Linear Measurements (Micrometry)
The first reported measurements performed with an optical microscope were undertaken in the late 1600s by the Dutch scientist Antonie van Leeuwenhoek, who used fine grains of sand as a gauge to determine the size of human erythrocytes. Since then, countless approaches have been employed for measuring linear, area, and volume specimen dimensions with the microscope (a practice known as micrometry or morphometrics), and a wide variety of useful techniques have emerged over the past few hundred years.
All measurements of length are based on a comparison of the object under scrutiny with another of known dimensions, or with a standardized, calibrated scale. In order to determine the length or width of a wooden board, for example, a ruler or measuring tape is placed in contact with the board and the dimensions are noted by direct comparison to the graduated numerical markings on the ruler.
This basic principle is applicable to the measurement of specimens observed in the microscope, but in practice, it is often not possible with a compound microscope to place a ruler in direct contact with the specimen (although this is often done in low-magnification stereomicroscopy). Alternative mechanisms for performing measurements at high magnifications in compound optical microscopy must be employed, and the most common of these is the application of eyepiece reticles in combination with stage micrometers. A majority of measurements made with compound microscopes fall into the size range of 0.2 micrometers to 25 millimeters (the average field diameter of widefield eyepieces). Horizontal distances below 0.2 micrometers are beneath the resolving power of the microscope, and lengths larger than the field of view of a widefield eyepiece are usually (and far more conveniently) measured with a stereomicroscope
Illustrated in Figure 1 is a modern microscope eyepiece (often termed an ocular) equipped with an internal reticle scale. Also presented in the figure is a stage micrometer, which contains a small metallized millimeter ruler that is subdivided into increments of 10 and 100 micrometers. Juxtaposing the graduations on the eyepiece reticle with those on the stage micrometer enables the microscopist to calibrate the reticle gauge and perform linear measurements on specimens.
The first reported measurements performed with an optical microscope were undertaken in the late 1600s by the Dutch scientist Antonie van Leeuwenhoek, who used fine grains of sand as a gauge to determine the size of human erythrocytes. Since then, countless approaches have been employed for measuring linear, area, and volume specimen dimensions with the microscope (a practice known as micrometry or morphometrics), and a wide variety of useful techniques have emerged over the past few hundred years. Many of these methods are of practical use, and can be segregated into several generalized categories, as outlined below:
Measurements obtained by direct comparison of the specimen dimensions to a micrometer scale in the x-y plane of the microscope (for example, the use of calibrated mechanical stages and specialized measuring microscopes). Mechanical stages enable movement in both the x and y axes, and often employ a vernier scale that allows reading of the stage displacement with an accuracy of 0.1 millimeter (the accuracy of the method).
Techniques that utilize projected real images and those made by means of a traditional or digital camera system combined with a stage micrometer. Because the micrometer scale is not viewed simultaneously with the specimen, an image of the micrometer must be recorded by means of a photomicrograph or a digital camera system. This technique is very reproducible, often yielding results that are accurate to a micrometer or less.
Linear comparisons obtained by projecting a measuring scale into the field of view or by inclusion of objects having a known size with the specimen. Often, homogeneous preparations of polystyrene or glass beads can be included with specimens, such as erythrocytes, to provide a size reference. Measurements are then performed utilizing a photomicrograph or digital image. The accuracy of this method is variable and depends on the homogeneity of the comparison objects.
Direct specimen measurements made by means of graduated scales located within the microscope, such as eyepieces containing fixed or moveable reticles (the most common method). Reticles must be calibrated together with a stage micrometer, but provide an accuracy of approximately 2-10 micrometers (3 to 5 percent, depending on magnification and the resolution of the stage micrometer).
Calibrated microscope slides and counting chambers are utilized for direct linear measurements or for counting the density of specimen particles. Accuracy depends on the separation distance between ruled lines, but averages between 10 and 50 micrometers.
Fixed dimensions of the microscope can be employed to produce a very rough estimate of specimen dimensions. By measuring or calculating the viewfield size, the relative linear dimensions of a mounted specimen can be determined.
Determination of vertical distances along the microscope optical axis (z-direction) by utilization of a calibrated fine focus adjustment on the microscope. This technique is often complicated by refraction artifacts and spherical aberration, but can provide an average accuracy level of several micrometers.
