One of the first
astronomical interferometerAn astronomical interferometer is an array of telescopes or mirror segments acting together to probe structures with higher resolution. Astronomical interferometers are widely used for optical astronomy, infrared astronomy, submillimetre astronomy and radio astronomy. Aperture synthesis can be used...
s was built on the
Mount Wilson ObservatoryThe Mount Wilson Observatory is an astronomical observatory in Los Angeles County, California. The MWO is located on Mount Wilson, a 5,715 foot peak in the San Gabriel Mountains near Pasadena, northeast of Los Angeles....
's reflector telescope in 1920 in order to measure the diameters of stars. The red giant star
BetelgeuseBetelgeuse is a semiregular variable star located approximately 640 light-years from the Earth. It is Alpha Orionis , but the second brightest star in the constellation Orion and the ninth brightest star in the night sky...
was among the first to have its diameter determined in this way. 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. In the late 1970s improvements in computer processing allowed for the first "fringe-tracking" interferometer, which operates fast enough to follow the blurring effects of
astronomical seeingAstronomical seeing refers to the blurring and twinkling of astronomical objects such as stars caused by turbulence in the Earth's atmosphere. It is the equivalent of looking at the bottom of a lake on a windy day. The astronomical seeing conditions on a given night at a given location describe how...
, 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 InterferometerThe Palomar Testbed Interferometer is a near-IR, long-baseline stellar interferometer located at Palomar Observatory in north San Diego County. It was built by Caltech/JPL and is intended to serve as a testbed for developing interferometric techniques to be used at the Keck Interferometer...
.
In the 1980s the
aperture synthesisAperture synthesis or synthesis imaging is a type of interferometry that mixes signals from a collection of telescopes to produce images having the same angular resolution as an instrument the size of the entire collection...
interferometric imaging technique was extended to visible light and infrared astronomy by the
Cavendish Astrophysics GroupThe Cavendish Astrophysics Group is based at the Cavendish Laboratory at the University of Cambridge. The group operates all of the telescopes at the Mullard Radio Astronomy Observatory except for the 32m MERLIN telescope, which is operated by Jodrell Bank.The group is the second largest of three...
, providing the first very high resolution images of nearby stars. In 1995 this imaging technique was demonstrated on
an array of separate optical telescopesCOAST, the Cambridge Optical Aperture Synthesis Telescope, is a multi-element optical astronomical interferometer with baselines of up to 100 metres, which uses aperture synthesis to observe stars with angular resolution as high as one thousandth of one arcsecond COAST, the Cambridge Optical...
for the first time, allowing a further improvement in resolution, and allowing even higher resolution
imaging of stellar surfaces. The same imaging technique has now been applied at the
Navy Prototype Optical InterferometerThe Navy Prototype Optical Interferometer is an astronomical interferometer operated by the US Naval Observatory , the Naval Research Laboratory and The Lowell Observatory. The facility is located on Anderson Mesa about 15 miles southeast of Flagstaff, Arizona...
and the
IOTAThe Infrared Optical Telescope Array began with an agreement in 1988 among five Institutions, the Smithsonian Astrophysical Observatory, Harvard University, the University of Massachusetts, the University of Wyoming, and MIT/Lincoln Laboratory, to build a two-telescope stellar interferometer for...
array. In the near future other arrays are expected to release their first interferometric images, including the
ISIThe Infrared Spatial Interferometer is an astronomical interferometer array of three 65 inch telescopes operating in the mid-infrared. The telescopes are fully mobile and their current site on Mount Wilson allows for placements as far as 70 m apart, giving the resolution of a telescope of that...
,
VLTVLT may stand for:* Very Large Telescope, a system of four large optical telescopes organized in an array formation, located in northern Chile...
I, the
CHARA arrayThe CHARA Array is an optical astronomical interferometer operated by The Center for High Angular Resolution Astronomy of the Georgia State University . CHARA is the World's highest angular resolution telescope at near-infrared wavelengths...
and the 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 InterferometerThe Palomar Testbed Interferometer is a near-IR, long-baseline stellar interferometer located at Palomar Observatory in north San Diego County. It was built by Caltech/JPL and is intended to serve as a testbed for developing interferometric techniques to be used at the Keck Interferometer...
and the
VLTVLT may stand for:* Very Large Telescope, a system of four large optical telescopes organized in an array formation, located in northern Chile...
