I've been using the simple question above, "What's Under the Curve", for many years now as a very basic way of illustrating the principle difference between imaging particle analysis and the bulk of automated particle analysis systems. Automated particle analysis has been around for quite a long time, beginning in the 1950's with the availability of Coulter (electrozone) Counters. Many people are familiar with these and other systems which are "volumetric" in nature: basically these systems measure something that is relative to particle volume and convert it to a single number, Equivalent Spherical Diameter (ESD), based upon an assumption that all particles are spherical in shape (see also the post entitled "Direct versus Indirect Particle Size Measurement").
The results obtained from these volumetric-based particle analyzers are most frequently expressed in a distribution graph (histogram) where the x-axis displays "ESD" and the y-axis represents either frequency or volume (most often volume). The particles measured are "binned" into size ranges for display, as shown in Figure 1. While this type of distribution histogram is quite useful in some ways, it unfortunately tells you absolutely nothing about the particles contained in each bin ("what's under the curve?") beyond their ESD. Remember that the ESD for a volumetric system is based upon the assumption that all particles are spherical in shape.
This assumption of spherical shape is actually not as much of a problem when dealing with a homogeneous (all particles of identical material) sample being analyzed. However, even in those samples, one might want to know the shape of the particles: are they uniform in shape? How uniform?, etc. Or perhaps one might want to know if the largest particles are simply very large particles of the material or perhaps they are agglomerates of smaller particles. With the volumetric systems, one has no way of answering these questions other than to take another sample and look at it under a microscope, which is very time consuming, especially in order to view enough particles to get a good statistical sample!
To further complicate things, a good percentage of "real world" samples that people want to do particle analysis on are heterogeneous in nature, consisting of several different particle types mixed together. Once again, the volumetric systems are of no help here, because all particles are treated equally and assumed to be spheres. In many cases, what is really desired is to obtain is an idea of what the mixture is composed of, which simply can not be accomplished with the volumetric approaches.
While imaging particle analysis also usually produces a graph similar to Figure 1, it goes well beyond just ESD by measuring many other shape and grey scale qualities for each particle at the same time, while also capturing an image of each particle. So now the user can choose a bin (or set of bins) from the histogram, and display "what's under the curve" by displaying the particle images associated with that bin. What becomes immediately apparent is that individual particles found in each bin can be very different in shape even though they share the same ESD value. Figure 2 shows this graphically by displaying two images with identical ESD that have completely different shapes!
So, the next time you are looking at a particle size distribution, ask yourself "What's Under the Curve?". There's a lot more information to be found underneath that distribution!