Colour Technology of Coatings by Wilhelm Kettler

Author:Wilhelm Kettler
Language: eng
Format: epub
Publisher: Vincentz Network
Published: 2017-03-29T16:00:00+00:00

3 Mie theory

Uwe Hempelmann

Scattering of electromagnetic waves by particles is one of the most important processes in physics and the underlying theory can be used to describe a great many phenomena. Mie published his theory on the absorption and scattering of an electromagnetic wave by a sphere in 1908.

It is sometimes called the Lorenz-Debye-Mie theory, because major preliminary work had already been done by Lorenz and Debye. The equations serve as a good approximation for characterising the absorption and scattering of pigment particles within a coating or a plastic.

Mie theory describes the absorption and scattering of a planar electromagnetic wave by a single spherical particle and accounts for scattering of the incident wavelength. It does not account for Raman scattering (inelastic scattering of light by atoms and molecules) and similar effects. Mie theory provides solutions for the Maxwell equations for surface waves on a particle. It has since been extended to cylindrical particles. Meanwhile, methods have been developed that describe the absorption and scattering of arbitrarily shaped particles; unfortunately, these entail much more complex calculations.

Our brief overview of Mie theory starts with a summary of the input parameters. The results of a Mie calculation are presented as a function of these parameters, which regrettably take some getting used to, but are necessary for showing the results in a presentable form.

The first input parameter is particle size, which determines the extent of Mie scattering; for our purposes, the particle radius will be denoted by a. In later equations describing absorption and scattering, the particle radius will be denoted by a, a parameter encompassing the refractive index of the medium and the wavelength of the incident radiation.

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