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A Stable Phantom Material for Optical and Acoustic Imaging
Published on: June 16, 2023
Reflectance of acoustic horns and solution of the inverse problem
Daniel M Rasetshwane1, Stephen T Neely, Jont B Allen
1Boys Town National Research Hospital, 555 North 30th Street, Omaha, Nebraska 68131, USA. daniel.rasetshwane@boystown.org
Abstract:
A method is described for solving the inverse problem of determining the profile of an acoustic horn when time-domain reflectance (TDR) is known only at the entrance. The method involves recasting Webster's horn equation in terms of forward and backward propagating wave variables. An essential feature of this method is a requirement that the backward propagating wave be continuous at the wave-front at all locations beyond the entrance. Derivation of the inverse solution raises questions about the meaning of causality in the context of wave propagation in non-uniform tubes. Exact reflectance expressions are presented for infinite exponential, conical and parabolic horns based on exact solutions of the horn equation. Diameter functions obtained with the inverse solution are a good match to all three horn profiles.
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