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CILAS LASER Particle sizing and shape analysis PARTICLE-SIZE-ANALYZER Particle size analyzer & SHAPE ANALYSIS
CILAS LASER Particle sizing and shape analysis
Particle size instrument

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ISO 9001/14001 Certificate


CILAS LASER Particle sizing and shape analysis


Assumptions Le laser

Fraunhofer Theory Spherical, non-porous and opaque particles,
Fraunhofer Theory Diameter d > wavelength l,
Fraunhofer Theory Particles are distant enough from each other,
Fraunhofer Theory Random motion,
Fraunhofer Theory All the particles diffract the light with the same efficiency, regardless of.

Characteristics of the Airy shapeLe laser

Characteristic of the Airy shape : 3d graph
Characteristic of the Airy shape : 2d graph

Fraunhofer Theory Circular,
Fraunhofer Theory Consisting in concentric rings I = f (a),
Fraunhofer Theory Spacing and size of the rings are linked to the particle size,
Fraunhofer Theory The fist zero angle is related to the diameter d by 1.22 l/d,
Fraunhofer Theory 75% of the total energy is concentrated in the first lobe.

Principle Le laser


Aspect of the diffraction pattern with respect to the particle size Le laser

for a large particle
for a small particle

The observation of the diffraction pattern at finite distance is done through a lens (L) placed between the laser source and the detector Le laser

The observation of the diffraction pattern at finite distance

Fraunhofer Theory The diffraction patterns of particles having the same size converge at the same point whatever them location with respect to the lens,
Fraunhofer Theory The first zero on the detector is 1.22 lf/d where f is the focal length.


The Fraunhofer theory is applicable for large particles compared to the wavelength l (diffusion and absorption are not considered). 
For smaller particles, it is appropriate to use Mie Theory.

Mie schema

The Mie model takes into account both diffraction and diffusion of the light around the particle in its medium. 
To use the Mie model, it is necessary to know the complex refractive index of both the sample and the medium. 
This complex index has a real part, which is the standard refractive index, and an imaginary part, which represents absorption. Complex index = m
Fraunhofer Theory m = a + b
Fraunhofer Theory a: real part
Fraunhofer Theory b: imaginary part

Because of the importance of this model, CILAS has crated a fast algorithm, which enables the user to get, within seconds, diffusion results using Mie theory and taking into account the complex index of the sample.