Size determination techniques using a light beam as a probe are broadly classified into imaging and non-imaging types. Techniques constituting the non-imaging methods of size determination can further be classified into numerous groups based upon the physical principle describing the interaction between the light beam and the particle and the information that can be deduced from that interaction. Laser diffraction instruments fall within this category of non-imaging type of instruments. Manufacturers produce instruments that are based upon the same general principles of laser diffraction but the use of different components, configurations, and algorithms gives rise to a broad selection of instruments with analysis capabilities covering a wide range of sizes and size distributions.

The underlying assumption in the design of laser diffraction instruments is that the scattered light pattern formed at the detector is a summation of the scattering pattern produced by each particle that is being sampled. Deconvolution of the resultant pattern can generate information about the scattering pattern produced by each particle and, upon inversion, information about the size of that particle. In order for this to be true, multiple scattering of light should not be permitted. Multiple scattering refers to the phenomenon where light scattered from one particle interacts with another particle and gets scattered again. This places an inherent limitation on the concentration of particles that can be analyzed. The concentration limit is determined by the design of the instrument and varies depending on the nature of the incident light source, optical geometry and light detection system. Laser diffraction instruments can be used for the analysis of dry powders, powders dispersed in aqueous or non-aqueous dispersants, and also finely divided aerosols. These instruments are mostly used for analysis of small sample quantities (typically, a few milligrams to a gram), though some are designed for, or have accessories that enable sampling from a moving stream and are thus, suited for size characterization and process control of an industrial production line.

Instruments are designed with capabilities for applying various optical models for deconvolution of the scattered pattern and size determination. Those using the Fraunhofer model for size analysis have typically a lower size limit of about 2 um and an upper limit of about 8000 um. However, it should be kept in mind that the Fraunhofer model is not valid below a size range of about 2 um to 4 um. In such instances it is better to use instruments that have capabilities for the Mie optical model. Instruments using this model typically enable analysis to about 0.1 um, and reliable analysis in even finer size ranges is possible depending upon the configuration of the optical elements and the detector array used in the instrument. 

The interaction of a particle and light incident upon it gives rise to four different but inherently related scattering phenomena, namely, diffraction, refraction, reflection and absorption of the incident beam. The magnitude of each phenomenon will vary depending upon the nature and size of the particle and the beam. Size analysis by interpretation of the scattered light patterns formed due to diffraction of the incident light is of primary interest in this chapter.

Diffraction of light occurs at the surface of the particle and can be thought of as the bending of light waves by the surface of the particle. Diffraction arises due to slight differences in the path length of the light waves created upon interaction with the particle surface. These differences in the path length cause constructive and destructive interference between the sinusoidal light waves leading to characteristic diffraction patterns. The diffracted waves are then scattered in different directions. The direction of scatter depends on the size and shape of the particle. Large, spherical particles scatter mostly in the forward direction. As the particle size gets smaller, the scattering occurs over a broader range of angles. This description is a very simplistic perspective. In practice, scattering is significantly more complex and is influenced by the nature of polarization of the incident light, optical properties of the particle and surface roughness of the particle. Numerous texts deal in detail with the underlying mathematics and physics of scattering and diffraction. Laser light scattering instruments are often referred to as Fraunhofer diffraction instruments, because instruments based on early designs processed the diffracted light scattered in the forward direction by the particles using the Fraunhofer approximation to deduce particle size from the scattered signal.

The development of instruments based on laser diffraction has been closely related to developments in technology that have enabled the miniaturization of laser light sources and photo-detector arrays and systems. Early particle size analysis instruments based on this principle used simple configurations of optical elements, such that the light scattered only in the forward direction, over a relatively narrow angle from the optic axis, was focussed on the detector system. Detector systems used in these instruments comprised of individual detector elements rather than multi-element arrays and thus, needed to be placed at discrete distances from each other. This also limited the number of detectors that could be placed to receive the scattered signal and so early instruments would process signals from a very narrow segment of the scattering cross-section and were thus limited for size analysis over a range of about 300 um to 2 um. Size determination of particles finer and coarser than these limits has been possible due to developments of both suitable hardware and signal processing algorithms. Multi-element detectors and arrays have enabled positioning of more detector elements closer to each other and over a wider scattering angle, contributing to the improved sensitivity and resolution in more recent instruments. The development of better optical configurations and techniques makes possible the analysis of signals scattered over a wider range of angles off the optic axis, and thus the analysis of finer particles. Processing of the signals scattered from the fine particles by algorithms based on the

Mie theory provide a more realistic estimation of the size of the fine particles. Instrument resolution and sensitivity for size calculation of the fine particles have been improved by other techniques including the use of 90° scattering configurations (additional detector elements at a 90° angle to the incident beam), and observing the changes in polarization of light after scattering.

Instruments for particle size determination based on closely related principles of light scattering are also available and may be confused with light diffraction instruments. These instruments include those based on single particle light interaction methods, where the interaction of a single particle with the light beam causes a reduction in the intensity of the light beam due to absorption and scattering of light by the particle. The reduction in transmitted light intensity (extinction) is translated into an electrical signal the strength of which correlates to the particle size. By the very nature of this technique, these instruments can be used only on extremely dilute suspensions. Other instruments are based upon the principle of quasi-elastic light scattering (QELS), a generic term encompassing a wide range of specific methods including photon correlation spectroscopy, dynamic light scattering, and heterodyne spectroscopy. These instruments are designed to make use of the Brownian motion of particles in suspension. Consequently, the measurement of variations in the intensity and frequency of the scattered light (incident light is monochromatic in nature) can be correlated to the Brownian motion and other dynamics of the particles that cause the scattering. Because of the dependence on Brownian motion and relaxation time associated with the random motion, these techniques are ideally suited for particles smaller than 1 um and require very dilute suspensions. Thus, only small quantities of sample powder (order of a few milligrams) are needed.

Laser Diffraction Instruments Strengths:

• Rapid analysis.

• Relatively simple specimen preparation.

• Some instruments can be used for both dry powders and powders in suspension.

• Some instruments can be used on-line and off-line.

• Relatively inexpensive.

• Do not require highly skilled operators.

Laser Diffraction Instruments Limitations: 

• Instrument performance and operation is highly dependent on instrument design (e.g., laser sources of different wavelengths, differing number and positions of detectors).

• Given the above reason, comparison of results from different instruments may be misleading.

• May require a precise knowledge of optical properties of specimen.

• Cannot distinguish between dispersed particles and agglomerates.

• Significant error and bias may be introduced in the particle size distribution results, if powder particle shapes deviate from spherical configurations.