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Inverse Scattering Solutions to the Exact Riccati Wave Equations by Iterative RYTOV Approximations and Internal Field Calculations

A fixed-point iterative method has been applied to solve the Riccati equation for ultrasonic waves. An algorithm is developed to calculate the exact field when an incident plane wave is scattered by a known object, whose refractive index and/or size are so large that the Born or Rytov approximations would not apply. Another algorithm is also developed which reconstructs the scattering potentials from given scattered phases measured by sets of linear detectors. Here, a fixed-point iterative scheme is also used to make the reconstruction as accurate as possible. The simulation results are shown for circularly symmetric cylindrical objects. Limitations of the fixed-point algorithm are demonstrated; a Newton type iterative algorithm without these limitations is suggested.