A Closed-Form Expression for the Point Spread Function in Synthetic Transmit Aperture Ultrasound Imaging

The Point Spread Function (PSF) is an essential tool used to characterize the resolution and response of an imaging system. This paper presents, for the first time, closed-form expressions for the PSF in Synthetic Transmit Aperture (STA) ultrasound imaging. The expressions were first derived under the assumption that the imaging depth is much larger than the aperture size and the PSF size, and then improved for the large-aperture configuration. The proposed PSF formulas include the position of the point object explicitly, and therefore are spatially varying. They can be applied to both off-axis locations and near-field regions. Field II simulations validated the PSF expressions. In addition to visual inspections, we used two quantitative metrics — the correlation coefficient and the central frequency of the PSF — to evaluate the agreement between the proposed method and Field II. We also studied the PSF behavior for a large-aperture configuration, where the small-aperture assumption used in the derivation doesn't hold. We found that rescaling the spectrum improved the performance of the proposed method for the large-aperture case. The proposed method can be applied to various applications, such as deconvolution of ultrasound images and quantitative ultrasound imaging.