The eyepiece is selected to examine the relayed image under conditions that are comfortable for the viewer. The magnifying power of the eyepiece generally does not exceed 10×. The field of view is then about 40° total, a convenient value for a relatively simple optical design. The observer places the eye at the exit pupil of the eyepiece, the point at which the light rays leaving the eyepiece come together. In most cases an eye relief (or distance from the exit pupil to the last element of the eyepiece) of about 1 cm is desirable. Too short an eye relief makes viewing difficult for observers who wear corrective eyeglasses.

Image capture

The objectives described above are usually intended to project an image through an eyepiece for direct viewing by an observer. The use of a photographic recording method permits the capture of a real image in a film holder or digital imaging system without an eyepiece lens. One approach is to remove the eyepiece and place the film holder or digital camera in the focal plane of the eyepiece, thus intercepting the image from the objective directly. A better approach is to use a specifically designed projection eyepiece, which can be adjusted to provide the appropriate magnification coupling the image to the film. Such an eyepiece can incorporate a change in the chromatic aberration correction to accommodate the requirements of the image-capture system.

Increasingly prevalent today is the use of an electronic detector such as a complementary metal-oxide semiconductor (CMOS) or charge-coupled device (CCD) chip to capture the magnified image as a digital signal. This signal can be transmitted to a computer and translated into an image on the monitor. Software allows the user to take single pictures, moving video sequences, or time-lapse sequences at the click of a mouse. These may be saved for conventional viewing, and image processing can be used to enhance the result. Analysis of area and particle size and distribution is easily done by conventional analytical means once the images have been digitally captured. The production of computer presentations, transmission via e-mail, and ease of printing are benefits that digital imaging brings to the modern microscopist.

The large N.A. of a microscope objective restricts the focusing requirements of the objective. The depth of focus is shown in the table as the accuracy with which the focal plane must be located in a direction along the axis of the microscope optics in order that the highest possible resolution can be obtained.

objective focal length (mm)	numerical aperture (N.A.)	maximum useful magnification in compound microscope	maximum resolution on object (mm)	objective depth of focus (mm)
32	0.10	100×	0.0025	0.025
16	0.25	250×	0.001	0.0038
8	0.50	500×	0.0005	0.00086
4	0.95	1,000×	0.00026	0.00024
3	1.38	1,500× (oil immersion)	0.00018	0.00010

High-power objectives pose several design problems. Because the focal length of an objective decreases as the N.A. and magnifying power increase, the working distance, or distance from the front of the objective to the top of the slide, is shorter for higher-power objectives. The need to use additional elements in the lens system for high magnifications further shortens the working distance to only 10 to 20 percent of the focal length. Thus, a 40× objective of 4-mm (0.2-inch) focal length may have a working distance of less than 0.4 mm (0.02 inch), so objectives with an increased working distance have been designed. These use a negative lens element between the object and the eyepiece, which has the added attraction of providing some field flattening as well. These objectives are especially of value in use with video systems.

In objectives with magnifying powers of 25× or greater, meniscus-shaped aplanatic elements are designed into the microscope objective in the space between the object and the pairs of doublets that carry out the relayed imaging. These aplanatic components have the property of converging the light without adding spherical aberration to the image and provide an increase in the N.A. without introducing significant aberration.

The highest-power microscope objective available is the immersion objective. When this type of objective is used, a drop of oil must be placed between the object on the microscope slide and the objective. The oil used has an R.I. that matches that of the glass in the first component of the objective.

The first component of immersion objectives is generally a hyper-hemisphere (a small optical surface shaped like a hemisphere but with a boundary curve exceeding 180°), which acts as an aplanatic coupler between the slide and the rest of the microscope objective. An immersion objective with a high N.A. typically consists of a hyper-hemisphere followed by one or two aplanatic collectors and then two or more sets of doublets. Such objectives are made with magnifying powers greater than 50×, the extreme being about 100×.

