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(optics) The design and use of optical inferometers; uses include precise measurement of wavelength, measurement of very small distances and thicknesses, study of hyperfine structure of spectral lines, precise measurement of indices of refraction, and determination of separations of binary stars and diameters of very large stars.
The design and use of optical interferometers. Optical interferometers based on both two-beam interference and multiple-beam interference of light are extremely powerful tools for metrology and spectroscopy. A wide variety of measurements can be performed, ranging from determining the shape of a surface to an accuracy of less than a millionth of an inch (25 nanometers) to determining the separation, by millions of kilometers, of binary stars. In spectroscopy, interferometry can be used to determine the hyperfine structure of spectrum lines. By using lasers in classical interferometers as well as holographic interferometers and speckle interferometers, it is possible to perform deformation, vibration, and contour measurements of diffuse objects that could not previously be performed. There are two basic classes of interferometers: division of wavefront and division of amplitude.
The Michelson interferometer (Fig. 1) is based on division of amplitude. Light from an extended source S is incident on a partially reflecting plate (beam splitter) P1. The light transmitted through P1 reflects off mirror M1 back to plate P1. The light which is reflected proceeds to M2 which reflects it back to P1. At P1, the two waves are again partially reflected and partially transmitted, and a portion of each wave proceeds to the receiver R, which may be a screen, a photocell, or a human eye. Depending on the difference between the distances from the beam splitter to the mirrors M1 and M2, the two beams will interfere constructively or destructively. Plate P2 compensates for the thickness of P1.
Michelson interferometer.
The function of the beam splitter is to superimpose (image) one mirror onto the other. When the mirrors' images are completely parallel, the interference fringes appear circular. If the mirrors are slightly inclined about a vertical axis, vertical fringes are formed across the field of view. These fringes can be formed in white light if the path difference in part of the field of view is made zero. Just as in other interference experiments, only a few fringes will appear in white light.
Twyman-Green interferometer
If the Michelson interferometer is used with a point source instead of an extended source, it is called a Twyman-Green interferometer. The use of the laser as the light source for the Twyman-Green interferometer has made it an extremely useful instrument for testing optical components. The great advantage of a laser source is that it makes it possible to obtain bright, good-contrast, interference fringes even if the path lengths for the two arms of the interferometer are quite different. See also Laser.
The Twyman-Green interferometer can be used to test a flat mirror. In this case, M1 in Fig. 1 is a reference surface and M2 is the flat surface being tested. If the test surface is perfectly flat, then straight, equally spaced fringes are obtained. Departure from the straight, equally spaced condition shows directly how the surface differs from being perfectly flat. A height change of half a wavelength will cause an optical path change of one wavelength and a deviation from fringe straightness of one fringe. Thus, the fringes give surface height information, just as a topographical map gives height or contour information.
The basic Twyman-Green interferometer can be modified to test concave-spherical mirrors. In the interferometer, the center of curvature of the surface under test is placed at the focus of a high-quality diverger lens so that the wavefront is reflected back onto itself. Likewise, a convex-spherical mirror can be tested. Also, if a high-quality spherical mirror is used, the high-quality diverger lens can be replaced with the lens to be tested.
One of the most commonly used interferometers in optical metrology is the Fizeau interferometer, which can be thought of as a folded Twyman-Green interferometer. In the Fizeau, the two surfaces being compared, which can be flat, spherical, or aspherical, are placed in close contact. The light reflected off these two surfaces produces interference fringes. For each fringe, the separation between the two surfaces is a constant. If the two surfaces match, straight, equally spaced fringes result. Surface height variations between the two surfaces cause the fringes to deviate from straightness or equal separation.
Mach-Zehnder interferometer
The Mach-Zehnder interferometer (Fig. 2) is a variation of the Michelson interferometer and, like the Michelson interferometer, depends on amplitude splitting of the wavefront. Light enters the instrument and is reflected and transmitted by the semitransparent mirror M1. The reflected portion proceeds to M3, where it is reflected through the cell C2 to the semitransparent mirror M4. Here it combines with the light transmitted by M1 to produce interference. The light transmitted by M1 passes through a cell C1, similar to C2, and is used to compensate for the windows of C2. The major application of this instrument is in studying airflow around models of aircraft, missiles, or projectiles.
Mach-Zehnder interferometer.
Shearing interferometers
In a lateral-shear interferometer a wavefront is interfered with a shifted version of itself. A bright fringe is obtained at the points where the slope of the wavefront times the shift between the two wavefronts is equal to an integer number of wavelengths. That is, for a given fringe the slope or derivative of the wavefront is a constant. For this reason a lateral-shear interferometer is often called a differential interferometer. Another type of shearing interferometer is a radial-shear interferometer. Here, a wavefront is interfered with an expanded version of itself. This interferometer is sensitive to radial slopes.
