Light Scattering in Fiber-based Materials : a foundation for characterization of structural properties

Abstract: Deeper knowledge of light propagation in fiber-based materials is fundamental in order to understand their optical appearance as well as for industrial applications. Light scattering measurements are appropriate in handling dynamic industrial environments and can provide information regarding structural properties. In general, on-line property measurements are best utilized by establishing an understanding of the underlying physics and using that knowledge in an optimal way to determine the parameters or properties sought after. Light scattering is affected by numerous parameters such as size, shape, concentration and refractive index of the scattering particles as well as the waveleng th of the incident source. In addition, anisotropic light diffusion in media which have a directional-dependency, such as structured fiber-based materials, are neither well understood nor well investigated.By approximating cellulose fibers as infinitely long, straigth cylinders it is possible to use an analytical solution to Maxwell’s equations to describe the scattering characteristics such as phase functions and scattering efficiency. This makes it possible to utilize both the wave nature of light and structural properties of the fiber network when modelling multiple light scattering. The developed model solves the radiative transfer equation numerically using theMonte Carlo method resulting in a description of multiple scattering in a sphere-cylinder media.The results show that scattering media consisting of infinite long, straigth, homogeneous or hollow cylinders scatter light very differently as compared with a media consisting of spherical particles. Both scattered intensity and the degree of depolarization are affected by a strong forward scattering behavior observed for cylindrical particles. This strong forward scattering behavior was also found to enhance lateral scattering in paper, and therefore predicts a larger extent of lateral light scattering than models using rotationally invariant single scattering phase functions. A strong relationship between anisotropic diffusion and to degree of in-plane fiber orientation was also observed using both measurements and simulations. In conclusion, it was found that the approximation of cellulose fibers as infinitely long, straigth cylinders is reasonable when modelling scattering in paper. The findings indicate that parameters such as geometrical properties, particle composition, fiber orientation and fiber orientation variations can be measured by monitoring scattered light intensity. The obtained knowledge provides a base for further development of on-line sensing techniques that meet industrial requirements. Since the theory is general, it is likewise relevant and applicable to other areas of material science where imaging or remote sensing techniques are of interest.