en>Jeldering: Add citation to Coppel for exponential dichotomy.

2014-08-18T19:47:17Z

Add citation to Coppel for exponential dichotomy.

← Older revision		Revision as of 21:47, 18 August 2014
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	~~{{merge to\|Degree of coherence\|date=September 2013}}~~		She is known by the title of Myrtle Shryock. What I adore performing is performing ceramics but I haven't made a dime with it. North Dakota is our birth place. I am a meter reader.<br><br>Feel free to visit my webpage - std testing at home [[http://nuvem.tk/altergalactica/AliceedMaurermy resource for this article]]
	The '''interferometric visibility''' (also known as "interference visibility" or "fringe visibility" or just "visibility") quantifies the contrast of [[Interference (wave propagation)\|interference]] in any system which has wave-like properties, such as [[optics]], [[quantum mechanics]], water waves, or electrical signals. Generally, two or more waves are combined and as the phase between them is changed (e.g. in an [[interferometer]]) the [[power (physics)\|power]] or [[intensity (physics)\|intensity]] (probability or population in [[quantum mechanics]]) of the resulting wave oscillates (forming an interference pattern). The ratio of the size or [[amplitude]] of these oscillations to the sum of the powers of the individual waves is defined as the visibility.

	~~==Visibility in optics==~~
	In linear optical [[interferometer]]s like the [[Mach-Zehnder interferometer]], [[Michelson interferometer]], and [[Sagnac interferometer]] interference manifests itself as oscillations in the outgoing intensity, also called "fringes". Under these circumstances, the interferometric visibility is also known as the "Michelson visibility" <ref>http://scienceworld.wolfram.com/physics/FringeVisibility.html</ref> or the "fringe visibility." For this type of interference, the sum of the intensities (or powers) of the two interfering waves equals the average of ~~the fringes. It follows that the visibility can be written as,~~

	~~:<math>\text{Visibility}(\text{real})=\frac{\text{amplitude}}{\text{average}}~~.~~</math>~~

	~~This can also be rewritten as~~

	~~:<math>\text{Visibility}(\text{real})=\frac{\max-\min}{\max+\min},</math>~~

	where max is the maximum of the oscillations and min the minimum of the oscillations. If the two optical fields are ideally [[monochromatic]] (consist of only single wavelength) point sources then the predicted visibility will be

	~~:<math>\text{Visibility}(\text{ideal}) = \frac{2\sqrt{I_1I_2}}{I_1+I_2},</math>~~

	where <math>I_1</math> and <math>I_2</math> indicates the intensity of the respective wave. Any dissimilarity between the optical fields will decrease the visibility from the ideal. In this sense, the visibility is a ~~measure of the [[Coherence (physics)\|coherence]] between two optical fields~~. ~~A more general formula for this~~ is ~~given by the [[degree of coherence]]. This definition of interference directly applies to the interference of water waves and electric signals~~.

	~~[[Image:visibility.png\|left\|thumb\|Visibility in~~ a ~~Mach-Zehnder, Michelson or Sagnac interferometer~~.]]
	[[Image:double slit visibility.png\|thumb\|Visibility is similarly defined in double-slit interference. However, now the max and min vary across the interference pattern. The example shows a visibility of 80% (i.e. 0.8).]]

	<br ~~style="clear:both" /~~>

	~~==Visibility in quantum mechanics==~~
	Since the [[Schrödinger equation]] is a [[wave equation]] and all objects can be considered waves in [[quantum mechanics]], interference is ubiquitous. Some examples: [[Bose-Einstein condensate]]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 interferometer]]s.~~

	[[Image:HOM visibility.png\|thumb\|Visibility in [[Hong–Ou–Mandel interference]]. At large delays the photons do not interfere. At zero delays, the detection of coincident photon pairs is suppressed.]]