Michelson stellar interferometer
A Michelson stellar interferometer can be used to measure the diameter of stars which are as small as 0.01 second of arc. This task is impossible with a ground-based optical telescope since the atmosphere limits the resolution of the largest telescope to not much better than 1 second of arc.
Fabry-Perot interferometer
All the interferometers discussed above are two-beam interferometers. The Fabry-Perot interferometer is a multiple-beam interferometer since the two glass plates are partially silvered on the inner surfaces, and the incoming wave is multiply reflected between the two surfaces. The position of the fringe maxima is the same for multiple beam interference as two-beam interference; however, as the reflectivity of the two surfaces increases and the number of interfering beams increases, the fringes become sharper.
Holographic interferometry
A wave recorded in a hologram is effectively stored for future reconstruction and use. Holographic interferometry is concerned with the formation and interpretation of the fringe pattern which appears when a wave, generated at some earlier time and stored in a hologram, is later reconstructed and caused to interfere with a comparison wave. It is the storage or time-delay aspect which gives the holographic method a unique advantage over conventional optical interferometry. See also Holography.
Speckle interferometry
A random intensity distribution, called a speckle pattern, is generated when light from a highly coherent source, such as a laser, is scattered by a rough surface. The use of speckle patterns in the study of object displacements, vibration, and distortion is becoming of more importance in the nondestructive testing of mechanical components. See also Speckle.
Phase-shifting interferometry
Electronic phase-measurement techniques can be used in interferometers such as the Twyman-Green, where the phase distribution across the interferogram is being measured. Phase-shifting interferometry is often used for these measurements since it provides for rapid precise measurement of the phase distribution. In phase-shifting interferometry, the phase of the reference beam in the interferometer is made to vary in a known manner. This can be achieved, for example, by mounting the reference mirror on a piezoelectric transducer. By varying the voltage on the transducer, the reference mirror is moved a known amount to change the phase of the reference beam a known amount. A solid-state detector array is used to detect the intensity distribution across the interference pattern. This intensity distribution is read into computer memory three or more times, and between each intensity measurement the phase of the reference beam is changed a known amount. From these three or more intensity measurements, the phase across the interference pattern can be determined to within a fraction of a degree.
Interferometry is an important tool in measurements concerned with extreme accuracy. This is because the measurement unit is the wavelength of light (which is less than 1 micrometre). It depends on the fact that two crossing light beams can (under certain conditions) produce a stationary pattern of light and dark bars (called interference fringes), at intervals that bear a simple relation to the wavelength used. Optical Interferometry has been a laboratory technique for over a century, but until the advent of the laser with its highly monochromatic beam it was difficult to find a light source capable of forming fringes over a distance of more than about a millimetre. Today, interferometry's main areas of application are in the measurement of displacements and distances, gas and fluid flow, temperature and pressure variation, in microscopy, spectroscopy, and the sensing of acceleration and rotation—and, of particular importance to the photographer, the control of lens fabrication to surface accuracies of fractions of a wavelength. Interference fringes occur when both beams originate from the same source (are mutually coherent). Where the beams cross they interact so that where wavecrests coincide they reinforce resulting in a bright fringe (constructive interference) and where crests coincide with troughs they cancel out and there is a dark fringe. A shift in the phase of one of the beams by half a wavelength results in a light fringe being replaced by a dark one and vice versa. This would indicate a change in one of the optical path lengths of about 0.25 μm (for green light).
Interferometers
In interferometric measurement, a number of different optical arrangements are employed. The two most important in imaging technologies are the Michelson and Mach-Zehnder interferometers.
Michelson interferometer. One of the earliest optical devices to use interference phenomena, it employs a partial mirror (a beamsplitter) to send two beams to mirrors at equal optical path distances from the source. On their return the beamsplitter acts as a beam combiner. The combination of the two beams produces an interference pattern that is observed through a telescope eyepiece (Fig. 1). This pattern may consist of either concentric rings or straight bars, depending on whether the mirrors are in exact alignment or (more usually) set at a very small angle. If one of the mirrors is moved slowly along the beam, the fringes will move across the field, and the exact distance moved can be measured by counting the number of fringes that move past the cross-hairs in the eyepiece. The main use of the basic instrument is to measure the coherence length of near-monochromatic light sources by measuring the optical path difference at which the fringe contrast falls to zero. An important variant is the Twyman-Green interferometer, in which an optical component to be tested (e.g. a photographic lens) is placed in one beam, and the fringes produced by the returning beams are examined for irregularities.
