Phased Array Beam Modeling Using a Discretely Orthogonal Gaussian Aperture Basis

A discretely orthogonal basis set is constructed from Gaussian functions of complex exponent. The basis set is then used in solving the Green function/boundary integral formulation of ultrasonic beam transmission through a water/solid interface, where ray theory is used to evaluate the Green function. Properties of the Gaussian function yield a highly efficient computational algorithm. It is outlined how the resulting algorithm eliminates problems associated with ray theory focusing caustics.