A frequency-domain method for implementing the synthetic aperture focusing technique is developed and demonstrated using computer simulation. As presented, the method is well suited to reconstructing ultrasonic reflectivity over a volumetric region of space using measurements made over an adjacent two-dimensional aperture. Extensive use is made of both one- and two-dimensional Fourier transformations to perform the temporal and spatial correlation required by the technique, making the method well suited to general-purpose computing hardware. Results are presented demonstrating both the lateral and axial resolution achieved by the method. The effect of limiting the reconstruction bandwidth is also demonstrated.

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An analysis is presented of the responses of a phase sensitive and a phase insensitive ultrasound receiver detecting a spatially nonuniform pressure distribution. The predicted output of each type of receiver is obtained numerically using a model of wave propagation based upon diffraction theory. Experimental verification of these predictions is obtained using a piezoelectric and an acoustoelectric receiver as a phase sensitive and a phase insensitive detector, respectively. Results are illustrated for transmission measurements of the frequency-dependent attenuation of an irregular plastic plate and for scattering measurements of the observed angular and spatial dependence of scattering from a pair of brass rods.

The acoustoelectric effect (i.e., the interaction of ultrasound with conduction electrons in a piezoelectric semiconductor} provides the basis for the construction of a finite aperture, phase insensitive receiver using a single crystal of cadmium sulfide. In this paper we present a formalism describing the operation of such a receiver. Criteria for the optimization of the device in terms of ultrasonic bandwidth, response time, sensitivity, and electrical and mechanical loading are presented. In an accompanying paper [J. Acoust. Soe. Am. 70, 1377-1386 (1981}], we discuss and demonstrate the merits of using a phase insensitive receiver when measurements of a phase distorted (spatially noncoherent} ultrasonic radiation must be made.