Mach-Zehnder interferometer
This device sends the two beams along paths forming a parallelogram, using a beamsplitter and a separate beam combiner (Fig. 2). One of the beams passes through an optical cell, often a wind tunnel work section. By examination of the interference pattern of the recombined beams it is possible to obtain data on fluid flow, shock waves, and convection currents, as changes in the density of a gas change the shape of the fringe patterns, showing the detail of the flow. Both the Michelson and Mach-Zehnder configurations are used as standard tests for assessing the stability of optical tables.
Holographic interferometry
A hologram is a record of the interference pattern generated by two mutually coherent laser beams, one unmodulated (the reference beam) and one modulated by reflection from the subject matter (the object beam). A double exposure with a small distortion or other movement introduced between the exposures results in a large moiré pattern on the holographic image that contours the distortion with fringes at half-wavelength intervals, thus making visible (and measurable) extremely small strains.
Speckle interferometry
Laser illumination of a surface produces a grainy effect known as laser speckle, caused by interference between rays reflected from adjacent points on the surface. The speckle pattern is unique to the surface and the position of the illuminating source, and changes if the subject matter is moved or distorted. This is the basis of speckle interferometry. The subject is illuminated by laser light and the image recorded by a television camera. A second image is recorded after the subject is stressed, and this image is then subtracted electronically from the first; the result, enhanced, is displayed on a screen or recorded as a photograph. Where the speckles have changed there will be reduced contrast, and where they remain unchanged (i.e. no subject movement) there will be increased contrast. Again, the result is fringes contouring the distortion. The technique can cope with larger distortions than holography can, and has the advantage of real-time observation, but the resolution is low. Speckle interferometry is often inaccurately called ‘TV holography’.
In interferometry, visual analysis allows a reading precision of about one-quarter of a wavelength, but digital analysis of the fringe pattern gives the greater precision needed for the testing of surfaces that must be accurate to a tiny fraction of a wavelength, such as astronomical telescope optics.
Although their main use is in industrial research, interferograms, in particular the holographic type, can form interesting and often beautiful patterns. A number of holographic artists have exploited the formation of attractive fringe patterns seen on holograms of vibrating objects and in portraiture using a double laser pulse to contour minute facial movements.
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Interferometry is the technique of superposing (interfering) two
or more waves, to detect differences between them. Interferometry is applied in a wide variety of
fields, including astronomy,
An interferometer works because two waves with the same frequency that have the same
phase will add to each other while two waves that have opposite phase will cancel out,
assuming both have the same amplitude. Early interferometers principally used white light sources (e.g., Young's double slit experiment of 1805). Modern researchers often
use monochromatic light sources like
There are many types of interferometers, but all work on the same basic principle.
In a Michelson (or Michelson-Morley) type interferometer, the basic building blocks are a monochromatic source (emitting light or matter waves), a detector, two mirrors and one semitransparent mirror (often called beam splitter). These are put together as shown in the figure.
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 one 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.
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 conservation of energy. However energy is conserved, because there is a re-distribution of energy at the detector in which the energy at the destructive sites are 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.
This type of interferometer was used in the Michelson-Morley experiment, to disprove the existence of the Luminiferous aether. Michelson interferometers are also used in astronomical interferometers (see astronomical section below) and gravitational wave detectors.
Interferometers are used in integrated optical circuits, in the form of a Mach-Zehnder interferometer, in which light interferes between two branches of a waveguide that are (typically) externally modulated to vary their relative phase. This interferometer's configuration consists of two beam splitters and two completely reflective mirrors. The source beam is split and the two resulting waves travel down separate paths. A slight tilt of one of the beam splitters will result in a path difference and a change in the interference pattern. The Mach-Zehnder interferometer can be very difficult to align, however its improved sensitivity enables a diverse number of applications.[1] The Mach-Zehnder interferometer can be the basis of a wide variety of devices, from RF modulators to sensors to optical switches.
A Sagnac Interferometer is an interferometry configuration in which a beam of light is split and the two beams are made to follow a trajectory in opposite directions. To act as a ring the trajectory must enclose an area. On return to the point of entry the light is allowed to exit the apparatus in such a way that an interference pattern is obtained.
In the Sagnac configuration, the position of the interference fringes is dependent on angular velocity of the setup. This dependence is caused by the rotation effectively shortening the path distance of one of the beams, while lengthening the other. A Sagnac interferometer has been used by Albert Michelson and Henry Gale to determine the angular velocity of the Earth. It can be used in navigation as a ring laser gyroscope, which is commonly found on fighter planes[2].
