Cross correlation phase aberration estimates with sparse arrays and parallel beamforming

2D arrays and parallel beamforming are useful technologies for 3D scanning. 2D arrays are also considered to be valuable for phase aberration correction. However, many researchers have investigated sparse 2D arrays to limit the number of needed beamforming channels. Therefore, the authors investigate whether sparse 2D arrays and parallel beamforming are compatible with cross correlation based phase aberration estimates. The van Cittert-Zernike theorem is applied to some models of transmit apertures for random and periodic sparse arrays and parallel beamforming. The theoretical results show that these approaches all degrade the performance of the cross correlation phase aberration estimator. The theoretical results are compared to experimental data from sparse 1D arrays, as well as measurements from a broad transmit beam suitable for parallel beam formation. The experimental measurements confirm the theoretical predictions.