Abstract It is possible to improve measurements with the Michelson interferometer by a photoelectric method, which allows extension out of the visible spectrum. The photomultiplier is the only useful detector for narrow weak lines ; it is supposed that fluctuations are due to shot-noise. Optimum conditions are calculated for measurements of fractional order of interference, and wavelength comparison : the diameter of the hole isolating the central part of the interference pattern, and the order of interference. The accuracy of wavelength intercomparison is limited at present not by photomultiplier quality but by interferometer imperfections.
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The Michelson interferometer is a common configuration for optical interferometry and was invented by Albert Abraham Michelson. Using a beam splitter , a light source is split into two arms.
Each of those light beams is reflected back toward the beamsplitter which then combines their amplitudes using the superposition principle. The resulting interference pattern that is not directed back toward the source is typically directed to some type of photoelectric detector or camera.
For different applications of the interferometer, the two light paths can be with different lengths or incorporate optical elements or even materials under test. The Michelson interferometer among other interferometer configurations is employed in many scientific experiments and became well known for its use by Albert Michelson and Edward Morley in the famous Michelson—Morley experiment  in a configuration which would have detected the earth's motion through the supposed luminiferous aether that most physicists at the time believed was the medium in which light waves propagated.
The null result of that experiment essentially disproved the existence of such an aether, leading eventually to the special theory of relativity and the revolution in physics at the beginning of the twentieth century.
In , another application of the Michelson interferometer, LIGO , made the first direct observation of gravitational waves. M is partially reflective, so part of the light is transmitted through to point B while some is reflected in the direction of A. Both beams recombine at point C' to produce an interference pattern incident on the detector at point E or on the retina of a person's eye.
If there is a slight angle between the two returning beams, for instance, then an imaging detector will record a sinusoidal fringe pattern as shown in Fig. If there is perfect spatial alignment between the returning beams, then there will not be any such pattern but rather a constant intensity over the beam dependent on the differential pathlength; this is difficult, requiring very precise control of the beam paths.
Narrowband spectral light from a discharge or even white light can also be used, however to obtain significant interference contrast it is required that the differential pathlength is reduced below the coherence length of the light source.
That can be only micrometers for white light, as discussed below. If a lossless beamsplitter is employed, then one can show that optical energy is conserved. At every point on the interference pattern, the power that is not directed to the detector at E is rather present in a beam not shown returning in the direction of the source. As shown in Fig.
The fringes can be interpreted as the result of interference between light coming from the two virtual images S' 1 and S' 2 of the original source S.
The characteristics of the interference pattern depend on the nature of the light source and the precise orientation of the mirrors and beam splitter. In Fig. If, as in Fig. If S is an extended source rather than a point source as illustrated, the fringes of Fig. White light has a tiny coherence length and is difficult to use in a Michelson or Mach—Zehnder interferometer. Even a narrowband or "quasi-monochromatic" spectral source requires careful attention to issues of chromatic dispersion when used to illuminate an interferometer.
The two optical paths must be practically equal for all wavelengths present in the source. This requirement can be met if both light paths cross an equal thickness of glass of the same dispersion. To equalize the dispersion, a so-called compensating plate identical to the substrate of the beam splitter may be inserted into the path of the vertical beam.
The requirement for dispersion equalization is eliminated by using extremely narrowband light from a laser. The extent of the fringes depends on the coherence length of the source. Single longitudinal mode lasers are highly coherent and can produce high contrast interference with differential pathlengths of millions or even billions of wavelengths. On the other hand, using white broadband light, the central fringe is sharp, but away from the central fringe the fringes are colored and rapidly become indistinct to the eye.
Early experimentalists attempting to detect the earth's velocity relative to the supposed luminiferous aether , such as Michelson and Morley  and Miller ,  used quasi-monochromatic light only for initial alignment and coarse path equalization of the interferometer.
A practical Fourier transform spectrometer would substitute corner cube reflectors for the flat mirrors of the conventional Michelson interferometer, but for simplicity, the illustration does not show this. An interferogram is generated by making measurements of the signal at many discrete positions of the moving mirror. A Fourier transform converts the interferogram into an actual spectrum.
When using a noisy detector, such as at infrared wavelengths, this offers an increase in signal to noise ratio while using only a single detector element; 2 the interferometer does not require a limited aperture as do grating or prism spectrometers, which require the incoming light to pass through a narrow slit in order to achieve high spectral resolution. This is an advantage when the incoming light is not of a single spatial mode.
