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The interferometric visibility (also known as interference visibility and fringe visibility, or just visibility when in context) is a measure of the contrast of ''
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 ...
'' in any system subject to
wave 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 tha ...
. Examples include as
optics Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of optical instruments, instruments that use or Photodetector, detect it. Optics usually describes t ...
,
quantum mechanics Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...
, water waves, sound waves, or electrical signals. Visibility is defined as the ratio of the
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 ...
of the
interference pattern In physics, interference is a phenomenon in which two coherent waves are combined by adding their intensities or displacements with due consideration for their phase difference. The resultant wave may have greater amplitude (constructive int ...
to the sum of the powers of the individual waves. The interferometric visibility gives a practical way to measure the
coherence 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 ...
of two waves (or one wave with itself). A theoretical definition of the coherence is given by the
degree of coherence In quantum optics, correlation functions are used to characterize the statistical and Coherence (physics), coherence properties – the ability of waves to interfere – of electromagnetic radiation, like optical light. Higher order coherence or ...
, using the notion of correlation. Generally, two or more waves are superimposed and as the phase difference between them varies, the
power Power may refer to: Common meanings * Power (physics), meaning "rate of doing work" ** Engine power, the power put out by an engine ** Electric power, a type of energy * Power (social and political), the ability to influence people or events Math ...
or
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 ...
(probability or population in
quantum mechanics Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...
) of the resulting wave oscillates, forming an interference pattern. The
pointwise In mathematics, the qualifier pointwise is used to indicate that a certain property is defined by considering each value f(x) of some Function (mathematics), function f. An important class of pointwise concepts are the ''pointwise operations'', that ...
definition may be expanded to a visibility function varying over time or space. For example, the phase difference varies as a function of space in a two-slit experiment. Alternately, the phase difference may be manually controlled by the operator, for example by adjusting a vernier knob in an
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 ...
.


Visibility in optics

In linear optical
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 (like the
Mach–Zehnder interferometer The Mach–Zehnder interferometer is a device used to determine the relative phase shift variations between two collimated beams derived by splitting light from a single source. The interferometer has been used, among other things, to measure p ...
,
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
Sagnac interferometer The Sagnac effect, also called Sagnac interference, named after French physicist Georges Sagnac, is a phenomenon encountered in interferometry that is elicited by rotation. The Sagnac effect manifests itself in a setup called a ring interferometer ...
), interference manifests itself as
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 ...
oscillations Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum ...
over time or space, also called '' fringes''. Under these circumstances, the interferometric visibility is also known as the "Michelson visibility" or the "fringe visibility." For this type of interference, the sum of the intensities (powers) of the two interfering waves equals the average intensity over a given time or space domain. The visibility is written as: :\nu=A/\bar, in terms of the amplitude
envelope An envelope is a common packaging item, usually made of thin, flat material. It is designed to contain a flat object, such as a letter (message), letter or Greeting card, card. Traditional envelopes are made from sheets of paper cut to one o ...
of the oscillating intensity and the average intensity: :A=(I_\max-I_\min)/2, :\bar=(I_\max+I_\min)/2. So it can be rewritten as: :\nu=\frac, where ''I''max is the maximum intensity of the oscillations and ''I''min the minimum intensity of the oscillations. :I_=I_ + I_+2*\sqrt*, \gamma , , :I_=I_ + I_-2*\sqrt*, \gamma , , If the two optical fields are ideally
monochromatic A monochrome or monochromatic image, object or palette is composed of one color (or values of one color). Images using only shades of grey are called grayscale (typically digital) or black-and-white (typically analog). In physics, mon ...
(consist of only single wavelength) point sources of the same polarization, then the predicted visibility will be :\nu=\frac, where I_1 and I_2 indicate the intensity of the respective wave. \gamma indicates the phase relationship of the original electric field. Any dissimilarity between the optical fields will decrease the visibility from the ideal. In this sense, the visibility is a measure of the
coherence 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 ...
between two optical fields. A theoretical definition for this is given by the
degree of coherence In quantum optics, correlation functions are used to characterize the statistical and Coherence (physics), coherence properties – the ability of waves to interfere – of electromagnetic radiation, like optical light. Higher order coherence or ...
. This definition of interference directly applies to the interference of water waves and electric signals.


Examples

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Visibility in quantum mechanics

Since 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 ...
is a
wave equation The wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields such as mechanical waves (e.g. water waves, sound waves and seismic waves) or electromagnetic waves (including light ...
and all objects can be considered waves in
quantum mechanics Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...
, interference is ubiquitous. Some examples:
Bose–Einstein condensate In condensed matter physics, a Bose–Einstein condensate (BEC) is a state of matter that is typically formed when a gas of bosons at very low Density, densities is cooled to temperatures very close to absolute zero#Relation with Bose–Einste ...
s can exhibit interference fringes. Atomic populations show interference in a Ramsey interferometer. Photons, atoms, electrons, neutrons, and molecules have exhibited interference in double-slit interferometers.


See also

*
Degree of coherence In quantum optics, correlation functions are used to characterize the statistical and Coherence (physics), coherence properties – the ability of waves to interfere – of electromagnetic radiation, like optical light. Higher order coherence or ...
*
Interferometry Interferometry is a technique which uses the ''interference (wave propagation), interference'' of Superposition principle, superimposed waves to extract information. Interferometry typically uses electromagnetic waves and is an important inves ...
*
Optical interferometry 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 opti ...
*
List of types of interferometers An interferometry, interferometer is a device for extracting information from the superposition of multiple waves. Field and linear interferometers *Air-wedge shearing interferometer *Astronomical interferometer / Michelson stellar interferomet ...
* Hong–Ou–Mandel effect


References


External links


Stedman Review of the Sagnac Effect
Interferometry