F-number optimization for synthetic aperture delay-multiply-and-sum reconstruction

The choices of transmit and receive f-numbers impact both ultrasound image contrast and spatial resolution. Although previous studies have evaluated the impact of receive f-number in delay-and-sum (DAS) plane wave imaging, there has not been a systematic study of f-numbers in DAS or delay-multiply-and-sum (DMAS) synthetic aperture (SA) imaging. In this study, we measured the impact on main lobe to side lobe energy ratio (MSER), generalized contrast-to-noise ratio (gCNR), and spatial resolution when varying receive and transmit f-numbers from 1 to 5 in 0.2 increments in DAS and DMAS reconstructed SA images. A wire target in a water tank and a standard imaging phantom were used to measure these metrics. From the water tank wire target images, higher MSER values were achieved with middle-range transmit f-numbers (2-4) and high receive f-numbers (>4) for both DAS and DMAS. From the phantom contrast target images, DAS produced images with high gCNR when using high transmit f-numbers (>4) and high receive f-numbers (>4). This came at the cost of reduced spatial resolution. DMAS produced images with high gCNR when using low transmit f-numbers (<3) and high receive fnumbers (>4). DMAS was not found to have as severe of a tradeoff in spatial resolution when seeking maximum gCNR. However, gCNR was typically lower for DMAS than DAS. For both DAS and DMAS, point target images had high spatial resolution when using low receive f-numbers (<2). Spatial resolution was typically higher for DMAS than DAS. Hanning apodization was found to produce similar trends as those found with rectangular apodization. These findings give insight on the behaviors of DAS and DMAS SA reconstruction algorithms and could be used to guide f-number selection.