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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editor: Gregory W. Faris
  • Vol. 4, Iss. 6 — May. 26, 2009

Higher-order perturbation theory for the diffusion equation in heterogeneous media: application to layered and slab geometries

Angelo Sassaroli, Fabrizio Martelli, and Sergio Fantini  »View Author Affiliations


Applied Optics, Vol. 48, Issue 10, pp. D62-D73 (2009)
http://dx.doi.org/10.1364/AO.48.000D62


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Abstract

We apply a previously proposed perturbation theory of the diffusion equation for studying light propagation through heterogeneous media in the presence of absorbing defects. The theory is based on the knowledge of (a) the geometric characteristics of a focal inclusion, (b) the mean optical path length inside the inclusion, and (c) the optical properties of the inclusion. The potential of this method is shown in the layered and slab geometries, where calculations are carried out up to the fourth order. The relative changes of intensity with respect to the unperturbed (heterogeneous) medium are predicted by the theory to within 10% for a wide range of contrasts d Δ μ a (up to d Δ μ a 0.4 0.8 ), where d is the effective diameter of the defect and Δ μ a the absorption contrast between defect and local background. We also show how the method of Padé approximants can be used to extend the validity of the theory for a larger range of absorption contrasts. Finally, we study the possibility of using the proposed method for calculating the effect of a colocalized scattering and absorbing perturbation.

© 2009 Optical Society of America

OCIS Codes
(170.3660) Medical optics and biotechnology : Light propagation in tissues
(170.5280) Medical optics and biotechnology : Photon migration
(170.7050) Medical optics and biotechnology : Turbid media

History
Original Manuscript: September 2, 2008
Revised Manuscript: November 21, 2008
Manuscript Accepted: November 29, 2008
Published: January 15, 2009

Virtual Issues
Vol. 4, Iss. 6 Virtual Journal for Biomedical Optics

Citation
Angelo Sassaroli, Fabrizio Martelli, and Sergio Fantini, "Higher-order perturbation theory for the diffusion equation in heterogeneous media: application to layered and slab geometries," Appl. Opt. 48, D62-D73 (2009)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=ao-48-10-D62

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