Proceedings of Ultrasonics International '91 (Butterworth-Heinemann, Oxford, UK, 1991), pp. 507-510.
16. R. L. Weaver, " Ultrasonic diffuse field measurements of grain size., " in Non-Destructive Testing and Evaluation in Manufacturing and Construction, edited by, H. L. M. D. Reis, (Hemisphere, New York, 1990), pp. 425-434.
17. R. L. Weaver, " Diffusivity of ultrasound in polycrystals., " J. Mech. Phys. Solids 38, 55-86 (1990).
18. F. J. Margetan, T. A. Gray, and R. B. Thompson, " A technique for quantitative measuring microstructurally induced ultrasonic noise., " in Review of Progress in Quantitative NDE, edited by, D. O. Thompson, and, D. E. Chimenti, (Plenum, New York, 1991), Vol. 10, pp. 1721-1728.
19. R. L. Weaver, " Anderson localization of ultrasound., " Wave Motion 12, 129-142 (1990).
20. R. L. Weaver, " Diffuse waves in finite plates., " J. Sound Vib. 94, 319-335 (1984).
21. R. L. Weaver, " Laboratory studies of diffuse waves in plates., " J. Acoust. Soc. Am. 79, 919-923 (1986).
22. J. A. Turner and R. L. Weaver, " Time dependence of multiply scattered diffuse ultrasound in polycrystalline media., " J. Acoust. Soc. Am. 97, 2639-2644 (1995).
23. J. A. Turner and R. L. Weaver, " Radiative transfer of ultrasound., " J. Acoust. Soc. Am. 96, 3654-3674 (1994).
24. J. A. Turner and R. L. Weaver, " Radiative transfer and multiple scattering of diffuse ultrasound in polycrystalline media., " J. Acoust. Soc. Am. 96, 3675-3683 (1994).
25. R. L. Weaver and W. Sachse, " Diffusion of ultrasound in a glass bead slurry., " J. Acoust. Soc. Am. 97, 2094-2102 (1995).
26. A. Tourin, M. Fink, and A. Derode, " Multiple scattering of sound., " Waves Random Media 10, R31-R60 (2000).
27. P. Anugonda, J. S. Wiehn, and J. A. Turner, " Diffusion of ultrasound in concrete., " Ultrasonics 39, 429-435 (2001).
28. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).
29. L. Tsang, J. A. Kong, and R. T. Shin, Theory of Microwave Remote Sensing (Wiley-Interscience, New York, 1985).
30. L. Tsang, J. Kong, and K. Ding, Scattering of Electromagnetic Waves: Theory and Applications (Wiley Interscience, New York, 2000).
31. L. Tsang and J. Kong, Scattering of Electromagnetic Waves: Advanced Topics (Wiley Interscience, New York, 2001).
32. 3D Radiative Transfer in Cloudy Atmosphere, edited by, A. Marshak, and, A. B. Davis, (Springer, Berlin, 2005).
33. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering (Cambridge University Press, Cambridge, 2006).
34. B. Davison, Neutron Transport Theory (Oxford-Clarendon Press, Oxford, 1957).
35. K. M. Case and P. F. Zweifel, Linear Transport Theory (Addison-Wesley, Reading, 1967).
36. G. I. Bell and S. Glasstone, Nuclear Transport Theory (Van Nostrand, New York, 1970).
37. L. Ryzhik, G. Papanicolaou, and J. B. Keller, " Transport equations for elastic and other waves in random media., " Wave Motion 24, 327-370 (1996).
38. N. Tŕgour̀s, R. Hennino, C. Lacombe, N. M. Shapiro, L. Margerin, M. Campilo, and B. A. V. Tiggelen, " Multiple scattering of seismic waves., " Ultrasonics 40, 269-274 (2002).
39. A. E. Malcom, J. A. Scales, and B. A. V. Tiggelen, " Extracting the Green function from diffuse, equipartioned waves., " Phys. Rev. E 70, 015601 (2004).
40. N. Tŕgour̀s and B. A. V. Tiggelen, " Generalized diffusion equation for multiple scattered elastic waves., " Waves Random Media 12, 21-38 (2002).