A number of the techniques that are commonly employed for the measurement of objects (specimens), both in the microscope and in everyday surroundings, involve the principle of a transfer scale. Direct comparison measurements require access to the object under scrutiny, and an accurate ruler or graduated scale. If a measurement is necessary and no suitable ruler is available for comparison, a transfer scale can often be employed to determine critical dimensions. The transfer scale may be any suitable substitute that can be placed in contact with the object, allowing the length (or width) of the object to be directly compared, or transferred, onto the transfer scale. The absolute dimension of the object is later determined by comparison to a calibrated scale (or ruler). If the transfer scale itself is marked with graduations in arbitrary units, then the graduations must be referenced to absolute units by comparison to a standard.
Conjugate Image-Forming Focal Planes
The principle of the transfer scale has been utilized in everyday activities since the earliest days of mankind, and can be applied to specimens studied in the microscope even though they may not be accessible for direct measurement with a standardized scale. There are various approaches for employing a transfer scale in microscopy, including placing the scale on a transparent material for use with a drawing tube, or conducting measurements directly on a projected image. An alternative method is to photograph or engrave the scale onto a glass element, which can be placed in the optical path at one of the image-forming conjugate planes of the microscope so that it can be observed in sharp focus superimposed on the specimen image. Before a quantitative measurement can be performed, the arbitrary divisions of the transfer scale must be calibrated by comparison to absolute graduations of a master scale, such as a stage micrometer.
A wide variety of specimens can be mounted directly onto a calibrated microscope scale, such as those imprinted on specialized measuring slides, and measurements can then be conducted by employing absolute units. If this is not possible, then the image of a transfer scale must be superimposed onto that of the specimen in the manner described above. The most common technique currently in use for measuring specimen features with an optical microscope is to compare feature size with the graduations of a scale that is strategically located in the microscope optical train. In order to conduct direct comparison measurements, the scale within the microscope must appear simultaneously in sharp focus with the specimen.
The critical requirement in superimposing a graduated scale onto the specimen, in such a manner that it can be imaged together with the specimen, is to place the scale in a suitable conjugate plane of the microscope. Two primary sets of principle conjugate focal planes occur along the optical axis of a properly focused and aligned compound microscope. One set of planes consists of four image-forming or field planes (see Figure 2), while the other consists of four illumination or aperture planes. Each plane within a set is termed conjugate with the other planes in the set because they are simultaneously in focus, and can be viewed superimposed upon one another when observing specimens through the microscope. An object placed in one plane of a conjugate set will appear in sharp focus at all other conjugate planes of the same set. Obviously, if a scale is to be visible and in focus while observing the image of a specimen, the scale must be placed in one of the image-forming set of planes.
Presented in Figure 2 are the common image-forming conjugate planes in a typical transmitted light microscope and a schematic drawing of the optical train (on the left-hand side of the figure). Potential measuring reticle locations in the optical pathway are the eyepiece fixed diaphragm, the specimen plane, and the field diaphragm. Reticles can also (theoretically) be positioned in the camera and/or retina image plane, but this procedure is difficult to accomplish, impractical, and usually not necessary. Note that the field diaphragm in the microscope vertical illuminator, utilized for epi-illumination, is also a suitable (but difficult to access) location for a reticle designed to perform measurements in reflected light microscopy.
From a consideration of the list of conjugate image-forming planes, it is apparent that one possible location for a scale is the plane of the illuminated field diaphragm. A scale placed in the plane of the field diaphragm will appear simultaneously in focus with a specimen on the microscope stage (see Figure 2). Although numerous techniques for inserting a measuring scale at this position have been reported, it is not easy to implement on many microscope designs, primarily due to the difficulty in gaining access to the iris diaphragm. A majority of modern microscopes are constructed with the field diaphragm located within the base of the instrument and inaccessible to the operator. Unless the scale can be located precisely in the plane of the field diaphragm, the condenser must be relocated along the optical axis (defocused) in order to bring the scale into focus. As a result, the altered microscope configuration may differ significantly from that required to achieve true Köhler illumination.
