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https://www.bettersizeinstruments.com/the-difference-between-mie-scattering-and-fraunhof.html

Mie scattering theory is induced from Maxwell's electromagnetic theory. It describes the analysis to the mechanism of light scattering from a smooth sphere. mie theory particle size distribution took into account optical properties (refractive index, absorptivity, and reflectivity) of the particle and the refractive index of the medium. Therefore, it can provide accurate analysis for samples with varies optical properties and offer more precise results for particle sizing. Mie scattering theory can be applied to sub-micron to millimeter particles. It is the theoretic foundation of particle size instrument. Although the calculation in Mie theory is complicated, this barrier has been overcome with the advance of computation techniques. Mie scattering theory is now adopted by nearly all brands of laser particle sizing instruments.

Fraunhofer diffraction is the optical theory used by inchoate laser particle sizing instruments. It is a simplified version of the Mie scattering theory. It does not consider the refractive index, absorptivity, and reflectivity of the particles and the medium; therefore, the calculation is simple and inchoate laser particle size analyzers adopted it. Fraunhofer diffraction can accurately describe the diffraction results for particles >25μm (40 times of laser wavelength). However, error occurred for particles <25μm and the smaller the particles are, the greater the error is. In order to compare the data with those obtained from inchoate instruments, most laser particle size analyzers still keep Fraunhofer diffraction as an option.