I) or through the use of nulling (as will be used by the Keck Interferometer and
DarwinDarwin is a European Space Agency program designed to directly detect Earth-like planets orbiting nearby stars, and search for evidence of life on these planets. The launch date will not be before 2016. The current design envisions three free-flying space telescopes, each at least 3 meters in...
).
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 100s of stars and many accurate stellar positions, COAST and
NPOIThe Navy Prototype Optical Interferometer is an astronomical interferometer operated by the US Naval Observatory , the Naval Research Laboratory and The Lowell Observatory. The facility is located on Anderson Mesa about 15 miles southeast of Flagstaff, Arizona...
producing many very high resolution images, and
ISIThe Infrared Spatial Interferometer is an astronomical interferometer array of three 65 inch telescopes operating in the mid-infrared. The telescopes are fully mobile and their current site on Mount Wilson allows for placements as far as 70 m apart, giving the resolution of a telescope of that...
measuring stars in the mid-infrared for the first time. Additional results included direct measurements of the sizes of and distances to Cepheid variable stars, and young stellar objects. At the beginning of the 21st Century, the VLTI and Keck Interferometer large-telescope arrays came into operation, and the first interferometric measurements of the brightest few extra-galactic targets were performed.
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 resolutionAngular resolution or 'spatial resolution' describes the resolving power of any image-forming device such as an optical or radio telescope, a microscope, a camera, or an eye.- Definition of terms :...
. 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 (
astrometryAstrometry is the branch of astronomy that relates to precise measurements and explanations of the positions and movements of stars and other celestial bodies...
) and for imaging the nearest
giant starA giant star is a star with substantially larger radius and luminosity than a main sequence star of the same surface temperature. Typically, giant stars have radii between 10 and 100 solar radii and luminosities between 10 and 1,000 times that of the Sun. Stars still more luminous than giants are...
s.
For details of individual instruments, see the
list of astronomical interferometers at visible and infrared wavelengths.
 |
 |
| A simple two-element optical interferometer. Light from two small telescopes (shown as lenses A lens is an optical device with perfect or approximate axial symmetry which transmits and refracts light, converging or diverging the beam. A simple lens is a lens consisting of a single optical element...
) is combined using beam splitters at detectors 1, 2, 3 and 4. The elements creating a 1/4 wave delay in the light allow the phase and amplitude of the interference visibility to be measured, which give information about the shape of the light source. |
A single large telescope with an aperture mask Aperture Masking Interferometry is a form of speckle interferometry, allowing diffraction limited imaging from ground-based telescopes. This technique allows ground based telescopes to reach the maximum possible resolution, allowing ground-based telescopes with large diameters to produce far...
over it (labelled Mask), only allowing light through two small holes. The optical paths to detectors 1, 2, 3 and 4 are the same as in the left-hand figure, so this setup will give identical results. By moving the holes in the aperture mask and taking repeated measurements, images can be created using aperture synthesisAperture synthesis or synthesis imaging is a type of interferometry that mixes signals from a collection of telescopes to produce images having the same angular resolution as an instrument the size of the entire collection...
which would have the same quality as would have been given by the right-hand telescope without the aperture mask. In an analogous way, the same image quality can be achieved by moving the small telescopes around in the left-hand figure - this is the basis of aperture synthesis, using widely separated small telescopes to simulate a giant telescope. |
In
astronomyAstronomy is the scientific study of celestial objects and phenomena that originate outside the Earth's atmosphere...
interferometry is used to combine signals from two or more
telescopeA telescope is an instrument designed for the observation of remote objects by the collection of electromagnetic radiation. The first known practically functioning telescopes were invented in the Netherlands at the beginning of the 17th century...
s to obtain measurements with higher resolution than could be obtained with either telescopes individually. This technique is the basis for
astronomical interferometerAn astronomical interferometer is an array of telescopes or mirror segments acting together to probe structures with higher resolution. Astronomical interferometers are widely used for optical astronomy, infrared astronomy, submillimetre astronomy and radio astronomy. Aperture synthesis can be used...
