Properties of Microscope Objectives
Three critical design characteristics of the objective set the ultimate resolution limit of the microscope. These include the wavelength of light used to illuminate the specimen, the angular aperture of the light cone captured by the objective, and the refractive index in the object space between the objective front lens and the specimen.
Presented in Figure 1 is a cut-away diagram of a microscope objective being illuminated by a simple two-lens Abbe condenser. Light passing through the condenser is organized into a cone of illumination that emanates onto the specimen and is then transmitted into the objective front lens element as a reversed cone. The size and shape of the illumination cone is a function of the combined numerical apertures of the objective and condenser. The objective angular aperture is denoted by the Greek letter θ and will be discussed in detail below.
Resolution for a diffraction-limited optical microscope can be described as the minimum detectable distance between two closely spaced specimen points:
R = λ/2n(sin(θ))
where R is the separation distance, λ is the illumination wavelength, n is the imaging medium refractive index, and θ is one-half of the objective angular aperture. In examining the equation, it becomes apparent that resolution is directly proportional to the illumination wavelength. The human eye responds to the wavelength region between 400 and 700 nanometers, which represents the visible light spectrum that is utilized for a majority of microscope observations. Resolution is also dependent upon the refractive index of the imaging medium and the objective angular aperture. Objectives are designed to image specimens either with air or a medium of higher refractive index between the front lens and the specimen. The field of view is often quite limited, and the front lens element of the objective is placed close to the specimen with which it must lie in optical contact. A gain in resolution by a factor of approximately 1.5 is attained when immersion oil is substituted for air as the imaging medium.
The last, but perhaps most important, factor in determining the resolution of an objective is the angular aperture, which has a practical upper limit of about 72 degrees (with a sine value of 0.95). When combined with refractive index, the product:
is known as the numerical aperture (abbreviated NA), and provides a convenient indicator of the resolution for any particular objective. Numerical aperture is generally the most important design criteria (other than magnification) to consider when selecting a microscope objective. Values range from 0.1 for very low magnification objectives (1x to 4x) to as much as 1.6 for high-performance objectives utilizing specialized immersion oils. As numerical aperture values increase for a series of objectives of the same magnification, we generally observe a greater light-gathering ability and increase in resolution. The microscopist should carefully choose the numerical aperture of an objective to match the magnification produced in the final image. Under the best circumstances, detail that is just resolved should be enlarged sufficiently to be viewed with comfort, but not to the point that empty magnification hampers observation of fine specimen detail.
Just as the brightness of illumination in a microscope is governed by the square of the working numerical aperture of the condenser, the brightness of an image produced by the objective is determined by the square of its numerical aperture. In addition, objective magnification also plays a role in determining image brightness, which is inversely proportional to the square of the lateral magnification. The square of the numerical aperture/magnification ratio expresses the light-gathering power of the objective when utilized with transmitted illumination. Because high numerical aperture objectives are often better corrected for aberration, they also collect more light and produce a brighter, more corrected image that is highly resolved. It should be noted that image brightness decreases rapidly as the magnification increases. In cases where the light level is a limiting factor, choose an objective with the highest numerical aperture, but having the lowest magnification factor capable of producing adequate resolution.
During assembly of the objective, lenses are first strategically spaced and lap-seated into cell mounts, then packaged into a central sleeve cylinder that is mounted internally within the objective barrel. Individual lenses are seated against a brass shoulder mount with the lens spinning in a precise lathe chuck, followed by burnishing with a thin rim of metal that locks the lens (or lens group) into place. Spherical aberration is corrected by selecting the optimum set of spacers to fit between the lower two lens mounts (the hemispherical and meniscus lens). The objective is parfocalized by translating the entire lens cluster upward or downward within the sleeve with locking nuts so that objectives housed on a multiple nosepiece can be interchanged without losing focus. Adjustment for coma is accomplished with three centering screws that can optimize the position of internal lens groups with respect to the optical axis of the objective.
Objective Specifications by Magnification
There is a wealth of information inscribed on the objective barrel. Briefly, each objective has inscribed on it the magnification (e.g. 10x, 20x or 40x etc.); the tube length for which the objective was designed to give its finest images (usually 160 millimeters or the Greek infinity symbol); and the thickness of cover glass protecting the specimen, which was assumed to have a constant value by the designer in correcting for spherical aberration (usually 0.17 millimeters). If the objective is designed to operate with a drop of oil between it and the specimen, the objective will be engraved OIL or OEL or HI (homogeneous immersion). In cases where these latter designations are not engraved on the objective, the objective is meant to be used dry, with air between the lowest part of the objective and the specimen. Objectives also always carry the engraving for the numerical aperture (NA) value. This may vary from 0.04 for low power objectives to 1.3 or 1.4 for high power oil-immersion apochromatic objectives. If the objective carries no designation of higher correction, one can usually assume it is an achromatic objective. More highly corrected objectives have inscriptions such as apochromat or apo, plan, FL, fluor, etc. Older objectives often have the focal length (lens-to-image distance) engraved on the barrel, which is a measure of the magnification. In modern microscopes, the objective is designed for a particular optical tube length, so including both the focal length and magnification on the barrel becomes somewhat redundant.
