Efficient three-dimensional imaging from a small cylindrical aperture

Abstract

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.

Effective ultrasonic virtual sources which can be positioned independently of physical aperture focus positions

“…Specifically, VS2 yielded a higher lateral resolution than a synthesized physical aperture and other virtual sources reported. [9][10][11][13][14][15][16][17][18][19] The high lateral resolution achieved is uniform regardless of the position depth. VS2 also mitigates the physical and electrical limitations of using smaller ultrasound array elements and a smaller pitch, such that a high echo signal-to-noise ratio as well as a high lateral resolution is obtained.…”

“…As shown in Figure 1a, the setting of a virtual source behind the transducer array 8,[13][14][15][16][17][18][19] yields a larger transmitted ultrasound intensity by firing plural elements rather than a physical source as used with the classical synthetic aperture method. In this report, this virtual source is referred to as VS1.…”

“…18 In this report, VS1 is dealt with as a point acoustic source 8 similarly to that originally reported. [13][14][15][16][17][18][19] Then, for the use of the synthetic aperture method, a spherical wave is considered as a generated wave. In this case, ultrasound to be transmitted from or received by the respective physical elements is weighted by decay weights which are determined by the reciprocal of the distance between the virtual source and the respective physical elements (see Figure 1a).…”

“…In this case, ultrasound to be transmitted from or received by the respective physical elements is weighted by decay weights which are determined by the reciprocal of the distance between the virtual source and the respective physical elements (see Figure 1a). Otherwise, the decay weights can also be determined more strictly by using the distances Virtual sources (VS1) set behind physical array elements for gaining a transmitted ultrasound intensity without removing a superficial region from the region of interest (ie, without shortening the axial length of the region of interest); [13][14][15][16][17][18][19] b) Virtual sources 9-12 set at the focus position of a physical aperture; c) Virtual sources (VS2) of which position is independent of physical apertures (ie, an arbitrary position ahead of physical array elements); 8 D) those realized by regular or random scatter material installed in transducers, by a scatter medium put between the transducer and target, or random scattering in a target tissue; 8 e) those (or receivers) realized in null spaces beside the short physical array aperture to obtain a large width for the region of interest and to obtain an arbitrarily shaped field of vision regardless of physical aperture geometry (eg, convex, linear between the point of interest and the physical elements and between the point of interest and the virtual source. Using the superposition theorem, VS1 can also be used for real-time beamforming for imaging and measurements, ie, so-called dynamic focusing and dynamic apodization.…”

“…13,14,17 Applications to other type apertures have also been reported, eg, a small cylindrical aperture. 19 In our case, using the same new viewpoint, another virtual source can also be obtained, and is constructed using an ultrasound random scatter, 2 a diffraction grating, or a hole. 8 That is, an arbitrary position ahead of the physical array elements is also used as a virtual source position, eg, in a target tissue or in some material put between the physical aperture and the target.…”