
In
physics
Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...
, interference is a phenomenon in which two
coherent
Coherence is, in general, a state or situation in which all the parts or ideas fit together well so that they form a united whole.
More specifically, coherence, coherency, or coherent may refer to the following:
Physics
* Coherence (physics ...
wave
In physics, mathematics, engineering, and related fields, a wave is a propagating dynamic disturbance (change from List of types of equilibrium, equilibrium) of one or more quantities. ''Periodic waves'' oscillate repeatedly about an equilibrium ...
s are combined by adding their intensities or displacements with due consideration for their
phase difference. The resultant wave may have greater amplitude (constructive interference) or lower amplitude (destructive interference) if the two waves are in phase or out of phase, respectively.
Interference effects can be observed with all types of waves, for example,
light
Light, visible light, or visible radiation is electromagnetic radiation that can be visual perception, perceived by the human eye. Visible light spans the visible spectrum and is usually defined as having wavelengths in the range of 400– ...
,
radio
Radio is the technology of communicating using radio waves. Radio waves are electromagnetic waves of frequency between 3 hertz (Hz) and 300 gigahertz (GHz). They are generated by an electronic device called a transmitter connec ...
,
acoustic,
surface water waves,
gravity wave
In fluid dynamics, gravity waves are waves in a fluid medium or at the interface between two media when the force of gravity or buoyancy tries to restore equilibrium. An example of such an interface is that between the atmosphere and the oc ...
s, or
matter wave
Matter waves are a central part of the theory of quantum mechanics, being half of wave–particle duality. At all scales where measurements have been practical, matter exhibits wave-like behavior. For example, a beam of electrons can be diffract ...
s as well as in loudspeakers as electrical waves.
Etymology
The word ''interference'' is derived from the
Latin
Latin ( or ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken by the Latins (Italic tribe), Latins in Latium (now known as Lazio), the lower Tiber area aroun ...
words ''inter'' which means "between" and ''fere'' which means "hit or strike", and was used in the context of wave superposition by
Thomas Young in 1801.
Mechanisms

The
principle of superposition of waves states that when two or more propagating waves of the same type are incident on the same point, the resultant
amplitude
The amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period). The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of am ...
at that point is equal to the
vector sum
In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude (or length) and direction. Euclidean vectors can be added and scal ...
of the amplitudes of the individual waves. If a
crest of a wave meets a crest of another wave of the same frequency at the same point, then the amplitude is the sum of the individual amplitudes—this is constructive interference. If a crest of one wave meets a trough of another wave, then the amplitude is equal to the difference in the individual amplitudes—this is known as destructive interference. In ideal mediums (water, air are almost ideal) energy is always conserved, at points of destructive interference, the wave amplitudes cancel each other out, and the energy is redistributed to other areas. For example, when two pebbles are dropped in a pond, a pattern is observable; but eventually waves continue, and only when they reach the shore is the energy absorbed away from the medium.

Constructive interference occurs when the
phase difference between the waves is an even multiple of (180°), whereas destructive interference occurs when the difference is an odd multiple of . If the difference between the phases is intermediate between these two extremes, then the magnitude of the displacement of the summed waves lies between the minimum and maximum values.
Consider, for example, what happens when two identical stones are dropped into a still pool of water at different locations. Each stone generates a circular wave propagating outwards from the point where the stone was dropped. When the two waves overlap, the net displacement at a particular point is the sum of the displacements of the individual waves. At some points, these will be in phase, and will produce a maximum displacement. In other places, the waves will be in anti-phase, and there will be no net displacement at these points. Thus, parts of the surface will be stationary—these are seen in the figure above and to the right as stationary blue-green lines radiating from the centre.
Interference of light is a unique phenomenon in that we can never observe superposition of the EM field directly as we can, for example, in water. Superposition in the EM field is an assumed phenomenon and necessary to explain how two light beams pass through each other and continue on their respective paths. Prime examples of light interference are the famous
double-slit experiment
In modern physics, the double-slit experiment demonstrates that light and matter can exhibit behavior of both classical particles and classical waves. This type of experiment was first performed by Thomas Young in 1801, as a demonstration of ...
,
laser speckle
Speckle, speckle pattern, or speckle noise designates the granular structure observed in coherent light, resulting from random interference. Speckle patterns are used in a wide range of metrology techniques, as they generally allow high sensitivi ...
