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Second-order iterative approach to inverse scattering: numerical results

Pierri1, Leone, Persico

  • 1Dipartimento di Ingegneria dell'Informazione, Seconda Universita di Napoli, Aversa, Italy. pierri@unina.it

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
|May 5, 2000
PubMed
Summary

A new iterative algorithm reconstructs dielectric profiles using quadratic inversion, offering improved accuracy over linear methods. This approach enhances dielectric profile function reconstruction from scattered field data.

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Area of Science:

  • Electromagnetics and Optics
  • Computational Physics
  • Inverse Problems

Background:

  • Accurate reconstruction of dielectric profiles is crucial for understanding material properties and electromagnetic wave interactions.
  • Existing linear iterative inversion algorithms face convergence limitations for certain profile functions.

Purpose of the Study:

  • To introduce and validate a novel iterative algorithm for dielectric profile reconstruction.
  • To compare the performance of the proposed quadratic inversion algorithm against traditional linear methods.

Main Methods:

  • Development of an iterative algorithm solving quadratic inversion problems at each step.
  • Second-order approximation of the scattering operator using a reference profile function.
  • Numerical simulations in scalar two-dimensional geometry using far-zone scattered field data.

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Main Results:

  • The proposed quadratic iterative algorithm demonstrates convergence to the actual solution.
  • Linear iterative inversion algorithms show convergence limitations for specific profile function classes.
  • The quadratic model reconstructs a broader class of functions compared to the linear model.

Conclusions:

  • The quadratic iterative algorithm provides a more robust and accurate method for dielectric profile reconstruction.
  • The enhanced approximation in the quadratic model is beneficial for profiles with larger norms.
  • The study confirms the theoretical advantages of the quadratic approach through numerical examples.