Michelson interferometer

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A Michelson interferometer for use on an optical table.

The Michelson interferometer is the most common configuration for optical interferometry and was invented by Albert Abraham Michelson. An interference pattern is produced by splitting a beam of light into two paths, bouncing the beams back and recombining them. The different paths may be of different lengths or be composed of different materials to create alternating interference fringes on a back detector. Michelson, along with Edward Morley, used this interferometer in the famous Michelson-Morley experiment (1887)[1] to show the constancy of the speed of light across multiple inertial frames, which removed the conceptual need for a luminiferous aether to provide a rest frame for light.

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[edit] Configuration

A Michelson interferometer consists of two highly polished mirrors M1 & M2. A source S emits monochromatic light that hits a half-silvered mirror, surface M, at point C. M is partially reflective, so one beam is transmitted through to point B while one is reflected in the direction of A. Both beams recombine at point C' to produce an interference pattern (assuming proper alignment) visible to the observer at point E. To the observer at point E, the effects observed would be the same as those produced by placing surfaces A and B' (the image of B on the surface M) on top of each other. Let's look at this interaction in more detail. Imagine that we have two surfaces M1 and M2 as diagrammed.

Path of light in Michelson interferometer.

There are two paths from the (light) source to the detector. One reflects off the semi-transparent mirror, goes to the top mirror and then reflects back, goes through the semi-transparent mirror, to the detector. The other first goes through the semi-transparent mirror, to the mirror on the right, reflects back to the semi-transparent mirror, then reflects from the semi-transparent mirror into the detector. The principle is when a parallel beam of light coming from a monochromatic extended light source is incident on a half silvered glass plate, it is divided into two beams of equal intensities by partial reflection and transmission. Both beams are coherent. In this experiment coherent waves are thus produced by the method of division of amplitude.

If these two paths differ by a whole number (including 0) of wavelengths, there is constructive interference and a strong signal at the detector. If they differ by a whole number and a half wavelengths (e.g., 0.5, 1.5, 2.5 ...) there is destructive interference and a weak signal. This might appear at first sight to violate the principle of conservation of energy. However energy is conserved, because there is a redistribution of energy at the central beam-splitter in which the energy at the destructive sites is re-distributed to the constructive sites. The effect of the interference is to alter the share of the reflected light which heads for the detector and the remainder which heads back in the direction of the source.

In the late 1800s, the interference pattern was obtained by using a gas discharge lamp, a filter, and a thin slot or pinhole. In one version of the Michelson-Morley experiment, the interferometer used starlight as the source of light. Starlight is temporally incoherent light, but since it is a point source of light it has spatial coherence and will produce an interference pattern.

[edit] Applications

The best known application of the Michelson Interferometer is the Michelson-Morley experiment that provided evidence for special relativity. However, this configuration can be used for an assortment of different applications.

The Michelson Interferometer has been used for the detection of gravitational waves, as a tunable narrow band filter, and as the core of Fourier transform spectroscopy. There are also some interesting applications as a "nulling" instrument that is used for detecting planets around nearby stars. For most purposes, however, the geometry of the Mach–Zehnder interferometer is more useful. For the same path lengths, it will obtain a minimum due to zero phase shift on the internal reflection.

A further application is to produce a delay line interferometer that converts phase modulation into amplitude modulation in DWDM networks.

Astronomical interferometry is principally conducted using Michelson (and sometimes other type) interferometers. Principle operational interferometric observatories which use this type of instrumentation include VLTI, NPOI, and CHARA.

Another application of the Michelson Interferometer is in the OCT (Optical coherence tomography) which is a medical imaging technique.

[edit] Atmospheric and Space Applications

The Michelson Interferometer has played an important role in studies of the upper atmosphere, revealing temperatures and winds, employing both space-borne, and ground-based instruments, by measuring the Doppler widths and shifts in the spectra of airglow and aurora. For example, the Wind Imaging Interferometer, WINDII, [2] on the Upper Atmosphere Research Satellite, UARS, (launched on September 12, 1991) measured the global wind and temperature patterns from 80 to 300 km by using the visible airglow emission from these altitudes as a target and employing optical Doppler interferometry to measure the small wavelength shifts of the narrow atomic and molecular airglow emission lines induced by the bulk velocity of the atmosphere carrying the emitting species. The instrument was an all-glass field-widened achromatically and thermally compensated phase-stepping Michelson interferometer, along with a bare CCD detector that imaged the airglow limb through the interferometer. A sequence of phase-stepped images was processed to derive the wind velocity for two orthogonal view directions, yielding the horizontal wind vector.

The principle of using a polarizing Michelson Interferometer as a narrow band filter was first described by Evans [3] who developed a birefringent photometer where the incoming light is split into two orthogonally polarized components by a polarizing beam splitter, sandwiched between two halves of a Michelson cube. This led to the first polarizing wide-field Michelson interferometer described by Title and Ramsey [4] which was used for solar observations; and led to the development of a refined instrument applied to measurements of oscillations in the sun’s atmosphere, employing a network of observatories around the Earth known as the Global Oscillations Network Group (GONG) [5].

The Polarizing Atmospheric Michelson Interferometer, PAMI, developed by Bird et al.[6], and discussed in Spectral Imaging of the Atmosphere[7], combines the polarization tuning technique of Title and Ramsey [8] with the Shepherd et al [9] technique of deriving winds and temperatures from emission rate measurements at sequential path differences, but the scanning system used by PAMI is much simpler than the moving mirror systems in that it has no internal moving parts, instead scanning with a polarizer external to the interferometer. The PAMI was demonstrated in an observation campaign [10] where its performance was compared to a Fabry-Perot spectrometer, and employed to measure E-region winds.

