Precise time-of-flight calculation for 3-D synthetic aperture focusing

Abstract

Abstract-Conventional linear arrays can be used for 3D ultrasound imaging, by moving the array in the elevation direction and stacking the planes in a volume. The point spread function (PSF) is larger in the elevation plane, as the aperture is smaller and has a fixed elevation focus. Resolution improvements in elevation can be achieved by applying synthetic aperture (SA) focusing to the beamformed in-plane RF-data. The method uses a virtual source (VS) placed at the elevation focus for post-beamforming. This has previously been done in two steps, in plane focusing followed by SA post-focusing in elevation, because of a lack of a simple expression for the exact time of flight (ToF). This paper presents a new method for calculating the ToF for a 3D case in a single step using a spherical defocused emission from a linear array. The method is evaluated using both simulated data obtained by Field II and phantom measurements using the RASMUS experimental scanner. For the simulation, scatterers were placed from 20 to 120 mm of depth. A point and a cyst phantom were scanned by translating a 7 MHz linear array in the elevation direction. For a point placed at (25,8, 75) mm relative to the transducer, the mean error between the calculated and estimated ToF is 0.0129 µs (0.09λ), and the standard deviation of the ToF error is 0.0049λ.

Ultrasound Pixel-Based Beamforming With Phase Alignments of Focused Beams

“…integrating data in out-of-focus regions, we apply the VSE calculation to the pre-beamformed signals. In this calculation, we follow suggestions in [6], [10] to discard the data outside the limited angle (regions (II) and (IV) in our analysis). The result is shown in Fig.…”

“…Outside this angle, the wave shape assumption is invalid. The VSE approach therefore requires that we discard these data, which could otherwise benefit the image reconstruction [6], [10]. The lack of a way to incorporate these data may create errors in the B-mode image especially when there is high echogenicity around the focal depth.…”

Three-dimensional synthetic aperture focusing using a rocking convex array transducer

“…The method presented in [21] describes the ToF calculation for a given 3-D-point for a linear array. This method has been implemented for a convex rocking array.…”

“…The effective aperture for a given depth can be calculated using (11), but this will create a complex expression if combined with (13). The effective aperture can also be calculated by approximating the intersection with the acceptance angle by…”

“…This paper presents the feasibility of implementing a direct 3-D time-of-flight (ToF) calculation on a rocking convex array for use with SAF to improve the elevation resolution. The ToF method has previously been used for improving the elevation resolution and contrast for a translated linear array [13]. The method uses the positions of 2 virtual sources (VS) to calculate the ToF in 3-D, but only a single interpolation step, as opposed to two interpolation steps used by previously described methods.…”