Using Mie Theory and the Fraunhofer Approximation
When setting up laser diffraction methods, users are faced with the decision as to whether to use Mie Theory or the Fraunhofer Approximation to calculate the particle size distribution results.
The Fraunhofer Approximation represents the easiest model to set-up as, in contrast to Mie Theory, it does not require the user to provide any optical property information. However, its use can lead to significant errors due to the assumptions it makes regarding the nature of the materials being measured. As such, users need to consider the following when selecting the Fraunhofer Model:
- Particle Absorption: If the particles show some transparency (absorption < 0.2), then the Fraunhofer approximation will tend to yield inaccurate results below 50µm in size. If the absorption is high (>0.2), good results may be obtained down to 2µm in size, although this does depend on the refractive index.
- Particle Refractive Index: If the refractive index different between the particle and the medium which surrounds it is low, then the Fraunhofer model can shown errors, even up to very large particle sizes (>200µm).
- Partikelform: If the particle size distribution contains material less than 2 microns in size then the Fraunhofer Approximation will lead to an incorrect assessment of the fine particle fraction.
The nature of the errors observed when using the Fraunhofer Approximation are not always predictable. In most instances an over-estimation of the fine particle fraction is observed, as shown here for a pharmaceutical material. However, it is also possible for the Fraunhofer model to underestimate the fine particle fraction, as is seen for materials such as calcium carbonate, because it incorrectly predicts the scattering efficiency of these particles.