,
anti-reflective coating
An antireflective, antiglare or anti-reflection (AR) coating is a type of optical coating applied to the surface of lens (optics), lenses, other optical elements, and photovoltaic cells to reduce reflection (physics), reflection. In typical ima ...
s and
interferometer
Interferometry is a technique which uses the '' interference'' of superimposed waves to extract information. Interferometry typically uses electromagnetic waves and is an important investigative technique in the fields of astronomy, fiber opt ...
s.
In addition to classical wave model for understanding optical interference, quantum
matter waves
Matter waves are a central part of the theory of quantum mechanics, being half of wave–particle duality. At all scales where measurements have been practical, matter exhibits wave-like behavior. For example, a beam of electrons can be diffract ...
also demonstrate interference.
Real-valued wave functions
The above can be demonstrated in one dimension by deriving the formula for the sum of two waves. The equation for the amplitude of a
sinusoid
A sine wave, sinusoidal wave, or sinusoid (symbol: ∿) is a periodic wave whose waveform (shape) is the trigonometric sine function. In mechanics, as a linear motion over time, this is '' simple harmonic motion''; as rotation, it correspond ...
al wave traveling to the right along the x-axis is
where
is the peak amplitude,
is the
wavenumber
In the physical sciences, the wavenumber (or wave number), also known as repetency, is the spatial frequency of a wave. Ordinary wavenumber is defined as the number of wave cycles divided by length; it is a physical quantity with dimension of ...
and
is the
angular frequency
In physics, angular frequency (symbol ''ω''), also called angular speed and angular rate, is a scalar measure of the angle rate (the angle per unit time) or the temporal rate of change of the phase argument of a sinusoidal waveform or sine ...
of the wave. Suppose a second wave of the same frequency and amplitude but with a different phase is also traveling to the right
where
is the phase difference between the waves in
radian
The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. It is defined such that one radian is the angle subtended at ...
s. The two waves will
superpose and add: the sum of the two waves is
Using the
trigonometric identity
In trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined. Geometrically, these are identities involvin ...
for the sum of two cosines:
this can be written
This represents a wave at the original frequency, traveling to the right like its components, whose amplitude is proportional to the cosine of
.
* ''Constructive interference'': If the phase difference is an even multiple of :
then
, so the sum of the two waves is a wave with twice the amplitude
* ''Destructive interference'': If the phase difference is an odd multiple of :
then
, so the sum of the two waves is zero
Between two plane waves
A simple form of interference pattern is obtained if two
plane wave
In physics
Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of ...
s of the same frequency intersect at an angle.
One wave is travelling horizontally, and the other is travelling downwards at an angle θ to the first wave. Assuming that the two waves are in phase at the point B, then the relative phase changes along the ''x''-axis. The phase difference at the point A is given by
It can be seen that the two waves are in phase when
and are half a cycle out of phase when
Constructive interference occurs when the waves are in phase, and destructive interference when they are half a cycle out of phase. Thus, an interference fringe pattern is produced, where the separation of the maxima is
and is known as the fringe spacing. The fringe spacing increases with increase in
wavelength
In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats.
In other words, it is the distance between consecutive corresponding points of the same ''phase (waves ...
, and with decreasing angle .
The fringes are observed wherever the two waves overlap and the fringe spacing is uniform throughout.
Between two spherical waves
A
point source
A point source is a single identifiable ''localized'' source of something. A point source has a negligible extent, distinguishing it from other source geometries. Sources are called point sources because, in mathematical modeling, these sources ...
produces a spherical wave. If the light from two point sources overlaps, the interference pattern maps out the way in which the phase difference between the two waves varies in space. This depends on the wavelength and on the separation of the point sources. The figure to the right shows interference between two spherical waves. The wavelength increases from top to bottom, and the distance between the sources increases from left to right.
When the plane of observation is far enough away, the fringe pattern will be a series of almost straight lines, since the waves will then be almost planar.
Multiple beams
Interference occurs when several waves are added together provided that the phase differences between them remain constant over the observation time.
It is sometimes desirable for several waves of the same frequency and amplitude to sum to zero (that is, interfere destructively, cancel). This is the principle behind, for example,
3-phase power and the
diffraction grating
In optics, a diffraction grating is an optical grating with a periodic structure that diffraction, diffracts light, or another type of electromagnetic radiation, into several beams traveling in different directions (i.e., different diffractio ...
