Fresnel approximations for acoustic fields of rectangularly symmetric sources

Journal of the Acoustical Society of America

Volumn 121, Issue 6, 2007, Pages 3311-3322

  Mast, T Douglas ^a  

^a University of Cincinnati   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; DIFFRACTION; ERROR ANALYSIS; GAUSSIAN NOISE (ELECTRONIC); NUMERICAL METHODS; VELOCITY DISTRIBUTION;

ERROR FUNCTIONS; FRESNEL APPROXIMATIONS; RADIATED FIELDS; SURFACE VELOCITY; TIME-HARMONIC SOURCES;

ACOUSTIC FIELDS;

ACOUSTICS; ARTICLE; GEOMETRY; PRIORITY JOURNAL; SOUND TRANSMISSION; SURFACE PROPERTY;

ACOUSTICS; MATHEMATICS; MODELS, THEORETICAL; RHEOLOGY; SOUND; SOUND LOCALIZATION; ULTRASONICS; ULTRASONOGRAPHY;

EID: 34249914231     PISSN: 00014966     EISSN: None     Source Type: Journal    
DOI: 10.1121/1.2726252     Document Type: Article

References (45)

1. C. Lafon, F. Prat, J. Y. Chapelon, F. Gorry, J. Margonari, Y. Theillere, and D. Cathignol, " Cylindrical thermal coagulation necrosis using an interstitial applicator with a plane ultrasonic transducer: in vitro and in vivo experiments versus computer simulations., " Int. J. Hyperthermia 16, 508-522 (2000).
2. R. Chopra, M. J. Bronskill, and F. S. Foster, " Feasibility of linear arrays for interstitial ultrasound thermal therapy., " Med. Phys. 27, 1281-1286 (2000).
3. T. D. Mast, I. R. S. Makin, W. Faidi, M. M. Runk, P. G. Barthe, and M. H. Slayton, " Bulk ablation of soft tissue with intense ultrasound: Modeling and experiments., " J. Acoust. Soc. Am. 118, 2715-2724 (2005).
4. Y. Li and J. A. Zagzebski, " A frequency domain model for generating B-mode images with array transducers., " IEEE Trans. Ultrason. Ferroelectr. Freq. Control 46, 690-699 (1999).
5. T. Jansson, T. D. Mast, H. W. Persson, and K. Lindström, " Frequency dependence of speckle in continuous-wave ultrasound with implications for blood perfusion measurements., " IEEE Trans. Ultrason. Ferroelectr. Freq. Control 49, 715-725 (2002).
6. J. A. Jensen, " Simulation of advanced ultrasound systems using Field II., " Proceedings of the 2004 IEEE International Symposium on Biomedical Imaging, Arlington, VA, April 2004, pp. 636-639.
7. Y.-T. Shen and J. C. Lacefield, " First-order speckle statistics of ultrasound breast images synthesized from a computational anatomy model., " Can. Acoust. 33, 86-87 (2005).
8. M. F. Insana, T. J. Hall, and L. T. Cook, " Backscatter coefficient estimation using array transducers., " IEEE Trans. Ultrason. Ferroelectr. Freq. Control 41, 714-723 (1994).
9. X. Chen, D. Phillips, K. Q. Schwarz, J. G. Mottley, and K. J. Parker, " The measurement of backscatter coefficient from a broadband pulse-echo system: A new formulation., " IEEE Trans. Ultrason. Ferroelectr. Freq. Control 44, 515-525 (1997).
10. T. T. Jansson, T. D. Mast, and R. C. Waag, " Measurements of differential scattering cross-section using a ring transducer., " J. Acoust. Soc. Am. 103, 3169-3179 (1998).
11. T. L. Szabo, Diagnostic Ultrasound Imaging: Inside Out (Elsevier, Burlington, MA, 2004), Chap..
12. P. R. Stepanishen and K. C. Benjamin, " Forward and backward projection of acoustic fields using FFT methods., " J. Acoust. Soc. Am. 71, 803-812 (1982).
13. E. G. Williams and J. D. Maynard, " Numerical evaluation of the Rayleigh integral for planar radiators using the FFT., " J. Acoust. Soc. Am. 72, 2020-2030 (1982).
14. P. R. Stepanishen, " The time-dependent force and radiation impedance on a piston in a rigid infinite planar baffle., " J. Acoust. Soc. Am. 49, 841-849 (1971).
15. J. C. Lockwood and J. G. Willette, " High-speed method for computing the exact solution for the pressure variations in the nearfield of a baffled piston., " J. Acoust. Soc. Am. 53, 735-741 (1973).
16. J. L. San Emeterio and L. G. Ullate, " Diffraction impulse-response of rectangular transducers., " J. Acoust. Soc. Am. 92, 651-662 (1992).
17. A. Neild and D. A. Hutchins, " A theoretical model for a finite-size acoustic receiver., " J. Acoust. Soc. Am. 155, 1546-1556 (2004).
18. R. J. McGough, " Rapid calculations of time-harmonic nearfield pressures produced by rectangular pistons., " J. Acoust. Soc. Am. 115, 1934-1941 (2004).
