A light microscope allows you to view very small objects, and to collect quantitative information as well. Measurements are made within the microscope's field of view, which is the entire area that you see when you look into the eyepiece. If you know the surface area of a field of view, for example, you can count the number of objects per unit area. Knowing the depth of a sample and the area in view, you can count the number of objects, such as cells in a suspension, per unit volume. Using an ocular measuring device, you can measure the linear dimensions (length and width) of a specimen.

This presentation will discuss how to calibrate a microscope for measurement, how to estimate field diameter, and how to count the number of objects in a single field.  We will cover use of a linear measuring device (called an eyepiece reticule), how to estimate vertical dimensions, and how to use a counting chamber to estimate number of objects per unit volume.

Microscopes make excellent measurement instruments, provided that the user knows how to calibrate them. A calibration device called a stage micrometer consists of a thick glass slide with a very precise scale etched into the surface. A typical scale is about 2 mm long, with a line marking each tenth of a millimeter. Usually, one end of the scale is more finely etched, into divisions of 0.01 - 0.02 mm. These etchings are included on only one end of the scale to keep the cost of micrometers—which are far more expensive than plain glass slides—a bit lower. We don’t place specimens directly on a stage micrometer, but rather use it to calibrate the true diameter of the field of view and/or to calibrate another scale, called a reticule, that is built into one ocular.

To determine field diameter using a stage micrometer, one places the stage micrometer on the microscope stage. Next, looking through the eyepiece (using the lowest magnification), one uses the mechanical stage controls to line up a major division of the scale with one edge of a microscope field so that the finely etched portion of the scale overlaps the other edge. By counting divisions, one can estimate true field diameter to the nearest 0.01 or 0.02 mm.  Once a microscope is calibrated at one magnification, it should not be necessary to repeat calibration for other objective lenses. The scale is inversely proportional to the magnification itself.  For example, if the field diameter at 40x total magnification is measured to be 5.2 mm, then the diameter at 400x must be 0.52 mm.
(field of view 1) X (magnification 1) = (field of view 2) X (magnification 2)

Knowing field diameter, one can determine the actual surface area of the specimen in view, count objects in the field, and determine the number of objects per unit area. For accuracy, one may count multiple randomly-selected fields. Often an object will overlap the edge of a field, and counting all overlapping objects results in overestimating the density. A good practice is to set criteria in advance for accepting or rejecting an object. For example, you can divide the field into four imaginary quadrants. If an object overlaps the top or right edge of the field it is accepted, but it is rejected if it overlaps the bottom or left of the field.

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).

An ocular micrometer scale, or reticule, is a scale etched on a glass disk and placed within an eyepiece. The scale is superimposed over any image seen in the microscope, allowing the user to measure any object in the field of view. Such measurement does require the reticule to be calibrated.

To calibrate and/or use an eyepiece reticule, start by focusing the eyepiece itself on the reticule. Looking through that eyepiece only, focus the microscope, then make the adjustment for the other eye as described previously. Then place and center a stage micrometer in the light path. To line up the ocular reticule with the stage micrometer, the eyepiece can be rotated in its tube (without changing focus) and the mechanical stage controls used so that the two images are superimposed. Then measure the distance over which the eyepiece reticule extends and divide by the number of divisions to determine distance per division.

For example, suppose that at 100x an ocular micrometer scale with 50 evenly spaced divisions is superimposed over a portion of stage micrometer that is 1.0 mm (1000 µm) long. In this case, each division of the reticule represents 1000 ÷ 50 = 20 µm per division. The calibration for other magnifications is inversely proportional to objective magnification. For example, if you have 20 µm per division at 100x, you have 5 µm per division at 400x.

(field of view 1) X (magnification 1) = (field of view 2) X (magnification 2)

Once an eyepiece reticule is calibrated, it can be used to measure the length or width of any visible object within the limits of resolution. The reticule is simply superimposed over the object to be measured. The translational stage controls are used to move the specimen itself since the reticule is in a fixed position. To line up the reticule, the eyepiece is rotated in its tube without changing its focus.

In the present example, the investigator wanted to know the diameter of a filament of the alga Spirogyra. First the investigator centered the image using the stage controls. The angle of the filament cannot be changed, however, so it then was necessary to rotate the eyepiece bearing the reticule so that the scale was perpendicular to the filament. The investigator estimated the filament to be 13 divisions wide. With a calibration of 20 micrometers per division, the estimated diameter is 260 µm, or 0.26 mm.

Note that the edges of the filament are indistinct. A different investigator might estimate its diameter as 12, or even 14 divisions. Limits of resolution must be taken into consideration when reporting such measurements. In addition, it can be useful to set criteria for standardizing the measurement. For example, always measuring to the outside edge on both sides of the specimen, or measuring one outside edge and one inside edge.

