Light scattering is a popular technique used for determining the particle size distribution of a material. In general, the scattering intensity detected by a detector placed at a distance much larger than the size of the scatterer (particle) is the resultant of the scattered electromagnetic radiation from different portions of the particle illuminated by a monochromatic light source. This scattering intensity pattern is specific to a material with certain physical properties and particle size distribution. Rigorous analytical solutions to determine the particle size distribution of materials are only available for spherical and rod-shaped particles using the Maxwell's equations. The Mie theory is the rigorous solution for light scattered from a sphere. For particles smaller than the wavelength of the incident light, the Mie theory is reduced to the Rayleigh theory. When particles are much larger than the wavelength of the incident light, the Mie theory simplifies to the Fraunhofer theory.

Modern light scattering instruments used for measuring particle size distribution rely mainly on the Mie theory to obtain analytical results. Thus, the basic assumption for the instruments is that particles are perfect spheres. Irregularly-shaped particles are very difficult to size because of the need to deconvolute multiple parameters.

According to the Mie theory, the scattering angular pattern is symmetrical along the axis of incident light for perfect spheres. That is, the light scattering pattern is the same for the same absolute value of the scattering angle. There are other interesting features for light scattered by a sphere. One of them is that the light intensity is higher for larger sphere at the same scattering angle. This implies that large particles can be distinguished from small particles by the strength of light reflected off their surfaces at the same angle. In addition, the light intensity gets lower as the scattering angle increases. However, this trend of angular dependence of light intensity is reduced when the particles are very small (in the nm range). The scattered angular light intensities are indistinguishable from each other when the particles are smaller than 50 nm. Another feature for light scattering of a sphere is that there are maxima and minima for the angular light intensity observed. The pattern is characteristic for a particle of a given size.

Although the angular light intensity (flux) distribution (pattern) is a complicated function of many variables, most are known constants in a direct instrumental measurement. Thus, as long as the light flux distribution is obtained, the particle size (diameter) can be worked out.

For particles smaller than the incident light wavelength, the Mie theory can be simplified to the Rayleigh theory. In this simplification, the intra-particle interference, which leads to the oscillation of the scattered light angular intensity can be neglected or approximated with a 1st-order function by a scattering form factor. Scattering form factors for many regular shapes have been derived and are available in the literature. The analytical formulae for the regular shapes are much simpler to solve than the Mie theory. The other big advantage in using the form factors is that the analytical equations are independent of the refractive index of the material. Size and shape are the only variables for a pre-determined experimental setup. For uniformly shaped small particles, as long as the shape is known (and the analytical solution exists for the particular shape), the size distribution can be obtained.

For the visible light wavelength range, this theory can be used for particles with sizes up to 100 nm.

When the particle is much larger than the wavelength of light or the materials are highly absorptive, the edge effect (diffraction) of particles contributes more to the total scattered light. For light source at a relatively far distance from the particles and when the light beams are homogenously parallel, only Fraunhofer diffraction occurs. If particles also have refractive indices much different from that of the medium (relative refractive index or m~<1.2) or are highly absorptive (typically with absorption coefficients>0.5), then the simpler Fraunhofer theory applies. In this theory, a particle is assumed to be producing a scattering pattern as it were an opaque circular disk of the same projected area placed normally to the axis of the incident beam. This assumption frees the need to know the material refractive index.

Since this theory only applies for large particles (typically>30 µm), scattering intensity is concentrated in the forward direction(~<10º). The scattering intensity and the particle size distribution are having the ratio of 1. Thus, if the light intensity distribution of the particle to be measured is known, its particle size can be determined. The Fraunhofer theory provides a much easier analytical solution for particle sizing as compared to the Mie theory. However, extra care must be taken in using this theory because for particles with smaller m values, even though they have large diameters, the effects of light transmitting or refracting through the particles can invalidate the application. In this kind of situation, the more rigorous Mie theory has to be used.

For particles smaller than the wavelength the incident light, the scattered light is not concentrated in the forward direction but spreads to the side and rear. The intensity of front scattering does not depend on the particle size but becomes almost constant. Therefore, even if particle size is different in this region, there will be no difference in the forward-scattered light and particle size need to be determined from light intensities scattered from other directions.