. In both of these cases, the result is achieved by uniform spacing of the phases.
It is easy to see that a set of waves will cancel if they have the same amplitude and their phases are spaced equally in angle. Using
phasor
In physics and engineering, a phasor (a portmanteau of phase vector) is a complex number representing a sinusoidal function whose amplitude and initial phase are time-invariant and whose angular frequency is fixed. It is related to a mor ...
s, each wave can be represented as
for
waves from
to
, where
To show that
one merely assumes the converse, then multiplies both sides by
The
Fabry–Pérot interferometer
In optics, a Fabry–Pérot interferometer (FPI) or etalon is an optical cavity made from two parallel reflecting surfaces (i.e.: thin mirrors). Optical waves can pass through the optical cavity only when they are in resonance with it. It is ...
uses interference between multiple reflections.
A
diffraction grating
In optics, a diffraction grating is an optical grating with a periodic structure that diffraction, diffracts light, or another type of electromagnetic radiation, into several beams traveling in different directions (i.e., different diffractio ...
can be considered to be a multiple-beam interferometer; since the peaks which it produces are generated by interference between the light transmitted by each of the elements in the grating; see
interference vs. diffraction for further discussion.
Complex valued wave functions
Mechanical
Mechanical may refer to:
Machine
* Machine (mechanical), a system of mechanisms that shape the actuator input to achieve a specific application of output forces and movement
* Mechanical calculator, a device used to perform the basic operations o ...
and
gravity waves
In fluid dynamics, gravity waves are waves in a fluid medium or at the interface between two media when the force of gravity or buoyancy tries to restore equilibrium. An example of such an interface is that between the atmosphere and the oc ...
can be directly observed: they are real-valued wave functions;
optical
Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultravio ...
and
matter waves
Matter waves are a central part of the theory of quantum mechanics, being half of wave–particle duality. At all scales where measurements have been practical, matter exhibits wave-like behavior. For example, a beam of electrons can be diffract ...
cannot be directly observed: they are complex valued
wave functions. Some of the differences between real valued and complex valued wave interference include:
- The interference involves different types of mathematical functions: A classical wave is a real function representing the displacement from an equilibrium position; an optical or quantum wavefunction is a
complex
Complex commonly refers to:
* Complexity, the behaviour of a system whose components interact in multiple ways so possible interactions are difficult to describe
** Complex system, a system composed of many components which may interact with each ...
function. A classical wave at any point can be positive or negative; the quantum probability function is non-negative.
- Any two different real waves in the same medium interfere; complex waves must be
coherent
Coherence is, in general, a state or situation in which all the parts or ideas fit together well so that they form a united whole.
More specifically, coherence, coherency, or coherent may refer to the following:
Physics
* Coherence (physics ...
to interfere. In practice this means the wave must come from the same source and have similar frequencies
- Real wave interference is obtained simply by adding the displacements from equilibrium (or amplitudes) of the two waves; In complex wave interference, we measure the modulus of the wavefunction squared.
Optical wave interference

Because the frequency of light waves (~10
14 Hz) is too high for currently available detectors to detect the variation of the electric field of the light, it is possible to observe only the
intensity
Intensity may refer to:
In colloquial use
* Strength (disambiguation)
*Amplitude
* Level (disambiguation)
* Magnitude (disambiguation)
In physical sciences
Physics
*Intensity (physics), power per unit area (W/m2)
*Field strength of electric, m ...
of an optical interference pattern. The intensity of the light at a given point is proportional to the square of the average amplitude of the wave. This can be expressed mathematically as follows. The displacement of the two waves at a point is:
where represents the magnitude of the displacement, represents the phase and represents the
angular frequency
In physics, angular frequency (symbol ''ω''), also called angular speed and angular rate, is a scalar measure of the angle rate (the angle per unit time) or the temporal rate of change of the phase argument of a sinusoidal waveform or sine ...
.
The displacement of the summed waves is
The intensity of the light at is given by
This can be expressed in terms of the intensities of the individual waves as
Thus, the interference pattern maps out the difference in phase between the two waves, with maxima occurring when the phase difference is a multiple of 2. If the two beams are of equal intensity, the maxima are four times as bright as the individual beams, and the minima have zero intensity.
Classically the two waves must have the same
polarization to give rise to interference fringes since it is not possible for waves of different polarizations to cancel one another out or add together. Instead, when waves of different polarization are added together, they give rise to a wave of a different
polarization state.
