Is the Kramers-Kronig causal relationship between ultrasonic attenuation and dispersion maintained when phase aberrations distort the field incident on a phase sensitive aperture?

Abstract

The objective of this investigation was to determine whether the causality-induced link between ultrasonic attenuation and dispersion remains valid when the measured signal loss arises as a consequence of phase cancellation at the face of a phase-sensitive receiver rather than from intrinsic losses within the medium under study. The frequency-dependent apparent attenuation and phase velocity were obtained from through-transmission measurements of two flat and parallel plastic polymer plates, PlexiglasTM and LexanTM, exhibiting an approximately linear with frequency attenuation coefficient and logarithmic with frequency phase velocity. Phase distortion was achieved by machining a step into one side of each plastic plate. Through-transmission measurements were performed in a water tank using 5 MHz center frequency single element planar transmitting and receiving transducers. The causal (Kramers-Kronig) link between apparent phase velocity and the apparent attenuation coefficient in the presence of phase distortion was examined for both plastics over a bandwidth ranging from 3 to 7 MHz. Results demonstrate that the Kramers-Kronig link between the apparent attenuation coefficient and apparent phase velocity dispersion remains causally consistent even in the presence of aberrating media.