Ly index as a function of wavelength for a glass sample of known thickness and for a. Fm Keywords: Spectral interferometry Michelson and Mach–Zehnder. 2 We can estimate the minimum and maximum thicknesses of SM ðlÞ ¼ 1 þ V I. Mach-Zehnder Interferometer 1014617 Instruction manual 07/15 ALF 1. Safety instructions The interferometer is intended for use with a class 2 He-Ne laser. Looking directly at the beam can cause burning of the retina and should be avoided at all costs. The safety instructions supplied with the.
This image demonstrates a simple but typical Michelson interferometer. The bright yellow line indicates the path of light.The Michelson interferometer is a common configuration for optical and was invented. Using a, 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.
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 in the famous (1887) in a configuration which would have detected the earth's motion through the supposed 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 and the revolution in physics at the beginning of the twentieth century. In 2015, another application of the Michelson interferometer, made the first direct observation of. That observation confirmed an important prediction of, validating the theory's prediction of space-time distortion in the context of large scale cosmic events (known as ). Path of in Michelson interferometer.A Michelson interferometer consists minimally of mirrors M 1 & M 2 and a M.In Fig 2, a source S emits light that hits the beam splitter (in this case, a plate beamsplitter) surface M at point C. 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.Fig. 2 shows use of a coherent (laser) source. Narrowband spectral light from a 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 of the light source. That can be only for white light, as discussed below.If a lossless beamsplitter is employed, then one can show that optical. 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. This photo shows the fringe pattern formed by the Michelson interferometer,using monochromatic light (sodium D lines).As shown in Fig. 3a and 3b, the observer has a direct view of mirror M 1 seen through the beam splitter, and sees a reflected image M' 2 of mirror M 2. 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. 3a, the optical elements are oriented so that S' 1 and S' 2 are in line with the observer, and the resulting interference pattern consists of circles centered on the normal to M 1 and M' 2 (fringes of equal ). If, as in Fig. 3b, M 1 and M' 2 are tilted with respect to each other, the interference fringes will generally take the shape of (hyperbolas), but if M 1 and M' 2 overlap, the fringes near the axis will be straight, parallel, and equally spaced (fringes of equal thickness). If S is an extended source rather than a point source as illustrated, the fringes of Fig. 3a must be observed with a telescope set at infinity, while the fringes of Fig. 3b will be localized on the mirrors.: 17 Source bandwidth.
Michelson interferometers using a white light sourceWhite light has a tiny and is difficult to use in a Michelson (or ) interferometer. Even a narrowband (or 'quasi-monochromatic') spectral source requires careful attention to issues of 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. In Fig. 4a, the horizontal beam crosses the beam splitter three times, while the vertical beam crosses the beam splitter once. 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.: 16 In Fig. 4b, we see using a cube beam splitter already equalizes the pathlengths in glass.
The requirement for dispersion equalization is eliminated by using extremely narrowband light from a laser.The extent of the fringes depends on the of the source. In Fig. 3b, the yellow used for the fringe illustration consists of a pair of closely spaced lines, implying that the interference pattern will blur after several hundred fringes.
Single longitudinal mode 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, such as Michelson and Morley (1887) and Miller (1933), used quasi-monochromatic light only for initial alignment and coarse path equalization of the interferometer. Thereafter they switched to white (broadband) light, since using they could measure the point of absolute phase equalization (rather than phase modulo 2π), thus setting the two arms' pathlengths equal. More importantly, in a white light interferometer, any subsequent 'fringe jump' (differential pathlength shift of one wavelength) would always be detected.Applications.