A Fabry-Pérot interferometer or etalon is typically made of a transparent plate with two reflecting surfaces, or two parallel highly-reflecting mirrors. (Technically the former is an etalon and the latter is an interferometer, but the terminology is often used inconsistently.) Its transmission spectrum as a function of wavelength exhibits peaks of large transmission corresponding to resonances of the etalon. It is named after Charles Fabry and Alfred Pérot.
Fabry-Pérot interferometers are widely used in telecommunications, lasers and spectroscopy for controlling and measuring the wavelength of light. Recent advances in fabrication technique allow the creation of very precise tunable Fabry-Pérot interferometers. Fabry-Pérot interferometers also form the most common type of optical cavity used in laser construction.
Coherent interferometry uses a coherent light source (for example, a helium-neon laser), and can make interference with large difference between the interferometer path length delays. The interference is capable of very accurate (nanometer) measurement by recovering the phase.
One of the most popular methods of interferometric phase recovery is phase-shifting by piezoelectric transducer (PZT) phase-stepping. By stepping the path length by a number of known phases (minimum of three) it is possible to recover the phase of the interference signal, with 2π = λ / 2.
Coherent interferometry suffers from a 2π ambiguity problem: that is, if between any two measurements the interferometric phase jumps by more than 2π the phase measurement is incorrect. However by combining interferometry results obtained using multiple wavelengths of illumination, such as in digital multi-wavelength holography, the ambiguity interval can be extended to indefinitely large dynamic ranges of measurement.
The applications of coherent interferometry are wide ranging: Nanometer surface profiling, Microfluidics, Mechanical stress/strain, Velocimetry, and high-definition metrology of large parts and assemblies in manufacturing.
In inertial navigation, ring laser gyroscopes are used that can detect rotation through optical interferometry of laser beams travelling around a circumference in opposite directions
In optical systems, a speckle pattern is a field-intensity pattern produced by the mutual interference of partially coherent beams that are subject to minute temporal and spatial fluctuations. This speckling effect is most commonly observed in the fields of fiber optics and astronomical speckle imaging.
A special application of optical interferometry using coherent light is holography, a technique for photographically recording and re-displaying three-dimensional scenes. The technique also lends itself to monitoring small deformations in single wavelength implementations as well as dimensional metrology of large parts and assemblies and larger surface defect detection when used in multi-wavelength implementations..
Low-coherence interferometry utilizes a light source with low temporal coherence such as white light (for example, LED/SLD, halogen lamp) or high specification femtosecond lasers. Interference will only be achieved when the path length delays of the interferometer are matched within the coherence time of the light source (note: using a femtosecond source is somewhat more intricate).
The chief benefit of low-coherence interferometry is that it does not suffer from the 2π ambiguity of coherent interferometry, and is therefore suited to profiling steps and rough surfaces. The axial resolution of the system is determined by the coherence length of the light source and is typically in the micrometer range.
Optical coherence tomography is a medical imaging technique based in low-coherence interferometry, where subsurface light reflections are resolved to give tomographic visualization. Recent advances have striven to combine the nanometer phase retrieval with the ranging cabability of low-coherence interferometry.
A famous use of white light interferometry is the precise measurement of geodetic standard baselines as invented by Yrjö Väisälä. Here, the light path is split in two, and one leg is "folded" between a mirror pair 1 m apart. The other leg bounces once off a mirror 6 m away. Only if the second path is precisely 6 times the first, will fringes be seen.
Starting from a standard quartz gauge of 1 m length, it is possible to measure distances up to 864 m by repeated multiplication. Baselines thus established are used to calibrate geodetic distance measurement equipment on, leading to a metrologically traceable scale for geodetic networks measured by these instruments.
More modern geodetic applications of laser interferometry are in calibrating the divisions on levelling staffs, and in monitoring the free fall of a reflective prism within a ballistic or absolute gravimeter, allowing determination of gravity, i.e., the acceleration of free fall, directly from the physical definition at a few parts in a billion accuracy.
In astronomy interferometry is used to combine signals from two or more telescopes to obtain measurements with higher resolution than could be obtained with either telescopes individually. This technique is the basis for astronomical interferometer arrays, which can make measurements of very small astronomical objects if the telescopes are spread out over a wide area. If a large number of telescopes are used a picture can be produced which has resolution similar to a single telescope with the diameter of the combined spread of telescopes. These include radio telescope arrays such as LOFAR and SKA, and more recently astronomical optical interferometer arrays such as COAST, NPOI and IOTA, resulting in the highest resolution optical images ever achieved in astronomy. The VLT Interferometer is expected to produce its first images using aperture synthesis soon, followed by other interferometers such as the CHARA array and the Magdalena Ridge Observatory Interferometer which may consist of up to 10 optical telescopes. If outrigger telescopes are built at the Keck Interferometer, it will also become capable of interferometric imaging.
