• DOI:10.1088/0266-5611/22/4/001
• Corpus ID: 800641

Inverse problem in refractive index based optical tomography

@article{Khan2005InversePI,
  title={Inverse problem in refractive index based optical tomography},
  author={Taufiquar R. Khan and Alan Thomas},
  journal={Inverse Problems},
  year={2005},
  volume={22},
  pages={1121-1137}
}

• T. Khan, Alan Thomas
• Published 1 October 2005
• Mathematics, Physics
• Inverse Problems

In optical tomography, conventionally the diffusion approximation to the radiative transport equation (RTE) with a constant refractive index is used to image highly scattering or turbid media. Diffusion optical tomography with a constant refractive index is rather difficult due to the exponential instability of the inverse problem. Therefore, it is beneficial to find a simple yet stable model that adequately describes the physics of radiative transport, for example, refractive index based optical tomography. In this paper, we formulate a refractive index based optical tomography inverse problem based on the diffusion approximation to the RTE with a spatially varying refractive index. We establish formally the theoretical framework for both the forward and the inverse problem. We simulate both the forward and the inverse problem using the finite-element method. We reconstruct the refractive index parameter in our model for the inverse problem. Our simulations indicate that refractive index based optical tomography shows promise at least for the reconstruction of refractive index inclusions with circular geometry.