Water-immersion lenses are also available. These use water as an immersion liquid and allow biologists to examine specimens in a watery medium without the burden of a cover slip confining the living organisms.

The illumination system of the standard optical microscope is designed to transmit light through a translucent object for viewing. In a modern microscope it consists of a light source, such as an electric lamp or a light-emitting diode, and a lens system forming the condenser.

The condenser is placed below the stage and concentrates the light, providing bright, uniform illumination in the region of the object under observation. Typically, the condenser focuses the image of the light source directly onto the plane of the specimen, a technique called critical illumination. Alternatively, the image of the source is focused onto the condenser, which is in turn focused onto the entrance pupil of the microscope objective, a system known as Köhler illumination. The advantage of the latter approach is that nonuniformities in the source are averaged in the imaging process. To obtain optimal use of the microscope, it is important that the light from the source both covers the object and fills the entrance aperture of the objective of the microscope with light.

Early microscopes had as their condenser a single lens, which was fixed in the end of the instrument facing the lamp (as in barrel microscopes) or mounted below the stage (as in the Bancks microscopes used by Robert Brown, Charles Darwin, and others). More-complex designs followed, their development driven by the peculiarly English obsession of observing fine details on diatom frustules. Achromatic condensers followed, but they are more troublesome to use because they need precise focusing, and the working distance is short.

Apart from condensers that are matched to specialized objectives (such as phase-contrast systems), others are available for specific applications. Thus, the dark-ground, or dark-field, condenser illuminates specimens against a black background and is eminently applicable to the observation of structures such as bacteria and flagellated cells in water. The use of colour filters, pioneered in the closing years of the 19th century by British microscopist Julius Rheinberg and now known as Rheinberg illumination, allows one to practice a form of dark-ground microscopy in which the background and the specimen are in contrasting colours. Although this technique is of no diagnostic benefit, the results can be spectacularly beautiful.

The microscope body tube separates the objective and the eyepiece and assures continuous alignment of the optics. It is a standardized length, anthropometrically related to the distance between the height of a bench or tabletop (on which the microscope stands) and the position of the seated observer’s eyes. It is typically fitted with a rotating turret that permits objectives of different powers to be interchanged with the assurance that the image position will be maintained. Traditionally, the length of the body tube has been defined as the distance from the upper end of the objective to the eyepiece end of the tube.

A standard body-tube length of 160 mm (6.3 inches) has been accepted for most uses. (Metallographic microscopes have a 250-mm [10-inch] body tube.) Microscope objectives are designed to minimize aberrations at the specified tube length. Use of other distances will affect the aberration balance for high-magnification objectives. Therefore, focusing of the traditional microscope requires moving the objective, the tube, and the eyepiece as a rigid unit. To achieve this, the entire tube is fitted with a rack-and-pinion mechanism that allows it, together with the objective and the eyepiece, to be moved toward or away from the specimen.

The specimen is usually mounted on a glass slide. Routine microscope slides were fixed at 3 × 1 inches during the Victorian era and are still produced at the metric equivalent of those dimensions (7.5 × 2.5 cm) today. The specimen, usually immersed in a material with an R.I. that matches that of the slide, is covered with a thin cover slip. The mechanical stage on which the slide lies is fitted with a pair of controls featuring a rack-and-pinion arrangement. This permits the glass slide to be moved across the stage in two directions, so that different areas of the specimen can be examined. Computer-controlled microscopes track the position of the slide and can return to designated areas of the specimen when required to do so.

The accuracy with which the focusing and the movement of the slide have to be maintained increases as the depth of focus of the objective decreases. For high-N.A. objectives, this depth of focus can be as small as 1 or 2 μm, which means that the mechanical components must provide stable motion at even smaller increments.