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
resolutionAngular resolution or 'spatial resolution' describes the resolving power of any image-forming device such as an optical or radio telescope, a microscope, a camera, or an eye.- Definition of terms :...
similar to a single telescope with the diameter of the combined spread of telescopes. These include
radio telescopeA radio telescope is a form of directional radio antenna used in radio astronomy. The same types of antennas are also used in tracking and collecting data from satellites and space probes...
arrays such as
VLAVLA may refer to:* Vertical Launch ASROC, a vertically launched version of an anti-submarine rocket * Very Large Array, a radio telescope array* Very Light Aircraft, a category of aircraft, per the European EASA CS-VLA specifications...
, VLBI,
SMAThe Submillimeter Array consists of eight 6 m diameter radio telescopes arranged as an interferometer for submillimeter wavelength observations...
,
LOFARLOFAR is the LOw Frequency ARray for radio astronomy. LOFAR is being built by ASTRON and will be operated by ASTRON's Radio Observatory...
and
SKAThe Square Kilometre Array is a radio telescope in development which will have a total collecting area of approximately one square kilometre. It will operate over a wide range of frequencies and its size will make it 50 times more sensitive than any other radio instrument...
, and more recently astronomical optical interferometer arrays such as COAST,
NPOIThe Navy Prototype Optical Interferometer is an astronomical interferometer operated by the US Naval Observatory , the Naval Research Laboratory and The Lowell Observatory. The facility is located on Anderson Mesa about 15 miles southeast of Flagstaff, Arizona...
and
IOTAThe Infrared Optical Telescope Array began with an agreement in 1988 among five Institutions, the Smithsonian Astrophysical Observatory, Harvard University, the University of Massachusetts, the University of Wyoming, and MIT/Lincoln Laboratory, to build a two-telescope stellar interferometer for...
, resulting in the highest resolution optical images ever achieved in astronomy. The
VLT InterferometerThe Very Large Telescope is a very large telescope made up of four separate optical telescopes organized in an array formation, built and operated by the European Southern Observatory at the Paranal Observatory on Cerro Paranal, a 2,635 m high mountain...
is expected to produce its first images using
aperture synthesisAperture synthesis or synthesis imaging is a type of interferometry that mixes signals from a collection of telescopes to produce images having the same angular resolution as an instrument the size of the entire collection...
soon, followed by other interferometers such as the
CHARA arrayThe CHARA Array is an optical astronomical interferometer operated by The Center for High Angular Resolution Astronomy of the Georgia State University . CHARA is the World's highest angular resolution telescope at near-infrared wavelengths...
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 synthesisAperture synthesis or synthesis imaging is a type of interferometry that mixes signals from a collection of telescopes to produce images having the same angular resolution as an instrument the size of the entire collection...
can be used to computationally simulate a large telescope aperture from either type of interferometer.
Astronomical direct-detection interferometry
One of the first
astronomical interferometerAn astronomical interferometer is an array of telescopes or mirror segments acting together to probe structures with higher resolution. Astronomical interferometers are widely used for optical astronomy, infrared astronomy, submillimetre astronomy and radio astronomy. Aperture synthesis can be used...
s was built on the
Mount Wilson ObservatoryThe Mount Wilson Observatory is an astronomical observatory in Los Angeles County, California. The MWO is located on Mount Wilson, a 5,715 foot peak in the San Gabriel Mountains near Pasadena, northeast of Los Angeles....
'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
BetelgeuseBetelgeuse is a semiregular variable star located approximately 640 light-years from the Earth. It is Alpha Orionis , but the second brightest star in the constellation Orion and the ninth brightest star in the night sky...
was among the first to have its diameter
determined in this way. In the late 1970s improvements in computer processing allowed for the first "fringe-tracking" interferometer, which operates fast enough to follow the blurring effects of
astronomical seeingAstronomical seeing refers to the blurring and twinkling of astronomical objects such as stars caused by turbulence in the Earth's atmosphere. It is the equivalent of looking at the bottom of a lake on a windy day. The astronomical seeing conditions on a given night at a given location describe how...
