An analytical prediction of the nonlinear diffractive fields of medical ultrasound tranducers

The nonlinear propagation of ultrasound in medical imaging has recently been exploited to improve image resolution and remove nearfield artifacts generated by overlying tissue structures. The images are formed using the second harmonic energy generated by nonlinear propagation. This propagation can be modeled using the KZK wave equation. The authors present an analytical solution to the KZK equation for a circular piston transducer. The solution is based on the method of slowly changing wave profile and is valid for moderate nonlinearity. The resulting analytical solution provides an easy way to estimate the generation of harmonics in the radiation pattern. Excellent agreement was found between the analytical predictions and experimental results