Interferometry

(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.

Michelson interferometer

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.

Fizeau interferometer

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.

Fig. 1

Fig. 2

Bibliography

• Jones, R., and Wykes, C., Holographic and Speckle Interferometry (2nd edn. 1989).
• Hariharan, P., Basics of Interferometry (1992)

This article needs additional citations for verification. Please help improve this article by adding reliable references. Unsourced material may be challenged and removed. (November 2008)

Interferometry is the technique of diagnosing the properties of two or more waves by studying the pattern of interference created by their superposition. The instrument used to interfere the waves together is called an interferometer. Interferometry is an important investigative technique in the fields of astronomy, fiber optics, engineering metrology, optical metrology, oceanography, seismology, quantum mechanics, nuclear and particle physics, plasma physics, and remote sensing.^[1]

Contents 1 Rudimentary principles 1.1 Heterodyne detection 1.2 Homodyne detection 2 Imaging interferometry 3 Applications 3.1 Astronomical interferometry 4 See also 5 References 6 Further reading

Rudimentary principles

See also: Interference

The light path through a Michelson interferometer.

Interferometry makes use of the principle of superposition to combine separate waves together in a way that will cause the result of their combination to have some meaningful property that is diagnostic of the original state of the waves. This works because when two waves with the same frequency combine, the resulting pattern is determined by the phase difference between the two waves—waves that are in phase will undergo constructive interference while waves that are out of phase will undergo destructive interference. Most interferometers use light or some other form of electromagnetic wave.^[2]

An idealized interferometric determination of wavelength obtained by looking at interference fringes between two coherent beams recombined after traveling different distances. (The source is symbolized as a light bulb, but actually is a laser.)

Typically a single incoming beam of light will be split into two identical beams by a grating or a partial mirror. Each of these beams will travel a different route, called a path, until they are recombined before arriving at a detector. The path difference, the difference in the distance traveled by each beam, creates a phase difference between them. It is this introduced phase difference that creates the interference pattern between the initially identical waves. If a single beam has been split along two paths then the phase difference is diagnostic of anything that changes the phase along the paths. This could be a physical change in the path length itself or a change in the refractive index along the path.

Heterodyne detection

Main article: Heterodyne detection

In heterodyne detection, one modulates, usually by a frequency shift, one of two beams prior to detection. A special case of heterodyne detection is optical heterodyne detection, which detects the interference at the beat frequency. The AC signal now oscillates between the minimum and maximum levels every cycle of the beat frequency. Since the modulation is known, the relative phase of the measured beat frequency can be measured very precisely even if the intensity levels of the beams are (slowly) drifting. This phase is identical in value to the phase one measures in the homodyne case. There are many additional benefits of optical heterodyne detection including improved signal to noise ratio^{[citation needed]} when one of the beams is weak.^{[clarification needed]}

Homodyne detection

Main article: Homodyne detection

In standard interferometry, the interference occurs between two beams at the same wavelength (or carrier frequency). The phase difference between the two beams results in a change in the intensity of the light on the detector. Measuring the resulting intensity of the light after the mixing of these two light beams is known as homodyne detection.

In homodyne detection for a given relative phase shift, the output is a constant (DC) signal level. This level is indirectly related to the phase shift. If the minimum and maximum possible values of the signal level are known (through calibration) then one can compute the relative phase shift. In practice, precise calibration is difficult since the optical beams 1) may not be perfectly aligned, 2) are not true plane waves, or 3) usually undergo unknown time varying attenuation on one arm of the interferometer.^{[citation needed]}

Imaging interferometry

The pattern of radiation across a region can be represented as a function of position i(x,y), i.e. an image. The pattern of incoming radiation i(x,y) can be transformed into the Fourier domain f(u,v). A single detector measures information from a single point in x,y space. An interferometer measures the difference in phase between two points in the x,y domain. This corresponds to a single point in the u,v domain. The signals from each set of detectors are combined in a device called a correlator. A single detector builds up a full image by scanning through the x,y coordinates. An interferometer builds up a full picture by measuring multiple points in u,v space. The image i(x,y) can then be restored by performing an inverse Fourier transform on the measured f(u,v) data. This technique is called aperture synthesis.

In the optical domain, direct phase detection is impossible so Optical heterodyne detection is used.^[3] Unscanned (staring) coherent optical imaging arrays have been made possible by a technique known as Synthetic array heterodyne detection (SAHD) and its practical implementation as rainbow heterodyne detection.^[3] A related technique is the time domain conjugate of SAHD, known as Fourier Transform Heterodyne detection.^[4]

Applications

Astronomical interferometry

Main article: Astronomical interferometer

The VLA interferometry

The angular resolution that a telescope can achieve is determined by its diffraction limit (which is proportional to its diameter). The larger the telescope, the better its resolution. However, the cost of building a telescope also scales with its size. The purpose of astronomical interferometry is to achieve high-resolution observations using a cost-effective cluster of comparatively small telescopes rather than a single very expensive monolithic telescope. The basic unit of an astronomical interferometry is a pair of telescopes. Each pair of telescopes is a basic interferometer. Their position in u,v space is referred to as a baseline.