Quantum mechanically the theories of Paul Dirac and Richard Feynman offer a more modern approach. Dirac showed that every quanta or photon of light acts on its own which he famously stated as "every photon interferes with itself". Richard Feynman showed that by evaluating a path integral where all possible paths are considered, that a number of higher probability paths will emerge. In thin films for example, film thickness which is not a multiple of light wavelength will not allow the quanta to traverse, only reflection is possible.
Light source requirements
The discussion above assumes that the waves which interfere with one another are monochromatic, i.e. have a single frequency—this requires that they are infinite in time. This is not, however, either practical or necessary. Two identical waves of finite duration whose frequency is fixed over that period will give rise to an interference pattern while they overlap. Two identical waves which consist of a narrow spectrum of frequency waves of finite duration (but shorter than their coherence time), will give a series of fringe patterns of slightly differing spacings, and provided the spread of spacings is significantly less than the average fringe spacing, a fringe pattern will again be observed during the time when the two waves overlap.
Conventional light sources emit waves of differing frequencies and at different times from different points in the source. If the light is split into two waves and then re-combined, each individual light wave may generate an interference pattern with its other half, but the individual fringe patterns generated will have different phases and spacings, and normally no overall fringe pattern will be observable. However, single-element light sources, such as
sodium- or
mercury-vapor lamps have emission lines with quite narrow frequency spectra. When these are spatially and colour filtered, and then split into two waves, they can be superimposed to generate interference fringes. All interferometry prior to the invention of the laser was done using such sources and had a wide range of successful applications.
A
laser beam
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word ''laser'' originated as an acronym for light amplification by stimulated emission of rad ...
generally approximates much more closely to a monochromatic source, and thus it is much more straightforward to generate interference fringes using a laser. The ease with which interference fringes can be observed with a laser beam can sometimes cause problems in that stray reflections may give spurious interference fringes which can result in errors.
Normally, a single laser beam is used in interferometry, though interference has been observed using two independent lasers whose frequencies were sufficiently matched to satisfy the phase requirements.
This has also been observed for widefield interference between two incoherent laser sources.
It is also possible to observe interference fringes using white light. A white light fringe pattern can be considered to be made up of a 'spectrum' of fringe patterns each of slightly different spacing. If all the fringe patterns are in phase in the centre, then the fringes will increase in size as the wavelength decreases and the summed intensity will show three to four fringes of varying colour. Young describes this very elegantly in his discussion of two slit interference. Since white light fringes are obtained only when the two waves have travelled equal distances from the light source, they can be very useful in interferometry, as they allow the zero path difference fringe to be identified.
Optical arrangements
To generate interference fringes, light from the source has to be divided into two waves which then have to be re-combined. Traditionally, interferometers have been classified as either amplitude-division or wavefront-division systems.
In an amplitude-division system, a
beam splitter
A beam splitter or beamsplitter is an optical instrument, optical device that splits a beam of light into a transmitted and a reflected beam. It is a crucial part of many optical experimental and measurement systems, such as Interferometry, int ...
is used to divide the light into two beams travelling in different directions, which are then superimposed to produce the interference pattern. The
Michelson interferometer
The Michelson interferometer is a common configuration for optical interferometry and was invented by the American physicist Albert Abraham Michelson in 1887. Using a beam splitter, a light source is split into two arms. Each of those light be ...
and the
Mach–Zehnder interferometer are examples of amplitude-division systems.
In wavefront-division systems, the wave is divided in space—examples are
Young's double slit interferometer and
Lloyd's mirror.
Interference can also be seen in everyday phenomena such as
iridescence
Iridescence (also known as goniochromism) is the phenomenon of certain surfaces that appear gradually to change colour as the angle of view or the angle of illumination changes. Iridescence is caused by wave interference of light in microstru ...
and
structural coloration
Structural coloration in animals, and a few plants, is the production of colour by microscopically structured surfaces fine enough to interfere with visible light instead of Biological pigment, pigments, although some structural coloration occu ...
. For example, the colours seen in a soap bubble arise from interference of light reflecting off the front and back surfaces of the thin soap film. Depending on the thickness of the film, different colours interfere constructively and destructively.
File:Samsung Galaxy A50 back 2.jpg, Smartphone with iridescent back panel
File:Dieselrainbow.jpg, An oil spill
File:Soap bubble sky.jpg, White light interference in a soap bubble.