Main article:Fig. 5 illustrates the operation of a Fourier transform spectrometer, which is essentially a Michelson interferometer with one mirror movable. (A practical Fourier transform spectrometer would substitute 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. Fourier transform spectrometers can offer significant advantages over dispersive ( i.e. Grating and prism) spectrometers under certain conditions. (1) The Michelson interferometer's detector in effect monitors all wavelengths simultaneously throughout the entire measurement. When using a noisy detector, such as at infrared wavelengths, this offers an increase in 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. For more information, see.Twyman–Green interferometer. Twyman–Green interferometer.The is a variation of the Michelson interferometer used to test small optical components, invented and patented by Twyman and Green in 1916.
The basic characteristics distinguishing it from the Michelson configuration are the use of a monochromatic point light source and a collimator. Michelson (1918) criticized the Twyman–Green configuration as being unsuitable for the testing of large optical components, since the available light sources had limited.
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. Decades later, the advent of laser light sources answered Michelson's objections.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. Fig. 6 illustrates a Twyman–Green interferometer set up to test a lens. 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. Laser unequal path interferometer The 'LUPI' is a Twyman–Green interferometer that uses a coherent laser light source. The high 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. A similar scheme has been used by Tajammal M in his PhD thesis (Manchester University UK, 1995) to balance two arms of an LDA system.
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This system used fibre optic direction coupler.Stellar measurements The is used for measuring the diameter of stars. In 1920, Michelson and used it to measure the diameter of, the first time the diameter of a star other than the sun was measured.Gravitational wave detection Michelson interferometry is one leading method for the direct. This involves detecting tiny in space itself, affecting two long arms of the interferometer unequally, due to a strong passing gravitational wave.
In 2015 the first detection of was accomplished using the instrument, a Michelson interferometer with 4 km arms. This was the first experimental validation of gravitational waves, predicted by 's. With additional interferometers placed on other continents, like the 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.
An even larger Michelson, to achieve greater sensitivity at low frequencies, is in the planning stages.Miscellaneous applications. Typical optical setup of single point OCTAnother application of the Michelson interferometer is in (OCT), a medical imaging technique using low-coherence interferometry to provide tomographic visualization of internal tissue microstructures. As seen in Fig. 8, the core of a typical OCT system is a Michelson interferometer. 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.
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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. Recent advances have striven to combine the nanometer phase retrieval of coherent interferometry with the ranging capability of low-coherence interferometry.Others applications include which convert phase modulation into amplitude modulation in networks, the characterization of high-frequency circuits., and low-cost THz power generation. Atmospheric and space applications The Michelson Interferometer has played an important role in studies of the, revealing temperatures and winds, employing both space-borne, and ground-based instruments, by measuring the and shifts in the spectra of airglow and aurora.
For example, the Wind Imaging Interferometer, WINDII, on the UpperAtmosphere 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 thebulk 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 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). Michelson (1881) wrote, '. When they the fringes using sodium light were of convenient width and of maximum sharpness, the sodium flame was removed and the lamp again substituted.
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.' . Shankland (1964) wrote concerning the 1881 experiment, p. 20: ' The interference fringes were found by first using a sodium light source and after adjustment for maximum visibility, the source was changed to white light and the colored fringes then located. White-light fringes were employed to facilitate observation of shifts in position of the interference pattern.' And concerning the 1887 experiment, p.
31: ' With this new interferometer, the magnitude of the expected shift of the white-light interference pattern was 0.4 of a fringe as the instrument was rotated through an angle of 90° in the horizontal plane. (The corresponding shift in the Potsdam interferometer had been 0.04 fringe.)'References.
This version reflects the comments of the coreparticipants as reviewed and incorporated in accordance with CORD's FIPSE-supportedCurriculum Morphing Project.MODULE 10-7MACH-ZEHNDERINTERFEROMETERSINTRODUCTIONThe Mach-Zehnder interferometer is an important diagnostic tool. It is most frequentlyused in the fields of plasma physics, aerodynamics, and heat transfer to measure density,pressure, and temperature changes in gases. Because of its relatively large and freelyaccessible working space and flexibility of location of the fringes, it is the mostsuitable interferometer to study the airflow around models of aerodynamic structures.This module will familiarize the student with the characteristics of the Mach-Zehnderinterferometer and some of its applications.
