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Author(s): Roberta Anding, MS, RD/LD, CDE
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#### Estimating Number of Objects Per Unit Area

Suppose you wish to estimate the number of structures per unit surface area of a specimen. For example, you might be interested in the number of stomata (microscopic pores that permit gas exchange through the epidermis) on a typical leaf of one species of deciduous tree, versus that of another species. One way to accomplish such an estimate is to make an impression of the lower leaf surface using a film of nail polish or white glue. After peeling the dried film from the leaf and flattening it on a slide under a coverslip the impressions of stomata can be seen clearly.

You will wish to estimate the number of stomata per microscope field, determine the surface area in the field of view using physically meaningful units, and obtain the number of stomata per unit area, based on measurements taken from several fields. The surface area is, of course, pi times the square of the radius of the field (Π r^2). For example, at 400x with field diameter of 0.52 mm, the magnified image covers 0.21 sq. mm. Notice that I rounded to two significant digits, since that is what I started with.  It would be silly to report the surface area calculation with full precision, which is 0.21237166 when taken to eight places because that is beyond the precision of our measurement tool.

We do have a problem when a stoma (singular term) overlaps the edge of the field. Do we count it or not? If you count all such structures, you will overestimate the density because, in effect, you are enlarging the surface area over which you make the count. One solution, which also applies to counting cells with a counting chamber such as a hemacytometer (originally designed to count blood cells), is to set criteria for accepting or rejecting a structure in the count. You might arbitrarily divide the field into four quadrants, pretending that there are invisible crosshairs in the field of view. You then can accept all structures that overlap the field in the upper right hand or lower left hand quadrants and reject those that overlap in the top left or bottom right hand quadrants. By setting criteria before viewing an image, you can produce an unbiased and accurate estimate of density. Supposing you counted 96 stomata in four fields at 400x, the the density, assuming it is uniform, is 113 stomata per sq. mm, which rounds to 110, or 1.1 x 10^2 stomata per sq. mm. (mm^2).

### National Space Biomedical Research Institute

This work was supported by National Space Biomedical Research Institute through NASA cooperative agreement NCC 9-58.