Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

European Journal of Physics

Analysis of the localization of Michelson interferometer fringes using Fourier optics and temporal coherence

Chittur Subramanian Narayanamurthy

Published Dec 5, 2008• 4 citations
Publisher

Abstract

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.

DOI
10.1088/0143-0807/30/1/015

Related papers

The relationship between the fringes produced by Young's slits and by the Michelson interferometer

Derek N. Stacey

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.

European Journal of Physics•Jan 1, 1991•2 citations

Real Fringes in the Sagnac and Michelson Interferometers

Alfred Zajac, Henry Sadowski, Seymour Licht

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.

American Journal of Physics•Oct 1, 1961•5 citations

On the formation of white-light interference fringes

Attila Pál Kovács, Katalin Varjú, K. Osvay +1 more

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.

American Journal of Physics•Nov 1, 1998•10 citations

Interference of Light in a Michelson-Morley Interferometer: A Quantum Optical Approach

Øystein Langangen, Asle Heide Vaskinn, B.-S. Skagerstam

The temporal coherence interference properties of light as revealed by single detector intensity measurements in a Michelson-Morley interferometer (MMI) is often described in terms of classical optics. We show, in a pedagogical manner, how such features of light also can be understood in terms of a more general quantum-optics framework. If a thermal reference source is used in the MMI local oscillator port in combination with a thermal source in the signal port, the interference pattern revealed by single detector intensity measurements shows a distinctive dependence on the differences in the temperature of the two sources. A related method has actually been used to perform high-precision measurements of the cosmic microwave background radiation. The general quantum-optics framework allows us to consider any initialquantum state. As an example, we consider the interference of single photons as a tool to determine the peak angular-frequency of a single-photon pulse interfering with a single-photon reference pulse. A similar consideration for laser pulses, in terms of coherent states, leads to a different response in the detector. The MMI experimental setup is therefore an example of an optical device where one, in terms of intensity measurements, can exhibit the difference between classical and quantum-mechanical light.

International Journal of Optics•Jan 1, 2012•3 citations

Interference of Light in Michelson-Morley Interferometer: A Quantum Optical Approach

Øystein Langangen, B.-S. Skagerstam, Asle Heide Vaskinn

We investigate how the temporal coherence interference properties of light in a Michelson-Morley interferometer (MMI), using only a single-photon detector, can be understood in a quantum-optics framework in a straightforward and pedagogical manner. For this purpose we make use of elementary quantum field theory and Glaubers theory for photon detection in order to calculate the expected interference pattern in the MMI. If a thermal reference source is used in the MMI local oscillator port in combination with a thermal source in the signal port, the interference pattern revealed by such an intensity measurement shows a distinctive dependence on the differences in the temperature of the two sources. The MMI can therefore be used in order to perform temperature measurements. A related method was actually used to carry out high precision measurements of the cosmic micro-wave background radiation on board of the COBE satellite. The theoretical framework allows us to consider any initial quantum state. The interference of single photons as a tool to determine the angular peak-frequency of a one-photon pulse interfering with a single-photon reference pulse is, e.g., considered. A similar consideration for coherent laser pulses leads to a different response in the detector. The MMI experimental setup is therefore in a sense an example of an optical device where one can exhibit the difference between classical and quantum-mechanical light using only intensity measurements.

arXiv:1102.4324•Feb 21, 2011•0 citations

A Statistical Introduction to Temporal Coherence Effects in Interferometers

Pierre H. Chavel, Jean‐Michel Jonathan

In paying tribute to the many contributions of Adolf Lohmann to optical science, we must highlight his inspiring talent as a lecturer and teacher as well as his ability to introduce original concepts and ideas.We have chosen to devote our contribution to one aspect of the teaching of physical optics. When teaching interferences, the lecturer always encounters the question:Why do two different frequencies never interfere? A two-beam interferometer illuminated by light of a different frequency on each arm does not show fringes. Or to be more precise, in the quite common case of thermal light sources,1 common experience shows that interferences between two different frequencies of the source spectrum cannot be observed. Interferences with light that is not strictly monochromatic are observed but merely result from the incoherent superposition of all component monochromatic interference intensities. Providing a convincing explanation of this fact in an elementary course is not easy because statistical tools are required that are only available to the students at a more advanced level—typically, senior undergraduate or graduate. However, a full account of the phenomenon based on solid statistical grounds is not even commonly found in textbooks designed for such advanced students. Such is the aim of the present chapter. Indeed, the superposition of two different frequencies should be expected to show a beat phenomenon in time. Nevertheless, common experience shows that interference effects are stationary in time and show no beat effect. If we start from the definition of interferences as the phenomenon whereby the intensity resulting from the superposition of two light beams differs from the sum of the two intensities, we are led to clarifying the temporal aspects in the detection of light beams. First, the common situation of describing the effect at a less advanced level is examined, together with the difficulties that automatically arise. After a review of the necessary statistical concepts such as, in particular, the Wiener-Khintchin theorem, the issue of what exactly is meant by average intensity and the associated “classical detection noise” is addressed, leading to a complete model of temporal coherence in thermal light.

