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American Journal of Physics

Real Fringes in the Sagnac and Michelson Interferometers

Alfred Zajac, Henry Sadowski, Seymour Licht

Published Oct 1, 1961• 5 citations

Abstract

In describing the Michelson interferometer, it is usually stated that in order to observe fringes an extended source must be used. It has to be realized, however, that this requirement applies only to the formation of virtual fringes. Actually two distinct sets of fringes exist; virtual and real. Rarely, if ever, is attention brought to the existence of the latter type. The existence of the real fringes was first noted by the authors using the Sagnac interferometer, which is described in this paper. This little-known interferometer and the Michelson interferometer are both amplitude-splitting types. Real fringes were obtained for both a point source and an extended source while virtual fringes were, of course, only visible for an extended source. Similar sets of real fringes were also observed for the Michelson interferometer using either an extended or a point source. An analysis of the formulation of real fringes is presented.

DOI: 10.1119/1.1937549

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In describing the Michelson interferometer, it is usually stated that in order to observe fringes an extended source must be used. It has to be realized, however, that this requirement applies only to the formation of virtual fringes. Actually two distinct sets of fringes exist; virtual and real. Rarely, if ever, is attention brought to the existence of the latter type. The existence of the real fringes was first noted by the authors using the Sagnac interferometer, which is described in this paper. This little-known interferometer and the Michelson interferometer are both amplitude-splitting types. Real fringes were obtained for both a point source and an extended source while virtual fringes were, of course, only visible for an extended source. Similar sets of real fringes were also observed for the Michelson interferometer using either an extended or a point source. An analysis of the formulation of real fringes is presented.

The author demonstrates a relationship between the pattern of straight interference fringes formed in Young's experiment and the circular fringes produced at infinity by a Michelson interferometer. The two patterns can both be considered to be produced by the interference of light from two coherent point sources. It is shown that the pattern given by these sources on a large sphere centred midway between them reduces to Young's fringes in the vicinity of zero path difference and to the Michelson pattern in the vicinity of maximum path difference.

Fringes formed in a Michelson interferometer never localize in any plane, in the detector plane and in the localization plane. Instead, the fringes are assumed to localize at infinity. Except for some explanation in Principles of Optics by Born and Wolf (1964 (New York: Macmillan)), the fringe localization phenomena of Michelson's interferometer have never been analysed seriously in any book. Because Michelson's interferometer is one of the important and fundamental optical experiments taught at both undergraduate and graduate levels, it would be appropriate to explain the localization of these fringes. In this paper, we analyse the localization of Michelson interferometer fringes using Fourier optics and temporal coherence, and show that they never localize at any plane even at infinity.

We describe an experiment in which the white-light interference fringes appearing at the output of a Michelson interferometer are observed through a spectrograph. In this manner the relative positions of monochromatic interference fringes come into sight and it allows a better understanding of the formation of the white-light fringes. A simple model is described for determining the shape of the spectrally resolved white-light interference fringes. An expression for the relationship between the slope of the fringes and the arm length difference of the interferometer is derived and is demonstrated experimentally. In addition, an intuitive explanation based on this experiment is given for the washing out of the white-light fringes.

The genesis of quantum optics can be found in the Dirac discussion on interference as disclosed in The Principles of Quantum Mechanics . This is a masterful and prophetic discussion that begins by considering a roughly monochromatic light source. The discussion continues by considering a beam of light consisting of a large number of photons. Besides Dirac, useful references on interferometry include Steel, Meaburn and Born and Wolf. The Hanbury Brown–Twiss effect originates in interferometric measurements performed by an “intensity interferometer” used for astronomical observations. A diagram of the stellar intensity interferometer used to determine the diameter of stars is depicted. Two-beam interferometers are optical devices that divide and then recombine a light beam. It is on recombination of the beams that interference occurs. The most well-known two-beam interferometers are the Sagnac interferometer, the Mach–Zehnder interferometer, and the Michelson interferometer.