'Interferometry' is the science and technique of superposing ('
interfering') two or more
waves, which creates an output wave different from the input waves; this in turn can be used to explore the differences between the input waves. Because interference is a very general phenomenon with waves, interferometry can be applied to a wide variety of fields, including
astronomy,
fiber optics, optical
metrology,
oceanography, seismology and various studies of
quantum mechanics. Interferometry can be applied to both one-dimensional waves such as time varying signals, or to multi-dimensional waves such as coherent images produced by laser illumination.
Interferometer
An 'interferometer' works on the principle that two
waves that coincide with the same
phase will add to each other while two waves that have opposite phases will cancel each other 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
lasers, and even the wave character of matter can be exploited to build interferometers. One of the first examples of matter interferometers were
electron interferometers, later followed by
neutron interferometers. Around 1990 the first
atom interferometers were demonstrated, later followed by interferometers employing
molecules. Currently it is not clear what the maximum particle size for interferometry might be.
The highest-resolution astronomical images are produced using interferometers (at both optical and radio wavelengths). In order to perform interferometric imaging in optical astronomy at least three telescopes are required (more are preferred). One familiar use of the technique is in radio and optical
interferometer telescopes.
Types of Interferometers
Main articles: List of types of interferometers
There are many other types of interferometers. They all work on the same basic principles, but the geometry is different for the different types of interferometers.
Michelson Interferometer
Main articles: Michelson interferometer
A Michelson interferometer.
A very common example of an interferometer is the
Michelson (or Michelson-Morley) type. Here 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.
The interferometer setup shown to the right was used in the famous
Michelson-Morley experiment that provided evidence for
special relativity. In
Michelson's day, the interference pattern was obtained by using a gas discharge lamp, a filter, and a thin slot or pinhole. In one version of the Michelson-
Morley experiment, they even ran the interferometer off starlight. Starlight is
temporally incoherent light, but since for small instruments it can be considered as a
point source of light it is spatially coherent and will produce an interference pattern. The
Michelson interferometer finds use not only in these experiments but also for other purposes, e.g., in
astronomical interferometers (see
astronomical section below) and
gravitational wave detectors.
Mach-Zehnder interferometer
A Mach-Zehnder interferometer.
Interferometers are perhaps even more widely 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.
Sagnac interferometer
A Sagnac interferometer.
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 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].
Fabry-Perot interferometer
A Fabry-Pérot interferometer or etalon
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.
Types of Interferometry
Coherent interferometry
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
.
Coherent interferometry suffers from a
ambiguity problem: that is, if between any two measurements the interferometric phase jumps by more than
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.
Inertial navigation
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
Speckle Interferometry
Main articles: Speckle pattern
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.
Holography
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
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
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.
Geodetic standard baseline measurements
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.
Astronomical Interferometry
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.
Astronomical direct-detection interferometry
A simple two-element optical interferometer.
A single large telescope with an
aperture mask over it (labelled 'Mask'), only allowing light through two small holes.
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.
Astronomical heterodyne interferometry
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).
Quantum effects
By using photons in
entangled states, it is possible to increase the precision of interferometry measurements. Using a pair of photons, sensitivity increases by 40%. Four photons further improves precision.
[3]
References
★
John E. Baldwin and
Chris A. Haniff. "The application of interferometry to optical astronomical imaging." ''Phil. Trans. A'', 360, 969-986, 2001. (
download PostScript file)
★ J. E. Baldwin, "Ground-based interferometry — the past decade and the one to come" in ''Interferometry for Optical Astronomy II'', volume 4838 of Proc. SPIE, page 1. 22-28 August 2002, Kona, Hawaii, SPIE Press, 2003. ([ftp://ftp.mrao.cam.ac.uk/pub/coast/spie4838-01-letter.ps download PostScript file])
★ J. D. Monnier, Optical interferometry in astronomy, Reports on Progress in Physics, 66, 789-857, 2003
IoP. (
download PDF file)
★ P. Hariharan, ''Optical Interferometry'', 2nd edition, Academic Press, San Diego, USA, 2003.
★ Adolf F. Fercher, Wolfgang Drexler, Christoph K. Hitzenberger and Theo Lasser, "Optical coherence tomography — principles and applications," ''Reports on Progress in Physics'' vol. 66, no. 2, pp. 239-303, 2003. Available:
iop.org.
★ E. Hecht, ''Optics'', 2nd Edition, Addison-Wesley Publishing Co., Reading, Mass, USA, 1987.
Notes
1. E. Hecht, Optics, 2nd Edition, Addison-Wesley Publishing Co., Reading, Mass, USA, 1987. p. 358
2. Sagnac Interferometer on Eric Weisstein's World of Physics Accessed Aug 1, 2006
3. Castelvecchi, D. (2007). Quantum Loophole, ''Science News'' vol. 171, p. 276 (references)
See also
★
List of astronomical interferometers at visible and infrared wavelengths
★
Astronomical interferometer
★
Aperture synthesis
★
History of astronomical interferometry
★
Interference
★
Very Long Baseline Interferometry
★
Optical coherence tomography
★
List of types of interferometers
External links
★
Coda-wave interferometry using
seismic waves.
★ Description of
astronomical interferometry.
★
The VLTI Delay Lines Article and images by Fred Kamphues/Mill House Engineering
★
Optical Long Baseline Interferometry Latest news about Optical Long Baseline Interferometry from JPL NASA
★
Stedman Review of the Sagnac Effect
★
List of papers which chart the historical development of astronomical interferometry
★
Description of one absolute gravimeter
★
Optical Long Baseline Interferometry News
★
Description of astronomical interferometry.
★
Interferometry/Moire in art by Richard Allen
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