Ultrasonic Reflectivity Imaging in Three Dimensions: Reconstruction with Spherical Transducer Arrays

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Abstract
Three-dimensional backprojection for reconstructing acoustic reflectivity within a volume is examined. The reflectivity data are acquired by means of a spherical array of point sources-receivers which encloses the object under study. Reconstruction of the image is obtained by back-projecting the recorded pulse-echo data over spherical surfaces in image space. An analytical expression for the point spread function (PSF) generated by the backprojection process has been derived. This expression was evaluated for several different choices of the acoustic pulse: a narrowband pulse, wideband pulse, and two analytically-derived optimum pulses which provide the best sidelobe response and a mainlobe width equal to approximately 0.4Λc, where Λc is the wavelength corresponding to the upper cutoff frequency of the pulse. Excellent agreement was obtained between the theoretical PSF's for the different pulses and those obtained by computer simulation. A number of potential advantages of direct three-dimensional reconstruction relative to two-dimensional tomographic techniques are discussed, including (1) high resolution in three dimensions (2) the possibility of incorporating refraction effects in the reconstruction process (3) reduced sensitivity to limited viewing anglesand (4) improved signal-to-noise ratio (thus minimizing requirements for data redundancy).

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