Conjugate Planes in Optical Microscopy

In a properly focused and aligned optical microscope, a review of the geometrical properties of the optical train demonstrates that there are two sets of principal conjugate focal planes that occur along the optical pathway through the microscope. One set consists of four field planes and is referred to as the field or image-forming conjugate set, while the other consists of four aperture planes and is referred to as the illumination conjugate set. Each plane within a set is said to be conjugate with the others in that set because they are simultaneously in focus and can be viewed superimposed upon one another when observing specimens through the microscope.

Figure 1 - Conjugate Planes in the Optical Microscope

Presented in Figure 1 is a cutaway diagram of a modern microscope (a Nikon Eclipse E600), which illustrates the strategic location of optical components comprising the two sets of conjugate planes in the optical pathways for both transmitted and incident (reflected or epi) illumination modes. Components that reside in the field set of conjugate planes are described in black text, while those comprising the aperture set are described in red text. Note that conjugate planes are illustrated for both observation and digital imaging (or photomicrography) modes. Table 1 lists the elements that make up each set of conjugate planes, including alternate nomenclature (listed in parentheses) that has often been employed and may be encountered in the literature. A minor difference exists in the relative location of the field and condenser apertures between the incident and transmitted modes of illumination, which will be explained later.

Table 1 - Conjugate Focus Planes

Aperture or Illuminating
Conjugate Plane Set
Field or Image-Forming
Conjugate Plane Set
Microscope Exit Pupil: Eye Iris Diaphragm,
Ramsden Disc, and Eyepoint
Retina of the Eye
Camera Image Plane
Objective Rear Focal Plane
(Objective Rear Aperture)
Intermediate Image Plane
(Eyepiece Fixed Diaphragm)
Condenser Aperture Diaphragm
(Condenser Front Focal Plane)
Specimen Plane
(Object Plane)
Lamp Filament Field Diaphragm
(Field Stop)
(Köhler Diaphragm)

In normal observation mode (using the eyepieces), the conjugate set of object or field planes can all be simultaneously viewed when the specimen is in focus. This observation mode is referred to as the orthoscopic mode, and the image is known as the orthoscopic image. Observing the other conjugate set of aperture or diffraction planes requires the ability to focus on the rear aperture of the objective, which may be accomplished by using an eyepiece telescope in place of an ocular, or a built-in Bertrand lens on microscopes that are so equipped. This observation mode is termed the conoscopic, aperture, or diffraction mode and the image observed at the objective rear aperture is known as the conoscopic image. Although the terms orthoscopic and conoscopic are scattered widely throughout the literature, many microscopists favor using normal mode and aperture mode because the latter nomenclature more clearly relates to the operation of the microscope. Planes belonging to the pair of conjugate sets alternate in succession through the optical train from the light source filament to the final microscope image produced on the retina or the image plane of an electronic sensor. A thorough understanding of the relationships between these conjugate plane sets, and their location within the microscope, is essential in understanding image formation and carrying out correct adjustment of illumination. In addition, the location of principal conjugate planes is often a key factor in the proper placement of optical components such as phase plates, differential interference contrast (DIC) Wollaston prisms, polarizers, modulators, filters, or graticules.

Figure 2 - Conjugate Planes in the Optical Microscope

The imaging and illumination ray paths through a microscope adjusted for Köhler illumination are presented in Figure 2, with the focal conjugates of each plane set indicated by crossover points of the ray traces. Illustrated diagrammatically in the figure is the reciprocal nature of the two sets of conjugate planes that occur in the microscope. The optical relationship between the conjugate plane sets is based upon the fact that, in the illuminating ray path (shown in red), the spherical wave fronts converge and are brought into focus onto the aperture planes, while in the imaging ray path (shown in yellow), the spherical waves converge into focused rays in the field planes. Light rays that are focused in one set of conjugate planes are nearly parallel when passing through the other set of conjugate planes. The reciprocal relationship between the two sets of conjugate planes determines how the two ray paths fundamentally interact in forming an image in the microscope, and it also has practical consequences for operation of the microscope.