	~~==See also==~~
	*[[degree of coherence]]
	*[[interferometry]]
	*[[optical interferometry]]
	*[[List of types of interferometers]]
	*[[~~Hong–Ou–Mandel effect]]~~

	~~== References ==~~
	~~<references />~~

	~~==External links==~~
	*[http://~~www.physics.berkeley~~.~~edu~~/~~research~~/~~packard/Competition/Gyros/LaserRingGyro/Steadman/StedmanReview1997.pdf Stedman Review of the Sagnac Effect]~~

	~~[[Category:Interferometers]]~~
	~~[[Category:Interferometry]]~~
	~~[[Category:Optics~~]]

en>Zfeinst: fix LaTeX parsing error

2011-10-09T22:24:09Z

fix LaTeX parsing error

New page

{{merge to|Degree of coherence|date=September 2013}}
The '''interferometric visibility''' (also known as "interference visibility" or "fringe visibility" or just "visibility") quantifies the contrast of [[Interference (wave propagation)|interference]] in any system which has wave-like properties, such as [[optics]], [[quantum mechanics]], water waves, or electrical signals. Generally, two or more waves are combined and as the phase between them is changed (e.g. in an [[interferometer]]) the [[power (physics)|power]] or [[intensity (physics)|intensity]] (probability or population in [[quantum mechanics]]) of the resulting wave oscillates (forming an interference pattern). The ratio of the size or [[amplitude]] of these oscillations to the sum of the powers of the individual waves is defined as the visibility.

==Visibility in optics==
In linear optical [[interferometer]]s like the [[Mach-Zehnder interferometer]], [[Michelson interferometer]], and [[Sagnac interferometer]] interference manifests itself as oscillations in the outgoing intensity, also called "fringes". Under these circumstances, the interferometric visibility is also known as the "Michelson visibility" <ref>http://scienceworld.wolfram.com/physics/FringeVisibility.html</ref> or the "fringe visibility." For this type of interference, the sum of the intensities (or powers) of the two interfering waves equals the average of the fringes. It follows that the visibility can be written as,

:<math>\text{Visibility}(\text{real})=\frac{\text{amplitude}}{\text{average}}.</math>

This can also be rewritten as

:<math>\text{Visibility}(\text{real})=\frac{\max-\min}{\max+\min},</math>

where max is the maximum of the oscillations and min the minimum of the oscillations. If the two optical fields are ideally [[monochromatic]] (consist of only single wavelength) point sources then the predicted visibility will be

:<math>\text{Visibility}(\text{ideal}) = \frac{2\sqrt{I_1I_2}}{I_1+I_2},</math>

where <math>I_1</math> and <math>I_2</math> indicates the intensity of the respective wave. Any dissimilarity between the optical fields will decrease the visibility from the ideal. In this sense, the visibility is a measure of the [[Coherence (physics)|coherence]] between two optical fields. A more general formula for this is given by the [[degree of coherence]]. This definition of interference directly applies to the interference of water waves and electric signals.

[[Image:visibility.png|left|thumb|Visibility in a Mach-Zehnder, Michelson or Sagnac interferometer.]]
[[Image:double slit visibility.png|thumb|Visibility is similarly defined in double-slit interference. However, now the max and min vary across the interference pattern. The example shows a visibility of 80% (i.e. 0.8).]]

<br style="clear:both" />

==Visibility in quantum mechanics==
Since the [[Schrödinger equation]] is a [[wave equation]] and all objects can be considered waves in [[quantum mechanics]], interference is ubiquitous. Some examples: [[Bose-Einstein condensate]]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 interferometer]]s.

[[Image:HOM visibility.png|thumb|Visibility in [[Hong–Ou–Mandel interference]]. At large delays the photons do not interfere. At zero delays, the detection of coincident photon pairs is suppressed.]]

==See also==
*[[degree of coherence]]
*[[interferometry]]
*[[optical interferometry]]
*[[List of types of interferometers]]
*[[Hong–Ou–Mandel effect]]

== References ==
<references />

==External links==
*[http://www.physics.berkeley.edu/research/packard/Competition/Gyros/LaserRingGyro/Steadman/StedmanReview1997.pdf Stedman Review of the Sagnac Effect]

[[Category:Interferometers]]
[[Category:Interferometry]]
[[Category:Optics]]

Exponential dichotomy - Revision history

en>Jeldering: Add citation to Coppel for exponential dichotomy.

en>Zfeinst: fix LaTeX parsing error