, 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 InterferometerThe Palomar Testbed Interferometer is a near-IR, long-baseline stellar interferometer located at Palomar Observatory in north San Diego County. It was built by Caltech/JPL and is intended to serve as a testbed for developing interferometric techniques to be used at the Keck Interferometer...
.
Techniques from Very Long Baseline Interferometry (VLBI), in which
a large aperture is synthesized computationallyAperture synthesis or synthesis imaging is a type of interferometry that mixes signals from a collection of telescopes to produce images having the same angular resolution as an instrument the size of the entire collection...
, were implemented at optical and infrared wavelengths in the 1980s by the
Cavendish Astrophysics GroupThe Cavendish Astrophysics Group is based at the Cavendish Laboratory at the University of Cambridge. The group operates all of the telescopes at the Mullard Radio Astronomy Observatory except for the 32m MERLIN telescope, which is operated by Jodrell Bank.The group is the second largest of three...
. This providing the first very high resolution images of nearby stars. In 1995 this technique was demonstrated on
an array of separate optical telescopesCOAST, the Cambridge Optical Aperture Synthesis Telescope, is a multi-element optical astronomical interferometer with baselines of up to 100 metres, which uses aperture synthesis to observe stars with angular resolution as high as one thousandth of one arcsecond COAST, the Cambridge Optical...
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 InterferometerThe Navy Prototype Optical Interferometer is an astronomical interferometer operated by the US Naval Observatory , the Naval Research Laboratory and The Lowell Observatory. The facility is located on Anderson Mesa about 15 miles southeast of Flagstaff, Arizona...
and the
IOTAThe Infrared Optical Telescope Array began with an agreement in 1988 among five Institutions, the Smithsonian Astrophysical Observatory, Harvard University, the University of Massachusetts, the University of Wyoming, and MIT/Lincoln Laboratory, to build a two-telescope stellar interferometer for...
array and soon the
VLTVLT may stand for:* Very Large Telescope, a system of four large optical telescopes organized in an array formation, located in northern Chile...
I,
CHARAThe CHARA Array is an optical astronomical interferometer operated by The Center for High Angular Resolution Astronomy of the Georgia State University . CHARA is the World's highest angular resolution telescope at near-infrared wavelengths...
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 InterferometerThe Palomar Testbed Interferometer is a near-IR, long-baseline stellar interferometer located at Palomar Observatory in north San Diego County. It was built by Caltech/JPL and is intended to serve as a testbed for developing interferometric techniques to be used at the Keck Interferometer...
and the
VLTVLT may stand for:* Very Large Telescope, a system of four large optical telescopes organized in an array formation, located in northern Chile...
I) or through the use of nulling (as will be used by the Keck Interferometer and
DarwinDarwin is a European Space Agency program designed to directly detect Earth-like planets orbiting nearby stars, and search for evidence of life on these planets. The launch date will not be before 2016. The current design envisions three free-flying space telescopes, each at least 3 meters in...
).
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
NPOIThe Navy Prototype Optical Interferometer is an astronomical interferometer operated by the US Naval Observatory , the Naval Research Laboratory and The Lowell Observatory. The facility is located on Anderson Mesa about 15 miles southeast of Flagstaff, Arizona...
producing many very high resolution images, and
ISIThe Infrared Spatial Interferometer is an astronomical interferometer array of three 65 inch telescopes operating in the mid-infrared. The telescopes are fully mobile and their current site on Mount Wilson allows for placements as far as 70 m apart, giving the resolution of a telescope of that...
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 resolutionAngular resolution or 'spatial resolution' describes the resolving power of any image-forming device such as an optical or radio telescope, a microscope, a camera, or an eye.- Definition of terms :...
. 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 (
astrometryAstrometry is the branch of astronomy that relates to precise measurements and explanations of the positions and movements of stars and other celestial bodies...
