Ultrasonic focusing through inhomogeneous media by application of the inverse scattering problem

A new approach is introduced for self-focusing phased arrays through inhomogeneous media for therapeutic and imaging applications. This algorithm utilizes solutions to the inverse scattering problem to estimate the impulse response (Green's function) of the desired focal point(s) at the elements of the array. This approach is a two-stage procedure, where in the first stage the Green's functions is estimated from measurements of the scattered field taken outside the region of interest. In the second stage, these estimates are used in the pseudoinverse method to compute excitation weights satisfying predefined set of constraints on the structure of the field at the focus points. These scalar, complex valued excitation weights are used to modulate the incident field for retransmission. The pseudoinverse pattern synthesis method requires knowing the Green's function between the focus points and the array, which is difficult to attain for an unknown inhomogeneous medium. However, the solution to the inverse scattering problem, the scattering function, can be used directly to compute the required inhomogeneous Green's function. This inverse scattering based self-focusing is noninvasive and does not require a strong point scatterer at or near the desired focus point. It simply requires measurements of the scattered field outside the region of interest. It can be used for high resolution imaging and enhanced therapeutic effects through inhomogeneous media without making any assumptions on the shape, size, or location of the inhomogeneity. This technique is outlined and numerical simulations are shown which validate this technique for single and multiple focusing using a circular array.