12 February 2009 Fourth order perturbation theory for the diffusion equation: continuous wave results for absorbing defects
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Abstract
We show the performance of a proposed perturbation theory of the diffusion equation for studying light propagation in optically heterogeneous media, i.e. characterized by a distribution of the absorption and the reduced scattering coefficient. In different geometries (cylindrical, slab, layered), we study the change of continuous wave intensity due to the presence of focal absorption perturbations. The results obtained with fourth order perturbation theory show a clear improved accuracy with respect to first order calculations for a range of the absorption contrasts of interest in the field of near infrared spectroscopy and diffuse optical tomography. The method of Padè Approximants is used to extend the limits of the proposed perturbation theory to a wider range of absorption contrasts. For validation of the theory, we show comparison with Monte Carlo simulations.
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Angelo Sassaroli, Angelo Sassaroli, Fabrizio Martelli, Fabrizio Martelli, Sergio Fantini, Sergio Fantini, } "Fourth order perturbation theory for the diffusion equation: continuous wave results for absorbing defects", Proc. SPIE 7174, Optical Tomography and Spectroscopy of Tissue VIII, 717402 (12 February 2009); doi: 10.1117/12.809070; https://doi.org/10.1117/12.809070
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