The intermediate image plane is an alternative location in the image-forming conjugate set at which a measuring scale can be inserted. This plane coincides with the eyepiece fixed diaphragm, which is generally easily accessible (Figure 2). Nearly any eyepiece can be fitted with a scale in the focal plane, converting the eyepiece into a measuring device for specimen features observed in the microscope. Eyepiece scales are often referred to as reticles, although the terms reticules, or graticules are commonly employed in the same sense and will frequently be encountered in the literature. The most common conventional eyepieces differ in respect to the physical location of the fixed diaphragm. Some eyepiece designs position the diaphragm in the center of the unit (between the lenses), while other models have a fixed diaphragm at the base of the eyepiece, beneath, and external, to the lens assembly. In both eyepiece styles, the field diaphragm is located at the intermediate image focal plane, but the external diaphragm design is preferred for measurement because any reticle, pointer, or other scale will be outside the optical system of the eyepiece.
One of the simplest eyepiece designs, known as the Huygenian (or Huygens) eyepiece, consists of two plano-convex lenses mounted with their convex faces oriented toward the objective (as illustrated in Figure 3). The lens nearest the eye is referred to as the eye lens, and the one closer to the objective is termed the field lens. Eyepieces of this type are uncorrected for optical aberration, and have the disadvantage that the image plane is located between the two lenses (internal diaphragm). Therefore, reticle accuracy is affected by aberrations of the eye lens alone, while the specimen image suffers from any optical defects arising in the field lens as well.
The Ramsden eyepiece has a construction motif similar to the Huygenian eyepiece, except that the field lens is oriented with the plane surface facing the objective (Figure 3). In addition, the focal plane and diaphragm are located outside the optical system (external diaphragm design), just beneath the field lens. A reticle or similar scale placed in the diaphragm will experience less distortion than with the Huygenian design, and any optical aberrations of the eyepiece will affect the specimen and reticle images equally. One of the primary applications of the Ramsden eyepiece is in micrometry.
A more highly corrected and refined version of the Ramsden design, known as the Kellnereyepiece, employs an achromatic doublet for the eye lens to more fully correct chromatic aberration of the field lens. Kellner eyepieces (not illustrated in Figure 3) also feature a high eye point, which is useful to operators wearing eyeglasses, but they introduce a small degree of distortion to the image. Because the lower focal plane is external to the optical system in the Kellner eyepiece, aberrations affect the intermediate image and eyepiece reticle equally, and therefore, this eyepiece style is ideal for conducting accurate measurements with the microscope. Many infinity-corrected microscopes are equipped by the manufacturers with Kellner-style eyepieces, which feature a removable fixed diaphragm tube threaded into the lower portion of the eyepiece barrel. Removal of the diaphragm tube and installation of a reticle can be easily accomplished in a few minutes without disassembly of the eyepiece internal lens element mounts.
Prior to the introduction of infinity-corrected optical systems, compensating eyepieces were utilized to assist in the correction of chromatic aberration. These eyepieces are generally constructed with two separate lenses, one or both of which are doublets or triplets (see Figure 3; widefield eyepiece). Compensating eyepieces can be identified by the color fringe appearing around the inside edge of the fixed diaphragm when the eyepiece is viewed in front of a bright light source (ordinary eyepieces display a blue fringe, while compensating eyepieces exhibit a yellow, orange, or blue fringe). Chromatic difference of magnification, an aberration common to all high-power objectives, can be corrected by coupling the optical system to a compensating eyepiece. In addition, compensating eyepieces are designed to correct image curvature to a limited extent.
The correct position for reticle placement is the field stop or fixed diaphragm of the eyepiece, which is located in the intermediate image focal plane. Modern eyepieces usually contain a retaining ring that can be unscrewed from the bottom of the eyepiece for insertion of a reticle. After the reticle is properly seated at the fixed diaphragm, the retaining ring is reinserted and tightened. Stereomicroscope eyepieces often contain spring-loaded holders used for mounting reticles. Cementing the reticle into the holder will ensure proper orientation, and the entire assembly is inserted into the eyepiece barrel and moved towards the eye lens until proper focus is achieved. The reticle holder will maintain a constant position due to spring tension of the holder on the sides of the eyepiece barrel. The focal point of the reticle can be altered to accommodate the observer's eye by translating the entire assembly up or down. Before using this type of reticle holder, the diaphragm of the eyepiece must be removed to allow the reticle holder to slip into the eyepiece tube.
