Point Spread Function Formation in Plane-Wave Imaging: A Theoretical Approximation in Fourier Migration

The point spread function (PSF) is often analyzed to determine the image quality of an ultrasound system. The formation of PSF is determined by practical factors, such as transducer aperture, element directivity, apodization, pitch, imaging position, and steering angle. Conventional numerical simulations provide an iterative approach to examine those factors' effects but cannot explain the inherent mechanism of PSF formation. This article presents a theoretical approximation of PSF formation for plane-wave imaging throughout the Fourier-based reconstruction process. Aforementioned factors are incorporated in the theory. The proposed theory is used to analyze the effects of those factors and presents a high degree of consistency with numerical simulations and experiments.