Gaussian-beam expansions for focused transducers

It is shown that a small set of Gaussian beams can efficiently represent the fields of ideal focused transducers. Each beam in the expression has two complex parameters related to the complex width and complex amplitude of the beam, i.e., four real parameters. For an N-beam expansion, a least-squares minimization algorithm chooses the 4N parameters to match the Gaussian-beam prediction to the data. One set of data is the pressure field calculated exactly with the Rayleigh integral for an unapodized transducer. As few as six beams give a very reasonable match to the data. The number of beams required for a good fit equals the number of lobes to be fit in the example. Another set of data is the pitch-catch voltage measured by two focused transducers facing each other at twice their focal distance and scanned past each other along a line perpendicular to their axes. >