Differential forms of the Kramers-Krönig dispersion relations.
Differential forms of the Kramers-Krönig dispersion relations provide an alternative to the integral Kramers-Krönig dispersion relations for comparison with finite-bandwidth experimental data. The differential forms of the Kramers-Krönig relations are developed in the context of tempered distributions. Results are illustrated for media with attenuation obeying an arbitrary frequency power law (alpha(omega) = alpha0 + alpha1(absolute value of omega)y). Dispersion predictions using the differential dispersion relations are compared to the measured dispersion for a series of specimens (two polymers, an egg yolk, and two liquids) exhibiting attenuation obeying a frequency power law (1.00 < or = y < or = 1.99), with very good agreement found. For this form of ultrasonic attenuation, the differential Kramers-Krönig dispersion prediction is found to be identical to the (integral) Kramers-Krönig dispersion prediction.
Waters
Kendall R
KR
Laboratory for Ultrasonics, Department of Physics, Washington University, St. Louis, MO 63130-4899, USA.
Hughes
Michael S
MS
Mobley
Joel
J
Miller
James G
JG
D000465:Algorithms; D000818:Animals; D002368:Castor Oil; D002642:Chick Embryo; D002645:Chickens; D004530:Egg Yolk / Q000000981:diagnostic imaging*; D007089:Image Enhancement / Q000379:methods*; D008954:Models, Biological; D008962:Models, Theoretical; D019904:Polymethyl Methacrylate; D012542:Scattering, Radiation; D012828:Silicones; D014463:Ultrasonography / Q000379:methods*
D012828:Silicones; D002368:Castor Oil; D019904:Polymethyl Methacrylate