Several approaches have been introduced to achieve such precise stable motion at reasonable cost. Some designers have eliminated the sliding mechanism of the body tube, incorporating adjustments for the vertical movement needed for focusing, as well as the lateral motion of the object, in a single mechanical system. An alternative approach has been to mount a relay objective doublet of 160 mm (6.3 inches) focal length into the lower end of the tube. This tube lens is designed to accept light from an image created by the objective at infinity. The objective itself is designed to have aberrations corrected for an infinite image distance. An advantage of this approach is that, since the relayed image is at infinity, the microscope objective itself, a very lightweight component, can be moved to effect focusing without upsetting the correction of aberrations.

In some microscopes the eyepiece is designed as a portion of a zoom lens, which permits continuous variation of the magnification over a limited range without loss of focus. Such microscopes are widely used in industry.

There are some obvious geometric limitations that apply to the design of microscope optics. The attainable resolution, or the smallest distance at which two points can be seen as separate when viewed through the microscope, is the first important property. This is generally set by the ability of the eye to discern detail, as well as by the basic physics of image formation.

The eye’s ability to discern detail is determined by several factors, including the level of illumination and the degree of contrast between light and dark regions on the object. Under reasonable light conditions, a normal eye with good visual acuity is capable of seeing two high-contrast points if they subtend a visual angle of at least one arc minute in size. Thus, at a nominal viewing distance of 25 cm (10 inches), the points must be at least 0.1 mm (0.004 inch) apart for the eye to see them as separate. With a simple magnifier of 10×, an observer can see two points separated by perhaps 0.01 mm (0.0004 inch); and with a compound microscope magnifying 100×, one might expect the observer to be able to distinguish two points only 0.001 mm (0.00004 inch) apart. However, an additional complication arises for the high magnifications encountered in a compound microscope. When the dimensions to be resolved approach the wavelength of light, consideration must be given to the effect of diffraction upon the eye’s ability to resolve details upon objects

The resolution and the light-collecting capability of the microscope are determined by the numerical aperture (N.A.) of the objective. The N.A. is defined as the sine of half the angle of the cone of light from each point of the object that can be accepted by the objective multiplied by the refractive index (R.I.) of the medium in which the object is immersed. Thus, the N.A. increases as the lens becomes larger or the R.I. increases. Typical values for microscope objective N.A.’s range from 0.1 for low-magnification objectives to 0.95 for dry objectives and 1.4 for oil-immersion objectives. A dry objective is one that works with the air between the specimen and the objective lens. An immersion objective requires a liquid, usually a transparent oil of the same R.I. as glass, to occupy the space between the object and the front element of the objective.

The limit of resolution is set by the wavelength of light and the N.A. The resolution can be improved either by increasing the N.A. of a lens or by using light with a shorter wavelength. In an immersion objective, the effective wavelength of the light is reduced by the index of refraction of the media within which the object being examined resides. The use of immersion imaging techniques in microscopy improves the resolution capabilities of the microscope.

Some cutting-edge types of light microscopy (beyond the techniques we discussed above) can produce very high-resolution images. However, if you want to see something very tiny at very high resolution, you may want to use a different, tried-and-true technique: electron microscopy.Electron microscopes differ from light microscopes in that they produce an image of a specimen by using a beam of electrons rather than a beam of light. Electrons have much a shorter wavelength than visible light, and this allows electron microscopes to produce higher-resolution images than standard light microscopes. Electron microscopes can be used to examine not just whole cells, but also the subcellular structures and compartments within them.One limitation, however, is that electron microscopy samples must be placed under vacuum in electron microscopy (and typically are prepared via an extensive fixation process). This means that live cells cannot be imaged.

Images of Salmonella bacteria taken via light microscopy and scanning electron microscopy. Much more detail can be seen in the scanning electron micrograph.Image credit: OpenStax Biology. Credit a: modification of work by CDC/Armed Forces Institute of Pathology, Charles N. Farmer, Rocky Mountain Laboratories; credit b: modification of work by NIAID, NIH; scale-bar data from Matt Russell.In the image above, you can compare how Salmonella bacteria look in a light micrograph (left) versus an image taken with an electron microscope (right). The bacteria show up as tiny purple dots in the light microscope image, whereas in the electron micrograph, you can clearly see their shape and surface texture, as well as details of the human cells they’re trying to invade.