As previously stated, linear measurements require the comparison of the object to be measured with a standardized scale, such as a ruler. In utilizing eyepiece reticles or micrometer eyepieces for measurements in the microscope, the arbitrary units of the transfer scale (reticle), which is superimposed upon the specimen image, must be converted to absolute units, such as millimeters or micrometers. Calibration of the reticle scale graduations is commonly performed by imaging a stage micrometer with the same objective to be used for specimen measurements. A proper calibration involves determining an absolute distance on the stage micrometer, imaged in place of a specimen, which corresponds to one division of the scale in the eyepiece reticle. This value is often referred to as the micrometer value, or calibration factor, for that particular objective. Once the value has been determined, the size of any specimen feature may be calculated by multiplying the number of eyepiece reticle divisions spanned by the feature with the calibration factor for the objective in use.
Stage micrometers designed for applications employing transmitted-light microscopes consist of a standard-sized microscope slide (1 x 3 inches) having a scale of defined length attached directly to the surface, or preferably, sandwiched beneath a cover glass of known thickness. Micrometers commonly have a graduated scale either one or two millimeters in length, subdivided into units that are one-tenth millimeter in length (100 micrometer units). Each 100 micrometer unit is further subdivided into ten equal sections, resulting in the smallest graduation representing ten micrometers.
The majority of microscope objectives are corrected for use with a coverslip of standard thickness (0.17 millimeters), and therefore, this is the most commonly employed coverslip thickness for stage micrometer scales. Micrometers are also available without a coverslip, and this type should be used with reflected light objectives that are corrected for zero-thickness coverslip (or the absence of a coverslip). Some stage micrometer designs utilize a metal plate, equal in size to a standard microscope slide, as a carrier for a small circular glass insert that is imprinted or engraved with the graduated scale.
The actual measuring scales may be manufactured by a photographic process, but the lines resulting from this method are not as sharp and accurately defined as those formed by physically engraving the lines. An alternative process for producing sharp micrometer lines is electrodeposition of a metallic film directly onto the glass surface of the microscope slide. On many stage micrometers, the scales are encircled by a black line that eases the task of locating the minute graduations, and to assist in rough focusing of the microscope. Although photographically produced micrometers are adequate for routine work, especially at lower magnifications, their lines are too ragged along the edges and are too wide for accurate measurements, or for use at high magnification. These micrometers should be restricted to rough measurements at low magnifications.
In applications utilizing epi-illumination (reflected light), the transparent glass stage micrometer design is not suitable, and scales that are engraved directly on highly polished metal are used instead. Microscope objectives utilized with epi-illumination, such as in reflected-light metallography, are usually corrected for use without a coverslip, and require a stage micrometer without a coverslip over the rulings for accurate measurements. As a result, the unprotected scales are vulnerable to damage and must be treated with great care to avoid scratching and contamination with dust, dirt, fingerprints, or other debris.
Eyepiece Reticle Calibration
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 4). 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 unnecessarily avoid 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 4(a) and 4(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 4(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 4). 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 4(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 4(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.
Eyepiece Reticles and Specialized Stage Micrometers
A wide variety of eyepiece reticles has been developed for numerous linear, area, and counting measurements with the microscope (see Figures 5 and 6). The simple crossline reticle (Figure 5(a)) is often employed as a location mark for measuring large specimens with a graduated mechanical stage. This type of reticle is also commonly found in microscopes equipped for crossed polarized illumination to assist the observer in determining the orientation of birefringent specimens in relation to the vibration axes of the polarizers. For linear measurements, either the horizontal or vertical line rule is superimposed over one edge of a specimen feature under study. Next, the graduated mechanical stage is translated in either the x or y direction until the opposite edge coincides with the reference line, and the size of the feature determined by examining the scale on the mechanical stage. Measurements that employ mechanical stages should be repeated from left to right (or top to bottom) and vice versa to compensate for backlash error in the stage gearset.
