Frequency-Dependent F-Number Suppresses Grating Lobes and Improves the Lateral Resolution in Coherent Plane-Wave Compounding

Ultrafast imaging modes, such as coherent plane-wave compounding (CPWC), increase image uniformity and reduce grating lobe artifacts by dynamic receive apertures. The focal length and the desired aperture width maintain a given ratio, which is called the F-number. Fixed F-numbers, however, exclude useful low-frequency components from the focusing and reduce the lateral resolution. Herein, this reduction is avoided by a frequency-dependent F-number. This F-number derives from the far-field directivity pattern of a focused aperture and can be expressed in closed form. The F-number, at low frequencies, widens the aperture to improve the lateral resolution. The F-number, at high frequencies, narrows the aperture to avoid lobe overlaps and suppress grating lobes. Phantom and in vivo experiments with a Fourier-domain beamforming algorithm validated the proposed F-number in CPWC. The lateral resolution, which was measured by the median lateral full-widths at half-maximum of wires, improved by up to 46.8% and 14.9% in a wire and a tissue phantom, respectively, in comparison to fixed F-numbers. Grating lobe artifacts, which were measured by the median peak signal-to-noise ratios of wires, reduced by up to 9.9 dB in comparison to the full aperture. The proposed F-number thus outperformed F-numbers that were recently derived from the directivity of the array elements.