Angle Resolved Light Scattering in Turbid Media : Analysis and Applications

Light scattering in turbid media is essential for such diverse application areas as paper and print, computer rendering, optical tomography, astrophysics and remote sensing. This thesis investigates angular variations of light reflected from plane-parallel turbid media using both mathematical models and reflectance measurements, and deals with several applications. The model of most widespread use in industry is the Kubelka-Munk model, which neglects angular variations in the reflected light. This thesis employs a numerical solution of the angle resolved radiative transfer problem to better understand how the angular variations are related to medium properties. It is found that the light is reflected anisotropically from all media encountered in practice, and that the angular variations depend on the medium absorption and transmittance and on the angular distribution of the incident light. If near-surface bulk scattering dominates, as in strongly absorbing or highly transmitting media or obliquely illuminated media, relatively more light is reflected in large polar (grazing) angles. These results are confirmed by measurements using a set of paper samples. The only situation with isotropic reflectance is when a non-transmitting, non-absorbing medium is illuminated diffusely. This is the only situation where the Kubelka-Munk model is exactly valid. The results also show that there is no such thing as an ideal bulk scattering diffusor, and these findings can affect calibration and measurement procedures defined in international standards.The implications of the presented results are studied for a set of applications including reflectance measurements, angle resolved color and point spreading. It is seen that differences in instrument detection and illumination geometry can result in measurement differences. The differences are small and if other sources of error - such as fluorescence and gloss - are not eliminated, the differences related to instrument geometry become difficult to discern. Furthermore, the angle resolved color of a set of paper samples is assessed both theoretically and experimentally. The chroma decreases and the lightness increases as the observation polar angle increases. The observed differences are clearly large, and it is an open issue how angle resolved color should be handled. Finally, the dependence of point spreading in turbid media on the medium parameters is studied. The asymmetry factor is varied while maintaining constant the optical response in a standardized measurement geometry. It is seen that the point spreading increases as forward scattering becomes more dominant, and that the effect is larger if the medium is low-absorbing with large mean free path. A generic model of point spreading must therefore capture the dependence on all of these medium parameters.This thesis shows that turbid media reflect light anisotropically, and angle resolved radiative transfer models are therefore necessary to capture this. Using simplified models can introduce errors in an uncontrolled manner. The results presented potentially have consequences for all applications dealing with light scattering, some of which are studied here