Horizontal and vertical reticle scales (Figure 5(b) through Figure 5(g)) are manufactured in a wide spectrum of configurations to suit any linear measurement requirement. Graduated horizontal scales (Figure 5(b)-5(e)) are the most common, and usually consist of a 10-millimeter scale subdivided into 8, 10 or 100 divisions. These reticles are useful for measurements of all specimen feature sizes, and often contain reference marks to aid calibration and measurement. Crossed micrometer scale reticles (Figure 5(f) and 5(g)) are employed for two-dimensional linear measurements, or for convenience when separate measurements are taken in a vertical and horizontal direction. Tapered gauge reticles (Figure 5(h)) consist of several ruled line pairs that have differing gaps between the lines in each pair. Engraved beside the line pair is a reference number for calibration of the reticle with a stage micrometer. Tapered gauge reticles are convenient for measuring the size of mixed fibers and similar specimens that have repeating feature dimensions.
Reticles designed to assist in the analysis of particles and fibers often contain grid squares, globes, concentric circles, and protractors, as illustrated in Figure 6. Square and grid reticles (Figure 6(a) through Figure 6(d)) are employed in the systematic measurement of small feature size or to count microbes, blood cells, and small particles. In most cases, a selected region of the specimen is counted and the result is multiplied over the entire area of interest to derive a quantitative result. One of the most common counting applications requires a Miller reticle (Figure 6(b)), which enables the operator to determine the number of particles in one of the smaller squares, then multiply the result to calculate the total number of particles contained within the reticle boundaries. Miller reticles are also useful to compare the proportion of large to small particles in a specimen. Whipple reticles (Figure 6(c)) are similar in design to the Miller reticle, but are intended to enable the measurement of smaller specimen features (pigment dispersions, colloidal particles, dust, and bacteria). Reticles designed for random analysis and stereology (the science of deriving three-dimensional data from a two-dimensional specimen) are available in several popular designs (Figure 6(d) is an example).
Circular and angular reticles (illustrated in Figure 6(e) through 6(h)) are available in a wide array of designs to accommodate numerous measurement requirements. Concentric circular reticles (Figure 6(e)) are employed to perform two-dimensional measurements similar to those undertaken with crossed scale linear reticles. However, in this case, the center of the (usually circular) specimen is placed to coincide with the center of the reticle. Similar reticles are inscribed with protractors, gauge sizes, and reference points in a variety of combinations (Figure 6(f) through Figure 6(h)) for estimating arcs, angles, and radii. Some reticles (Figure 6(f)) contain both linear and angular rules for simultaneous measurements of specimen features. Typical specimens measured with these reticles are abrasives, fertilizers, fibers, fine dust, pigments, plant seeds, coal silica, sand grains, soil particles, and similar particles.
In the semiconductor industry, the size and position of microscopic features on masks and wafers is critical to fabrication assembly lines. The linewidth standard is a calibration standard (stage micrometer) utilized to maintain consistency between measurements conducted at different plants in remote locations. A soda-lime glass plate of defined dimensions is coated with anti-reflective chrome having a thickness between 110 and 130 nanometers and an optical density between 2.6 and 3.4. At the center of the standard is a clear rectangle measuring 4 x 5 millimeters, along with the letters NPL (an acronym for the National Physical Laboratory in Teddington, England), which enables easy identification of the plate center. Linewidths are arranged in eight pattern groupings consisting of opaque and clear lines having nominal widths ranging from 0.25 to 10 micrometers.
Another class of stage micrometers, which is popular and often employed in objective calibration for quantitative microscopy, are resolution targets designed to measure the performance of the microscope optical system. Resolution targets consist of custom layouts containing positive, negative, and/or semi-opaque pattern groupings, often arranged as several lines and numbers having varying widths and lengths or in test stars. The resolution capability of a high performance microscope objective can often be accurately estimated by careful investigation of results obtained from a suitable resolution target.
Included in the broad category of stage micrometers are calibration scales (previously discussed in detail), finder reticles, and counting chambers (see Figure 7). Finder reticles are utilized for locating a region of interest on a specimen, while counting chambers are designed to enable particle and cell counts in a specific volume of liquid. Counting chambers are widely employed for counting blood cells and spermatozoa, and consist of a thick glass slide (Figure 7) having a central polished and ruled platform. The platform is positioned a short distance (typically 0.1 millimeter) beneath twin polished coverslip supports to create a chamber that can be filled with a precise quantity of fluid. In practice, a clean glass coverslip is placed over the chamber and centrally positioned on the polished supports. The gap between the ruled counting platform and the coverslip equals 100 micrometers, and the ruled (engraved) face is divided into squares of exact dimension. As a result, the volume of the liquid placed in the chamber can be easily calculated to yield an accurate analysis of the number of particles (cells) per unit volume in a suspension.
