Reproducibility Problem for Particle Size Analysis Solved

During the current era of increasing globalization, manufacturing operations are being located around tile world. Companies that manufacture or use powdered materials may need to produce identical products at many different plants on several continents. This can create quality control headaches that underscore the importance of having effective methods and instrumentation for measuring and controlling product quality.

Until recently, companies found it frustrating to use laser light scattering instruments to monitor particle size distribution in different plants due to the inadequate resolution and repeatability of previously available instruments. Instruments located at different plants, even of the same brand and model, are often unable to produce matching analyses for identical samples. This means that the objective of improved product quality has not been realized by these companies, in spite of sometimes considerable investment in these instruments. This situation has now changed.

Back To Basics

On the surface, this problem is puzzling because light scattering theory is based oil fundamental principles and instruments measuring particle size distribution using light scattering should always produce similar results from similar light scattering patterns. College textbooks such as Born and Wolf's "Principles of Optics" derive the equations dealing with the propagation and scattering of light beginning with Maxwell's equations which are the fundamental equations dealing with the properties of electromagnetic fields. The light scattering pattern measured during a laser particle size analysis should be well defined, repeatable, and predictable. Why then, do light scattering instruments from different manufacturers and even from the same manufacturer give different results for the same material?

The Causes

The obvious answer is that the differences are because different instrument vendors have implemented their instruments differently, with different detection systems, different numbers of detectors, different data reduction methods, and even different sample handling systems. Yet there are many examples of the same brand model, and, therefore, design of instruments giving different results. (This is a well known, but seldom discussed "secret" of the industry.)

Tile Scattered Light

A not so obvious answer is that the previously available instruments have been designed in a way that prevents them from measuring tile scattered light in enough detail and with the accuracy necessary to extract all of the information inherent in the light scattering pattern. In fact, the detector systems used are the same technology used in the earliest laser light scattering instruments in the 1970's. These instruments use "ring detectors" based on photodiode technology, dividing the incredibly richly detailed light scattering pattern into a relatively small number of measurements made by anywhere from 32 to 128 detectors. To illustrate the effect of such a small number of detectors, look at a high resolution photograph on your computer screen (say, 4k by 4k pixels) and see how much detail is there. Then use a photo editor to reduce the resolution to 128 by 128 pixels. The scene is no longer recognizable and cannot be recovered because most of the information in the original image has been lost.

Signal to Noise Ratio

A second problem with tile legacy laser light scattering technology is that the signal to noise ratio for low intensity areas of the light scattering pattern makes it very difficult to measure the intensity accurately. The net result is a low resolution representation of the original light scattering pattern with inadequate measurement accuracy.

Dynamic Range

A third problem of previous instruments is that the dynamic range of the light scattering intensity pattern is so large (in the order of a billion to one) that photodiode technology cannot be used at a high enough resolution to significantly improve the situation. Making higher resolution ring detectors would require making individual detectors significantly smaller. However, measuring low intensity regions of the light scattering pattern requires increasing the photodiode area so that the photodiode signal is high enough to be detected. The legacy technology is at an impasse.

A Breakthrough Solution

Micromeritics recognized the limitations of the old technology. A breakthrough technology was needed, not just another variation on the same outdated theme. This technology was found to be available as an outgrowth of the space program in the form of a scientific charge coupled device, or CCD. CCDs were originally developed and used for astronomical imaging and have been steadily increasing in performance and quality. Recent photographs from the Cassini space probe and the current level of performance of the Hubble Space telescope show what can be accomplished with these devices.

Astronomical imaging requires the ability to accurately measure a very wide range of intensities, and digital techniques have been developed that allow multiple exposures to be digitially combined This permits both high  and low intensity light levels to be imaged in the same region while maintaining accurate intensity measurements. Another technique developed by astronomers enables multiple images taken over a wide field of view to be combined to produce a detailed panorama of the entire scene.

