Interferometric visibility
1847015
223895372
2008-07-06T11:30:45Z
QuantumCyclops
7427173
/* See also */
The '''interferometric visibility''' (also known as "interference visibility" or "fringe visibility" or just "visibility") quantifies the contrast of [[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]] (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 "Mach-Zehnder visibility" 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>Visibility(real)=\frac{amplitude}{average}.</math>
This can also be rewritten as,
:<math>Visibility(real)=\frac{max-min}{max+min},</math>
where ''max'' is the maximum of the oscillations (also called fringes) and ''min'' the minimum of the oscillations. If two optical fields are identical (have the same colour, shape, direction, polarization, time profile, etc.) then the predicted visibility will be
:<math>Visibility(ideal)=\frac{2\sqrt{I_1I_2}}{I_1+I_2},</math>
where I 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: [[BEC]]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]]
==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]]
[[de:Interferenzkontrast]]