Convolutional modeling of diffraction effects in pulse-echo ultrasound imaging.

A model is presented for pulse-echo imaging of three-dimensional, linear, weakly-scattering continuum media by ultrasound array transducers. The model accounts for the diffracted fields of focused array subapertures in both transmit and receive modes, multiple transmit and receive focal zones, frequency-dependent attenuation, and aberration caused by mismatched medium and beamformer sound speeds. For a given medium reflectivity function, computation of a B-scan requires evaluation of a depth-dependent transmit/receive beam product, followed by two one-dimensional convolutions and a one-dimensional summation. Numerical results obtained using analytic expressions for transmit and receive beams agree favorably with measured B-scan images and speckle statistics.