It will also give practical experience inbuilding, aligning, and using this versatile optical device.MODULE PREREQUISITESThe student should have completed Module 1-1 through 1-6 of Course 1,'Introduction to Lasers'; Modules 6-1 through 6-8 of Course 6, 'Laser andElectro-Optic Components'; and have a basic knowledge of laser safety, including eyehazards and electrical safety, as well as knowledge of algebra and interference of opticalwaves. The student should also be able to operate a HeNe laser and adjust a beam-expandingtelescope.Upon completion of this module, the student should be able to:1. Demonstrate knowledge of Mach-Zehnder interferometers by drawing and labeling adiagram as shown in the text. Explain the basic design of the instrument and how itoperates, including the following items:a.
Interference between emerging beams to form a fringe pattern on the screen.b. Effect on fringe pattern when a parallel glass plate is inserted into one of thebeams.c. Reason for fringe localization.d. Use of fringe localization in the examination of airflow over the model of anaircraft wing.2. Assemble a Mach-Zehnder interferometer and align the interferometer using a HeNelaser and beam-expanding telescope according to procedures outlined in the text.3. With the Mach-Zehnder interferometer as previously assembled, perform experimentsaccording to given procedures to accomplish the following tasks:a. Observe the fringe pattern on a screen.b.
Measure the index of refraction of a gas.c. Observe and measure the optical fringe inaccuracies in a flat plate of glass.The Mach-Zehnder interferometer is basically a very simple device. A schematic diagramof the instrument and associated optical equipment is shown in Figure 1.
The light beamfrom a source, say a HeNe laser, is first expanded by a telescope. The expanded laser beamis divided at the 50% reflecting/50% transmitting surface of a plane parallel glass plate P 1into two beams of equal intensity. After reflection at the 100% reflecting plan mirrors M 1and M 2, the two beams are recombined at the 50% reflecting/50%transmitting surface of plane parallel plate P 2. The recombined beamsemerge from P 2 and are intercepted by a well-corrected positive lens L 2,which brings both beams to the focus at S ¢. This willalways be true if the four reflecting surfaces, whose centers are at the corners of aparallelogram, are perfectly parallel. (Figure 1 shows a rectangle which is a special caseof the parallelogram.)Fig. 1Typical construction of a Mach-Zehnder interferometerWhen all reflecting surfaces are perfectly parallel, the recombined beams do notproduce interference fringes.
If, on the other hand, the four reflecting surfaces are onlyapproximately parallel, the recombined beams will interfere and produce interferencefringes. The exact location of the fringes depends on the size of the light source Sand the relative alignment of the four reflecting surfaces.Let us briefly consider the mechanism of interference as it applies to the Mach-Zehnderinterferometer. The two beams of light of equal amplitude and wavelength originating fromthe same source are brought to a focus at S ¢and S ²if the reflecting surfaces are nearly parallel to each other.As indicated in Figure 2, the light from the images S ¢andS ²proceeds on, and the beams interfere in much thesame way as in Youngs famous double slit experiment.
In a plane (the screen) at aright angle to the direction of propagation of the combined beams, an interference fringepattern will be observed. This means that bright lines will be seen where the peaks of thewaves reinforce and dark lines where the troughs of the waves from one beam coincide withthe peaks of the waves from the other beam. The end result is a series of nearly parallellight and dark lines varying sinusoidally in intensity. If the intensity were measured asa function of position across the beams, the pattern shown in Figure 2b would be observed.Fig. 2Production of interference fringeson a Mach-Zehnder interferometer.If the reflecting surfaces are adjusted so that the images S ¢and S ²lie on a horizontal line (into the paper),the fringes will be vertical; if S ¢and S ²lie on a vertical line (in the plane of the paper), thefringes will be horizontal. Fringe spacingthat is, the distance between light lines(or dark lines)depends on the distance between S ¢andS ². For instance, fringe spacing can be increased(more nearly equal path lengths) by adjusting one mirror in such a way that the distancebetween S ¢and S ²isdecreased.
