NikonUSA NikonNet MicroscopyU NikonMall NikonSchool
Search
Go

Basic Concepts and Formulas in Microscopy

In order to realize the full potential of the optical microscope, one must have a firm grasp of the fundamental physical principles surrounding its operation. Important topics for understanding the microscope, such as resolution, numerical aperture, depth of field, image brightness, objective working distance, field of view, conjugate planes, and the useful magnification range, are discussed in the review articles linked below.

Innovations in Light Microscopy - Evolution of the optical microscope over the past centuries has been driven by scientists who wish to observe and measure phenomena that were smaller, fainter, and deeper inside tissue than ever before. Although the new instruments on the market have brought the microscope to a high level of development, we will probably never reach that goal as long as scientific research continues. Future needs will require innovations that we cannot yet even foresee, but the best of today's instruments provide the user with vastly more performance and versatility than were possible just a few years ago.

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.

Microscope Alignment for Köhler Illumination - Perhaps one of the most misunderstood and often neglected concepts in optical microscopy is proper configuration of the microscope with regards to illumination, which is a critical parameter that must be fulfilled in order to achieve optimum performance. The intensity and wavelength spectrum of light emitted by the illumination source is of significant importance, but even more essential is that light emitted from various locations on the lamp filament be collected and focused at the plane of the condenser aperture diaphragm. This interactive tutorial reviews both the filament and condenser alignment procedures necessary to achieve Köhler illumination.

Depth of Field and Depth of Focus - The depth of field is the thickness of the specimen that is acceptably sharp at a given focus level. In contrast, depth of focus refers to the range over which the image plane can be moved while an acceptable amount of sharpness is maintained. The two concepts are often incorrectly used interchangeably when referring to the depth of field of a microscope objective.

Field of View - The diameter of the field in an optical microscope is expressed by the field-of-view number, or simply the field number, which is the diameter of the view field in millimeters measured in the intermediate image plane. In most cases, the eyepiece field diaphragm opening diameter determines the view field size.

Refractive Index (Index of Refraction) - Refractive index is a value calculated from the ratio of the speed of light in a vacuum to that in a second medium of greater density. The refractive index variable is most commonly symbolized by the letter n or n' in descriptive text and mathematical equations.

Numerical Aperture - The numerical aperture of a microscope objective is a measure of its ability to gather light and resolve fine specimen detail at a fixed object distance. All modern microscope objectives have the numerical aperture value inscribed on the lens barrel, which allows determination of the smallest specimen detail resolvable by the objective and an approximate indication of the depth of field.

Resolution - The resolving power of a microscope is the most important feature of the optical system and influences the ability to distinguish between fine details of a particular specimen. As discussed in this section, the primary factor in determining resolution is the objective numerical aperture, but resolution is also dependent upon the type of specimen, coherence of illumination, degree of aberration correction, and other factors such as contrast enhancing methodology either in the optical system of the microscope or in the specimen itself.

Useful Magnification Range - The range of useful magnification for an objective/eyepiece combination is defined by the numerical aperture of the system. There is a minimum magnification necessary for the detail present in an image to be resolved, and this value is usually rather arbitrarily set to a value between 500 and 1000 times the numerical aperture (500 or 1000 x NA) of the objective.

Working Distance and Parfocal Length - Microscope objectives are generally designed with a short free working distance, which is defined as the distance from the front lens element of the objective to the closest surface of the coverslip when the specimen is in sharp focus. The parfocal length represents the distance between the specimen plane and the shoulder of the flange by which the objective is supported on the revolving nosepiece.

Image Brightness - Regardless of the imaging mode utilized in optical microscopy, image brightness is governed by the light-gathering power of the objective, which is a function of numerical aperture. Just as the brightness of illumination is determined by the square of the condenser working numerical aperture, the image brightness is proportional to the square of the objective numerical aperture.

Coverslip Correction - Non-immersion high-dry microscope objectives having a numerical aperture exceeding 0.75 are prone to introduction of aberration when imaging through coverslips that deviate from standard thickness and refractive index. To prevent artifacts, many objectives are equipped with correction collars that help compensate for coverslip thickness variations.

Adjustment of Objective Correction Collars - Most microscope objectives are designed to be used with a cover glass that has a standard thickness of 0.17 millimeters and a refractive index of 1.515, which is satisfactory when the objective numerical aperture is 0.4 or less. However, when using high numerical aperture dry objectives (numerical aperture of 0.8 or greater), cover glass thickness variations of only a few micrometers result in dramatic image degradation due to aberration, which grows worse with increasing cover glass thickness. To compensate for this error, the more highly corrected objectives are equipped with a correction collar to allow adjustment of the central lens group position to coincide with fluctuations in cover glass thickness. This interactive tutorial explores how a correction collar is adjusted to achieve maximum image quality.

Focusing and Alignment of Arc Lamps - Mercury and xenon arc lamps are now widely utilized as illumination sources for a large number of investigations in widefield fluorescence microscopy. Visitors can gain practice aligning and focusing the arc lamp in a Mercury or Xenon Burner with this interactive tutorial, which simulates how the lamp is adjusted in a fluorescence microscope.

Linear Measurements (Micrometry) - Performing measurements at high magnifications in compound optical microscopy is generally conducted by 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.

Basic Microscope Ergonomics - In order to view specimens and record data, microscope operators must assume an unusual but exacting position, with little possibility to move the head or the body. They are often forced to assume an awkward work posture such as the head bent over the eye tubes, the upper part of the body bent forward, the hand reaching high up for a focusing control, or with the wrists bent in an unnatural position.

Laser Safety - The two major concerns in safe laser operation are exposure to the beam and the electrical hazards associated with high voltages within the laser and its power supply. While there are no known cases of a laser beam contributing to a person's death, there have been several instances of deaths attributable to contact with high voltage laser-related components. Beams of sufficiently high power can burn the skin, or in some cases create a hazard by burning or damaging other materials, but the primary concern with regard to the laser beam is potential damage to the eyes, which are the part of the body most sensitive to light.

Principles and Applications of Interferometry - The foundation for interferometry (often referred to as microinterferometry) dates back to the Nineteenth Century with the introduction of the first interference microscope, which was based on the principles of the Jamin interferometer. Since that period, a number of commercial interference microscopes, both with transmitted and reflected light capabilities, have been produced by a number of manufacturers. Primarily designed to yield quantitative data from interference images, these microscopes utilize various technologies to determine parameters such as refractive index, birefringence, and thickness for a wide spectrum of materials.

  • Two Beam Interferometry - A two-beam interferometer functions by dividing originally coherent light into two beams of equal intensity, directing one beam onto the reference mirror and the other onto the specimen, and measuring the optical path difference (the difference in optical distances) between the resulting two reflected light waves.

  • Multiple-Beam Interferometry - The technique of multiple-beam interferometry is based upon situating two surfaces of high reflectivity in close proximity and using a lens to converge beams which have undergone multiple-reflection between the surfaces.

Contributing Authors

Kenneth R. Spring - Scientific Consultant, Lusby, Maryland, 20657.

Hiroshi Komatsu - Institute for Materials Research, Tohoku University, Sendai, Japan.

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