Measurement Techniques

Direct Measurements. Particle diameters can be measured directly in an optical microscope with the use of a filar micrometer eyepiece. This eyepiece contains a scale and a movable cross hair that is operated by a calibrated knob on the side of the eyepiece. A particle is moved so that one side touches one of the fixed scale markings, and the cross hair is moved to touch the other side of the particle. The difference between the two readings is the Feret's diameter of the particle. The eyepiece is calibrated with an optical stage micrometer. This technique is time consuming, and because absolute measurements are not required for accurate size analysis, eyepiece graticules are usually used for direct measurements.

Figure 7 shows typical examples of eyepiece graticules. These patterns are etched on glass disks that are positioned in the back focal plane of the microscope ocular and are therefore in the same focal plane as the particle images. Using one of these gauges, the size range, into which the actual diameter of a particle falls, can be measured easily. Feret's diameter, projected area diameter, or perimeter diameter are measured conveniently with graticules. Where measurements are made from photographs, projected images, or cathode ray tube screens, simple scales or plastic overlay graticules can be used to measure any of the accepted diameters.

Fig. 7 Eyepiece graticules

Image shearing eyepieces are used directly within the optical microscope. This device divides the optical beam into two parts by using mirrors and/or prisms. The distance between the two formed images is adjusted by shearing of the prisms, which is controlled by a micrometer dial on the side of the eyepiece. The maximum horizontal intercept is measured when the two images barely touch. With this device, a particle does not have to be moved to a particular position within the field of view to be measured.

The micrometer can be set to a given diameter, and the number of particles larger or smaller than this measurement can be counted, as determined by whether or not the images are touching. Red and green filters facilitate this by coloring the two images.

Semiautomatic Techniques. Many devices are available to shorten the time required to complete a particle size analysis. Most of these instruments record the number of particles in a size range, as judged by the analyst.

Adjustable light spot analyzers use a circle of light projected onto a photograph. The diameter of the circle can be adjusted by a diaphragm; a foot switch causes one of a bank of registers to record the diameter according to the diaphragm setting. Each particle on the photograph is passed under the light, which is adjusted to measure the projected area diameter or the perimeter diameter.

A transparent electronic graticule is a plastic sheet on which various size circles have been drawn. Under each circle, an electrical contact is connected to one of a bank of registers. When a contact is touched by the analyst with a pencil contact, the register advances one number. This device can be used with photographs, back-projected images, and cathode ray tube screens. The analyst decides which circle best represents the diameter of a particle and touches the corresponding contact.

Recording calipers work in the same manner, with a bank of registers connected to the caliper spread adjuster. Any particles of the prescribed diameter can be recorded with this device.

Recording micrometer eyepieces use a similar recording mechanism, but work directly within the optical microscope. Two movable cross hairs that move toward or away from each other with the turn of a micrometer screw are used to bracket a particle; a button is subsequently pushed to record the diameter. This technique is particularly useful when the depth of field prevents photography of the particles, because each particle can be sharply focused before measuring.

Sensitive surfaces connected to computers facilitate counting from photographs. The computer can be programmed to record diameters when the opposite sides of particles are touched with a pointer, or specific areas of the particle are touched. The computer consequently compiles data to suit user requirements.

Automatic techniques are used for counting large numbers of particles directly within the microscope. The main limitations of these techniques are the inability to distinguish particles that are touching and the fastidious sample preparation that is required.

Spot scanning devices use the moving spot from a cathode ray tube, which is projected through the microscope onto the specimen. When the spot passes over a particle, the light beam is interrupted, and a photocell records the particle. Particles are sized by scanning with different spot sizes. This technique also has been used on photographs, so electron micrographs can be used.

The slit scanning method projects the microscope image onto a slit. The microscope slide is mechanically scanned, and the signal produced as the particle images pass the slit is recorded. The width of the slit can be varied to eliminate coincidence and overlap.

Quantitative image analyzers are computer-controlled devices that use television cameras for direct analysis within an optical microscope. Analysis of photographs can also be accomplished. A quantitative image analyzer can be connected directly to a scanning electron microscope to control the scanning system. Particles can be counted according to their maximum horizontal chords, vertical chords, perimeters, or areas.

Data Presentation. Table 1 shows the most precise form of presenting particle size data. However, graphical representations are more concise and visually show the mean and deviation from the mean. Some graphical presentations can yield specific values for descriptive constants such as the mean, median, and the standard deviation.

Table 1 Particle size data


No. of

Particles, %




percent less

range, tlm

than size













































A histogram is a bar graph that illustrates the frequency of occurrence as a function of the size range. Figure 8 shows a typical histogram for a log-normal size distribution. The smooth curve drawn through the histogram is a valid size-frequency curve if sufficient particles are counted and the number of size intervals is at least ten.

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