Exploring the particle size measurement landscape is challenging and time-consuming. There are several methods of particle sizing used by different industries. With over a decade of expertise in particle sizing technology, we know the difficulty the users face to determine the best method for their process. To assist you, we have created a detailed review of industry-standard methods such as laser diffraction and cutting-edge direct imagining particle size analysers, to give you an appreciation of factors to consider in your particle size distribution (PSD).

Laser diffraction is a method of calculating the PSD of sample material by analysing the scatter pattern of light from a sample. As the light interacts with particles, it scatters in a pattern that is detected and measured by an array of sensors. The angle and intensity of the scatter pattern correlate with the size of the particle size and makes it possible to infer particle size information from the scattered light mathematically. The particle size information for a given sample is presented as a volume fraction distribution based on the diameter of the sphere of the equivalent volume of the observed particle.

The fundamental principle governing the determination of particle size by laser diffraction is the interaction of light with a particle. When light meets a particle, the incident light is altered in a way that is usually characteristic of that particle type. Some of the interactions which can take place include reflection, refraction, absorption, and diffraction, as seen in the figure below.

Figure: Modes of the interaction of incident light with particles and surfaces.

As light interacts with the particle surface, it undergoes diffraction, resulting in a distribution of scattered light, which is measured by an array of detectors and predictive models to infer particle size. The two main factors that influence scattering are light wavelength and particle size; smaller particles result in a broader scattered light distribution, for example.

Our in-house advanced particle size analyser Eyecon_{2}, which is a **direct imaging device**, calculates particle size distributions based on the measurement of individual particles within a sample image. The images captured are processed by the software **EyePASS™** where the particle detection algorithm identifies and measures individual particles within the captured image.

Laser diffraction uses three predictive models to describe the relationship between particle size and light scattering - *Fraunhofer approximation* model, *Rayleigh scattering* model, and *Mie scattering* model. These models vary in their approach, and so each has suitable particle sizes over which they can accurately predict. The choice of which model to use is therefore influenced by the particle size range of interest, but
also the degree of complexity of each model.

*Rayleigh* and *Mie* scattering theories are independent theories that describe two different situations. Rayleigh scattering occurs when the particle is smaller in size than the wavelength of the incident light. In comparison, Mie scattering occurs when the particle is much larger than the wavelength of the incident light. The *Fraunhofer approximation* is a related and simplified approximation to Mie theory and as such is applicable only to particles in and above the micrometre *(µm)* range, opposed to the nanometre* (nm)* range for the two former theories.

For example, Eyecon_{2} measures a multitude of particle parameters and values that are trended in real-time with live histogram and S-curve results. This allows *Eyecon _{2} to quickly get to work* once installed without requiring complex modeling

We learned earlier that the angle and intensity of scattered light are directly related to the size of the particle. Larger particles scatter light at lower angles and with greater intensity than smaller ones. Depending on the particle, differing angular distributions can occur, which effectively dictates the predictive model that should be used.

However, both the Rayleigh and Mie equations contain several other dependencies such as refractive index and empirical constants. This leads to the requirement of a significant amount of prior knowledge of the measurement environment. While the refractive index is readily measurable, the empirical constants are not so. Typically, manufacturers will calibrate the instrument with known particles, solving the equations in advance and creating solution matrices relating scattered light intensity to the most probable particle size.

Eyecon_{2} identifies particles and **EyePASS™** software fits them with an ellipse that is constructed based on the crossover of light which is used by the algorithm to determine edge
detection. This approach results in a tighter, smaller volume fit than the cubed diameter of an equivalent circle that fit the same particle. This allows Eyecon_{2} to more accurately calculate particle volume which will affect the subsequently calculated D-Values.

As with any scientific method, there a few restrictions, caveats, and difficulties surrounding the use of laser diffraction and direct imagining particle size analysers for PSD. We have detailed some limitation for each measurement system below:

**Laser diffraction: **

The optical properties of the sample and the surrounding medium must be known before the optical model can be established.

The refractive index of a particle may not permit the use of laser diffraction

**Direct image analysis:**

The focal length of the system may be limited, meaning samples must be adequately close to being measurable.

The measurement system may also be sensitive to transparent materials such as glass and may lead to reduced accuracy in measurement.

For more information, view our detailed application note where we deep dive further into laser diffraction and many more industry-standard PSD measurement methods.