Image of an electron microscope. It is very large, roughly the size of an industrial stove.Image credit: OpenStax Biology. Modification of work by Evan Bench.There are two major types of electron microscopy. In scanning electron microscopy (SEM), a beam of electrons moves back and forth across the surface of a cell or tissue, creating a detailed image of the 3D surface. This type of microscopy was used to take the image of the Salmonella bacteria shown at right, above.In transmission electron microscopy (TEM), in contrast, the sample is cut into extremely thin slices (for instance, using a diamond cutting edge) before imaging, and the electron beam passes through the slice rather than skimming over its surface^55start superscript, 5, end superscript. TEM is often used to obtain detailed images of the internal structures of cells.Electron microscopes, like the one above, are significantly bulkier and more expensive than standard light microscopes, perhaps not surprisingly given the subatomic particles they have to handle!

Most student microscopes are classified as light microscopes. In a light microscope, visible light passes through the specimen (the biological sample you are looking at) and is bent through the lens system, allowing the user to see a magnified image. A benefit of light microscopy is that it can often be performed on living cells, so it’s possible to watch cells carrying out their normal behaviors (e.g., migrating or dividing) under the microscope.

A light microscope, of the sort commonly found in high school and undergraduate biology labs.Image credit: OpenStax Biology. Modification of work by “GcG”/Wikimedia Commons.Student lab microscopes tend to be brightfield microscopes, meaning that visible light is passed through the sample and used to form an image directly, without any modifications. Slightly more sophisticated forms of light microscopy use optical tricks to enhance contrast, making details of cells and tissues easier to see.Another type of light microscopy is fluorescence microscopy, which is used to image samples that fluoresce (absorb one wavelength of light and emit another). Light of one wavelength is used to excite the fluorescent molecules, and the light of a different wavelength that they emit is collected and used to form a picture. In most cases, the part of a cell or tissue that we want to look at isn’t naturally fluorescent, and instead must be labeled with a fluorescent dye or tag before it goes on the microscope.The leaf picture at the start of the article was taken using a specialized kind of fluorescence microscopy called confocal microscopy. A confocal microscope uses a laser to excite a thin layer of the sample and collects only the emitted light coming from the target layer, producing a sharp image without interference from fluorescent molecules in the surrounding layers.

There are several types of magnifiers available. The choice of an optical design for a magnifier depends upon the required power and the intended application of the magnifier.

For low powers, about 2–10×, a simple double convex lens is applicable. (Early simple microscopes such as Leeuwenhoek’s magnified up to 300×.) The image can be improved if the lens has specific aspheric surfaces, as can be easily obtained in a plastic molded lens. A reduction of distortion is noted when an aspheric lens is used, and the manufacture of such low-power aspheric plastic magnifiers is a major industry. For higher powers of 10–50×, there are a number of forms for magnifiers in which the simple magnifier is replaced by a compound lens made up of several lenses mounted together.

A direct improvement in the distortion that may be expected from a magnifier can be obtained by the use of two simple lenses, usually plano-convex (flat on one side, outward-curved on the other, with the curved surfaces facing each other). This type of magnifier is based upon the eyepiece of the Huygenian telescope, in which the lateral chromatic aberration is corrected by spacing the elements a focal length apart. Since the imaging properties are provided and shared by two components, the spherical aberration and the distortion of the magnifier are greatly reduced over those of a simple lens of the same power.

A Coddington lens combines two lens elements into a single thick element, with a groove cut in the centre of the element to select the portion of the imaging light with the lowest aberrations. This was a simple and inexpensive design but suffers from the requirement that the working distance of the magnifier be very short.

