Interferometry

Interferometry

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Encyclopedia
Interferometry refers to a family of techniques in which electromagnetic waves
Electromagnetic radiation
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...

 are superimposed in order to extract information about the waves. An instrument used to interfere waves is called an interferometer. Interferometry is an important investigative technique in the fields of astronomy
Astronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...

, fiber optics
Optical fiber
An optical fiber is a flexible, transparent fiber made of a pure glass not much wider than a human hair. It functions as a waveguide, or "light pipe", to transmit light between the two ends of the fiber. The field of applied science and engineering concerned with the design and application of...

, engineering metrology
Metrology
Metrology is the science of measurement. Metrology includes all theoretical and practical aspects of measurement. The word comes from Greek μέτρον , "measure" + "λόγος" , amongst others meaning "speech, oration, discourse, quote, study, calculation, reason"...

, optical metrology, oceanography
Oceanography
Oceanography , also called oceanology or marine science, is the branch of Earth science that studies the ocean...

, seismology, quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

, nuclear
Nuclear physics
Nuclear physics is the field of physics that studies the building blocks and interactions of atomic nuclei. The most commonly known applications of nuclear physics are nuclear power generation and nuclear weapons technology, but the research has provided application in many fields, including those...

 and particle physics
Particle physics
Particle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...

, plasma physics, remote sensing and biomolecular interactions
Interactome
Interactome is defined as the whole set of molecular interactions in cells. It is usually displayed as a directed graph. Molecular interactions can occur between molecules belonging to different biochemical families and also within a given family...

.

Basic principles


Interferometry makes use of the principle of superposition to combine separate waves 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
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...

 combine, the resulting pattern is determined by the phase
Phase (waves)
Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.-Formula:The phase of an oscillation or wave refers to a sinusoidal function such as the following:...

 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
Light
Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...

 or some other form of electromagnetic wave.

Typically a single incoming beam of coherent
Coherence (physics)
In physics, coherence is a property of waves that enables stationary interference. More generally, coherence describes all properties of the correlation between physical quantities of a wave....

 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
Path length
In chemistry, the path length is defined as the distance that light travels through a sample in an analytical cell. Typically, a sample cell is made of quartz, glass, or a plastic rhombic cuvette with a volume typically ranging from 0.1 mL to 10 mL or larger used in a spectrophotometer. For the...

 itself or a change in the refractive index
Refractive index
In optics the refractive index or index of refraction of a substance or medium is a measure of the speed of light in that medium. It is expressed as a ratio of the speed of light in vacuum relative to that in the considered medium....

 along the path.

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
Optical heterodyne detection
Optical heterodyne detection is an important special case of heterodyne detection. In heterodyne detection, a signal of interest at some frequency is non-linearly mixed with a reference "local oscillator" that is set at a close-by frequency...

, 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.

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.

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
Fourier transform
In mathematics, Fourier analysis is a subject area which grew from the study of Fourier series. The subject began with the study of the way general functions may be represented by sums of simpler trigonometric functions...

 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.

In the optical domain, direct phase detection is now possible astronomers have combined the visible light from six telescopes to produce a single image before Optical heterodyne detection
Optical heterodyne detection
Optical heterodyne detection is an important special case of heterodyne detection. In heterodyne detection, a signal of interest at some frequency is non-linearly mixed with a reference "local oscillator" that is set at a close-by frequency...

 was used. 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. A related technique is the time domain conjugate of SAHD, known as Fourier transform heterodyne detection.

Astronomical interferometry




The angular resolution
Angular resolution
Angular resolution, or spatial resolution, describes the ability of any image-forming device such as an optical or radio telescope, a microscope, a camera, or an eye, to distinguish small details of an object...

 that a telescope
Telescope
A telescope is an instrument that aids in the observation of remote objects by collecting electromagnetic radiation . The first known practical telescopes were invented in the Netherlands at the beginning of the 1600s , using glass lenses...

 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 used a single baseline to measure the amount of power on a particular small angular scale. Later astronomical interferometers were arrays 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
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...

.

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
Very Large Array
The Very Large Array is a radio astronomy observatory located on the Plains of San Agustin, between the towns of Magdalena and Datil, some fifty miles west of Socorro, New Mexico, USA...

 and MERLIN
MERLIN
The Multi-Element Radio Linked Interferometer Network is an interferometer array of radio telescopes spread across England. The array is run from Jodrell Bank Observatory in Cheshire by the University of Manchester on behalf of STFC as a National Facility.The array consists of up to seven radio...

. 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
Atacama Large Millimeter Array
The Atacama Large Millimeter/sub-millimeter Array is an array of radio telescopes in the Atacama desert of northern Chile. Since a high and dry site is crucial to millimeter wavelength operations, the array is being constructed on the Chajnantor plateau at 5000 metres altitude...

, currently under construction. Optical astronomical interferometers have traditionally been specialized instruments, but recent developments have broadened their capabilities.

See also


  • List of types of interferometers
    • Fabry–Pérot interferometer
    • Fizeau–Foucault apparatus
    • Michelson interferometer
      Michelson interferometer
      The Michelson interferometer is the most common configuration for optical interferometry and was invented by Albert Abraham Michelson. An interference pattern is produced by splitting a beam of light into two paths, bouncing the beams back and recombining them...

  • List of astronomical interferometers at visible and infrared wavelengths
  • Angle-resolved low-coherence interferometry
    Angle-resolved low-coherence interferometry
    For the electrical device, see ALCIAngle-resolved low-coherence interferometry is an emerging biomedical imaging technology which uses the properties of scattered light to measure the average size of cell structures, including cell nuclei...

  • Astronomical interferometer
    Astronomical interferometer
    An astronomical interferometer is an array of telescopes or mirror segments acting together to probe structures with higher resolution by means of interferometry....

  • Aperture synthesis
    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...

  • Bose–Einstein correlations
  • Coherence
    Coherence (physics)
    In physics, coherence is a property of waves that enables stationary interference. More generally, coherence describes all properties of the correlation between physical quantities of a wave....

  • Dual polarisation interferometry
    Dual Polarisation Interferometry
    Dual polarization interferometry is an analytical technique that can probe molecular scale layers adsorbed to the surface of a waveguide by using the evanescent wave of a laser beam confined to the waveguide...

  • Interference
  • Interferometric microscopy
    Interferometric microscopy
    Interferometric microscopy or Imaging interferometric microscopy is the concept of microscopy whichis related to holography, synthetic-aperture imaging, and off-axis-dark-field illumination techniques....

  • Optical coherence tomography
    Optical coherence tomography
    Optical coherence tomography is an optical signal acquisition and processing method. It captures micrometer-resolution, three-dimensional images from within optical scattering media . Optical coherence tomography is an interferometric technique, typically employing near-infrared light...

  • Optical heterodyne detection
    Optical heterodyne detection
    Optical heterodyne detection is an important special case of heterodyne detection. In heterodyne detection, a signal of interest at some frequency is non-linearly mixed with a reference "local oscillator" that is set at a close-by frequency...

  • Optical interferometry
    Optical interferometry
    Optical interferometry combines two or more light waves in an opticalinstrument in such a way that interference occurs between them.Early interferometers used white light sources and also monochromatic light from atomic sources...

  • Phase interferometry
  • Very Long Baseline Interferometry
    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...