Effect of changing the transmit aperture on the spatial coherence of backscatter for the nonlinearly generated second harmonic

The present work measures the effective apodizations for the fundamental and second harmonic and uses the Van Cittert-Zernike theorem to predict the spatial coherence of the second harmonic portion of backscatter. Two-dimensional pseudo-array scans of a transverse cross section of the finite amplitude ultrasonic fields generated by rectangular and circular apertures were performed with a hydrophone. Three transmit apodization functions were investigated: rectangular, Riesz, and trapezoidal. An effective apodization was obtained by backpropagating the values measured from within the transmit focal zone using a linear angular spectrum approach. In all cases the effective apodization at 2f was narrower than the transmit apodization. Our results demonstrate that choices of apodization can be identified that yield better spatial coherence at the second harmonic than at the fundamental.