Astronomical interferometers come in two types -- direct detection and heterodyne. These differ only in the way that the signal is transmitted. Aperture synthesis can be used to computationally simulate a large telescope aperture from either type of interferometer.
One of the first astronomical interferometers was built on the Mount Wilson Observatory's reflector telescope in order to measure the diameters of stars. This method was extended to measurements using separated telescopes by Labeyrie (1975) to the visible. The red giant star Betelgeuse was among the first to have its diameter determined in this way. In the late 1970's improvements in computer processing allowed for the first "fringe-tracking" interferometer, which operates fast enough to follow the blurring effects of astronomical seeing, leading to the Mk I, II and III series of interferometers. Similar techniques have now been applied at other astronomical telescope arrays, including the Keck Interferometer and the Palomar Testbed Interferometer.
Techniques from Very Long Baseline Interferometry (VLBI), in which a large aperture is synthesized computationally, were implemented at optical and infrared wavelengths in the 1980s by the Cavendish Astrophysics Group. This providing the first very high resolution images of nearby stars. In 1995 this technique was demonstrated on an array of separate optical telescopes as a Michelson Interferometer for the first time, allowing a further improvement in resolution, and allowing even higher resolution imaging of stellar surfaces. The same technique has now been applied at a number of other astronomical telescope arrays, including the Navy Prototype Optical Interferometer and the IOTA array and soon the VLTI, CHARA and MRO Interferometers.
Projects are now beginning that will use interferometers to search for extrasolar planets, either by astrometric measurements of the reciprocal motion of the star (as used by the Palomar Testbed Interferometer and the VLTI) or through the use of nulling (as will be used by the Keck Interferometer and Darwin).
A detailed description of the development of astronomical optical interferometry can be found here. Impressive results were obtained in the 1990s, with the Mark III measuring diameters of 100 stars and many accurate stellar positions, COAST and NPOI producing many very high resolution images, and ISI measuring stars in the mid-infrared for the first time. Additional results include direct measurements of the sizes of and distances to Cepheid variable stars, and young stellar objects.
Interferometers are mostly seen by astronomers as very specialized instruments, capable of a very limited range of observations. It is often said that an interferometer achieves the effect of a telescope the size of the distance between the apertures; this is only true in the limited sense of angular resolution. The combined effects of limited aperture area and atmospheric turbulence generally limit interferometers to observations of comparatively bright stars and active galactic nuclei. However, they have proven useful for making very high precision measurements of simple stellar parameters such as size and position (astrometry) and for imaging the nearest giant stars.
For details of individual instruments, see the list of astronomical interferometers at visible and infrared wavelengths.
Radio wavelengths are much longer than optical wavelengths, and the observing stations in radio astronomical interferometers are correspondingly further apart. The very large distances do not always allow any usable transmission of radio waves received at the telescopes to some central interferometry point. For this reason many telescopes instead record the radio waves onto a storage medium. The recordings are then transferred to a central correlator station where the waves are interfered. Historically the recordings were analog and were made on magnetic tapes. This was quickly superseded by the current method of digitizing the radio waves, and then either storing the data onto computer hard disks for later shipping, or streaming the digital data directly over a telecommunications network e.g. over the Internet to the correlator station. Radio arrays with a very broad bandwidth, and also some older arrays, transmit the data in analogue form either electrically or through fibre-optics. A similar approach is also used at some submillimetre and infrared interferometers, such as the Infrared Spatial Interferometer. Some early radio interferometers operated as intensity interferometers, transmitting measurements of the signal intensity over electrical cables to a central correlator. A similar approach was used at optical wavelengths by the Narrabri Stellar Intensity Interferometer to make the first large-scale survey of stellar diameters in the 1970s.
At the correlator station, the actual interferometer is synthesized by processing the digital signals using correlator hardware or software. Common correlator types are the FX and XF correlators. The current trend is towards software correlators running on consumer PCs or similar commodity hardware. There also exist some radio astronomy amateur digital interferometers with correlator, such as the ALLBIN of the European Radio Astronomy Club.
As the usual radio astronomy interferometer is digital it does have a few shortcomings, some due to sampling and quantization effects, in addition to the obvious need for much more computing power, as compared to analog correlation. The output of both digital and analog correlator can be used to computationally synthesize the interferometer aperture in the same way as with direct detection interferometers (see above).
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