Table 1 lists working distance and numerical aperture as a function of magnification for the four most common classes of objectives: achromats, plan achromats, plan fluorites, and plan apochromats. Note that dry objectives all have a numerical aperture value of less than 1.0 and only objectives designed for liquid immersion media have a numerical aperture that exceeds this value.
When a manufacturer's set of matched objectives, e.g. all achromatic objectives of various magnifications (a single subset of the objectives listed in Table 1), are mounted on the nosepiece, they are usually designed to project an image to approximately the same plane in the body tube. Thus, changing objectives by rotating the nosepiece usually requires only minimal use of the fine adjustment knob to re-establish sharp focus. Such a set of objectives is described as being parfocal, a useful convenience and safety feature. Matched sets of objectives are also designed to be parcentric, so that a specimen centered in the field of view for one objective remains centered when the nosepiece is rotated to bring another objective into use.
For many years, objective lenses designed for biological applications from most manufacturers all conformed to an international standard of parfocal distance. Thus, a majority of objectives had a parfocal distance of 45.0 millimeters and were considered interchangeable. With the migration to infinity-corrected tube lengths, a new set of design criteria emerged to correct for aberrations in the objective and tube lenses. Coupled to an increased demand for greater flexibility to accommodate the need for ever-greater working distances with higher numerical apertures and field sizes, interchangeability between objective lenses from different manufacturers disappeared. This transition is exemplified by the modern Nikon CFI-60 optical system that features "Chrome Free" objectives, tube lenses, and eyepieces. Each component in the CFI-60 system is separately corrected without one being utilized to achieve correction for another. The tube length is set to infinity (parallel light path) using a tube lens, and the parfocal distance has been increased to 60 millimeters. Even the objective mounting thread size has been altered from 20.32 to 25 millimeters to meet new requirements of the optical system.
The field diameter in an optical microscope is expressed by the field-of-view number or simply field number, which is the diameter of the viewfield expressed in millimeters and measured at the intermediate image plane. The field diameter in the object (specimen) plane becomes the field number divided by the magnification of the objective. Although the field number is often limited by the magnification and diameter of the ocular (eyepiece) field diaphragm, there is clearly a limit that is also imposed by the design of the objective. In early microscope objectives, the maximum usable field diameter was limited to about 18 millimeters (or considerably less for high magnification eyepieces), but modern plan apochromats and other specialized flat-field objectives often have a usable field that can range between 22 and 28 millimeters or more when combined with wide-field eyepieces. Unfortunately, the maximum useful field number is not generally engraved on the objective barrel and is also not commonly listed in microscope catalogs.
The axial range through which an objective can be focused without any appreciable change in image sharpness is referred to as the depth of field. This value varies radically from low to high numerical aperture objectives, usually decreasing with increasing numerical aperture (see Table 2 and Figure 2). At high numerical apertures, the depth of field is determined primarily by wave optics, while at lower numerical apertures, the geometrical optical "circle of confusion" dominates. The total depth of field is given by the sum of the wave and geometrical optical depths of field as:
dtot = λn/NA2 + (n/M×NA)e
where λ is the wavelength of illumination, n is the refractive index of the imaging medium, NA is the objective numerical aperture, M is the objective lateral magnification, and e is the smallest distance that can be resolved by a detector that is placed in the image plane of the objective. Notice that the diffraction-limited depth of field (the first term on the right-hand side of the equation) shrinks inversely with the square of the numerical aperture, while the lateral limit of resolution is reduced with the first power of the numerical aperture. The result is that axial resolution and the thickness of optical sections are affected by the system numerical aperture much more than is the lateral resolution of the microscope (see Table 2).
