Linear measurements performed with a compound optical microscope generally cover a length range of approximately 25 millimeters down to 0.2 micrometer, upper and lower boundaries that are determined primarily by the maximum viewfield diameter and the microscope limit of resolution. This interactive tutorial explores calibration of various eyepiece reticles with a stage micrometer, and demonstrates how the reticle can then be employed to determine linear specimen dimensions.
The tutorial initializes with a horizontal graduated scale eyepiece reticle, having eight major division rules (the Standard Scale reticle), appearing in the viewport superimposed over a stage micrometer at a randomly-selected Objective Magnification. To operate the tutorial, use the X-Translation and Y-Translation sliders to maneuver the stage micrometer rulings behind the eyepiece reticle. Control of the stage micrometer translational resolution is determined by the Slider Translation Adjustment radio buttons, which enable Coarse (default) and Fine positioning of the micrometer graduated rules with respect to those of the reticle. After the micrometer has been placed behind the reticle with the sliders in Coarse mode, click on the Fine radio button and carefully match one of the micrometer rules (preferably a numbered 100-micrometer interval line) with the far left-hand rule of the eyepiece reticle (numbered "0" on the default reticle).
Once the reticle and the stage micrometer rulings have been aligned, use the mouse cursor to click on the superimposed rules at the left-hand rule (the rule labeled "0") of the eyepiece reticle to establish a calibration baseline. A red line (the baseline) will appear where the cursor is positioned when the mouse button is clicked. Next, move the cursor to another position to the right of the baseline at a location where the reticle and stage micrometer rules are again in perfect alignment. Click the mouse button again, and a second red line (the calibration line) will appear. The distance (in micrometers) between the baseline and calibration line will be displayed on the lower right-hand side of the viewport in a yellow box entitled Micrometer Length. Simultaneously, the calculated value (also in micrometers) between major reticle rulings (entitled Reticle Subdivision) will appear on the lower left-hand side of the viewport in a yellow box. The latter value can now be utilized to measure specimen dimensions.
After the reticle has been calibrated, click on the Specimen radio button, located on the upper right-hand side of the viewport, and a specimen will appear in the viewport (selected from the Choose A Specimen pull-down menu). In order to measure a specimen feature, align the edge of the feature with the left-hand rule on the eyepiece reticle (the rule labeled "0") using the X-Translation and Y-Translation sliders. Next, click the mouse cursor on the opposite edge of the specimen feature to perform the measurement. The measured specimen dimension (in micrometers) will appear at the lower right-hand side of the viewport in a yellow box entitled Specimen Measurement. A new specimen can be measured using the same calibration (and objective magnification) by selecting a candidate from the Choose A Specimen pull-down menu. To increase visibility of the reticle when it is superimposed over a specimen, choose a new reticle color (red is the default) from the Reticle Color pull-down menu (choices are black, white, red, and yellow).
Additional objective/eyepiece reticle calibrations can be performed by selecting a different magnification from the Objective Magnification pull-down menu. In addition, a new reticle can be selected from the Choose A Reticle menu. Either of these actions (choosing a new magnification or a new reticle) will re-initialize the tutorial and enable the visitor to start another calibration.
The linear reticles (Standard Scale, Crosshair, Pinwheel) are used for linear measurements, while the grid reticles (Squared Grid, Counting Grid, Concentric Circles, and Miller Squares) are employed for particle counting. The latter reticles can also be calibrated in the manner described above for linear measurements. The Thickness Gauge reticle is useful for comparing relative sizes of fibers and particles. This reticle is calibrated by aligning the rule set numbered 20 with graduations on the stage micrometer.
Calibration of an eyepiece reticle (determination of the micrometer graduation relationship) for a particular objective is typically conducted by following the recommended procedure described below (also see Figure 1). Note that calibration of an eyepiece reticle holds only for the specific objective/eyepiece combination being tested, and for the specific mechanical tube length of the microscope. To avoid unnecessarily repeating the procedure, the calibration information for each combination should be recorded and stored in a convenient location near the microscope workstation.
- After ensuring the microscope is aligned and configured for Köhler illumination, insert the proper reticle into the microscope eyepiece and adjust the eye lens so that the engraved scale on the surface of the glass reticle disk appears sharply focused. Carefully check the orientation of the reticle to verify that the numbers positioned above or below the engraved lines are not reversed. This task can be accomplished by holding the eyepiece in front of a bright light source and peering through the eye lens. Finally, adjust the microscope binocular interpupillary spacing and record this value for subsequent measurements. If the microscope is equipped with compensating adjustments on both eyepieces (as is the case with most modern microscopes), the reticle calibration values will be correct for any interpupillary spacing.
- Place a stage micrometer on the microscope stage and bring the micrometer scale into focus using the microscope coarse and fine focus control knobs. Detecting the scale and translating it into the center of the viewfield is facilitated by the use of a low power objective to first locate the circle surrounding the scale, and then the scale itself. The ring encircling the micrometer scale is visible with the naked eye and should be used to position the stage micrometer in the center of the microscope optical path (stage aperture). In addition, several stage micrometer designs have a line engraved from the ring to the edge of the scale, which is also helpful in locating the scale when using high magnification objectives. Rotate the desired objective into position and ensure that both scales (the stage micrometer and the eyepiece reticle) are visible in the viewfield in simultaneous focus.
