Point Response of a Linear Pulse - Echo Imaging System with Gaussian Transducer

Pulse echo B - Scan imaging systems have been used for years in medical diagnosis. The theroy of such
systems have been investigated by several researchers. In this paper, we introduce a new model for B - Scan
imaging system based on Gaussian type transducer. An imaging system is normally identified by its point response
function. This function describes the image of a single physical point object. Generally, derivation of the point
response requires extensive mathematical operations and complex integrations; and normally it can not be
expressed in closed form. Numerical solution to the problem is not always feasable. In this paper, we present an
approximate, but practical, method for derivation of the point response of a linear pulse echo system in closed
form. The transducer model used here, is assumed to have Gaussian field distribution, and defined by 5
parameters: width, length, center frequency. band width, and the time delay The point response is derived in a
rather simple form, suitable for mally applications. It can accurately represent an imging system with true
Gaussian transducer within the far field region. Also, by proper adjustment of the prameters, this function can be
used as a tool in approximate modelling of non - Gaussian imaging systems.