The clearance distance between the closest surface of the cover glass and the objective front lens is termed the working distance. In situations where the specimen is designed to be imaged without a cover glass, the working distance is measured at the actual surface of the specimen. Generally, working distance decreases in a series of matched objectives as the magnification and numerical aperture increase (see Table 1). Objectives intended to view specimens with air as the imaging medium should have working distances as long as possible, provided that numerical aperture requirements are satisfied. Immersion objectives, on the other hand, should have shallower working distances in order to contain the immersion liquid between the front lens and the specimen. Many objectives designed with close working distances have a spring-loaded retraction stopper that allows the front lens assembly to be retracted by pushing it into the objective body and twisting to lock it into place. Such an accessory is convenient when the objective is rotated in the nosepiece so it will not drag immersion oil across the surface of a clean slide. Twisting the retraction stopper in the opposite direction releases the lens assembly for use. In some applications (see below), a long free working distance is indispensable, and special objectives are designed for such use despite the difficulty involved in achieving large numerical apertures and the necessary degree of optical correction.
One of the most significant advances in objective design during recent years is the improvement in antireflection coating technology, which helps to reduce unwanted reflections that occur when light passes through a lens system. Each uncoated air-glass interface can reflect between four and five percent of an incident light beam normal to the surface, resulting in a transmission value of 95-96 percent at normal incidence. Application of a quarter-wavelength thick antireflection coating having the appropriate refractive index can increase this value by three to four percent. As objectives become more sophisticated with an ever-increasing number of lens elements, the need to eliminate internal reflections grows correspondingly. Some modern objective lenses with a high degree of correction can contain as many as 15 lens elements having many air-glass interfaces. If the lenses were uncoated, the reflection losses of axial rays alone would drop transmittance values to around 50 percent. The single-layer lens coatings once utilized to reduce glare and improve transmission have now been supplanted by multilayer coatings that produce transmission values exceeding 99.9 percent in the visible spectral range.
Depth of Field and Image Depth
Illustrated in Figure 3 is a schematic drawing of light waves reflecting and/or passing through a lens element coated with two antireflection layers. The incident wave strikes the first layer (Layer A in Figure 3) at an angle, resulting in part of the light being reflected (R(o)) and part being transmitted through the first layer. Upon encountering the second antireflection layer (Layer B), another portion of the light is reflected at the same angle and interferes with light reflected from the first layer. Some of the remaining light waves continue on to the glass surface where they are again both reflected and transmitted. Light reflected from the glass surface interferes (both constructively and destructively) with light reflected from the antireflection layers. The refractive indices of the antireflection layers vary from that of the glass and the surrounding medium (air). As the light waves pass through the antireflection layers and glass surface, a majority of the light (depending upon the incident angle--usual normal to the lens in optical microscopy) is ultimately transmitted through the glass and focused to form an image.
Magnesium fluoride is one of many materials utilized in thin-layer optical antireflection coatings, but most microscope manufacturers now produce their own proprietary formulations. The general result is a dramatic improvement in contrast and transmission of visible wavelengths with a concurrent destructive interference in harmonically-related frequencies lying outside the transmission band. These specialized coatings can be easily damaged by mis-handling and the microscopist should be aware of this vulnerability. Multilayer antireflection coatings have a slightly greenish tint, as opposed to the purplish tint of single-layer coatings, an observation that can be employed to distinguish between coatings. The surface layer of antireflection coatings used on internal lenses is often much softer than corresponding coatings designed to protect external lens surfaces. Great care should be taken when cleaning optical surfaces that have been coated with thin films, especially if the microscope has been disassembled and the internal lens elements are subject to scrutiny.
The focal length of a lens system is defined as the distance from the lens center to a point where parallel rays are focused on the optical axis (often termed the principal focal point). An imaginary plane perpendicular to the principal focal point is called the focal plane of the lens system. Every lens has two principal focal points for light entering each side, one in front and one at the rear. By convention, the objective focal plane that is nearer to the front lens element is known as the front focal plane and the focal plane located behind the objective is termed the rear focal plane (see Figure 4). The actual position of the rear focal plane varies with objective construction, but is generally situated somewhere inside the objective barrel for high magnification objectives. Objectives of lower magnification often have a rear focal plane that is exterior to the barrel, located in the thread area or within the microscope nosepiece.
As light rays pass through an objective, they are restricted by the rear aperture or exit pupil of the objective, as illustrated in Figure 4. The diameter of this aperture varies between 12 millimeters for low magnification objectives down to around 5 millimeters for the highest power apochromatic objectives. Aperture size is extremely critical for epi-illumination applications that rely on the objective to act as both an imaging system and condenser, where the exit pupil also becomes an entrance pupil. The image of the light source must completely fill the objective rear aperture to produce even illumination across the viewfield. If the light source image is smaller than the aperture, the viewfield will experience vignetting from uneven illumination. On the other hand, if the light source image is larger than the rear aperture, some light does not enter the objective and the intensity of illumination is reduced.
Kenneth R. Spring - Scientific Consultant, Lusby, Maryland, 20657.
Michael W. Davidson - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310.