Quantum interference
Quantum interference – the observed
wave-behavior of matter – resembles
optical interference. Let
be a
wavefunction
In quantum physics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common symbols for a wave function are the Greek letters and (lower-case and capital psi (letter) ...
solution of the
Schrödinger equation
The Schrödinger equation is a partial differential equation that governs the wave function of a non-relativistic quantum-mechanical system. Its discovery was a significant landmark in the development of quantum mechanics. It is named after E ...
for a quantum mechanical object. Then the
probability
Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an e ...
of observing the object in the interval
complex conjugation
In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign. That is, if a and b are real numbers, then the complex conjugate of a + bi is a - ...
. Quantum interference concerns the issue of this probability when the wavefunction is expressed as a sum or
linear superposition
The superposition principle, also known as superposition property, states that, for all linear systems, the net response caused by two or more stimuli is the sum of the responses that would have been caused by each stimulus individually. So th ...
of two terms
\Psi (x, t) = \Psi_A (x, t) + \Psi_B (x, t):
P( ,b = \int_a^b , \Psi (x, t), ^2 = \int_a^b (, \Psi_A (x, t), ^2 + , \Psi_B (x, t), ^2 + \Psi_A^* (x, t) \Psi_B (x, t) + \Psi_A (x, t) \Psi_B^* (x, t)) dx
Usually,
\Psi_A (x, t) and
\Psi_B (x, t) correspond to distinct situations A and B. When this is the case, the equation
\Psi (x, t) = \Psi_A (x, t) + \Psi_B (x, t) indicates that the object can be in situation A or situation B. The above equation can then be interpreted as: The probability of finding the object at
x is the probability of finding the object at
x when it is in situation A plus the probability of finding the object at
x when it is in situation B plus an extra term. This extra term, which is called the ''quantum interference term'', is
\Psi_A^* (x, t) \Psi_B (x, t) + \Psi_A (x, t) \Psi_B^* (x, t) in the above equation. As in the
classical wave case above, the quantum interference term can add (constructive interference) or subtract (destructive interference) from
, \Psi_A (x, t), ^2 + , \Psi_B (x, t), ^2 in the above equation depending on whether the quantum interference term is positive or negative. If this term is absent for all
x, then there is no quantum mechanical interference associated with situations A and B.
The best known example of quantum interference is the
double-slit experiment
In modern physics, the double-slit experiment demonstrates that light and matter can exhibit behavior of both classical particles and classical waves. This type of experiment was first performed by Thomas Young in 1801, as a demonstration of ...
. In this experiment,
matter waves
Matter waves are a central part of the theory of quantum mechanics, being half of wave–particle duality. At all scales where measurements have been practical, matter exhibits wave-like behavior. For example, a beam of electrons can be diffract ...
from electrons, atoms or molecules approach a barrier with two slits in it. One slit becomes
\Psi_A (x, t) and the other becomes
\Psi_B (x, t). The interference pattern occurs on the far side, observed by detectors suitable to the particles originating the
matter wave
Matter waves are a central part of the theory of quantum mechanics, being half of wave–particle duality. At all scales where measurements have been practical, matter exhibits wave-like behavior. For example, a beam of electrons can be diffract ...
.
The pattern matches the optical double slit pattern.
Applications
Beat
In
acoustics
Acoustics is a branch of physics that deals with the study of mechanical waves in gases, liquids, and solids including topics such as vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician ...
, a beat is an
interference
Interference is the act of interfering, invading, or poaching. Interference may also refer to:
Communications
* Interference (communication), anything which alters, modifies, or disrupts a message
* Adjacent-channel interference, caused by extra ...
pattern between two
sound
In physics, sound is a vibration that propagates as an acoustic wave through a transmission medium such as a gas, liquid or solid.
In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by the br ...
s of slightly different
frequencies
Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...
, ''perceived'' as a periodic variation in
volume
Volume is a measure of regions in three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch) ...
whose rate is the
difference of the two frequencies.
