Interferometry
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Interferometry is the science of combining (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 the wave phenomenon of interference is very general, interferometry can be applied to a wide variety of fields, including astronomy, fiber optics, optical metrology, oceanography and various studies of quantum mechanics. Interferometry can be applied to both one-dimensional (such as time signals) or mutli-dimensional (such as coherent images produced by laser illumination) waves.
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[edit] 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. 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 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.
[edit] 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.
[edit] 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 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 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.
[edit] 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 this sensitivity adds to its 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.
[edit] 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].
[edit] Fabry-Perot interferometer
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.
[edit] Types of Interferometry
[edit] 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 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.
[edit] 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.
[edit] Speckle Interferometry
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.
[edit] 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 dimesional metrology of large parts and assemblies and larger surface defect detection when used in multi-wavelength implementations..
[edit] 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 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.
[edit] 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.
[edit] 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 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.
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 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.
[edit] Applications
[edit] Astronomical Applications
In astronomy (such as with the Keck telescopes), interferometry is used to combine light 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 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.
[edit] 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.
- E. Hecht, Optics, 2nd Edition, Addison-Wesley Publishing Co., Reading, Mass, USA, 1987.
[edit] External References
[edit] Notes
- ^ E. Hecht, Optics, 2nd Edition, Addison-Wesley Publishing Co., Reading, Mass, USA, 1987. p. 358
[edit] Books
- Basics of Interferometry, 2E by P. Hariharan Outstanding introduction to the world of optical interferometry with summaries at the beginning and end of each chapter, several appendices with essential information, and worked numerical problems / Practical details enrich understanding for readers new to this material / New chapters on white-light microscopy for medical imaging and interference with single photons(quantum optics)
[edit] 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
[edit] 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.
