coherence

View more Science videos

The attribute of two or more waves, or parts of a wave, whose relative phase is constant during the resolving time of the observer. The concept has been developed most extensively in optics, but is applicable to all wave phenomena.

Consider two waves, with the same mean angular frequency ω, given by Eqs. (1) and (2). It is convenient, and no restriction,
1.

2.
to choose both A and B real. These expressions as they stand could describe de Broglie waves in quantum mechanics. For real waves, such as components of the electric field in light or radio beams, or the pressure oscillations in sound, it is necessary to retain only the real parts of these and subsequent expressions. The frequency spectrum is assumed to be narrow, in the sense that a Fourier analysis of expressions (1) and (2) gives appreciable contributions only for angular frequencies close to ω. This assumption means that, on the average, δ_A(t) and δ_B(t) do not change much per period. See also Electromagnetic radiation; Quantum mechanics; Sound.

Suppose that the waves are detected by an apparatus with resolving time T, that is, T is the shortest interval between two events for which the events do not seem to be simultaneous. For the human eye and ear, T is about 0.1 s, while a fast electronic device might have a T of 10⁻¹⁰ s. If the relative phase δ(t), given by Eq. (3), does not, on the average, change noticeably during
3.
T, then the waves are coherent. If during T there are sufficient random fluctuations for all values of δ(t), modulus 2π, to be equally probable, then the waves are incoherent. If during T there are noticeable random fluctuations in δ(t), but not enough to make the waves completely incoherent, then the waves are partially coherent. These distinctions are not useful unless T is specified. On the one hand, only waves that have existed forever and that fill all of space can have absolutely fixed frequency and phase. On the other hand, two independent sound waves in the phases change appreciably in 0.01 s would seem incoherent to the human ear, but would seem highly coherent to a fast electronic device.

The degree of coherence is related to the interference patterns that can be observed when the two beams are combined. See also Interference of waves.

Coherence is also used to describe relations between phases within the same beam. Suppose that a wave represented by Eq. (1) is passing a fixed observer characterized by a resolving time T. The phase δ_A may fluctuate, perhaps because the source of the wave contains many independent radiators. The coherence time Δt_W of the wave is defined to be the average time required for δ_A(t) to fluctuate appreciably at the position of the observer. If Δt_W is much greater than T, the wave is coherent; if Δt_W is of the order of T, the wave is partially coherent; and if Δt_W is much less than T, the wave is incoherent. These concepts are very close to those developed above.

Extended sources give partial coherence and produce interference fringes with visibility V less than unity. A. A. Michelson exploited this fact with his stellar interferometer, a modified double-slit arrangement with movable mirrors that permit adjustment of the effective separation D′ of the slits. It can be shown that if the source is a uniform disk of angular diameter θ, then the smallest value of D′ that gives zero V is 1.22λ/θ. The same approach has also been applied in radio astronomy. A different technique, developed by R. Hanbury Brown and R. Q. Twiss, measures the correlation between the intensifies received by separated detectors with fast electronics. See also Interferometry.

Because they are highly coherent sources, lasers and masers provide very large intensities per unit frequency. See also Laser.

Photon statistics is concerned with the probability distribution describing the number of photons incident on a detector, or present in a cavity. By extension, it deals with the correlation properties of beams of light.

According to the quantum theory of electromagnetism, quantum electrodynamics, light is made up of particles called photons, each of which possesses an energy E of ℏω, where ℏ is Planck's constant divided by 2π and ω is the angular frequency of the light (the frequency multiplied by 2π). In general, however, the photon number is an intrinsically uncertain quantity. It is impossible to precisely specify both the phase φ = ωt of a wave and the number of photons n ≈ E/(ℏω) that it contains; the uncertainties of these two conjugate variables must satisfy . For a beam to be coherent in the sense of having a well-defined phase, it must not be describable in terms of a fixed number of particles. (Lacking a fixed phase, a single photon may interfere only with itself, not with other photons.) See also Photon; Quantum electrodynamics.

The most familiar example of this uncertainty is shot noise, the randomness of the arrival times of individual photons. There is no correlation between photons in the coherent state emitted by a classical source such as an ideal laser or radio transmitter, so the number of photons detected obeys Poisson statistics, displaying an uncertainty equal to the square root of the mean. The shot noise constitutes the dominant source of noise at low light levels, and may become an important factor in optical communications as well as in high-precision optical devices (notably those that search for gravitational radiation). See also Distribution (probability); Electrical noise.

noun

Logical agreement among parts: congruity, consistence, consistency. See agree/disagree.

Definition: agreement
Antonyms: disagreement, incoherence, incongruity, nonsense, unintelligibility

LearnThatWord.com is a free vocabulary and spelling program where you only pay for results!

• Order, Hierarchy, and Systems - coherence: logical or natural consistency

Look up coherence, coherency, or coherent in Wiktionary, the free dictionary.

Coherence, coherency, or coherent can refer to:

Contents 1 In physics 2 In mathematics 3 In financial economics 4 In philosophy 5 In computational science 6 As name of IT products 7 Other uses 8 See also

In physics

• Coherence (physics)
• Coherence time

In mathematics

• Mutual coherence (linear algebra), sometimes referred to as coherence
• Coherence (philosophical gambling strategy), a concept in Bayesian statistics
• Coherence (signal processing)
• Coherence (statistics)
• Coherence condition
• Coherent sampling, a relationship used in Fast Fourier Transforms
• Coherent sheaf

In financial economics

• Coherent risk measures, a class of risk measures

In philosophy

• Coherentism is an epistemological theory
• There is also the coherence theory of truth

In computational science

• Cache coherence, a special case of memory coherence
• Coherence (programming language), an experimental programming language based upon Subtext
• Memory coherence, a concept in computer architecture

As name of IT products

• Coherence (software), a component of Parallels Desktop for Mac, the Windows virtualization software
• Coherence (UPNP), some free DLNA/UPnP tools (MediaServer/MediaRender) with a Python framework
• Coherent (operating system), a UNIX-clone operating system
• Oracle Coherence, an in-memory data grid product from Oracle

Other uses

• Coherence (cognitive science), a property of mental/cognitive states
• Coherence (linguistics), what makes a text semantically meaningful
• Coherence (music theory), a synonym for strict Rothenberg propriety in diatonic set theory
• Coherence time (communications systems), duration when a communication channel can be assumed to be constant
• Coherent (company), a company specializing in equipment to make and measure coherent light

See also

• Cohesion (disambiguation)
• Mutual coherence (disambiguation)

This disambiguation page lists articles associated with the same title. If an internal link led you here, you may wish to change the link to point directly to the intended article.

This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)