With
tuning instruments that can produce sustained tones, beats can be readily recognized. Tuning two tones to a
unison
Unison (stylised as UNISON) is a Great Britain, British trade union. Along with Unite the Union, Unite, Unison is one of the two largest trade unions in the United Kingdom, with over 1.2 million members who work predominantly in public servic ...
will present a peculiar effect: when the two tones are close in pitch but not identical, the difference in frequency generates the beating. The volume varies like in a
tremolo
In music, ''tremolo'' (), or ''tremolando'' (), is a trembling effect. There are multiple types of tremolo: a rapid repetition of a note, an alternation between two different notes, or a variation in volume.
Tremolos may be either ''measured'' ...
as the sounds alternately interfere constructively and destructively. As the two tones gradually approach unison, the beating slows down and may become so slow as to be imperceptible. As the two tones get further apart, their beat frequency starts to approach the range of human pitch perception, the beating starts to sound like a note, and a
is produced. This combination tone can also be referred to as a
missing fundamental
The pitch being perceived with the first harmonic being absent in the waveform is called the missing fundamental phenomenon.
It is established in psychoacoustics that the auditory system, with its natural tendency to distinguish a tone from anoth ...
, as the beat frequency of any two tones is equivalent to the frequency of their implied fundamental frequency.
Interferometry
Interferometry has played an important role in the advancement of physics, and also has a wide range of applications in physical and engineering measurement. The impact on physics and the applications span various types of waves.
Optical interferometry
Thomas Young's double slit interferometer in 1803 demonstrated interference fringes when two small holes were illuminated by light from another small hole which was illuminated by sunlight. Young was able to estimate the wavelength of different colours in the spectrum from the spacing of the fringes. The experiment played a major role in the general acceptance of the wave theory of light.
[
In quantum mechanics, this experiment is considered to demonstrate the inseparability of the wave and particle natures of light and other quantum particles (]wave–particle duality
Wave–particle duality is the concept in quantum mechanics that fundamental entities of the universe, like photons and electrons, exhibit particle or wave (physics), wave properties according to the experimental circumstances. It expresses the in ...
). Richard Feynman
Richard Phillips Feynman (; May 11, 1918 – February 15, 1988) was an American theoretical physicist. He is best known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics, the physics of t ...
was fond of saying that all of quantum mechanics can be gleaned from carefully thinking through the implications of this single experiment.
The results of the Michelson–Morley experiment
The Michelson–Morley experiment was an attempt to measure the motion of the Earth relative to the luminiferous aether, a supposed medium permeating space that was thought to be the carrier of light waves. The experiment was performed between ...
are generally considered to be the first strong evidence against the theory of a luminiferous aether
Luminiferous aether or ether (''luminiferous'' meaning 'light-bearing') was the postulated Transmission medium, medium for the propagation of light. It was invoked to explain the ability of the apparently wave-based light to propagate through empt ...
and in favor of special relativity
In physics, the special theory of relativity, or special relativity for short, is a scientific theory of the relationship between Spacetime, space and time. In Albert Einstein's 1905 paper, Annus Mirabilis papers#Special relativity,
"On the Ele ...
.
Interferometry has been used in defining and calibrating length standards. When the metre was defined as the distance between two marks on a platinum-iridium bar, Michelson and Benoît used interferometry to measure the wavelength of the red cadmium
Cadmium is a chemical element; it has chemical symbol, symbol Cd and atomic number 48. This soft, silvery-white metal is chemically similar to the two other stable metals in group 12 element, group 12, zinc and mercury (element), mercury. Like z ...
line in the new standard, and also showed that it could be used as a length standard. Sixty years later, in 1960, the metre in the new SI system was defined to be equal to 1,650,763.73 wavelengths of the orange-red emission line in the electromagnetic spectrum of the krypton-86 atom in a vacuum. This definition was replaced in 1983 by defining the metre as the distance travelled by light in vacuum during a specific time interval. Interferometry is still fundamental in establishing the calibration
In measurement technology and metrology, calibration is the comparison of measurement values delivered by a device under test with those of a calibration standard of known accuracy. Such a standard could be another measurement device of known ...
chain in length measurement.
Interferometry is used in the calibration of slip gauges (called gauge blocks in the US) and in coordinate-measuring machines. It is also used in the testing of optical components.[RS Longhurst, ''Geometrical and Physical Optics'', 1968, Longmans, London.]
Radio interferometry
In 1946, a technique called astronomical interferometry was developed. Astronomical radio interferometers usually consist either of arrays of parabolic dishes or two-dimensional arrays of omni-directional antennas. All of the telescopes in the array are widely separated and are usually connected together using coaxial cable
Coaxial cable, or coax (pronounced ), is a type of electrical cable consisting of an inner Electrical conductor, conductor surrounded by a concentric conducting Electromagnetic shielding, shield, with the two separated by a dielectric (Insulat ...
