Penetration of light into multiple scattering media: model calculations and reflectance experiments. Part I: the axial transfer

The article presents two general equations of radiation penetration into layers of diffuse reflectors. One of the equations describes the depth origins of reflection, the other the depth profiles of absorption. The equations are evaluated within the theory of radiative transfer applying various degrees of analytical approximations and Monte Carlo simulations. The data are presented for different scattering and absorption coefficients, arbitrary layer thicknesses, collimated and diffused irradiation, and anisotropic forward scattering. The calculated mean depths of reflection are always lower than the mean depths of absorption. For nearly non-absorbing layers, the mean depths of absorption are about one third of the physical layer thickness. In contrast, penetration saturates for strong absorbers at very low depth levels. From the simulated data, methods are derived for the determination of the penetration depth from reflectance and transmittance data of thin layers or from radially diffused reflectance profiles upon spot irradiation. The methods are experimentally verified for a series of metal oxide powders with particle sizes ranging from much smaller to much larger than the wavelength of irradiation and for microcrystalline cellulose stained with different concentrations of an organic dye.