More-complex magnifiers, such as the Steinheil or Hastings forms, use three or more elements to achieve better correction for chromatic aberrations and distortion. In general, a better approach is the use of aspheric surfaces and fewer elements.

Mirrors are also used. Reflecting microscopes, in which the image is magnified through concave mirrors rather than convex lenses, were brought to their peak of perfection in 1947 by British physicist C.R. Burch, who made a series of giant instruments that used ultraviolet rays. There is no chromatic aberration using a reflector, and distortion and spherical aberration are controlled through the introduction of a carefully contoured aspheric magnifying mirror. Present-day reflecting microscopes are confined to analytical instruments using infrared rays.

Principles

The simple microscope consists of a single lens traditionally called a loupe. The most familiar present-day example is a reading or magnifying glass. Present-day higher-magnification lenses are often made with two glass elements that produce a colour-corrected image. They can be worn around the neck packaged in a cylindrical form that can be held in place immediately in front of the eye. These are generally referred to as eye loupes or jewelers’ lenses. The traditional simple microscope was made with a single magnifying lens, which was often of sufficient optical quality to allow the study of microscopical organisms including Hydra and protists.

Magnification

It is instinctive, when one wishes to examine the details of an object, to bring it as near as possible to the eye. The closer the object is to the eye, the larger the angle that it subtends at the eye, and thus the larger the object appears. If an object is brought too close, however, the eye can no longer form a clear image. The use of the magnifying lens between the observer and the object enables the formation of a “virtual image” that can be viewed in comfort. To obtain the best possible image, the magnifier should be placed directly in front of the eye. The object of interest is then brought toward the eye until a clear image of the object is seen.

Without lenses, the highest possible magnification is when the object is brought to the closest position at which a clear virtual image is observed. For many people, this image distance is about 25 cm (10 inches). As people age, the nearest point of distinct vision recedes to greater distances, thus making a magnifier a useful adjunct to vision for older people.

The magnifying power, or extent to which the object being viewed appears enlarged, and the field of view, or size of the object that can be viewed, are related by the geometry of the optical system. A working value for the magnifying power of a lens can be found by dividing the least distance of distinct vision by the lens’ focal length, which is the distance from the lens to the plane at which the incoming light is focused. Thus, for example, a lens with a least distance of distinct vision of 25 cm and a focal length of 5 cm (2 inches) will have a magnifying power of about 5×.

If the diameter of the magnifying lens is sufficient to fill or exceed the diameter of the pupil of the eye, the virtual image that is viewed will appear to be of substantially the same brightness as the original object. The field of view of the magnifier will be determined by the extent to which the magnifying lens exceeds this working diameter and also by the distance separating the lens from the eye. The clarity of the magnified virtual image will depend upon the aberrations present in the lens, its contour, and the manner in which it is used.

Aberration

Various aberrations influence the sharpness or quality of the image. Chromatic aberrations produce coloured fringes about the high-contrast regions of the image, because longer wavelengths of light (such as red) are brought to focus in a plane slightly farther from the lens than shorter wavelengths (such as blue). Spherical aberration produces an image in which the centre of the field of view is in focus when the periphery may not be and is a consequence of using lenses with spherical (rather than nonspherical, or aspheric) surfaces. Distortion produces curved images from straight lines in the object. The type and degree of distortion visible is intimately related to the possible spherical aberration in the magnifier and is usually most severe in high-powered lenses.

The aberrations of a lens increase as the relative aperture (i.e., the working diameter divided by the focal length) of the lens is increased. Therefore, the aberrations of a lens whose diameter is twice the focal length will be worse than those of a lens whose diameter is less than the focal length. There is thus a conflict between a short focal length, which permits a high magnifying power but small field of view, and a longer focal length, which provides a lower magnifying power but a larger linear field of view. (Leeuwenhoek’s high-powered lenses of the 1670s had a focal length—and thus a working distance—of a few millimetres. This made them difficult to use, but they provided remarkable images that were not bettered for a century.)