) and for imaging the nearest
giant starA giant star is a star with substantially larger radius and luminosity than a main sequence star of the same surface temperature. Typically, giant stars have radii between 10 and 100 solar radii and luminosities between 10 and 1,000 times that of the Sun. Stars still more luminous than giants are...
s.
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
submillimetreSubmillimetre astronomy or submillimeter astronomy is the branch of observational astronomy that is conducted at submillimetre wavelengths of the electromagnetic spectrum. Astronomers place the submillimetre waveband between the far-infrared and microwave wavebands, typically taken to be between a...
and
infraredInfrared radiation is electromagnetic radiation whose wavelength is longer than that of visible light , but shorter than that of terahertz radiation and microwaves...
interferometers, such as the
Infrared Spatial InterferometerThe Infrared Spatial Interferometer is an astronomical interferometer array of three 65 inch telescopes operating in the mid-infrared. The telescopes are fully mobile and their current site on Mount Wilson allows for placements as far as 70 m apart, giving the resolution of a telescope of that...
. Some early radio interferometers operated as
intensity interferometerAn intensity interferometer is the name given to devices that use the Hanbury-Brown and Twiss effect. In astronomy, the most common use of such an astronomical interferometer is to determine the apparent angular diameter of a radio source or star...
s, 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 InterferometerThe Narrabri Stellar Intensity Interferometer was the first astronomical instrument to measure the diameters of a large number of stars at visible wavelengths. It was designed by Robert Hanbury Brown, who received the Hughes Medal in 1971 for this work...
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 apertureAperture synthesis or synthesis imaging is a type of interferometry that mixes signals from a collection of telescopes to produce images having the same angular resolution as an instrument the size of the entire collection...
in the same way as with direct detection interferometers (see above).
Interferometry as ELINT technique
Interferometry is used in direction finding systems where high accuracy is needed (1° or so). The ELINT system measures the phase of the RF signal received in different antennas and calculates the Direction Of Arrival (
DOADOA is often an acronym for Dead on arrival and Dead or Alive.
DOA may also refer to:- Film :*D.O.A. , a film noir**D.O.A. , a remake of the 1950 film...
) by using the phase difference.
See also
- List of astronomical interferometers at visible and infrared wavelengths
- Interferometry
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...
- Astronomical interferometer
An astronomical interferometer is an array of telescopes or mirror segments acting together to probe structures with higher resolution. Astronomical interferometers are widely used for optical astronomy, infrared astronomy, submillimetre astronomy and radio astronomy. Aperture synthesis can be used...
- Aperture synthesis
Aperture synthesis or synthesis imaging is a type of interferometry that mixes signals from a collection of telescopes to produce images having the same angular resolution as an instrument the size of the entire collection...
- History of astronomical interferometry
- Interference
In physics, interference is the addition of two or more waves that results in a new wave pattern.Interference usually refers to the interaction of waves that are correlated or coherent with each other, either because they come from the same source or because they have the same or nearly the same...
- Very Long Baseline Interferometry
Very Long Baseline Interferometry is a type of astronomical interferometry used in radio astronomy. It allows observations of an object that are made simultaneously by many telescopes to be combined, emulating a telescope with a size equal to the maximum separation between the telescopes.Data...
- Optical coherence tomography
Optical coherence tomography is an optical signal acquisition and processing method allowing extremely high-quality, micrometer-resolution, three-dimensional images from within optical scattering media to be obtained...
- List of types of interferometers
- Astronomical interferometer
An astronomical interferometer is an array of telescopes or mirror segments acting together to probe structures with higher resolution. Astronomical interferometers are widely used for optical astronomy, infrared astronomy, submillimetre astronomy and radio astronomy. Aperture synthesis can be used...
- History of astronomical interferometry
- List of astronomical interferometers at visible and infrared wavelengths
Further reading
- John E. Baldwin
John Evan Baldwin has worked at the Cavendish Astrophysics Group since 1954. He played a pivotal role in the development of interferometry in Radio Astronomy, and later astronomical optical interferometry and lucky imaging...
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
The Institute of Physics is a scientific charity devoted to increasing the practice, understanding and application of physics,and is the UK and Ireland's main professional body for physicists...
. (download PDF file)
- 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)
External links