The most common type of counting chamber, which is designed for counting blood cells, is known as a hemacytometer (see Figure 7). Several different hemacytometer grid patterns are offered by manufacturers, but most contain a large square boundary subdivided into smaller squares to assist counting. Hemacytometers are generally utilized for counting and measuring particles smaller than about 50 to 100 micrometers. Often, the specimen to be counted must be accurately diluted with serial dilution pipettes prior to filling the counting chamber to avoid an excessive number of particles, which can be difficult to count. A particle density of 5 to 10 particles per smaller square is considered the optimum concentration for quantitative analysis.
Filar Eyepiece Micrometer
The standard eyepiece reticle, when combined with a precision stage micrometer, provides a rapid, convenient, and accurate means of conducting measurements in the microscope. However, for easier and more precise measurements (with greater objectivity), a specialized vernier micrometer eyepiece, known as the Filar eyepiece micrometer, is often considered essential. This specialized eyepiece micrometer utilizes the same principle as a standard eyepiece and reticle combination, but features a moveable line rule (or line rule group) in addition to a fixed or mobile graduated scale positioned in the focal plane. The Filar micrometer avoids the necessity to estimate fractions of a division on a stage micrometer (a difficult and subjective maneuver), which can lead to considerable error.
The mobile line rule group in a Filar micrometer is designed to translate across the field of view, traversing a fixed vernier scale, by means of a precision screw mechanism that is operated by rotating an external drum. In general applications, a single rule or other reference point (depending upon the particular design) is aligned with one end of the specimen feature to be measured and a reading of the calibrated drum is noted. The drum is then rotated to move the reference line across the specimen feature, and a second reading is taken on the drum scale. The difference between the two readings yields an apparent linear dimension of the specimen feature measured, and when calibrated with a stage micrometer, enables an absolute determination of the feature size.
Some Filar micrometer design variations incorporate an additional movement of the reticle scale by the external drum, which allows zeroing of the drum scale after the reference line has been positioned at the first edge of the object to be measured. This feature enables each measurement to begin with the drum scale on zero, and avoids the necessity of determining the difference of the two drum readings. For most Filar micrometers, the primary reticle scale has a travel distance of 10 millimeters. The scale is also divided into 100 graduations with each division representing 0.1 millimeter. The drum of the micrometer screw is also divided into 100 intervals, so that one interval of the drum division corresponds to 0.1 interval of the eyepiece scale. Full rotation of the drum translates the measuring rule (line) across one interval of the eyepiece scale.
Several modern Filar eyepiece micrometer styles contain an internal zoom lens system that eases calibration of the micrometer with different objectives. The lower portion of the eyepiece contains a graduated ring that can be rotated to optically alter the effective tube length in order to superimpose graduations of the stage micrometer directly onto the internal scale of the Filar micrometer.
Axial Linear Measurements
Measurements of specimen depth, along the optical (or z) axis of the microscope, can be performed with microscopes having graduated fine focus knobs. Prior to conducting axial measurements, the value of each division on the graduated focus knob must be determined. In many cases, the manufacturer can provide this information, but it can also be measured experimentally using a glass coverslip. Carefully measure the thickness of the coverslip with a machinist's micrometer or dial caliper (as accurately as possible), and then place a mark on each side of the coverslip with a felt-tipped pen and lay it onto the surface of a standard microscope slide. Focus on the mark placed on the upper surface of the coverslip and note the position of the fine focus knob graduations with respect to a reference point. Locate and focus on the lower surface mark and record the fine focus knob position once again. The axial distance corresponding to each division of the fine focus knob is equal to the thickness of the cover glass (in micrometers) divided by the total number of knob graduations traversed from the top to the bottom of the coverslip.
In order to measure specimen axial dimensions, the feature of interest is located in the viewfield and the microscope focused on the bottom surface of the specimen. After achieving focus, the exact position of the focus knob is recorded. Next, focus is shifted to the upper specimen surface and the new focus knob value then subtracted from the one obtained from imaging the bottom surface. Specimen dimensions can be calculated by multiplying the number of focus knob increments by the calibration factor discussed above or supplied by the manufacturer.
