Spatial coherence of the nonlinearly generated second harmonic portion of backscatter for a clinical imaging system

Correlation-based approaches to phase aberration correction rely on the spatial coherence of backscattered signals. The spatial coherence of backscatter from speckle-producing targets is predicted by the auto correlation of the transmit apodization (Van Cittert-Zernike theorem). Work by others indicates that the second harmonic beam has a wider mainlobe with lower sidelobes than a beam transmitted at 2f. The purpose of this paper is to demonstrate that the spatial coherence of backscatter for the second harmonic is different from that of the fundamental, as would be anticipated from applying the Van Cittert-Zernike theorem to the reported measurements of the second harmonic field. Another objective of this work is to introduce the concept of the effective apodization and to verify that the effective apodization of the second harmonic is narrower than the transmit apodization. The spatial coherence of backscatter was measured using three clinical arrays with a modified clinical imaging system. The spatial coherence results were verified using a pseudo-array scan in a transverse plane of the transmitted field with a hydrophone. An effective apodization was determined by backpropagating these values using a linear angular spectrum approach. The spatial coherence for the harmonic portion of backscatter differed systematically and significantly from the auto correlation of the transmit apodization.