Differential forms of the Kramers-Krönig dispersion relations

IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control

Volumn 50, Issue 1, 2003, Pages 68-76

  Waters, Kendall R ^a   Hughes, Michael S ^b   Mobley, Joel ^c   Miller, James G ^a  

^a WASHINGTON UNIVERSITY   (United States)

^b WASHINGTON UNIVERSITY SCHOOL OF MEDICINE   (United States)

^c OAK RIDGE NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; COMPUTER SIMULATION; DIFFERENTIAL EQUATIONS; EIGENVALUES AND EIGENFUNCTIONS; INTEGRAL EQUATIONS; LIQUIDS; MATHEMATICAL TRANSFORMATIONS; POLYMETHYL METHACRYLATES; POLYSTYRENES; ULTRASONIC MEASUREMENT; ULTRASONIC PROPAGATION;

DIFFERENTIAL FORMS; EGG YOLK; KRAMERS-KRONIG DISPERSION RELATIONS;

ULTRASONIC DISPERSION;

CASTOR OIL; POLY(METHYL METHACRYLATE); SILICONE DERIVATIVE;

ALGORITHM; ANIMAL; ARTICLE; BIOLOGICAL MODEL; CHICK EMBRYO; CHICKEN; COMPARATIVE STUDY; ECHOGRAPHY; EGG YOLK; IMAGE ENHANCEMENT; METHODOLOGY; RADIATION SCATTERING; THEORETICAL MODEL; VALIDATION STUDY;

ALGORITHMS; ANIMALS; CASTOR OIL; CHICK EMBRYO; CHICKENS; EGG YOLK; IMAGE ENHANCEMENT; MODELS, BIOLOGICAL; MODELS, THEORETICAL; POLYMETHYL METHACRYLATE; SCATTERING, RADIATION; SILICONES; ULTRASONOGRAPHY;

EID: 0037268701     PISSN: 08853010     EISSN: None     Source Type: Journal    
DOI: 10.1109/TUFFC.2003.1176526     Document Type: Article

References (27)

1. K. R. Waters, M. S. Hughes, J. Mobley, G. H. Brandenburger, and J. G. Miller, "On the applicability of Kramers-Krönig relations for media with attenuation obeying a frequency power law," J. Acoust. Soc. Amer., vol. 108, pp. 556-563, 2000.
2. K. R. Waters, M. S. Hughes, G. H. Brandenburger, and J. G. Miller, "On a time-domain representation of the Kramers-Krönig dispersion relations," J. Acoust. Soc. Amer., vol. 108, pp. 2114-2119, 2000.
3. T. L. Szabo, "Time domain wave equations for lossy media obeying a frequency power law," J. Acoust. Soc. Amer., vol. 96, pp. 491-500, 1994.
4. T. L. Szabo, "Causal theories and data for acoustic attenuation obeying a frequency power law," J. Acoust. Soc. Amer., vol. 97, pp. 14-24, 1995.
5. M. O'Donnell, E. T. Jaynes, and J. G. Miller, "General relationships between ultrasonic attenuation and dispersion," J. Acoust. Soc. Amer., vol. 63, pp. 1935-1937, 1978.
6. M. O'Donnell, E. T. Jaynes, and J. G. Miller, "Kramers-Krönig relationship between ultrasonic attenuation and phase velocity," J. Acoust. Soc. Amer., vol. 69, pp. 696-701, 1981.
7. P. He, "Simulation of ultrasound pulse propagation in lossy media obeying a frequency power law," IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 45, pp. 114-125, 1998.
8. J. Mobley, K. R. Waters, M. S. Hughes, C. S. Hall, J. N. Marsh, G. H. Brandenburger, and J. G. Miller, "Kramers-Krönig relations in ultrasonics: Applications to finite-bandwidth data of encapsulated microbubbles," J. Acoust. Soc. Amer., vol. 108, pp. 2091-2106, 2000.
9. J. B. Bronzan, G. L. Kane, and U. P. Sukhatme, "Obtaining real parts of scattering amplitudes directly from cross section data using derivative analyticity relations," Phys. Lett. B, vol. 49B, pp. 272-276, 1974.
10. N. Akashi, J. Kushibiki, and F. Dunn, "Acoustic properties of egg yolk and albumen in the frequency range 20-400 MHz," J. Acoust. Soc. Amer., vol. 102, pp. 3774-3778, 1997.
11. R. M. Arthur and K. V. Gurumurthy, "A single-pole model for the propagation of ultrasound in soft tissue," J. Acoust. Soc. Amer., vol. 77, pp. 1589-1597, 1985.
12. B. Hosten, "Heterogeneous structure of modes and Kramers-Krönig relationship in anisotropic viscoelastic materials," J. Acoust. Soc. Amer., vol. 104, pp. 1382-1388, 1998.
13. M. S. Hughes, S. M. Handley, and J. G. Miller, "Nearly local Kramers-Krönig relations applied to porous epoxy," in Proc. IEEE Ultrason. Symp., pp. 1041-1045, 1987.
14. D. Zellouf, Y. Jayet, N. Saint-Pierre, J. Tatibouet, and J. C. Baboux, "Ultrasonic spectroscopy in polymeric materials. Application of the Kramers-Krönig relations," J. Appl. Phys., vol. 80, pp. 2728-2732, 1996.
15. J. Heidrich and E. Kazes, "Derivative analyticity relations," Lett. Nuovo Cimento, vol. 12, pp. 365-367, 1975.
16. G. Matthiae, "Proton and antiproton cross-sections at high-energies," Rep. Prog. Phys., vol. 57, pp. 743-790, 1994.
17. J. Fischer and P. Kolár, "Differential dispersion forms of the dispersion integral," Czech. J. Phys. B, vol. 37, pp. 297-311, 1987.
18. P. Kolár and J. Fischer, "On the validity and practical applicability of derivative analyticity relations," J. Math. Phys., vol. 25, pp. 2538-2544, 1984.
19. U. Sukhatme, G. L. Kane, R. Blankenbecler, and M. Davier, "Extensions of the derivative dispersion relations for amplitude analysis," Phys. Rev. D, vol. 12, pp. 3431-3440, 1975.
20. A. F. Martini, M. J. Menon, J. T. S. Paes, and M. J. S. Neto, "Differential dispersion relations and elementary amplitudes in a multiple diffraction model," Phys. Rev. D, vol. 59, p. 116006, 1999.
21. M. J. Menon, A. E. Motter, and B. M. Pimentel, "Differential dispersion relations with an arbitrary number of subtractions: A recursive approach," Phys. Lett. B, vol. 451, pp. 207-210, 1999.
22. L. Schwartz, Mathematics for the Physical Sciences. rev. ed. Paris: Hermann, 1966.
23. H. M. Nussenzveig, Causality and Dispersion Relations. New York: Academic, 1972.
24. E. J. Beltrami and M. R. Wohlers, Distributions and the Boundary Values of Analytic Functions. New York: Academic, 1966.
25. M. J. Lighthill, Introduction to Fourier Analysis and Generalised Functions. 1st ed. Cambridge: Cambridge Univ. Press, 1958.
26. H. B. Dwight, Tables of Integrals and Other Mathematical Data. 4th ed. New York: MacMillan, 1961.
27. K. R. Waters, "On the application of the generalized Kramers-Krönig dispersion relations to ultrasonic propagation," Ph.D. dissertation, Washington University, Saint Louis, MO, 2000.