The arccos and Lommel formulations—approximate closed-form diffraction corrections

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Title: The arccos and Lommel formulations—approximate closed-form diffraction corrections
Author: Daly, Charles; Rao, Navalgund
Abstract: A closed-form frequency-domain formalism for spatially integrated diffraction corrections is proposed. Spatially integrated diffraction corrections are necessary when trying to characterize material with ultrasonic probing. In the case of piston transducers and point receivers, the Lommel diffraction formulation is used when the excitation is monochromatic, and the arccos diffraction formulation is used when the excitation is impulsive. The Lommel and arccos formulations are usually treated separately; here, they are connected. Specifically, the arccos diffraction formulation and Lommel diffraction formulation are shown to form an approximate Fourier transform pair. Since the Lommel formulation is amenable to closed-form spatial integration, Lommel functions are used to derive diffraction corrections for unfocused piston transducers operating in receiveonly (one-way) mode or transmit/receive (two-way) mode. Results obtained from the proposed closed-form frequency-domain formalism are qualitatively compared with results based on the closed-form time-domain or impulse-response formalism. It will be shown that the proposed frequency-domain formalism has theoretical and practical value. Finally, specific computational considerations are discussed as necessary.
Description: Copyright © 1999 Acoustical Society of America.
Record URI: http://hdl.handle.net/1850/3206
Date: 1999-06

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