Illumination is perhaps the most critical factor in determining the overall performance of the optical microscope. The full aperture and field of the instrument is usually best achieved by adjusting the illumination system following the principles first introduced by August Köhler in the late nineteenth century. It is under the conditions of Köhler illumination that the requirements are met for having two separate sets of conjugate focal planes, field planes and aperture planes, in precise physical locations in the microscope. The details of adjusting a given microscope to satisfy the Köhler illumination conditions depend to some extent upon how the individual manufacturer meets the requirements, and are not discussed here.

The basic requirements of Köhler illumination are very simple. A collector lens on the lamp housing is required to focus light emitted from the various points on the lamp filament at the front aperture of the condenser while completely filling the aperture. Simultaneously, the condenser must be focused to bring the two sets of conjugate focal planes (when the specimen is also focused) into specific locations along the optical axis of the microscope. Meeting these conditions will result in a bright, evenly illuminated specimen plane, even with an inherently uneven light source such as a tungsten-halogen lamp filament (the filament will not be in focus in the specimen plane). With the specimen and condenser in focus, the focal conjugates will be in the correct position so that resolution and contrast can be optimized by adjusting the field and condenser aperture diaphragms.

Figure 3 - Image-Forming Conjugate Plane Locations

The concept that specific planes in the optical path of the microscope are conjugate indicates that they are equal. That is, whatever appears in focus in one plane of a conjugate set will appear in focus in all the other planes belonging to the same set. On the other hand, the reciprocal nature of the two sets of microscope conjugate planes requires that an object appearing in focus in one set of planes, will not be focused in the other set. The existence of two interrelated optical paths and two sets of image planes characterize Köhler illumination and is the foundation that allows the various adjustable diaphragms and aperture stops in the microscope to be used to control both the cone angle of illumination, and the size, brightness and uniformity of illumination of the field of view. The planes belonging to the field set are sometimes referred to as the field-limiting planes because a diaphragm placed in any one of these planes will limit the diameter of the image field. Figure 3 illustrates each of these planes, which will be focused and coincident with the specimen image. The aperture planes may be considered aperture-limiting because the numerical aperture of the optical system can be controlled by fixed or adjustable (iris) diaphragms inserted at any of these positions. Components containing the set of aperture planes, which are not in focus with the specimen image, are presented (removed from their locations in the microscope) in Figure 4.

Figure 4 - Aperture Conjugate Plane Locations

A microscopist may not be aware that in the normal observation mode, the specimen image is actually a combined view of four in-focus conjugate image planes (including the specimen plane) whose optical characteristics are determined or modulated by another set of four out-of-focus aperture planes. In a properly adjusted microscope, this fact can be easily ignored. However, the mechanism of the image formation becomes much more apparent, and of immediate practical interest, if there is something seriously wrong with the image. Knowledge of the location and image-forming function of each of the conjugate image and aperture planes is critical in troubleshooting problems that arise in the microscope image. It is also necessary for proper placement and use of filters, stops, phase rings, DIC prisms, and other optical components so that they do not introduce problems. Modern microscope design takes into consideration the location of the conjugate planes and the need for the microscopist to have access to them.

One of the more common ways in which the conjugate nature of the various field planes (including the specimen) and aperture planes (including the illumination source) is exploited, is in the placement of filters and other illumination-modifying optical components. These optical elements are likely to be contaminated with dust or fingerprints, due to frequent handling, and are often not optically designed to be included with the objective, oculars, and other elements of the optical path that are intended to form the focused final image. Therefore, auxiliary components should never be placed in any plane conjugate with the specimen, because any defects, dust, or debris may appear in the final image of the specimen formed at the retina or at a camera imaging plane.

