Efficient three-dimensional imaging from a small cylindrical aperture

Small-diameter cylindrical imaging platforms, such as those being considered in the development of in vivo ultrasonic microprobes, pose unique image formation challenges. The curved apertures they provide are incompatible with many of the commonly used frequency-domain synthetic aperture imaging algorithms. At the same time, their frequently small diameters place limits on the available aperture and the angular resolution that may be achieved. We obtain a three-dimensional, frequency-domain imaging algorithm for this geometry by making suitable approximations to the point spread function for wave propagation in cylindrical coordinates and obtaining its Fourier transform by analogy with the equivalent problem in Cartesian coordinates. For the most effective use of aperture, we propose using a focused transducer to place a virtual source a short distance from the probe. The focus is treated as a diverging source by the imaging algorithm, which then forms images on deeper cylindrical shells. This approach retains the simplicity and potential angular resolution of a single element, yet permits full use of the available probe aperture and a higher energy output. Computer simulations and experimental results using wire targets show that this imaging technique attains the resolution limit dictated by the operating wavelength and the transducer characteristics.