An explicit expression for point spread function in Synthetic Transmit Aperture ultrasound imaging

The point spread function (PSF)  is the most essential tool used to describe an imaging system. It can describe the spatial resolution and contrast transfer of an imaging system. There are only a few studies on the PSF of ultrasound imaging systems due to the nature of ultrasound image reconstruction, which is not accessible for theoretical analysis. The primary goal of this paper is to derive an explicit expression for the PSF in Synthetic Transmit Aperture ultrasound imaging. The results were compared with Field II simulation and the previous k-space theoretical paper. The proposed method agrees better with Field II simulation than the k-space method. The proposed theory has less than a 1\%  difference of the maximum spatial frequency, and the k space theory has more than 9\% for the same set of configurations compared to Field II results.