Modeling of ultrasonic scattering experiments with applications to system and transducer characterization
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The voltage signal output by the receiver electronics, which represents the observable quantity in an ultrasonic scattering experiment, is written as a product, in the frequency domain, of two factors: the system efficiency and the scattering coefficient. The system efficiency represents the combined electrical properties of both the generator and receiver electronics and is a function of frequency only. The scattering coefficient represents the acoustic nature of the experiment (the radiation, propagation, scattering and reception of ultrasonic waves) and depends on the distributed field properties of the transducers involved and their locations and orientations, on the number and type of scattering obstacles and their locations and orientations, on the acoustic properties of the media through which the waves travel, and on the nature and shape of any interfaces through which the waves pass. Based on a generalized principle of electroacoustic reciprocity, formulae are developed for the evaluation of the scattering coefficient. The most general of these involve an integration over either the volume or the surface of the scattering obstacle. More specific formulae are also developed which express the scattering coefficient in terms of either the spherical wave transition matrix or the plane wave scattering amplitude of the obstacle;In order to demonstrate the use of the formulae developed, the calculation of the scattering coefficient is considered for two common ultrasonic scattering experiments. The first experiment involves the pulse-echo scattering from an infinite, flat elastic plate immersed in water. This arrangement is often used for the measurement of the velocity and attenuation of elastic waves, and also as a reference experiment for the determination of the system efficiency. The second experiment involves the pulse-echo scattering from an elastic sphere immersed in water. Particular attention is given to the specular reflection component of the scattering, which is demonstrated to be approximately equivalent to a point measurement of the pressure field radiated by the transducer. This approximation is subsequently used as the basis for obtaining experimental data for transducer characterization. The characterization itself is based on expanding in a set of basis functions, each weighted by an unknown coefficient, the normal velocity profile across the plane flush with the face of the probe. Values for the coefficients are obtained by determining the best fit between the experimental pressure data and the pressure calculated from the assumed velocity profile. Results are presented for two commercially manufactured immersion transducers, one planar (unfocused) and the other focused.