However, the system cannot really measure to that small a level because of sampling. The Nyquist–Shannon sampling theorem
states that in the conversion of a continuous signal to a discrete signal, one can only resolve the original signal by sampling
at two times the rate of the original sample. To use the previous example, one can only resolve a 2.5 µm signal by sampling
at a minimum rate of 1.25 µm. Using the same example, with a 2.5-µm minimum pixel size, the smallest object the system can
possibly resolve is 5 µm in size. In terms of particle analysis, the term "resolve" would apply only to counting a particle,
and not to any higher-level description of the particle, such as shape. Indeed, the higher the order of the measurement desired,
the more resolution is needed (3).
As a result of diffraction limitations inherent to microscopy-based systems and sampling theory as discussed above, dynamic
particle imaging systems are limited to counting particles no smaller than 1 µm in size, and being able to differentiate shape
information for particles no smaller than 2–3 µm in size (4). To image particles smaller than these limits requires electron
microscopy, where the sample size and number of particles that can be imaged are extremely limited, and therefore statistically
significant numbers of particles cannot be achieved. Other synthetic image techniques, in which an image is produced by sampling
another characteristic (e.g., Brownian motion, or atomic force microscopy), can also be used for smaller particles, but these
are not direct optical images.
The second factor to consider when using dynamic imaging particle analysis is the effect of thresholding. Not only are digital
images quantized in the spatial domain in terms of a limited number of pixels, but each pixel is quantized in terms of gray-scale
(or color in the case of color imaging) resolution, also. In most typical systems, the gray-scale (i.e., intensity) value
of each pixel is limited to 256 levels or eight bits. In a color system, there are eight bits each of red, green, and blue.
To make rapid measurement calculations on the image data in particle image analysis, the gray-scale intensity is reduced to
a single bit (i.e., on or off) through a thresholding process. In imaging particle analysis, this thresholding is performed
by comparing each pixel of an incoming image that may contain particles with the same pixel of a background image taken when
no particles were present in the system. Because most systems are "bright-field" or backlit, a particle in the optical path
will reduce the amount of light passing through to the camera sensor, therefore the incoming pixel intensity will be darker
(i.e., a smaller number) than the background calibrated value for the same pixel. For this reason, most imaging particle analysis
systems will define a threshold as either a delta value or percent value darker than the background.
For opaque particles, thresholding in this fashion (i.e., in which pixels are darker than the background) works quite well.
However, as previously mentioned, protein aggregates are semitransparent and amorphous. In fact, because of the way light
is bent through the structure of the aggregate, many of the pixels within the aggregate will be brighter than the background.
Therefore, if only a dark threshold is used, the result will be that a single aggregate will be chopped up into multiple small
particles by the thresholding process. This technique results in a severe overcounting of small particles and undercounting
of large particles (5).