Early astronomical interferometry was involved with a single baseline being used to measure the amount of power on a particular small angular scale. Later astronomical interferometers were telescope arrays consisting of a set of telescopes, usually identical, arranged in a pattern on the ground. A limited number of baselines will result in insufficient coverage in u,v space. This can be alleviated by using the rotation of the Earth to rotate the array relative to the sky. This causes the points in u,v space that each baseline points at to change with time. Thus, a single baseline can measure information along a track in u,v space just by taking repeated measurements. This technique is called Earth-rotation synthesis. It is even possible to have a baseline of tens, hundreds, or even thousands of kilometers by using a technique called very long baseline interferometry.

The longer the wavelength of incoming radiation, the easier it is to measure its phase information. For this reason, early imaging interferometry was almost exclusively done with long wavelength radio telescopes. Examples of radio interferometers include the VLA and MERLIN. As the speed of correlators and associated technologies have improved, the minimum radiation wavelength observable by interferometry has decreased. There have been several submillimeter interferometers, with the largest, the Atacama Large Millimeter Array, currently under construction. Optical astronomical interferometers have traditionally been specialized instruments, but recent developments have broadened their capabilities.^{[citation needed]}

See also

• Optical heterodyne detection
• List of astronomical interferometers at visible and infrared wavelengths
• Optical interferometry
• Angle-resolved low-coherence interferometry
• Astronomical interferometer
• Aperture synthesis
• History of astronomical interferometry
• Interference
• Very Long Baseline Interferometry
• Optical coherence tomography
• List of types of interferometers
• Phase interferometry
• Dual Polarisation Interferometry
• Bose-Einstein correlations

References

1. ^ Bunch, Bryan H; Alexander Hellemans (April 2004). The history of science and technology. Houghton Mifflin Harcourt. pp. 695. ISBN 9780618221233. http://books.google.com/books?id=MlQ7NK9dw7IC&pg=PA695. 
2. ^ Pal, Bishnu P. (1992, 2005). Fundamentals of fibre optics in telecommunication and sensor systems. Delhi: New Age International Ltd.publishers. pp. 663 (read section 3). ISBN 8122404693. http://books.google.com/books?id=Oj7CWNPDLroC&pg=PA663. 
3. ^ ^{a b} Strauss C. E. M., "Synthetic-array heterodyne detection: a single-element detector acts as an array", Opt. Lett. 19, 1609-1611 (1994)
4. ^ Cooke BJ et al., "Laser field imaging through Fourier transform heterodyne"Laser Radar Technology and Applications IV, Vol. 3707, No. 1. (1999), pp. 390-408.

Further reading

Hariharan, P. (2003). Optical Interferometry (2nd edition ed.). San Diego, USA: Academic Press. http://www.astro.lsa.umich.edu/~monnier/Publications/ROP2003_final.pdf. 

v • d • e Radio astronomy Main articles Astronomical interferometer / History · Very Long Baseline Interferometry · Radio telescope · Radio window · Astronomical radio source Notable radio telescopes List of radio telescopes Single dish Arecibo Observatory (Puerto Rico) · Effelsberg Telescope (Germany) · Green Bank Telescope (West Virginia, USA)  · Lovell Telescope (UK) · Parkes Observatory (Australia) Interferometers Combined Array for Research in Millimeter-wave Astronomy (Cedar Flat, CA)  · European VLBI Network (Europe) · Giant Metrewave Radio Telescope (India) · MERLIN (UK) · Molonglo Observatory Synthesis Telescope (Canberra, Australia) · One-Mile Telescope (UK) · Very Large Array (New Mexico, USA) · Very Long Baseline Array (USA) · Westerbork Synthesis Radio Telescope (Netherlands) Proposed/in-progress telescopes Five hundred meter Aperture Spherical Telescope (China) · Allen Telescope Array (California, USA) · Atacama Large Millimeter Array (Chile) · LOFAR (Netherlands) · Murchison Widefield Array (Australia) · PaST (China) · Square Kilometre Array (TBD) Observatories Algonquin Radio Observatory (CAN) · Haystack Observatory (US) · Jodrell Bank Observatory (UK) · Mullard Radio Astronomy Observatory (UK) · National Radio Astronomy Observatory (USA) · Special Astrophysical Observatory of the Russian Academy of Science (Russia) People Arthur Covington · Antony Hewish · Karl Guthe Jansky · Bernard Lovell · Jan Oort · Groete Reber · Martin Ryle Related articles Cosmic microwave background radiation · SETI · Interferometry · Radio propagation · Aperture synthesis · Wow! signal Other types of astronomical observation: Optical astronomy · Submillimetre astronomy · Infrared astronomy · High-energy astronomy See also: Radio telescope category list

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