Point Counting Techniques

In discussing the Principle of counting techniques, the idea was introduced of using a point to represent a unit of area, and to count points to estimate areas.

In practice, transparent overlays are generally applied to micrographs of interest, where the overlay has the array of points used for counting purposes. The question of what form these points takes is really up to the user, but most people find that points do not really work that well, for they can be difficult to see with real micrographs.

Crosshairs seem to work better:

And it is then a small step to go back to a grid, but where the focus is on the corners of the squares rather than what is within them.

The use of a grid has an added benefit. Related counting methods that depend on having lines across the field can be used to estimate feature perimeters (which in 3-dimensional terms provides a measure of surface area), so the grid supports them too.

Performing area counts

So to estimate the area of the green profiles it is merely necessary to count those corners of the grid that hit the profiles. These are marked in red here:

In other words, 4 for the left profile and 6 for the right one. So the number of points hitting the profiles is 10, whereas the total number of points in the grid over our test area (the box) is 144, i.e.

P	= number of points hitting profiles
	= 10
P_t	= total number of reference points
	= 144
P/P_t	= area fraction
	= 7%

The results of point counting are generally expressed in a fractional sense as the fractions are independent of magnification.

If the particular section (or sections) is representative, then it is possible to extrapolate from the area fraction to the volume fraction (V/V_t). The number is of course the same.

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