  Fixed $F$-numbers reduce grating lobe artifacts in fast pulse-echo ultrasound
imaging. Such $F$-numbers result in dynamic receive subapertures whose widths
vary with the focal position. These subapertures, however, ignore useful
low-frequency components in the excluded radio frequency (RF) signals and,
thus, reduce the lateral resolution. Here, we propose a frequency-dependent
$F$-number to simultaneously suppress grating lobe artifacts and maintain the
lateral resolution. This $F$-number, at high frequencies, reduces the receive
subaperture to remove spatially undersampled components of the RF signals and
suppress grating lobes. The $F$-number, at low frequencies, enlarges the
receive subaperture to use the components of all RF signals and maintain the
lateral resolution. Experiments validated the proposed $F$-number and
demonstrated improvements in the contrast and the widths of wire targets of up
to 3.2 % and 12.8 %, respectively.
