The light propagation within an absorbing medium and the reflection and refraction at the interface of two absorbing media are studied. By using the unit vectors denoting the planes of constant field amplitude and constant phase respectively, the light propagation and attenuation are described by the effective refractive indices which depend on both the complex refractive index of the medium and the angle between the unit vectors. With the expression for the light propagation, the corresponding Snell＇s law and the expression of Fresnel coefficients are obtained, which can be applied to describe the reflection-refraction event at the interface between an arbitrary combination of transparent and absorbing media.
Using the classical Mie scattering theory, we compute the energy density of an arbitrary partial wave （e.g., the nth order） and then determine that the interaction between an incident planar wave and a sphere of radius a is the one between the sphere and those partial waves the order of which satisfies n ≤ ka. We also provide a simple expression to describe the diffracted wave in which the angle-dependent functions are employed. The difference between the accurate and the approximate expressions is demonstrated by numerical calculation.
The optical measurement technique based on Mie scattering has been applied to various areas, in which single scattering at low particle concentration is assumed. Nevertheless, since multiple scattering is usually unavoidable in online measurements, we present in this work a multiple scattering calculation method, in which a layer model is employed. The three-dimensional particle system is divided into a pile of layers the number of which is automatically determined, depending on the obscuration of the particle system. The calculation is found to be fast, reasonable and reliable.
