Photon flux gradients in layered turbid media: application to biological tissues

Estimation of photon flux gradients in biological tissues is necessary in many photobiological studies. A straightforward application of two-flux theories of light propagation in intensely scattering media to biological tissues is in many cases not adequate for two reasons: First biological tissues are layered objects with different absorption and scattering in different layers where there is no possibility of measuring photon fluxes within the object. Second, the multiple reflections at the boundaries make significant contributions to the photon fluxes. This paper presents a procedure for estimating, on the basis of measured transmission and remission, phenomenological absorption and scattering coefficients, the thickness of the layers, and the photon flux gradients in a two-layered tissue. The method, which is based on a combined treatment of the Kubelka-Munk equations for both layers, accounts for multiple reflections and does not require any measurements within the object. An example of application to a green leaf is given.