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

While depth of field is generally measured in macroscopic units such as meters and feet, depth of focus is typically measured in microscopic units such as fractions of a millimeter or thousandths of an inch. In optometry depth of focus is usually measured in dioptres.

There is a wealth of information inscribed on the barrel of each objective, which can be broken down into several categories. These include the linear magnification, numerical aperture value, optical corrections, microscope body tube length, the type of medium the objective is designed for, and other critical factors in deciding if the objective will perform as needed. A more detailed discussion of these properties is provided below and in links to other pages dealing with specific issues.

Illustrated in Figure 4 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 4) 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.

Multilayer Antireflection Coatings - 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 (flare and ghosts) that occur when light passes through a lens system, and ensure high-contrast images. 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. These specialized coatings are also used on the phase plates in phase contrast objectives to maximize contrast.

Microscope manufacturers offer a wide range of objective designs to meet the performance needs of specialized imaging methods, to compensate for cover glass thickness variations, and to increase the effective working distance of the objective. Often, the function of a particular objective is not obvious simply by looking at the construction of the objective. Finite microscope objectives are designed to project a diffraction-limited image at a fixed plane (the intermediate image plane), which is dictated by the microscope tube length and located at a pre-specified distance from the rear focal plane of the objective. Microscope objectives are usually designed to be used with a specific group of oculars and/or tube lenses strategically placed to assist in the removal of residual optical errors. As an example, older Nikon and Olympus compensating eyepieces were used with high numerical aperture fluorite and apochromatic objectives to eliminate lateral chromatic aberration and improve flatness of field. Newer microscopes (from Nikon and Olympus) have objectives that are fully corrected and do not require additional corrections from the eyepieces or tube lenses.

Annealing of optical glass for the manufacture of objectives is critical in order to remove stress, improve transmission, and reduce the level of other internal imperfections. Some of the glass formulations intended for apochromat lens construction are slow-cooled and annealed for extended periods, often exceeding six months. True apochromat objectives are manufactured with a combination of natural fluorite and other glasses that have reduced transmission in the near-ultraviolet region.

The same factors that determine depth of field also determine depth of focus, but these factors can have different effects than they have in depth of field. Both depth of field and depth of focus increase with smaller apertures. For distant subjects (beyond macro range), depth of focus is relatively insensitive to focal length and subject distance, for a fixed f-number. In the macro region, depth of focus increases with longer focal length or closer subject distance, while depth of field decreases.

Parfocal Distance - This is another specification that can often vary by manufacturer. Most companies produce objectives that have a 45 millimeter parfocal distance, which is designed to minimize refocusing when magnifications are changed.

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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.

Although not common today, other types of adjustable objectives have been manufactured in the past. Perhaps the most interesting example is the compound "zoom" objective that has a variable magnification, usually from about 4x to 15x. These objectives have a short barrel with poorly designed optics that have significant aberration problems and are not very practical for photomicrography or serious quantitative microscopy.

In astronomy, the depth of focus Δ f {\displaystyle \Delta f} is the amount of defocus that introduces a ± λ / 4 {\displaystyle \pm \lambda /4} wavefront error. It can be calculated as[4][5]

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For many years, natural fluorite was commonly used in the manufacture of fluorite (semi-apochromat) and apochromat objectives. Unfortunately, many newly developed fluorescence techniques often rely on ultraviolet excitation at wavelengths significantly below 400 nanometers, which is severely compromised by autofluorescence that occurs from natural organic constituents present in this mineral. Also, the tendency of natural fluorite to exhibit widespread localized regions of crystallinity can seriously degrade performance in polarized light microscopy. Many of these problems are circumvented with new, more advanced materials, such as fluorocrown glass.

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The phrase depth of focus is sometimes erroneously used to refer to depth of field (DOF), which is the distance from the lens in acceptable focus, whereas the true meaning of depth of focus refers to the zone behind the lens wherein the film plane or sensor is placed to produce an in-focus image. Depth of field depends on the focus distance, while depth of focus does not.

The objective depicted on the left in Figure 3 has a parfocal distance of 45mm and is labeled with an immersion medium color code in addition to the magnification color code. Parfocal distance is measured from the nosepiece objective mounting hole to the point of focus on the specimen as illustrated in the figure. The objective on the right in Figure 3 has a longer parfocal distance of 60 millimeters, which is the result of its being produced to the Nikon CFI60 200/60/25 Specification, again deviating from the practice of other manufacturers such as Olympus and Zeiss, who still produce objectives with a 45mm parfocal distance. Most manufacturers also make their objective nosepieces parcentric, meaning that when a specimen is centered in the field of view for one objective, it remains centered when the nosepiece is rotated to bring another objective into use.

Depth of focus can have two slightly different meanings. The first is the distance over which the image plane can be displaced while a single object plane remains in acceptably sharp focus;[1][2][clarify] the second is the image-side conjugate of depth of field.[2][clarify] With the first meaning, the depth of focus is symmetrical about the image plane; with the second, the depth of focus is slightly greater on the far side of the image plane.