•Mar 25, 2017•2 citations
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.
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.
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.
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 temporal coherence interference properties of light as revealed by single detector intensity measurements in a Michelson-Morley interferometer (MMI) is often described in terms of classical optics. We show, in a pedagogical manner, how such features of light also can be understood in terms of a more general quantum-optics framework. If a thermal reference source is used in the MMI local oscillator port in combination with a thermal source in the signal port, the interference pattern revealed by single detector intensity measurements shows a distinctive dependence on the differences in the temperature of the two sources. A related method has actually been used to perform high-precision measurements of the cosmic microwave background radiation. The general quantum-optics framework allows us to consider any initialquantum state. As an example, we consider the interference of single photons as a tool to determine the peak angular-frequency of a single-photon pulse interfering with a single-photon reference pulse. A similar consideration for laser pulses, in terms of coherent states, leads to a different response in the detector. The MMI experimental setup is therefore an example of an optical device where one, in terms of intensity measurements, can exhibit the difference between classical and quantum-mechanical light.
We investigate how the temporal coherence interference properties of light in a Michelson-Morley interferometer (MMI), using only a single-photon detector, can be understood in a quantum-optics framework in a straightforward and pedagogical manner. For this purpose we make use of elementary quantum field theory and Glaubers theory for photon detection in order to calculate the expected interference pattern in the MMI. If a thermal reference source is used in the MMI local oscillator port in combination with a thermal source in the signal port, the interference pattern revealed by such an intensity measurement shows a distinctive dependence on the differences in the temperature of the two sources. The MMI can therefore be used in order to perform temperature measurements. A related method was actually used to carry out high precision measurements of the cosmic micro-wave background radiation on board of the COBE satellite. The theoretical framework allows us to consider any initial quantum state. The interference of single photons as a tool to determine the angular peak-frequency of a one-photon pulse interfering with a single-photon reference pulse is, e.g., considered. A similar consideration for coherent laser pulses leads to a different response in the detector. The MMI experimental setup is therefore in a sense an example of an optical device where one can exhibit the difference between classical and quantum-mechanical light using only intensity measurements.
In paying tribute to the many contributions of Adolf Lohmann to optical science, we must highlight his inspiring talent as a lecturer and teacher as well as his ability to introduce original concepts and ideas.We have chosen to devote our contribution to one aspect of the teaching of physical optics. When teaching interferences, the lecturer always encounters the question:Why do two different frequencies never interfere? A two-beam interferometer illuminated by light of a different frequency on each arm does not show fringes. Or to be more precise, in the quite common case of thermal light sources,1 common experience shows that interferences between two different frequencies of the source spectrum cannot be observed. Interferences with light that is not strictly monochromatic are observed but merely result from the incoherent superposition of all component monochromatic interference intensities. Providing a convincing explanation of this fact in an elementary course is not easy because statistical tools are required that are only available to the students at a more advanced level—typically, senior undergraduate or graduate. However, a full account of the phenomenon based on solid statistical grounds is not even commonly found in textbooks designed for such advanced students. Such is the aim of the present chapter. Indeed, the superposition of two different frequencies should be expected to show a beat phenomenon in time. Nevertheless, common experience shows that interference effects are stationary in time and show no beat effect. If we start from the definition of interferences as the phenomenon whereby the intensity resulting from the superposition of two light beams differs from the sum of the two intensities, we are led to clarifying the temporal aspects in the detection of light beams. First, the common situation of describing the effect at a less advanced level is examined, together with the difficulties that automatically arise. After a review of the necessary statistical concepts such as, in particular, the Wiener-Khintchin theorem, the issue of what exactly is meant by average intensity and the associated “classical detection noise” is addressed, leading to a complete model of temporal coherence in thermal light.