If lens L 2 is removed, fringes will still be observed, butthe coherent sources S ¢and S ²are now virtual and located at infinity.What happens to the fringes if the length of the optical path of one of the beams ischanged (say the test beam P 1 M 2 P 3 inFigure 1) by inserting a plane parallel glass plate into the path of the beam? By causingone beam to propagate through the plane parallel glass plate, a new phase shift isintroduced between S ¢and S ²which causes a shift of the fringes. The extent of the shift is a sensitive measure ofthe change of the optical path length over the two dimensional fields of view.For example, by inserting a glass slide only 0.0002 millimeter thick into one of thebeams (which is assumed to originate from a HeNe laser at 632.8 nm), the fringe patternwould reverse itself; that is, the dark and light lines would exchange positions.Example A demonstrates how the Mach-Zehnder interferometer can be used to calculate thethickness of a glass slide that will cause a reversal in the fringe pattern. Example A: Reversal inFringe PatternCaused by Glass Slide ThicknessGiven:The index of refraction of the glass slide is1.5. To produce a reversal in the fringe pattern, the following condition must be met:where:phase change = p (180 ° ) = ( k ¢ k) dk ¢=k =d = The thickness of the slide.Find:Assume l = 0.63 ´ 10 4cm (HeNe laser).The thickness of a glass slide that will cause a reversal in the fringe pattern.Solution:d d = 6.3 ´ 10 5 cm, or 6.3 ´ 10 4 mmLet us illustrate the sensitivity of this device with one more example. The index ofrefraction of fluids depends on the temperature, among other things. If we fill a cell oflength L = 10 cm with water and insert this cell into the test volume between M 2 P 2and an identical air-filled cell into the path M 1 P 1 ofFigure 1, and raise the water temperature by 1/20°C, we would observe a full shift of onefringe corresponding to an optical path length change D nLof l ( l = 632.8 nm).
Since 1/10fringe shift can be accurately measured, it is possible to measure temperature changes ofwater by as little as 1/200°C. Thus, the interferometer can act as a very sensitivethermometer.Before turning our attention to the more technical aspects of the Mach-Zehnderinterferometer, such as its construction, alignment, and use, let us discuss one final butvery important characteristic of this device. If, instead of the well-collimated beamwhich is essentially derived from a point source, we had to work with an extended sourceof light, fringes may still be observed. But now they will be sharp only in a particularplane. The reason for this is that instead of the two coherent point images S ¢and S ²in Figure 2, we nowhave many pairs of coherent points, covering the whole extent of the images centered aboutS ¢and S ².It is possible to show that for extended sources, fringes are located in the region inwhich the two emerging rays originating from the same incident may meet.
This principle isillustrated in Figure 3a where mirror M 2 has been rotatedcounterclockwise by a small amount.Fig. 3Fringe localization with extended sourcesIt can be seen that only the reflected beam to P 2 will be affected.The reference beam propagating through the outer part of the interferometer is notaffected and arrives at P 2 as before. The beams of light indicated byrays 1 and 2 emerging from P 2 will no longer intersect.
However, byextending both rays back through beam splitter P 2, as is done in Figure3a, it can be seen that the virtual rays intersect at a point between M 2and P 2. The region where these virtual rays meet becomes the virtualregion of fringe localization. This region of fringe localization can be moved anywherebetween mirror M 2 and beam splitter P 2 by simplyrotating P 2 clockwise a small amount. The effect of a small rotation of P 2on the virtual location of the fringes is shown in Figure 3b.
