Analyzing Light Scattering Data

In laser diffraction, particle size distributions are calculated by comparing a sample’s scattering pattern with an appropriate optical model using a mathematical inversion process. Traditionally two different models are used: the Fraunhofer Approximation and Mie Theory.

Mie Theory provides a rigorous solution for the calculation of particle size distributions from light scattering data and is based on Maxwell’s electromagnetic field equations. It predicts scattering intensities for all particles, small or large, transparent or opaque within the following assumptions:

• The particles being measured are spherical
• The suspension is dilute, such at the scattered light is measured before it is re-scattered by other particles.
• The optical properties of the particles and the medium surrounding them is know
• The particles are homogeneous

“..... the Mie theory offers the best general solution.”
(ISO13320-1)

Mie Theory predicts the primary scattering response observed from the surface of the particle, with the intensity predicted by the refractive index difference between the particle and the dispersion medium. It also predicts how the particle’s absorption affects the secondary scattering signal caused by light refraction within the particle – this is especially important for particles below 50 microns in diameter and is extremely important when the particle is transparent, as stated in the international standard for laser diffraction measurements (ISO13320-1 (1999)).

The Fraunhofer Approximation was used in early laser diffraction instruments, mainly because it is simpler to calculate and does not require input of the sample’s optical properties. It is based on similar assumptions to Mie Theory, but additionally assumes that:

• The particles being measured are opaque discs
• Light is scattered only a narrow angles.
• That particles of all sizes scatter light with the same efficiency
• The refractive index difference between the particle and surrounding medium is infinite.

These approximations hold at large particle sizes (above 50 microns in size) but are increasingly in error when measuring fine particles.

More Information :

	Analyzing Irregular Particles
	Using Mie Theory and the Fraunhofer Approximation