Interferometry
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Interferometry is the applied science of combining two or more waves, which are said to interfere with each other. In wave terms the interference pattern is a state with amplitude and phase which depends on the amplitude and phase of all the contributing waves. Although the wave phenomenon of interference is very general, in applications the word interferometry is used for a small number of specialist niches, including optical metrology, studies of quantum mechanics such as neutron interferometry and amongst astronomers as described below.
In astronomy (such as with the Keck telescopes), this is used to combine light from two or more telescopes to obtain measurements with higher resolution than could be obtained with either telescope individually. This technique is the basis for astronomical interferometer arrays which, spread out over a wide area, can together produce a picture with resolution similar or equivalent to a single telescope with the diameter of the combined spread of telescopes. These include radio telescope arrays 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.
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Interferometer
An interferometer works on the principle that two waves that coincide with the same phase will amplify each other while two waves that have opposite phases will cancel each other out. In the beginning, most interferometers used white light sources (e.g., Young's double slit experiment of 1805). Nowadays 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 deploying molecules. Currently it is not clear yet what the maximum particle size for interferometry might be.
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 first 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 incoherent light, but since it is a point source of light it will produce an interference pattern. The Michelson interferometer finds use not only in these experiments but also for other purposes, e.g., in gravitational wave detection.
There are many other types of interferometers. They all work on the same basic principles, but the geometry is different for the different types. One familar use of the technique is in radio and optical interferometer telescopes. However, 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. Such components are the basis of a wide variety of devices, from RF modulators to sensors to optical switches.
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).
Some other geometries include the Sagnac interferometer and Fabry-Perot interferometer.
Coherent interferometry
Coherent interferometry uses a coherent light source (for example, helium--neon), 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 <math>2 \pi = \lambda / 2</math>.
Coherent interferometry suffers from a <math>2 \pi</math> ambiguity problem: that is, if between any two measurements the interferometric phase jumps by more than <math>2 \pi</math> the phase measurement is incorrect.
The applications of coherent interferometry are wide ranging: Nanometer surface profiling, Microfluidics, Mechanical stress/strain, Velocimetry.
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 (Sagnac interferometer). The effect is amplified by using optic fibres wound around thousands of times.
Speckle Interferometry
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.
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 <math>2 \pi</math> 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 optical interferometry
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 Johnson, Betz and Towns (1974) in the infrared and by Labeyrie (1975) in the visible. The red giant star Betelgeuse was among the first to have its diameter determined in this way. In the late 1970's improvments 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.
In the 1980s the aperture synthesis interferometric imaging technique was extended to visible light and infrared astronomy by the Cavendish Astrophysics Group, providing the first very high resolution images of nearby stars. In 1995 this technique was demonstrated on an array of separate optical telescopes 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.
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. (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.
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.de:Interferometrie
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