Riccati equations for scattering matrices on level surfaces

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Abstract

Layer stripping based on the Riccati equation for the scattering matrix is a natural approach to the solution of the inverse scattering problem for the Helmholtz equation. But it has so far failed to work in two and three dimensions. This paper examines a cause of failure and establishes a Riccati equation for the scattering matrix on the level surfaces of the index of refraction. The new Riccati equation overcomes a common drawback shared by the traditional Riccati equations - the waves are unnaturally forced to propagate with a Green's function of an artificially fixed background wave number, and this man-made mismatch will mix and deform the propagating and evanescent modes, which skews the regularization of the backward solve of the Riccati equations for layer stripping.

Original languageEnglish (US)
Pages (from-to)1745-1756
Number of pages12
JournalInverse Problems
Volume21
Issue number5
DOIs
StatePublished - Oct 1 2005

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Mathematical Physics
  • Computer Science Applications
  • Applied Mathematics

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