Suppose that at a total magnification of 400x, each division of an ocular scale is determined to be 2.5 µm wide. Suppose you then use the scale to estimate the length of a flagellum of an individual Chlamydomonas reinhardi. Let us further suppose that after superimposing a line over the apparent origin of the flagellum, the end appears to reach 4.5 divisions from the beginning. The calculated length, then, comes out to 4.5 x 2.5 = 11.25 µm. Is that the length that you should report?

The quantity, 11.25 µm, implies an accuracy to the nearest hundredth of a micrometer. One hundredth of a micrometer is just 10 nanometers, or 10 billionths of a meter.  Ten nanometers is the diameter of some molecules, or even atoms. Obviously, you cannot resolve molecules with the aid of a light microscope. In fact, it takes very high magnifications to image a molecule in an electron microscope, which provides far greater resolution than a light microscope.

The calibration, 2.5 µm per division, doesn't mean each division is accurate to half a micrometer. It only means that we use that calibration as a multiplier. A final result should be reported with an accuracy that reflects the precision of the instrument. The very best resolution we might expect at 400x is to the nearest 1 µm, and then only under ideal conditions. The length of this flagellum should be reported as 11 µm.

Suppose now that you intend to measure diameters of a couple of dozen filaments or so, in order to report a mean value. You would record the length with full precision, which in this case is 11.25 µm. After collecting the raw data and determining mean diameter you then suppress excess digits. For example, suppose you collect data from 23 cells and obtain a mean value of 11.9022 µm. The mean should be reported as 12 µm. You must not report the mean as 12.0 µm, which implies an accuracy to the nearest tenth of a micrometer.

To measure a vertical dimension using the fine focus, one must be able to focus separately on the top, and on the bottom of a specimen. For example, to measure the depth of liquid under a cover slip, it is necessary to measure the distance from the top of the slide to the bottom of the cover slip. To do so while lowering the focus requires one to focus on the bottom of the cover slip (or on a small object attached to it). While keeping track of the distance traveled, one then focuses on the top of the slide or on a small object on top of the slide.

It is easiest to measure the depth of an object that provides distinctly different cross sectional views from top to bottom. For example, the amoeboid protists known as Difflugia develop a shell, called a test, that encloses the cell. The test is usually textured and curved, and it is semi-transparent. When the organism is active, pseudopodia protrude from an aperture in the base of the test.

Depending on the type of microscope you are using, you will either raise the stage or lower the nosepiece until the object comes into view. When the central part of the test comes into focus, you are looking at the very top. When the aperture appears in focus, you are viewing the bottom of the test. The tips of the pseudopodia are attached to the surface of the slide. When you measure the distance traveled in the vertical direction from the top of the test to the tip of the pseudopodia, you have measured the height of the organism.

I would not rely too heavily on the precision of measurements using a fine focus control. For one thing, depth of focus limits the accuracy with which one can estimate a position. There also is the matter of hysteresis. We have hysteresis when the direction of change has a significant effect on a result. If I focus precisely on a specimen, then de-focus by moving the stage down a precise number of turns, the specimen is not in focus when I move the stage back up the exact number of turns. No machinery is perfect. Hysteresis results from slippage, for example, as a knob is turned. To minimize the effect, one should approach calibrated positions by moving a control in the same direction each time.

Another way to estimate vertical distance is to consider the volume of material under a cover slip. For example, suppose you have a square cover slip of 22 x 22 mm and you place it over a 40 µl drop of aqueous sample. One milliliter (1000 microliters) of pure water at standard temperature and pressure has a volume of 1 cubic centimeter, while a microliter has volume of one cubic millimeter. Forty microliters, therefore, have a volume of 40 cubic millimeters. The surface area under your cover slip is 484 sq. mm, so the space under your cover slip is 40 ÷ 484 = 0.082 mm. Assuming the liquid is spread out evenly under the cover slip and rounding to reflect precision, the space under the cover slip is 80 micrometers deep.

A counting chamber is a specialized microscope slide with an etched surface in the form of a grid, along with supports for a cover slip, so that the space between the grid and the bottom of the cover slip is precisely calibrated. Cover slips for counting chambers are specially made and are thicker than those for conventional microscopy, since they must be heavy enough to overcome the surface tension of a drop of liquid. Counting chambers are used for determining the number of cells per unit volume.

One type of counting chamber is called a hemacytometer because it was designed for counting the formed elements (red cells, white cells, and/or platelets) in blood samples. A clean 0.4 mm thick coverslip is placed over the clean grid and a suspension is introduced into one of the V-shaped wells with a Pasteur or other type of pipet. The area under the cover slip fills by capillary action. Enough liquid should be introduced so that the mirrored surface is just covered. Overfilling can "float" the cover slip, leading to an inaccurate count. The charged counting chamber is then placed on the microscope stage and the counting grid is brought into focus at low power. It is essential to be extremely careful with higher power objectives, since the counting chamber is much thicker than a conventional slide.