Laser Diffraction Methods
Over the past 30 years Laser Diffraction has developed into the leading principle for particle size analysis of all kinds of aerosols, suspensions, emulsions, and sprays in laboratory and process environments.
The scattering of unpolarized laser light by a single spherical particle can be mathematically described by
 |
(1) |
I(q) is the total scattered intensity as function of angle q with respect to the forward direction, I0 is the illuminating intensity, k is the wavenumber 2p/l, a is the distance from the scatterer to the detector and S1(q) and S2(q) are dimensionless, complex functions describing the change and amplitude in the perpendicular and the parallel polarized light. Different algorithms have been developed to calculate I(q). The Lorenz-Mie theory is based on the assumption of spherical, isotropic and homogenous particles and that all particles can be described by a common complex refractive index m = n-ik. m has to be precisely known for the evaluation which is difficult in practice especially for the imaginary part k,and inapplicable for mixtures with components having different refractive indices.
The Fraunhofer theory considers only the scattering at the contour of the particle and the near forward direction. No pre-knowledge of the refractive index is required and I(q) simplifies to
 |
(2) |
with the dimensionless size parameter a =px/l. This theory does not predict polarization or account for light transmission through the particle.
For a single spherical particle, the diffraction pattern shows a typical ring structure. The distance r0 of the first minimum to the centre is depending on the particle size, as shown in FIG. 1. In particle sizing instruments the acquisition of the intensity distribution of the diffracted light is usually performed with the help of a multi-element photo-detector.
FIG. 1 Diffraction patterns of laser light in forward direction for two different particle sizes.
Simultaneous diffraction on more than one particle results in a superposition of the diffraction patterns of the individual particles provided that particles are moving and diffraction between the particles is averaged out. This simplifies the evaluation, so a parameter-free and model-independent mathematical algorithm for the inversion process could already be introduced in 1983 [M. Heuer and K. Leschonski: Results obtained with a new Instrument for the Measurement of Particle Size Distributions from Diffraction Patterns; Part. Charact. 2 (1985) pp. 7-13.].
Today the method is standardized [ISO 13320-1: 1999 Particle size analysis - Laser diffraction methods - Part 1: General principles], and many companies offer instruments, usually with the choice of Fraunhofer and/or Mie theory for the evaluation of the PSD. As low-angle laser light scattering has been combined with 90° or back scattering, the combination of different wavelengths, polarization ratio, white light scattering etc., the size ranges of the instruments have been expanded and is now from below 0.1µm to about 1cm. Laser diffraction is currently the fastest method for particle sizing at highest reproducibility. In combination with dry dispersion it can handle large amounts of sample which makes this method well suitable for process applications.
