Abstract
A new hybrid scattering series is derived that incorporates as special cases both the Born and Rytov scattering series, and includes a parameter so that the behavior can be continuously varied between the two series. The parameter enables the error to be shifted between the Born and Rytov error terms to improve accuracy. The linearized hybrid approximation is derived as well as its condition of validity. Higher order terms of the hybrid series are also found. Also included is the integral equation that defines the exact solution to the forward scattering problem as well as its Fréchet derivative, which is used for the solution of inverse multiple scattering problems. Finally, the linearized hybrid approximation is demonstrated by simulations of inverse scattering off of uniform circular cylinders, where it is shown that the hybrid approximation achieves smaller error than either the Born or Rytov approximations alone.
Highlights
The mathematics of inverse scattering problems is important to optical imaging and microscopy, medical imaging, radar, acoustics, geophysics, and many other disciplines
Inverse scattering is the inference of properties of an inhomogeneous medium from detection of waves that are scattered by the medium
This work presents a new series that synthesizes two well-known scattering series into one. It is shown how two approximations typically used for linearized inverse scattering, the Born and Rytov approximations, are two extremes of a more generalized family of hybrid approximations, some of which can achieve better accuracy for particular inverse scattering problems than either the Born or Rytov approximations alone
Summary
The mathematics of inverse scattering problems is important to optical imaging and microscopy, medical imaging, radar, acoustics, geophysics, and many other disciplines. Such a generalized definition of the complex phase may be useful in inverse scattering problems where multiple scattering can not be neglected It will be shown a complex phase defined with an intermediate value of n can be used to incorporate both the Born and Rytov models in the search for a solution to inverse scattering problems. This will add a degree of flexibility that may enable inverse scattering problems to be solved where the scatterer has high contrast and large extent For this reason, results pertaining to the application of the hybrid approximation to multiple scattering methods such as higher order terms of the hybrid series are included in this work.
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