Building on these techniques from the space program has enabled Micromeritics to produce an instrument that can accurately measure a light scattering pattern over 45 degrees of scattering angle with a dynamic intensity range of 1 x 1010 to 1 at an effective resolution of over 15,000,000 pixels. This is as compared to 128 data points or so on legacy instruments. The level of detail, accuracy, and resolution of the Saturn DigiSizer enables the extraction of all available information from the static light scattering pattern. For the first time, users can measure the same material on multiple instruments located at different points around the world and get the same, highly detailed size distribution measurement on each instrument. The Saturn DigiSizer is able to produce correct, repeatable results based on first principles of light propagation and is able to do this reliably from instrument to instrument, as illustrated in Figure 1.

Multiple instruments give the same results – a sampling of 31 different DigiSizers, all running a garnet standard material, shows excellent reproducability

Figure 1. Multiple instruments give the same results – a sampling of 31 different DigiSizers, all running a garnet standard material, shows excellent reproducability

Mie and Fraunhofer Theory

Depending on tile size range of the particles being analyzed, one of two light scattering theories has typically been selected for interpreting the light scattering pattern and converting it to a size distribution. The two theories are Fraunhofer Theory, which is useful if all particles are larger than about 10 micrometers, and Mie Theory which gives accurate results for particles both above and below 10 micrometers. The primary difference between the two theories is that Fraunhofer is based on the action of light diffracting around the particles and Mie adds the effects of tile refraction of light through the particles and the absorption (or reflection) of light by the particles. An accurate measure of the refractive index is needed to get accurate results from Mie Theory. Tile refractive index is measured as a real part (representing the refraction of light through the particle) and an imaginary part (representing tile amount of light absorbed or reflected by tile particle). Obtaining a useful measurement of tile refractive index is difficult for many materials, so sonic manufacturers of legacy instruments have downplayed the usefulness of Mie Theory. Even on instruments that are able to provide a Mie analysis, obtaining the refractive index has been a problem. Micromeritics has developed techniques for easily determining the effective refractive index that make Mie analysis so easy to use that many customers are using it for all their analyses. Of course, Fraunhofer is still available and gives excellent results on the Saturn DigiSizer for larger particles.

Unique Capabilities

The Saturn DigiSizer has such a high degree of accuracy and resolution that it is sensitive to even small errors in the value of the refractive index. Legacy instruments are relatively insensitive to the value of refractive index since there isn't enough resolution to detect subtle differences in the light scattering pattern. In addition, refractive index values are often published for different wavelengths than used by light scattering instruments, plus the effective value can actually change due to variations in particle shape and surface texture. The amount of porosity in a particle can even make a difference. A high performance instrument such as the Saturn DigiSizer can detect these differences. For these reasons, the optimum value of the real and imaginary parts of the refractive index must be known at the wavelength of tile Saturn DigiSizer's laser diode (658 nm). Micromeritics incorporates in its instrument an analytical tool that simplifies determining the optimum refractive index values.

Mathematical Deconvolution

The technique used to determine the size distribution from the measured light scattering pattern is mathematical deconvolution. This technique uses a series of models based on the refractive index and scattering angles to determine the size distribution that would produce a light scattering pattern that closely fits the measured light scattering pattern. The difference in fit between the calculated and measured light scattering pattern for this distribution is the residual error and the correct model (based on the complex refractive index) is the one with the smallest residual error. This property of mathematical deconvolution is the basis for the method of determining the refractive index for an unknown material A software tool we have developed and used examines a range of real and imaginary refractive index values over a range of scattering angles and develops light scattering models for all of these values. It performs the deconvolution for all of these models and then compares the results to the measured data to determine how well the models fit the data. The optimum model, and therefore the correct effective refractive index values, will produce an excellent fit to experimental data with a smooth, noise free size distribution.


This refractive index scanning technique is very powerful and makes it practical to measure accurately the effective refractive index of samples. By combining this technique for optimizing the real and imaginary refractive index values with breakthrough technology and performance, Micromeritics is now able to provide paid laboratory analysis for size distribution measurement using the Saturn DigiSizer. With the optimum models identified by their internal analysis tool, Micromeritics is confident that the results produced by our Material Analysis Laboratory will match the results obtained on any Saturn DigiSizer located anywhere in the world. Micromeritics' customers are finally able to set up unified standards for the size distribution of their products produced at multiple locations and reduce their quality control headaches.

This information has been sourced, reviewed and adapted from materials provided by Micromeritics Instrument Corporation.

For more information on this source, please visit Micromeritics Instrument Corporation.



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