Axial measurements are complicated by specimen depth of field fluctuations, which are partially determined by the objective numerical aperture and magnification factor. Several additional factors, which must be addressed, are refraction artifacts and spherical aberration that often occur when specimens of significant thickness are imaged through aqueous solutions or other (mounting) media having inhomogeneous refractive index. It should also be noted that axial measurements combine quantitative analysis of a micrometer scale coupled to the subjective determination of best specimen focus. For this reason, many microscopists do not rely on this technique for accurate measurements.
Even if a significant amount of care is taken in operating the microscope and in the calibration of the reticles utilized for conducting measurements, there are several possible sources of error that can affect the calibration process, as well as the actual measurement of specimen features. An important consideration when using a stage micrometer to calibrate an eyepiece reticle is to include as many of the stage micrometer graduations as possible in the calculation. This will minimize errors due to variations in the individual graduation intervals, in addition to the potential error in precisely identifying the edges of individual lines. Averaging over several intervals becomes problematic when calibrating high magnification objectives because fewer graduations can be simultaneously imaged in the microscope viewfield. It is never advisable to rely on the accuracy of one ten-micrometer division alone because the widths of individual graduations can be expected to vary slightly from one span to another.
The quality of the graduations on a stage micrometer has a significant effect on the accuracy with which a calibration can be conducted, and this is especially true at high magnifications. As previously stated, micrometers produced by processes such as thin film deposition usually have much finer lines with better-defined edges than those produced photographically, and can provide improved accuracy and precision. Photographically-produced micrometer scales are more economical, but the ragged edges of the lines, coupled with the occurrence of randomly distributed isolated silver grains between the lines, make such micrometers unsuitable for precise measurements.
Measurement errors can occur if an objective having significant curvature of field or image distortion is employed to perform measurements. With modern objectives, this source of error is not as common as it was in the past; however, it is still advisable to use flat-field or plan objectives whenever possible. If an objective having some field distortion must be utilized, restricting measurements to the central portion of the viewfield will minimize measurement errors.
Problems in measurement can also occur due to difficulty in precisely aligning eyepiece reticle lines with those of the stage micrometer used for the calibration. A precision, graduated mechanical stage (see Figure 9) can be utilized to make this procedure much easier to accomplish. Modern graduated stages are ruled in millimeters on both axes and contain verniers for translation readings to within 0.1 millimeter. These stages are quite suitable for large (exceeding several millimeters) measurements in both the x and ydirections.
It is critical that both scales (reticle and stage micrometer) are imaged as sharply as possible, and as previously suggested, it is preferable to utilize as many divisions of the stage micrometer as can be observed in the field of view for the calibration. The alignment of the lines of the eyepiece reticle with those of the micrometer should be made consistently from the same edge of the stage micrometer line rules, and not at the center (which cannot be reproducibly identified).
An important factor that should be considered as a potential source of measurement error is the subjectivity involved in setting a reference line at the edge of a specimen feature. It should be borne in mind that measurements conducted in the microscope utilize an optical image of the specimen and not the specimen itself. The contrast mechanism employed in imaging, the type and quality of illumination, and the numerical aperture and other properties of the objective all affect the appearance of specimen feature edges from which measurements are often taken. In addition, if diffraction artifacts are present in the image, the selection of feature edges for placement of a measurement reference line can be highly uncertain.
Using digital imaging or traditional photomicrography techniques, linear specimen dimensions can be determined by direct measurement of specific features and comparison to the image of a stage micrometer at the same magnification. For example, a specimen photographed with a 10x objective can be measured by consecutively acquiring a second photograph of the stage micrometer at the same magnification. Using a ruler or similar measuring device, the microscopist can then directly measure the specimen feature and calculate the dimensions using the photograph of the stage micrometer. The technique is equally useful for digital images, where computer software can be utilized in place of a ruler to compare specimen images with a stage micrometer when the two images are captured at identical pixel resolution.
In the measurement of opaque objects, the subjective assessment of image brightness at the transition from bright background to dark specimen can result in errors in identifying a sharp edge under the different intensity gradients that occur with various illumination conditions. It is difficult to account for all of the possible sources of error in practical microscopy, but an awareness of potential pitfalls can help prevent large errors or inconsistencies, especially when comparing measurements that have been made utilizing different instrumental techniques and equipment.
Thomas J. Fellers and Michael W. Davidson - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310.