Gaussian-beam modeling of ultrasonic transducers using near-field experimental data
We wish to develop a model for the pitch-catch response of real transducers which is both accurate and efficient. Wen and Breazeale [1, 2] have shown that the fields of a uniformly active, planar disk transducer can be modelled by a small number of coaxial Gaussian beams (eg, 10 or 15). Margetan, Thompson and Gray  have similarly modelled the fields of a uniformly active, planar disk transducer in terms of Hermite Gaussian beams, and further picked the radius of the ideal transducer to match the main lobe of experimental data collected with a very small receiver,to approximate a point probe. Here we use the expansion of Wen and Breazeale and reciprocity to model the pitch-catch response of two transducers facing each other and having parallel axes, as a function of the displacement vector between the two transducers. Further, we fit this pitch-catch model directly to experimental pitch-catch data by choosing the parameters of the Gaussian beams, without assuming that the transducers are uniformly active, planar disks. Finally we show that the model developed by fitting over one set of displacements accurately describes the experiments over a disjoint set.