The Twyman—Green interferometer is a variation of the Michelson interferometer used to test small optical components, invented and patented by Twyman and Green in The basic characteristics distinguishing it from the Michelson configuration are the use of a monochromatic point light source and a collimator.
Michelson criticized the Twyman—Green configuration as being unsuitable for the testing of large optical components, since the available light sources had limited coherence length. Michelson pointed out that constraints on geometry forced by the limited coherence length required the use of a reference mirror of equal size to the test mirror, making the Twyman—Green impractical for many purposes. The use of a figured reference mirror in one arm allows the Twyman—Green interferometer to be used for testing various forms of optical component, such as lenses or telescope mirrors.
A point source of monochromatic light is expanded by a diverging lens not shown , then is collimated into a parallel beam. A convex spherical mirror is positioned so that its center of curvature coincides with the focus of the lens being tested. The emergent beam is recorded by an imaging system for analysis.
The high coherence length of a laser allows unequal path lengths in the test and reference arms and permits economical use of the Twyman—Green configuration in testing large optical components. This system used fibre optic direction coupler.
The Michelson stellar interferometer is used for measuring the diameter of stars. In , Michelson and Francis G. Pease used it to measure the diameter of Betelgeuse , the first time the diameter of a star other than the sun was measured. Michelson interferometry is the leading method for the direct detection of gravitational waves. This involves detecting tiny strains in space itself, affecting two long arms of the interferometer unequally, due to a strong passing gravitational wave.
With additional interferometers placed on other continents, like the Virgo placed in Europe, it became possible to calculate the direction where the gravitational waves originate, from the tiny time difference when the signals arrive at each station. Compared with Lyot filters, which use birefringent elements, Michelson interferometers have a relatively low temperature sensitivity.
On the negative side, Michelson interferometers have a relatively restricted wavelength range, and require use of prefilters which restrict transmittance. Another application of the Michelson interferometer is in optical coherence tomography OCT , a medical imaging technique using low-coherence interferometry to provide tomographic visualization of internal tissue microstructures. As seen in Fig. One interferometer arm is focused onto the tissue sample and scans the sample in an X-Y longitudinal raster pattern.
The other interferometer arm is bounced off a reference mirror. Reflected light from the tissue sample is combined with reflected light from the reference. Because of the low coherence of the light source, interferometric signal is observed only over a limited depth of sample. X-Y scanning therefore records one thin optical slice of the sample at a time. By performing multiple scans, moving the reference mirror between each scan, an entire three-dimensional image of the tissue can be reconstructed.
Others applications include delay line interferometer which convert phase modulation into amplitude modulation in DWDM networks, the characterization of high-frequency circuits. 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.
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  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  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. 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 See Fig. 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.
In one example of the use of the MDI, Stanford scientists reported the detection of several sunspot regions in the deep interior of the Sun, 1—2 days before they appeared on the solar disc. This is a Michelson interferometer in which the mirror in one arm is replaced with a Gires—Tournois etalon. Because the phase change from the Gires—Tournois etalon is an almost step-like function of wavelength, the resulting interferometer has special characteristics.
It has an application in fiber-optic communications as an optical interleaver. Both mirrors in a Michelson interferometer can be replaced with Gires—Tournois etalons. The step-like relation of phase to wavelength is thereby more pronounced, and this can be used to construct an asymmetric optical interleaver.
For this reason the interference pattern in twin-beam interferometer changes drastically. The nontrivial features of phase fluctuations in optical phase-conjugating mirror had been studied via Michelson interferometer with two independent PC-mirrors. From Wikipedia, the free encyclopedia. Main article: Fourier transform spectroscopy. The screw m was then slowly turned till the bands reappeared.
They were then of course colored, except the central band, which was nearly black. White-light fringes were employed to facilitate observation of shifts in position of the interference pattern. The corresponding shift in the Potsdam interferometer had been 0. American Journal of Science. Bibcode : AmJS Physical Review Letters. Bibcode : PhRvL. Basics of Interferometry, Second Edition. American Journal of Physics. Bibcode : AmJPh.. Retrieved 3 April Block Engineering. Retrieved 26 April Bibcode : PNAS Optical Shop Testing.
From Wikimedia Commons, the free media repository. Albert A. Media in category "Michelson interferometer" The following files are in this category, out of total. Colored and monochrome fringes. Experience 4 miroirs. Fig-Gequetschtes ifo D RS. Fig-Squeezed ifo E RS.