- Translate the stage, using the x-y movement control knobs or handles, and/or rotate the eyepiece (and its reticle) to bring the two scales into parallel alignment (Figure 1(a) and 1(b)). Modern mechanical stages are often provided with a limited degree of rotational movement around the microscope optical axis. In this case, loosen the thumbscrew (usually located at the front of the stage, beneath the specimen platform) and rotate the stage until the micrometer and the eyepiece reticle are parallel.
- Position the eyepiece reticle directly over the micrometer (with the stage controls) and align the left-hand rule in the reticle with one of the longer, numbered (100 micrometer) division lines on the stage micrometer (Figure 1(b)). Depending upon the objective magnification factor and eyepiece field diameter, a distance ranging between 150 micrometers and 4 millimeters (twice the length of the stage micrometer scale) will be visible in the eyepieces. Over a distance of 100 to 1000 micrometers (10 to 100 rules) on the stage micrometer, determine two points at which the reticle and micrometer scales exactly match (see Figure 1). For the most accurate measurements, utilize the largest possible range of divisions on both scales. Only occasionally do reticle and stage micrometer graduations coincide over the entire length visible in the eyepieces, but this is often the case with reticles manufactured for specific eyepieces. Finally, determine the apparent length of the eyepiece scale in reference to the divisions on the stage micrometer.
- The micrometer value for the objective in use can be calculated by dividing the known length of the selected region of stage micrometer by the corresponding number of divisions of the eyepiece scale. The result will yield the distance per graduation on the reticle scale for the objective, a quantity often termed the calibration constant. The reticle superimposed on a stage micrometer in Figure 1(b) illustrates alignment of the left-hand rule (marked 0) on the reticle with the stage micrometer division marked 20. Overlap of the two rules is indicated by a red line for clarity. The next area of overlap occurs where the rule labeled 30 on the stage micrometer coincides with the 7.5 mark on the eyepiece reticle. Thus, a 100-micrometer region of the stage micrometer equals 7.5 reticle divisions. Each division of the eyepiece reticle, therefore, corresponds to 13.3 micrometers, for the particular objective/eyepiece combination being calibrated. The number of significant figures appropriate for calculation of the reticle calibration should be carefully scrutinized. Because the minimum resolvable distance in an optical microscope is approximately 0.2 micrometers (under optimal circumstances), a linear measurement below this value cannot be accurately determined.
- When conducting precise measurements using a stereomicroscope equipped with a zoom optical system, it is necessary to use a stage micrometer for each zoom setting on the microscope. Although many microscope zoom rings and control knobs are graduated with the nominal objective magnification, it is virtually impossible to return the zoom control to exactly the same position, a necessary condition for accurate measurements.
- After the eyepiece reticle has been calibrated with the stage micrometer, specimen linear dimensions can be measured. For all measurements, the highest magnification objective should be chosen that enables the entire specimen feature of interest to fall within the span of the reticle scale. Orient the reticle scale to coincide with the contour of the specimen region under scrutiny. Next, move the specimen until the left edge coincides with a numbered line on the eyepiece reticle, and count the number of scale divisions spanned by the target region. Carefully estimate any fraction of a division. To increase accuracy, conduct several measurements on large specimens. When circular or oval specimens are being measured (such as blood cells, yeast, bacteria, etc.), record the dimensions of at least 20 candidates from different fields. The specimen being examined in Figure 1(c) is a human scalp hair shaft, which is approximately 93 micrometers in diameter (measured with a calibrated reticle, as discussed above).
The calibration procedure just described must, of course, be repeated for each objective that is to be employed for linear measurements. It should be noted that magnification varies by a few percent for similar objectives (even from the same manufacturer) inscribed with the same magnification factor (for example, 10x), so each objective should be independently measured. If the microscope is regularly used with a number of different objectives, it may be more convenient to plot calibration curves for each objective in graphical form. This provides an easy mechanism to rapidly determine feature sizes while working with the microscope, without having to repeat the arithmetic when applying the micrometer values for all of the objectives used to conduct measurements.
The calibration procedure described above provides a factor that is valid for a specific optical combination, without requiring knowledge of the actual objective magnification, which usually differs from the nominal power that is imprinted on the objective barrel. In utilizing an objective that contains a correction collar to accommodate variations in coverslip thickness, it is important to remember that the magnifying power changes with different settings of the collar. Therefore, a calibration factor determined for such an objective is only valid at the correction collar setting employed for the calibration. Objectives having adjustable collars provide correction for a wide range of coverslip thickness, but also exhibit magnification changes ranging up to 15 percent over the entire adjustment range.
Matthew Parry-Hill, Thomas J. Fellers, and Michael W. Davidson - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310.