Quadratic equalization: a method for producing extended uniform depth of focus in high frame rate medical ultrasound B-scans

This work describes a new and novel method for achieving the beneficial imaging effects that can be obtained from the coherent superposition of multiple firings with a uniform distribution of transmit foci, with a single transmit firing. It is demonstrated that a sine amplitude modulation of the transmit windowing function with an argument quadratic in the transducer coordinates is essentially equivalent to a synthetic image generated from the coherent superposition of an infinite number of firings with their transmit foci uniformly covering the full range of an extended B-scan. Using these methods, simulation results give range compensated peaks of the range energy impulse response (measure of image brightness) that are flat within ∼ ±0.2 dB over the range scan of the B-mode image at fractional bandwidths commensurate with range resolutions down to ∼ 0.25 mm.