More recently, the Helioseismic and Magnetic Imager (HMI), on the Solar Dynamics Observatory, employs two Michelson Interferometers with a polarizer and other tunable elements, to study solar variability and to characterize the Sun's interior along with the various components of magnetic activity. HMI takes high-resolution measurements of the longitudinal and vector magnetic field over the entire visible disk thus extending the capabilities of its predecessor, the SOHO's MDI instrument.[11]. HMI produces data to determine the interior sources and mechanisms of solar variability and how the physical processes inside the Sun are related to surface magnetic field and activity. It also produces data to enable estimates of the coronal magnetic field for studies of variability in the extended solar atmosphere. HMI observations will help establish the relationships between the internal dynamics and magnetic activity in order to understand solar variability and its effects.[12]

Stanford scientists [13] reported the detection of several sunspot regions in the deep interior of the Sun, 1-2 days before they appear on the solar disc. The detection of sunspots in the solar interior may thus provide valuable warnings about upcoming surface magnetic activity which could be used to improve and extend the predictions of space weather forecasts.

[edit] Nonlinear Michelson interferometer

Nonlinear Michelson interferometer, also known as Step-phase Michelson interferometer is a generalized Michelson interferometer in which one mirror in one arm is replaced with a Gires–Tournois interferometer[14] (Interferometer useful for the compression of frequency-modulated light pulse) or Gires–Tournois etalon. The field coming from Gires–Tournois etalon interferes with the plane field reflected from the ordinary reflector. Because the phase change from the Gires–Tournois etalon depends on wavelength and shows step-like behavior, nonlinear Michelson interferometer has particular applications. One notable application in fiber-optic communications is an optical interleaver.

The two mirrors in a Michelson interferometer can be replaced with two Gires–Tournois etalons. Such a nonlinear Michelson interferometer exhibits stronger nonlinearity, which can be used to construct an asymmetric optical interleaver.

LUPI

A variation of the Michelson that uses a small spherical reference mirror in one arm is often called a LUPI – laser unequal path interferometer. This setup needs a laser source, be it a tube laser or laser diodes – green or red.

This configuration is used to test large/small telescope mirrors.

A detailed write up on the first LUPI can be seen in the August 1972 issue of Applied Optics Vol 11 #8 pp 1872–74.There specifications are given for allowable cube beamsplitter (not single plate) thickness to be used with specific mirror focal length combinations with total allowable aberration limits for that setup detailed.

[edit] See also

[edit] References

  1. ^ Albert Michelson, Edward Morley (1887). "On the Relative Motion of the Earth and the Luminiferous Ether". American Journal of Science: 333–345. https://secure.wikimedia.org/wikisource/en/wiki/Index:On_the_Relative_Motion_of_the_Earth_and_the_Luminiferous_Ether.djvu. 
  2. ^ Shepherd, G. G.; et al. (1993). "WINDII, the Wind Imaging Interferometer on the Upper Atmosphere Research Satellite". J. Geophys. Res. 98(D6): 10,725–10,750. 
  3. ^ Evans, J. W. (1947). "The birefringent filter". J. Opt. Soc. Am. 39 229. 
  4. ^ Title, A. M.; Ramsey, H. E. (1980). "Improvements in birefringent filters. 6: Analog birefringent elements". Appl. Opt. 19, p. 2046. 
  5. ^ Harvey, J.; et al. (1996). "The Global Oscillation Network Group (GONG) Project". Science 272: 1284–1286. Bibcode 1996Sci...272.1284H. doi:10.1126/science.272.5266.1284. 
  6. ^ Bird, J.; et al. (1995). "A polarizing Michelson interferometer for measuring thermospheric winds". Meas. Sci. Technol 6(9): 1368–1378. 
  7. ^ Shepherd, G. G. (2002). Spectral Imaging of the Atmosphere. Academic Press. ISBN 0-12-639481-4. 
  8. ^ Title, A. M.; Ramsey, H. E. (1980). "Improvements in birefringent filters. 6: Analog birefringent elements". Appl. Opt. 19, p. 2046. 
  9. ^ Shepherd, G. G.; et al. (1985). "WAMDII: wide angle Michelson Doppler imaging interferometer for Spacelab". Appl. Opt. 24, p. 1571. 
  10. ^ Bird, J.; G. G. Shepherd, C. A. Tepley (1995). "Comparison of lower thermospheric winds measured by a Polarizing Michelson Interferometer and a Fabry-Perot spectrometer during the AIDA campaign". Journal of Atmospheric and Terrestrial Physics 55(3): 313–324. 
  11. ^ Dean Pesnell; Kevin Addison (5 February 2010). "SDO - Solar Dynamics Observatory: SDO Instruments". NASA. http://sdo.gsfc.nasa.gov/mission/instruments.php. Retrieved 2010-02-13. 
  12. ^ Solar Physics Research Group. "Helioseismic and Magnetic Imager Investigation". Stanford Universtity. http://hmi.stanford.edu/Description/HMI_Overview.html. Retrieved 2010-02-13. 
  13. ^ Ilonidis, S.; et al. (1996). "Detection of Emerging Sunspot Regions in the Solar Interior". Science 272 19 August 2011: 993-996.DOI:10.1126: 993–996. 
  14. ^ F. Gires, and P. Tournois (1964). "Interféromètre utilisable pour la compression d'impulsions lumineuses modulées en fréquence". Comptes Rendus de l'Académie des Sciences de Paris 258: 6112–6115. 

[edit] External links

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