, waveguide
A waveguide is a structure that guides waves by restricting the transmission of energy to one direction. Common types of waveguides include acoustic waveguides which direct sound, optical waveguides which direct light, and radio-frequency w ...
, optical fiber
An optical fiber, or optical fibre, is a flexible glass or plastic fiber that can transmit light from one end to the other. Such fibers find wide usage in fiber-optic communications, where they permit transmission over longer distances and at ...
, or other type of transmission line
In electrical engineering, a transmission line is a specialized cable or other structure designed to conduct electromagnetic waves in a contained manner. The term applies when the conductors are long enough that the wave nature of the transmis ...
. Interferometry increases the total signal collected, but its primary purpose is to vastly increase the resolution through a process called 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. At each separation and ...
. This technique works by superposing (interfering) the signal waves from the different telescopes on the principle that waves that coincide with the same phase will add to each other while two waves that have opposite phases will cancel each other out. This creates a combined telescope that is equivalent in resolution (though not in sensitivity) to a single antenna whose diameter is equal to the spacing of the antennas farthest apart in the array.
Acoustic interferometry
An acoustic interferometer is an instrument for measuring the physical characteristics of sound waves in a gas or liquid, such velocity
Velocity is a measurement of speed in a certain direction of motion. It is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of physical objects. Velocity is a vector (geometry), vector Physical q ...
, wavelength, absorption, or impedance. A vibrating crystal
A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macros ...
creates ultrasonic waves that are radiated into the medium. The waves strike a reflector placed parallel to the crystal, reflected back to the source and measured.
See also
* Active noise control
Active noise control (ANC), also known as noise cancellation (NC), or active noise reduction (ANR), is a method for reducing unwanted sound by the addition of a second sound specifically designed to cancel the first. The concept was first deve ...
* Beat (acoustics)
In acoustics, a beat is an interference pattern between two sounds of slightly different frequencies, ''perceived'' as a periodic variation in volume whose rate is the difference of the two frequencies.
With tuning instruments that can produc ...
* Coherence (physics)
Coherence expresses the potential for two waves to Wave interference, interfere. Two Monochromatic radiation, monochromatic beams from a single source always interfere. Wave sources are not strictly monochromatic: they may be ''partly coherent''. ...
* Diffraction
Diffraction is the deviation of waves from straight-line propagation without any change in their energy due to an obstacle or through an aperture. The diffracting object or aperture effectively becomes a secondary source of the Wave propagation ...
* Haidinger fringes
* Interference lithography
Interference lithography (or holographic lithography) is a technique that uses coherent light (such as light from a laser) for patterning regular arrays of fine features without the use of complex optics, optical systems or photomasks.
Basic prin ...
* Interference visibility
* Interferometer
Interferometry is a technique which uses the '' interference'' of superimposed waves to extract information. Interferometry typically uses electromagnetic waves and is an important investigative technique in the fields of astronomy, fiber opt ...
* Lloyd's Mirror
* Moiré pattern
In mathematics, physics, and art, moiré patterns ( , , ) or moiré fringes are large-scale wave interference, interference patterns that can be produced when a partially opaque grating, ruled pattern with transparent gaps is overlaid on ano ...
* Multipath interference
In radio communication, multipath is the radio propagation, propagation phenomenon that results in radio signals reaching the receiving antenna (electronics), antenna by two or more paths. Causes of multipath include atmospheric ducting, ionosph ...
* Newton's rings
* Optical path length
In optics, optical path length (OPL, denoted ''Λ'' in equations), also known as optical length or optical distance, is the length that light needs to travel through a vacuum to create the same phase difference as it would have when traveling throu ...
* Thin-film interference
Thin-film interference is a natural phenomenon in which light waves reflected by the upper and lower boundaries of a thin film Interference (wave propagation), interfere with one another, increasing reflection at some wavelengths and decreasing it ...
* Rayleigh roughness criterion
* Upfade
References
External links
Easy JavaScript Simulation Model of One Dimensional Wave Interference
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{{DEFAULTSORT:Interference (Wave Propagation)
Wave mechanics
ca:Interferència (propagació d'ones)#Interferència òptica