CILAS FRAUNHOFER / MIE

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ISO 13320
21 CFR-11

FRAUNHOFER / MIE
Reference powders

FRAUNHOFER THEORY

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

Characteristic of the Airy shape

Characteristic of the Airy shape : 3d graph

Characteristic of the Airy shape : 2d graph

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

Principle

Principle

Aspect of the diffraction pattern with respect to the particle size

System

System
for a large particle

System

System
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

$The observation of the diffraction pattern at finite distance$

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

MIE THEORY

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
m = a + b
a : real part
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.

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