In the optical microscope, image formation occurs at the intermediate image plane through interference between direct light that has passed through the specimen unaltered and light diffracted by minute features present in the specimen. The image produced by an objective lens is conjugate with the specimen, meaning that each image point is geometrically related to a corresponding point in the specimen. It follows that each point in the specimen is therefore represented by a corresponding point in the image.
Image resolution and contrast in the microscope can only be fully understood by considering light as a train of waves. Light emitted by a particular point on a specimen is not actually focused to an infinitely small point in the conjugate image plane, but instead light waves converge and interfere near the focal plane to produce a three-dimensional diffraction pattern. The ensemble of individual diffraction patterns spatially oriented in two dimensions, often termed Airy patterns, is what constitutes the image observed when viewing specimens through the eyepieces of a microscope. These and related concepts are discussed more fully in the sections listed below.
Overview of Image Formation - When direct or undeviated light from a specimen is projected by the objective, it is spread evenly across the entire image plane at the diaphragm of the eyepiece. The light diffracted by the specimen is brought to focus at various localized sites on the same image plane, and there the diffracted light causes destructive interference. A consequence is the reduction in light intensity resulting in more or less dark areas. These patterns of light and dark are what we recognize as an image of the specimen. Since our eyes are sensitive to variations in brightness, the image then becomes a more or less faithful reconstitution of the original specimen.
Airy Pattern Formation - When an image is formed in the focused image plane of an optical microscope, every point in the specimen is represented by an Airy diffraction pattern having a finite spread. This occurs because light waves emitted from a point source are not focused into an infinitely small point by the objective, but converge together and interfere near the intermediate image plane to produce a three-dimensional Fraunhofer diffraction pattern.
Airy Pattern Basics - When the diffraction pattern formed by a specimen in the microscope is sectioned in the focal plane, it is observed as the classical two-dimensional diffraction spectrum known as the Airy pattern. This tutorial explores how Airy pattern size changes with objective numerical aperture and the wavelength of illumination; it also simulates the close approach of two Airy patterns.
Light Diffraction Through a Periodic Grating - A model for the diffraction of visible light through a periodic grating is an excellent tool with which to address both the theoretical and practical aspects of image formation in optical microscopy. Light passing through the grating is diffracted according to the wavelength of the incident light beam and the periodicity of the line grating. This interactive tutorial explores the mechanics of periodic diffraction gratings when utilized to interpret the Abbe theory of image formation in the optical microscope.
Numerical Aperture and Image Resolution - The image formed by a perfect, aberration-free objective lens at the intermediate image plane of a microscope is a diffraction pattern produced by spherical waves exiting the rear aperture and converging on the focal point. This tutorial explores the effects of objective numerical aperture on the resolution of the central bright disks present in the diffraction pattern, commonly known as Airy disks.
Conoscopic Images of Periodic Gratings - The purpose of this tutorial is to explore the reciprocal relationship between line spacings in a periodic grid (simulating a specimen) and the separation of the conoscopic image at the objective aperture plane. When the line grating has broad periodic spacings, several images of the condenser iris aperture appear in the objective rear focal plane. If white light is used to illuminate the line grating, higher order diffracted images of the aperture appear with a blue fringe closer to the zeroth order (central) image and with a green-yellow-red spectrum appearing further out towards the objective aperture periphery.
Spatial Frequency and Image Resolution - When a line grating is imaged in the microscope, a series of conoscopic images representing the condenser iris opening can be seen at the objective rear focal plane. This tutorial explores the relationship between the distance separating these iris opening images and the periodic spacing (spatial frequency) of lines in the grating.
Airy Patterns and the Rayleigh Criterion - Airy diffraction pattern sizes and their corresponding radial intensity distribution functions are sensitive to both objective numerical aperture and the wavelength of illuminating light. For a well-corrected objective with a uniform circular aperture, two adjacent points are just resolved when the centers of their Airy patterns are separated by a distance r. This tutorial examines how Airy disk sizes, at the limit of optical resolution, vary with changes in objective numerical aperture and illumination wavelength and how these changes affect the resolution of the objective.
Axial Resolution and Depth of Field - The lateral resolution for an Airy diffraction pattern generated by a point light source is defined within a single plane of focus at the intermediate image position in an optical microscope. In fact, the diffraction image of a point source extends periodically and symmetrically above and below this plane into a three-dimensional pattern that expands and spreads out from the center along the optical axis. This tutorial explores the structure of cross sections taken along the optical axis of the microscope near the focal plane using a virtual high numerical aperture objective free from spherical aberration.
Periodic Diffraction Images - When a microscope objective forms a diffraction-limited image of an object, it produces a three-dimensional diffraction pattern that is periodic both along the optical axis and laterally within the intermediate image plane. This tutorial explores diffraction images produced by a periodic object at several focal depths.
Selected Literature References - An understanding of the distribution of light intensity throughout images observed in the optical microscope involves the laws of physical optics. Of primary consideration is the diffraction pattern exhibited by the specimen, which is composed of an array of elementary constituents known as the Airy disk. These and related concepts are reviewed in the reference materials listed in this section.
Mortimer Abramowitz - Olympus America, Inc., Two Corporate Center Drive., Melville, New York, 11747.
Kenneth R. Spring - Scientific Consultant, Lusby, Maryland, 20657.
Brian O. Flynn, Kirill I. Tchourioukanov, and Michael W. Davidson - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310.
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