Light scattering from mesoscopic objects in diffusive media

No direct imaging is possible in turbid media, where light propagates diffusively over length scales larger than the mean free path l. The diffuse intensity is, however, sensitive to the presence of any kind of object embedded in the medium, e.g. obstacles or defects. The long-ranged effects of isolated objects in an otherwise homogeneous, non-absorbing medium can be described by a stationary diffusion equation. In analogy with electrostatics, the influence of a single embedded object on the intensity held is parametrized in terms of a multipole expansion. An absorbing object is chiefly characterized by a negative charge, while the leading effect of a non-absorbing object is due to its dipole moment. The associated intrinsic characteristics of the object are its capacitance Q or its effective radius R-eff and its polarizability P. These quantities can be evaluated within the diffusion approximation for large enough objects. The situation of mesoscopic objects, with a size comparable to the mean free path, requires a more careful treatment, for which the appropriate framework is provided by radiative transfer theory. This formalism is worked out in detail: in the case of spherical and cylindrical objects of radius R, of the following kinds: (i) totally absorbing (black), (ii) transparent, (iii) totally reflecting. The capacitance. effective radius, and polarizability of these objects differ from the predictions of the diffusion approximation by a size factor, which only depends on the ratio R/l. The analytic form of the size factors is derived for small and large objects, while accurate numerical results are obtained for objects of intermediate size (R similar to l). For cases (i) and (ii) the size factor is smaller than one and monotonically increasing with R/l, while for case (iii) it is larger than one and decreasing with R/l.