In contrast, measurement graticules, scales, pointers, and other devices that are intended to be in focus and registered on the specimen must be placed at one of the field conjugate planes in order to be imaged with the specimen. For practical reasons, most of the commercially available measuring graticules are designed to be placed at the eyepiece field stop, coincident with the real intermediate image plane. Figure 5 illustrates a microscope viewfield containing three simultaneously focused conjugate planes that will appear, in focus, on the retina of the eye or the imaging plane of a camera. Phase plates, and their corresponding annuli, are intended to control the light path (not to appear in the specimen image), and are placed at conjugate planes in the aperture series. The phase plate is usually placed at the rear aperture (at or very near the rear focal plane) of the objective, so placing the correct annulus at the previous conjugate plane of the aperture series (the front aperture of the substage condenser) will ensure that the images of the two components are superimposed in the illumination optical path. Likewise, Wollaston prisms, which shear and recombine light beams in differential interference contrast microscopy, are placed in the condenser front focal plane and objective rear focal plane for the same reason. Polarizers and analyzers, utilized in polarized light and DIC microscopy, are generally placed far away from either conjugate plane set to avoid introducing contaminating dust or fingerprints into the specimen image or degrading the illumination conditions.

Figure 5 - Optical Microscope Conjugate Planes

If problems arise that affect the image quality obtained in the microscope, two avenues should be explored when attempting to correct them. In the normal microscope view through the eyepieces, the conjugate field planes are observed in focus. If dust or other imperfections appear distinct and in sharp focus with the image, then the source of the problem is probably one of the glass components located in or very near the field planes of the microscope optical path. The most likely components to contain dust and debris (that can be observed with the specimen) are the specimen slide itself, the eye lenses of the eyepieces, the objective front lens, the condenser top lens, graticules, and any lenses near the field diaphragm. Often, it is a simple matter to rotate the eyepieces, objective, and condenser and determine if the offending debris rotates in the viewfield, thereby confirming its location.

If this technique does not identify the problem, then the best way to continue troubleshooting is by observing the rear focal plane of the objective to evaluate possible obstructions or misalignments in the illumination path. This aperture, or conoscopic, view is obtained by replacing a normal eyepiece with a specialized eyepiece telescope or using a Bertrand lens (built into the microscope observation head). Although, it is possible to simply remove an eyepiece and peer down the observation tube at the rear aperture of the objective, the image is too small to easily evaluate without a telescope. Observing the aperture planes in this manner will reveal any obstructions such as poorly-centered lenses, dirt or contaminants in the lenses, illumination irregularities such as a poorly centered lamp filament, air bubbles that might be present in immersion oil, and improper adjustment of the condenser diaphragm. The condenser aperture diaphragm determines the effective numerical aperture of the objective-condenser combination, and should normally be adjusted to fill about 70 to 80 percent of the objective rear aperture with light, as an optimum compromise between maximum resolution, depth of field, and adequate contrast.

Figure 6 - Conjugate Planes in the Incident Light Optical System

As stated previously, use of the incident (reflected light) illumination mode requires a minor change in the arrangement of the field and aperture diaphragms in the microscope. This adjustment is necessary because, with incident illumination, the objective plays a dual role and also functions as the condenser, which requires an aperture diaphragm that does not lie in the imaging ray path between the objective lens and the eye or camera. To meet this requirement, lenses in the illumination system are employed to create a conjugate plane between the lamp and the field diaphragm for placement of an aperture diaphragm that is conjugate with the lamp filament. The aperture diaphragm is then projected by relay lenses and mirrors into the rear focal plane (exit pupil) of the objective where these two conjugate planes become coincident. Figure 6 illustrates the illuminating ray path (shown in red) and the imaging ray path (shown in yellow) in an incident light system.

The best image quality can be achieved in the microscope only with a thorough understanding of the central role played by the two sets of reciprocal conjugate focal planes. For optimum results, the microscopist must be familiar with their interrelationships and where they are located in the microscope when the conditions required for Köhler illumination are met. With this understanding, the primary optical components of the microscope, as well as any accessories that might be added, can be utilized in a manner that exploits the reciprocal nature of the conjugate plane sets to maximum benefit.

Contributing Authors

Thomas J. Fellers and Michael W. Davidson - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310.

Share this article:

Conjugate Planes in Optical Microscopy