Glass Design - The quality of glass formulations has been paramount in the evolution of modern microscope optics, and there are currently several hundred of optical glasses available for the design of microscope objectives. The suitability of glass for the demanding optical performance of a microscope objective is a function of its physical properties such as refractive index, dispersion, light transmission, contaminant concentrations, residual autofluorescence, and overall homogeneity throughout the mixture. Care must be taken by optical designers to ensure that glass utilized in high-performance objectives has a high transmission in the near-ultraviolet region and also produces high extinction factors for applications such as polarized light or differential interference contrast.

Extra Low Dispersion (ED) glass was introduced as a major advancement in lens design with optical qualities similar to the mineral fluorite but without its mechanical and optical demerits. This glass has allowed manufacturers to create higher quality objectives with lens elements that have superior optical corrections and performance. Because the chemical and optical properties of many glasses are of a proprietary nature, documentation is difficult or impossible to obtain. For this reason the literature is often vague about the specific properties of glasses utilized in the construction of microscope objectives.

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Depth of focus is a lens optics concept that measures the tolerance of placement of the image plane (the film plane in a camera) in relation to the lens. In a camera, depth of focus indicates the tolerance of the film's displacement within the camera and is therefore sometimes referred to as "lens-to-film tolerance".

The simple formula is often used as a guideline, as it is much easier to calculate, and in many cases, the difference from the exact formula is insignificant. Moreover, the simple formula will always err on the conservative side (i.e., depth of focus will always be greater than calculated).

Most manufacturers have now transitioned to infinity-corrected objectives that project emerging rays in parallel bundles from every azimuth to infinity. These objectives require a tube lens in the light path to bring the image into focus at the intermediate image plane. Infinity-corrected and finite-tube length microscope objectives are not interchangeable and must be matched not only to a specific type of microscope, but often to a particular microscope from a single manufacturer. For example, Nikon infinity-corrected objectives are not interchangeable with Olympus infinity-corrected objectives, not only because of tube length differences, but also because the mounting threads are not the same pitch or diameter. Objectives usually contain an inscription denoting the tube focal length as will be discussed.

Other features found on specialized objectives are variable working distance (LWD) and numerical aperture settings that are adjustable by turning the correction collar on the body of the objective as illustrated in Figure 2. The plan fluor objective on the left has a variable immersion medium/numerical aperture setting that allows the objective to be used with both air and an alternative liquid immersion medium, glycerin. The plan apo objective on the right has an adjustable working distance control (termed a "correction collar") that allows the objective to image specimens through glass coverslips of variable thickness. This is especially important in dry objectives with high numerical aperture that are particularly susceptible to spherical and other aberrations that can impair resolution and contrast when used with a cover glass whose thickness differs from the specified design value.

The magnification depends on the focal length and the subject distance, and sometimes it can be difficult to estimate. When the magnification is small, the formula simplifies to

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Identification of the properties of individual objectives is usually very easy because important parameters are often inscribed on the outer housing (or barrel) of the objective itself as illustrated in Figure 1. This figure depicts a typical 60x plan apochromat objective, including common engravings that contain all of the specifications necessary to determine what the objective is designed for and the conditions necessary for proper use.

Investigate how the size of the light cone entering the objective front lens changes with the objective numerical aperture value.

where t is the total depth of focus, N is the lens f-number, c is the circle of confusion, v is the image distance, and f is the lens focal length. In most cases, the image distance (not to be confused with subject distance) is not easily determined; the depth of focus can also be given in terms of magnification m:

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Discover how internal lens elements in a high numerical aperture dry objective may be adjusted to correct for fluctuations in cover glass thickness.

Special Features - Objectives often have additional special features that are specific to a particular manufacturer and type of objective. The plan apochromat objective illustrated in Figure 1 has a spring-loaded front lens to prevent damage when the objective is accidentally driven onto the surface of a microscope slide.

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From the discussion above it is apparent that objectives are the most important optical element of a compound microscope. It is for this reason that so much effort is invested in making sure that they are well-labeled and suited for the task at hand. We will explore other properties and aspects of microscope objectives in other sections of this tutorial.

Following historical convention, the circle of confusion is sometimes taken as the lens focal length divided by 1000 (with the result in same units as the focal length);[2][3] this formula makes most sense in the case of normal lens (as opposed to wide-angle or telephoto), where the focal length is a representation of the format size. This practice is now deprecated; it is more common to base the circle of confusion on the format size (for example, the diagonal divided by 1000 or 1500).[3]

The choice to place gels or other filters behind the lens becomes a much more critical decision when dealing with smaller formats. Placement of items behind the lens will alter the optics pathway, shifting the focal plane. Therefore, often this insertion must be done in concert with stopping down the lens in order to compensate enough to make any shift negligible given a greater depth of focus. It is often advised in 35 mm motion-picture filmmaking not to use filters behind the lens if the lens is wider than 25 mm.

In small-format cameras, the smaller circle of confusion limit yields a proportionately smaller depth of focus. In motion-picture cameras, different lens mount and camera gate combinations have exact flange focal distance measurements to which lenses are calibrated.

Explore how variations in the refractive index of the imaging medium effect the ability of an objective to capture light rays emanating from the specimen.

Cements employed in building multiple lens elements usually have a thickness around 5-10 microns, which can be a source of artifacts in groups that have three or more lens elements cemented together. Doublets, triplets, and other multiple lens arrangements can display spurious absorption, transmission, and fluorescence characteristics that will disqualify the lenses for certain applications.