In this way, one canactually place the fringes at infinity or before or behind beam splitter P 2.This flexibility in fringe localization gives the Mach-Zehnder interferometer one veryimportant advantage over many other interferometers. For instance, when the Mach-Zehnderinterferometer is used for the examination of airflow around a section of an aircraftwing, a model of the wing is enclosed in a test cell that is located in one leg of theinterferometer. Once the model is in position, a high-velocity airstream is blown past it.The airstream forms a pressure pattern around the model which causes local changes in theindex of refraction which, in turn, can be measured from the resultant change in thefringe pattern.For this kind of experimental work, it is necessary to photograph both the interferencefringes and test model simultaneously so that both are in focus.
Therefore, it isnecessary that the fringes be located (or localized) in the region where the test objectis located. The plane where the object and the fringes more or less coincide can now beimaged on a screen or on a photographic plate.In the case of a wind tunnel or shock-wave tube experiment, photographs of the fringepattern are obtained with and without gas flow.
The change of fringes, that is, the numberof times the intensity at a selected point P changes from say bright to dark tobright, is counted. This number, which is designated by D m, is given by Equation 1.D m =Equation 1.
Where:l = The wavelengthof the probe beam.L = The length of the test cell.n = The index of refraction of the undisturbed gas in the cell.n ¢= The new index ofrefraction under flow conditions.It is important to note at this point that Equation 1 applies only to thesituation where n ¢and n are bothconstant along the path of the ray passing through the cell. When the refractive index isnot constant, the expression for D m becomesconsiderably more complicated.In summary, the use of the Mach-Zehnder interferometer has increased considerably sincethe advent of the laser. Where:D m = Thenumber of fringes moving past the reference mark on the screen.L = The length of the test cell.A typical measurement for air at STP with a test cell of L = 5 cm, l = 632.8 nm, and D m = 21 resulted in an index of refraction of1.000253. This procedure can be repeated at several pressures and a plot of refractiveindex versus pressure obtained.EXPERIMENT 3: Measurement of the Polishing Inaccuracies with a Mach-ZehnderInterferometer.In the preparation of optically flat plates, it becomes necessary to check thespecimen periodically for flatness. This is generally done by laying the specimen on anoptical flat and viewing the fringes under a mercury lamp.
This test for flatness orpolishing inaccuracies of an optical plate can also be performed with the Mach-Zehnderinterferometer.For such a measurement, it is necessary that the fringes be localized at the positionof the specimen, normally between M 2 and P 2, asdiscussed previously, so that they both can be focused on the screen or photographicplate. Therefore, the plane of the fringes must be moved to the plane of the specimen.This adjustment is performed by rotation of both M 2 and P 2and is largely done by trial and error (and a great deal of patience).This time-consuming adjustment can be accomplished more quickly with the help of a highpower zoom telescope (around 60X). A diffusing plate of glass must be placed at the exitend of the beam-expanding telescope.
A neutral density filter is placed between the HeNelaser and the beam-expanding telescope (see Figure 6). (At this point, particular cautionmust be exercised to reduce the light intensity in order to avoid eye damage.) The zoomtelescope is then focused through plate P 2 on the specimen.
Using thelow magnification, the depth of field of the telescope may be sufficiently large that boththe specimen and fringes are in focus. Plate P 2 is slowly rotated tobring the fringe plane closer to the specimen. The magnification of the telescope is nowincreased, which reduces the depth of field. Plate P 2 is again adjustedto move the fringe plane closer to the location of the specimen.
At the final maximummagnification, the fringes can be located to within a few centimeters of the specimen.This procedure will ensure maximum resolution and sharpness of fringes. This completes thealignment of the interferometer.Fig. 6Arrangement for determining optical quality of a test plateThe final step in this experiment consists of an examination of the fringe pattern atthe specimen. Depending on the polishing imperfections, the fringe pattern may resemble acontour map. The difference in the thickness D L from one point to another point on the specimen is determined bycounting the number of fringes D m between these two points and using Equation 3.D L =Equation 3.