Recovery of optical parameters in multiple-layered diffusive media: Theory and experiments

Diffuse photon density waves have lately been used both to characterize diffusive media and to locate and characterize hidden objects, such as tumors, in soft tissue. In practice, most biological media of medical interest consist of various layers with different optical properties, such as the fat layer in the breast or the different layers present in the skin. Also, most experimental setups consist of a multilayered system, where the medium to be characterized (i.e., the patient’s organ) is usually bounded by optically diffusive plates. Incorrect modeling of interfaces may induce errors comparable to the weak signals obtained from tumors embedded deep in highly heterogeneous tissue and lead to significant reconstruction artifacts. To provide a means to analyze the data acquired in these configurations, the basic expressions for the reflection and transmission coefficients for diffusive-diffusive and diffusive-nondiffusive interfaces are presented. A comparison is made between a diffusive slab and an ordinary dielectric slab, thus establishing the limiting distance between the two interfaces of the slab for multiple reflections between them to be considered important. A rigorous formulation for multiple-layered (M-layered) diffusive media is put forward, and a method for solving any M-layered medium is shown. The theory presented is used to characterize a two-layered medium from transmission measurements, showing that the coefficients of scattering, µ’s, and absorption, µa, are retrieved with great accuracy. Finally, we demonstrate the simultaneous retrieval of both µ’s and µa.