Quantitative microscopy dates to the mid-19th century and is based upon the realization that in a randomly- selected sampling of a polished section, the ratio of the area of a mineral to that of all minerals is a consistent estimate of its volume fraction [18]. Similarly, the perimeter area fraction in two dimensions provides an estimate of the surface area exposure of the constituent phases.
With the digital SEM images, use of the entire image allows measurements of the perimeter and phase surface areas after the image has been segmented into the constituent phases. Image analysis operations on the composite image sum the number of pixels for each discrete phase color to measure the area fraction of each constituent. Similarly, the outer layer of pixels may also be summed to provide an estimate of each phase's surface area. For comparison to other data, such as X-ray powder diffraction, mass percentages may be calculated by multiplying the volume fractions by the specific gravity of the corresponding clinker phase, and normalizing the totals to 100%.