41. N. P. Tŕgour̀s and B. A. V. Tiggelen, " Quasi-two-dimensional transfer of elastic waves., " Phys. Rev. E 66, 036601 (2002).
42. S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).
43. L. Cohen, Time-Frequency Analysis (Prentice Hall, Englewood Cliffs, NJ, 1995).
44. E. Wigner, " On the quantum correction for thermodynamic equilibrium., " Phys. Rev. 40, 749-759 (1932).
45. R. L. Weaver, " The effect of an undamped finite degree of freedom 'fuzzy' substructure: Numerical solutions and theoretical discussion., " J. Acoust. Soc. Am. 100, 3159-3164 (1996).
46. U. Frisch, " Wave propagation in random media., " in Probabilistic Methods in Applied Mathematics, edited by, A. T. Barucha-Reid, (Academic, New York, 1968), Vol. 1, pp. 75-198.
47. P. J. Loughlin and L. Cohen, " A Wigner approximation for wave propagation (L)., " J. Acoust. Soc. Am. 118, 1268-1271 (2005).
48. L. Borcea, G. Papanicolaou, and C. Tsogka, " Adaptive interferometric imaging in clutter and optimal illumination., " Inverse Probl. 22, 1405-1436 (2006).
49. D. T. Smithey, M. Beck, and M. G. Raymer, " Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: Application to squeezed states and the vacuum., " Phys. Rev. Lett. 70, 1244-1247 (1993).
50. A. Wax, S. Bali, and J. E. Thomas, " Time-resolved phase-space distribution for light backscattered from a disordered medium., " Phys. Rev. Lett. 85, 66-69 (2000).
51. F. Reil and J. E. Thomas, " Observation of phase conjugation of light arising from enhanced backscattering in a random media., " Phys. Rev. Lett. 95, 143903 (2005).
52. R. B. Thompson and T. A. Gray, " A model relating ultrasonic scattering measurement through liquid-solid interfaces to unbounded medium scattering amplitudes., " J. Acoust. Soc. Am. 74, 1279-1290 (1983).
53. R. B. Thompson and E. F. Lopes, " The effects of focusing and refraction on Gaussian ultrasonic beams., " J. Nondestruct. Eval. 4, 107-123 (1984).
54. B. D. Cook and W. J. Arnoult III, " Gaussian-Laguerre/Hermite formulation for the nearfield of an ultrasonic transducer., " J. Acoust. Soc. Am. 59, 9-11 (1976).
55. A. D. Kim and A. Ishimaru, " Optical diffusion of focused beam wave pulse in discrete random media., " Proc. SPIE 3914, 423-434 (2000).
56. J. A. Turner, " Elastic wave propagation and scattering in heterogeneous, anisotropic media: Textured polycrystalline materials., " J. Acoust. Soc. Am. 106, 541-552 (1999).
57. R. B. Thompson, " Elastic wave propagation in random polycrystals: Fundamentals and application to nondestructive evaluation., " in Imaging of Complex Media with Acoustic and Seismic Waves, Topics in Applied Physics, edited by, M. Fink,,, W. A. Kuperman,,, J. Montagner,, and, A. Tourin, (2002), Vol. 84, pp. 233-257.
58. F. J. Margetan, P. Haldipur, L. Yu, and R. B. Thompson, " Looking for multiple scattering effects in backscattered ultrasonic grain noise from jetengine nickel alloys., " Review of Quantitative Nondestructive Evaluation, edited by, D. O. Thompson, and, D. E. Chimenti,, (American Institute of Physics, Melville, New York, 2005), Vol. 24, pp. 75-82.
59. F. J. Margetan, R. Roberts, and R. B. Thompson, " Estimates of signal-to-microstructural-noise ratios in ultrasonic inspections of metals., " Review of Quantitative Nondestrictive Evaluation, edited by, D. O. Thompson, and, D. E. Chimenti,, (American Institute of Physics, Melville, NY, 2006), Vol. 25, pp. 1193-1200.
60. Matlab, The Language of Technical Computing (The Math Works, Inc., Natick, MA, 2001).
61. Wolfram Research, I., Mathematica, version 4.0 (Wolfram Research, Inc., Champaign, IL, 1999).