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On the inverse problem in optical coherence tomography.

Callum M Macdonald1, Simon R Arridge2, Peter R T Munro3

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Retrieving sample refractive index with optical coherence tomography is ill-posed due to limited viewing angles. Both weak scattering and non-linear approaches show solution non-uniqueness, limiting observable data.

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Area of Science:

  • Biomedical Optics
  • Inverse Problems
  • Optical Coherence Tomography

Background:

  • Optical coherence tomography (OCT) is a valuable imaging technique.
  • Retrieving detailed sample properties like refractive index from OCT data presents significant challenges.
  • The inverse problem in OCT is known to be ill-posed, limiting its practical applications.

Purpose of the Study:

  • To investigate the limitations of the inverse problem in retrieving refractive index information using OCT.
  • To compare two distinct approaches for solving the inverse problem: diffraction tomography and a variational method.
  • To illustrate the non-uniqueness and ill-posed nature of the inverse problem, even in non-linear scattering scenarios.

Main Methods:

  • Theoretical analysis using diffraction tomography under a weak scattering approximation.
  • Investigation of the full non-linear inverse problem employing a variational approach.
  • Comparative analysis of solutions obtained from both diffraction-tomography and variational methods using examples.

Main Results:

  • Limited viewing angles in reflection geometry are a primary cause of the ill-posed nature of the inverse problem.
  • Both weak scattering (linear) and strong scattering (non-linear) scenarios exhibit solution non-uniqueness.
  • Observable spatial Fourier components of the sample are restricted to a limited support, irrespective of the scattering strength.

Conclusions:

  • The inverse problem of refractive index retrieval in OCT is fundamentally ill-posed due to geometric limitations.
  • The non-uniqueness of solutions persists across different scattering regimes, impacting the accuracy of reconstructed refractive index maps.
  • Understanding these limitations is crucial for developing more robust OCT-based material characterization techniques.