LASER DIFFRACTION

Microtrac has played a leading role in the development of light scattering particle size measurement. Commencing 25 years ago, diffraction measurements have been central to the Microtrac product line. A description of the basic diffraction concepts and the technology used in the S3000 is presented below.

Basic Concept   |   Young's Equation   |   S3000 Tri-Laser   |   Evaluating Light   |   2001 Angular Light Scattering Publication

Note: For all illustration thumbnails below click to enlarge

One method of describing the phenomenon of the development of a pattern of light that is related to a dimension has been shown by Young in his "double slit experiment" in which the wavelength of light could be determined. In this experiment, monochromatic light was directed to a card containing two very small slits cut very close to each other. The waves may interact destructively (180⁰ out of phase or peak of one wavelet superimposed on a valley of another wave) or they may interact constructively when in phase (peak of one wave superimposed on the valley of another wave). As the wavelets propagate in the forward direction the interference continues.

A card placed in front of the advancing superimposed waves will produce a pattern of lines (Figure 1.) due to interference. The pattern begins at the center where highly intense light is located. A dark line resulting from destructive interference follows. The next line is bright and is a result of constructive interference of the wavelets. The pattern of lines is related to the wavelength of the illuminating light and the distance between the slits. This can be expressed by the formula:

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Figure 1

This equation developed by Young provides the basis for determining the wavelength of light, but is also related to the distance between the holes or the size of a particle where the diameter equals the distance. The equation also established the concept of interference patterns that was used by Bragg to experimentally verify the concept of diffraction (bending) of light from layers of atoms in a crystal.

The issues involving light scattering particle size are much more complex, but these concepts form the basis that light is scattered from particles into a definite pattern. The pattern is developed primarily by diffraction, which spreads out more for fine particles and less for larger particles.

The issue for particle size measurement is the ability to interpret the pattern from a mixture of particle sizes covering a wide range of particle sizes (Figure 2). The mixed pattern is mathematically analyzed to ascertain the particle sizes present.

Only a single pattern of light will correspond to a given particle size distribution. To compute the distribution, Microtrac uses an advanced form of interative deconvolution mathematics that has high sensitivity and resolving capabilities without noise and spurious ("ghost") peaks.

Use of a single wavelength source of laser light is required to apply the mathematics to the fullest capability possible. The Tri-laser, single wavelength system allows the same computations to be used over the entire angular range of the diffraction pattern.

This avoids "connecting points" between distributions developed by different wavelengths of light and the requirement for multiple Mie scattering treatments (Mie scattering is wavelength dependent). For a complete explanation of the principles, order a copy of the publication given at the end of this document.

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Figure 2

The advanced S3000 Tri-Laser uses a detector system located at a precise distance from the point where the particles interact with the light. A series of small silicon detectors produces electrical current when light illuminates them (Figure 2). The detectors also respond to the amount of light (intensity) reaching them, which is related to the amount present of a particular particle size.

The angles of light determined from the illuminated detectors and the intensity of the current produced provide the basis for providing the distribution of particle sizes as well as the quantity of each present. The laser light (l = 780nm) in the S3000 allows for measurement of larger particles by detecting the light scattered over an angular range of 0.02 to approximately 45 degrees.

Very small particles scatter light at very wide angles. In order to illuminate the smallest particles and detect the scattered light, lasers are strategically placed (Figure 3) at angles that allow detectors to be used more than one time. This arrangement reduces optical components (design elegance and simplicity) and reduces instrument space requirements (small lab bench foot-print). This combination provides an optical instrument having extremely stable alignment as well as being extremely portable.

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Figure 2

Figure 3

Diffraction of light occurs at the edge of particles, but many substances have particles that are transparent and allow light to pass though. This phenomenon is termed refraction. Particles passing through the laser beam of the S3000 are constantly tumbling and pose different faces of the particle to be exposed to the incident light.

In the case of spheres, all orientations of the particles are identical. Any light passing through the particle will exit at the same place and illuminate the same place on the detector. For particles that are not spherical, the constant tumbling will cause the refracted light to illuminate a variety of detector locations. This light also will undergo reflection inside the particle.

As shown in Figure 4, the entire pattern of light reaching the detector contains diffracted and refracted light. The refracted light does not contain information of value in determining size over all of the sizes measured by the S3000 and thus must be eliminated by proper corrections. Since spheres represent well-defined shapes, the effect of refracted light is easily corrected by the concepts proffered by Gustave Mie (Mie theory). It has been estimated that spherical particle products represent only 2% of all substances and makes the use of Mie corrections limited. The more common effect is light refracted and diffracted by particles that are not spherical. Figure 5 shows the difference that can be expected when light is refracted by the two shapes. The patterns as shown are quite different meaning that spherical particles require different treatments than non-spherical particles.

The Microtrac S3000 and Ultrafine Particle Analyzer use Mie scattering calculations that are related to the shape as defined as spherical or non-spherical. The selection is made very easily as part of the measurement set-up. It is based upon guidelines provided in the on-line operator's manual.

Only Microtrac Particle Size Analyzers treat the refracted light according to the rigorous treatment proposed by Mie for spherical particles and as well when the particles are not spherical, using a modified Mie approach. The Microtrac technical staff is also available to assist in this decision as well as answer other questions.

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Figure 4

Figure 5

Introductory paragraph of publication presented at the 2001 Pittsburgh Conference, New Orleans, LA. Order the complete document from Microtrac, Inc by contacting:

Michael Trainer
Microtrac Inc.
148 Keystone Drive
Montgomeryville, PA 18936

Measurement of the Angular Scattered Light Distribution

Angular (or static) light scattering techniques are applicable over the particle size range from .02 microns to above 3000 microns. The particle size distribution is determined by measuring the scattered light intensity as a function of scattering angle. A typical static light scattering configuration is shown in Figure 1. A laser beam illuminates a group of particles, which may be dispersed in a liquid or gas stream. Light scattered by the particles, and the incident beam of light, are focused onto an optical detector array, which measures the angular distribution of scattered light. Each point on the array collects a single angle of scattered light, from all the particles in the beam; and the angular resolution is independent of the sample volume size. The detector array sums all of the scattered light distributions from individual particles in the ensemble. This composite distribution is mathematically inverted to obtain the particle size distribution, using a theoretical model for the scattering process. The most widely used model is based on Mie theory, which solves Maxwell's equations exactly for the boundary conditions of a spherical particle.

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Figure 1