Influence of the Processes Parameters on the Properties of The ...

Chapter 3.
Analytical Methods and Designs <strong>of</strong> Experiments
also caters <strong>the</strong> light refraction with <strong>the</strong> particle (secondary scattering) which is very important when particle
diameter is below 50 μm. This is also mentioned in <strong>the</strong> standard for laser diffraction measurements (ISO
133201) [Kippax, 2005]. According to Lorenz-Mie’ <strong>the</strong>ory <strong>the</strong> scattering patterns <strong>of</strong> spheres are symmetric
with axis <strong>of</strong> <strong>the</strong> incident light. Scattering minima and maxima are in different angles, if <strong>the</strong> properties <strong>of</strong> <strong>the</strong>
particles vary. Figure 3.9, shows <strong>the</strong> diffraction patterns <strong>of</strong> two particles with different sizes [Xu, 2000].
With large particle (solid line) <strong>the</strong> peak <strong>of</strong> intensity is stronger than with small particle (dashed line) and <strong>the</strong>
minimum intensity is much closer to axis <strong>of</strong> <strong>the</strong> incident light. The intensity peaks are in <strong>the</strong> same locations
in <strong>the</strong> both positive and negative angles because <strong>the</strong> symmetrical nature <strong>of</strong> scattering. Very illustrative way
<strong>of</strong> displaying <strong>the</strong> intensity distribution is also a radial graph as in Figure 3.9. The bold trace describes <strong>the</strong>
intensity <strong>of</strong> scattered light in different angles [Xu, 2000].
Figure 3.9: Scattering patterns <strong>of</strong> two particles <strong>of</strong> a different size.
[Xu, 2000]
3.2.3 Fraunh<strong>of</strong>er’ Theory
Fraunh<strong>of</strong>er’ <strong>the</strong>ory covers <strong>the</strong> light diffraction in <strong>the</strong> aperture which is described in Fresnel-
Kirch<strong>of</strong>f’ diffraction integral [Brittain, 2003]. In Fresnel diffraction (Figure 3.10-A), distances from <strong>the</strong>
point source and <strong>the</strong> screen to <strong>the</strong> obstacle forming <strong>the</strong> diffraction pattern are relatively short. In Fraunh<strong>of</strong>er’
diffraction (Figure 3.10-B), <strong>the</strong> distances are much longer and all lines from <strong>the</strong> source to <strong>the</strong> obstacle and
forward to <strong>the</strong> screen can be considered parallel. In Figure 3.10-C, <strong>the</strong> lens forms smaller image <strong>of</strong> <strong>the</strong> same
diffraction pattern which would be formed on <strong>the</strong> screen extremely far without <strong>the</strong> lens [Young and
Freedman, 2000].
(A) (B) (C)
Figure 3.10: Principles <strong>of</strong> Fresnel’ diffraction (A) and Fraunh<strong>of</strong>er’ diffraction (B and C).
[Young and Freedman, 2000]
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