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 mus (0.09A), and the standard deviation of the ToF error is 0.0049A. SA focusing improves both contrast and resolution. For simulated scatterers at depths of 40 and 70 mm the FWHM is 83.6% and 46.8% of the FWHM without elevation SA focusing. The main-lobe to side-lobe energy ratio (MLSLR) for the scatterers is 32.3 dB and 29.1 dB. The measurement of a PSF phantom at a depth of 65 mm shows a relative FWHM of 27.8%. For an elevation sampling distance of 0.63 mm, the MLSLR for the two simulated scatterers is 26.4 dB and 27.9 dB. For the point phantom the MLSLR is 16.3 dB. If the elevation sampling distance is increased to 0.99 mm, the two simulated scatterers have a MLSLR of 21.1 dB and 15.8 dB respectively, and the point pha- ntom has an MLSLR of 5.2 dB. The cyst phantom shows an improvement of 5.8 dB in contrast to noise ratio, for a 4 mm cyst, when elevation focusing is applied.
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