19. P. Faure, D. Cathignol, and J. Y. Chapelon, " On the pressure field of a transducer in the form of a curved strip., " J. Acoust. Soc. Am. 95, 628-637 (1994).
20. K. B. Ocheltree and L. A. Frizzell, " Sound field calculation for rectangular sources., " IEEE Trans. Ultrason. Ferroelectr. Freq. Control 46, 242-248 (1989).
21. C. Lee and P. J. Benkeser, " A computationally efficient method for the calculation of the transient field of acoustic radiators., " J. Acoust. Soc. Am. 96, 545-551 (1994).
22. B. Ü. Karbeyaz, E. L. Miller, and R. O. Cleveland, " Semi-analytical computation of the acoustic field of a segment of a cylindrically concave transducer in lossless and attenuating media., " J. Acoust. Soc. Am. 121, 1226-1237 (2007).
23. J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Co., Greenwood Village, CO, 2005), Chap..
24. A. Freedman, " Sound field of a rectangular piston., " J. Acoust. Soc. Am. 32, 197-209 (1960).
25. T. L. Szabo, " Generalized Fourier transform diffraction theory for parabolically anisotropic media., " J. Acoust. Soc. Am. 63, 28-34 (1978).
26. D. Ding, Y. Zhang, and J. Liu, " Some extensions of the Gaussian beam expansion: Radiation fields of the rectangular and the elliptical transducer., " J. Acoust. Soc. Am. 113, 3043-3048 (2003).
27. B. D. Cook and W. J. Arnoult III, " Gaussian-Laguerre/Hermite formula for the nearfield of an ultrasonic transducer., " J. Acoust. Soc. Am. 59, 9-11 (1976).
28. J. J. Wen and M. A. Breazeale, " A diffraction beam field expressed as the superposition of Gaussian beams., " J. Acoust. Soc. Am. 83, 1752-1756 (1988).
29. A. Sahin and A. C. Baker, " Ultrasonic pressure fields due to rectangular apertures., " J. Acoust. Soc. Am. 96, 552-556 (1994).
30. K. Sha, J. Yang, and W.-S. Gan, " A complex virtual source approach for calculating the diffraction beam field generated by a rectangular planar source., " IEEE Trans. Ultrason. Ferroelectr. Freq. Control 50, 890-897 (2003).
31. A. D. Pierce, Acoustics: An Introduction to its Physical Principles and Applications, 2nd ed. (Acoustical Society of America, Melville, NY, 1989), Chap..
32. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (National Bureau of Standards, Washington, DC, 1972), Chap..
33. S. Zhang and J. Jin, Computation of Special Functions (Wiley, New York, 1996), Chap..
34. S. Wolfram, The Mathematica Book, 4th ed. (Cambridge University Press, New York, 1999), pp. 766, 1125, 1143.
35. T. D. Mast and F. Yu, " Simplified expansions for radiation from a baffled circular piston., " J. Acoust. Soc. Am. 118, 3457-3464 (2005).
36. N. F. Declercq and J. Degneck, " The Laplace transform to describe bounded inhomogeneous waves., " J. Acoust. Soc. Am. 116, 51-60 (2004).
37. M. Greenspan, " Piston radiator: Some extensions of the theory., " J. Acoust. Soc. Am. 65, 608-621 (1979).
38. I. M. Mason, " Anisotropy, diffraction scaling, surface wave lenses, and focusing., " J. Acoust. Soc. Am. 53, 1123-1128 (1973).
39. T. Lawu, M. Tabei, and M. Ueda, " Near-field ultrasonic scattering from a cavity in steel considering the velocity amplitude on the transducer face using an error function model., " J. Acoust. Soc. Am. 104, 1242-1245 (1998).
40. J. Naze Tjøtta and S. Tjøtta, " Nearfield and farfield of pulsed acoustic radiators., " J. Acoust. Soc. Am. 118, 3457-3464 (2005).
41. W. H. Southwell, " Validity of the Fresnel approximation in the near field., " J. Opt. Soc. Am. 71, 7-14 (1998).
42. G. Poppe and C. Wijers, " More efficient computation of the complex error function., " ACM Trans. Math. Softw. 16, 38-46 (1990).
43. J. A. C. Weideman, " Computation of the complex error function., " SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 31, 1497-1518 (1994).
44. I. R. S. Makin, T. D. Mast, W. Faidi, M. M. Runk, P. G. Barthe, and M. H. Slayton, " Miniaturized ultrasound arrays for interstitial ablation and imaging., " Ultrasound Med. Biol. 31, 1539-1550 (2005).
45. J. A. Campbell and R. C. Waag, " Normalization of ultrasonic scattering measurements to obtain average differential scattering cross sections for tissues., " J. Acoust. Soc. Am. 74, 393-399 (1983).