The most familiar example of this uncertainty is shot noise, the randomness of the arrival times of individual photons. (Lacking a fixed phase, a single photon may interfere only with itself, not with other photons.) See Photon, Quantum electrodynamics 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. It is impossible to precisely specify both the phase &phgr = &ohgr t of a wave and the number of photons n &ap E/(ℏ&ohgr ) that it contains the uncertainties of these two conjugate variables must satisfy Δ nΔ&phgr ≥ &half. In general, however, the photon number is an intrinsically uncertain quantity. By extension, it deals with the correlation properties of beams of light.Īccording to the quantum theory of electromagnetism, quantum electrodynamics, light is made up of particles called photons, each of which possesses an energy E of ℏ&ohgr, where ℏ is Planck's constant divided by 2&pgr and &ohgr is the angular frequency of the light (the frequency multiplied by 2&pgr ). Photon statistics is concerned with the probability distribution describing the number of photons incident on a detector, or present in a cavity. See Interferometryīecause they are highly coherent sources, lasers and masers provide very large intensities per unit frequency. Twiss, measures the correlation between the intensifies received by separated detectors with fast electronics. The same approach has also been applied in radio astronomy. 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. 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. These concepts are very close to those developed above.Įxtended sources give partial coherence and produce interference fringes with visibility V less than unity. If Δ t W is much greater than T, the wave is coherent if Δ t W is of the order of T, the wave is partially coherent and if Δ t W is much less than T, the wave is incoherent. The coherence time Δ t 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. The phase δ A may fluctuate, perhaps because the source of the wave contains many independent radiators. (1) is passing a fixed observer characterized by a resolving time T. See Interference of wavesĬoherence is also used to describe relations between phases within the same beam. The degree of coherence is related to the interference patterns that can be observed when the two beams are combined. 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. On the one hand, only waves that have existed forever and that fill all of space can have absolutely fixed frequency and phase. These distinctions are not useful unless T is specified. 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. If during T there are sufficient random fluctuations for all values of δ( t), modulus 2&pgr, to be equally probable, then the waves are incoherent. (3) does not, on the average, change noticeably during T, then the waves are coherent. If the relative phase δ( t), given by Eq. 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.

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. See Electromagnetic radiation, Quantum mechanics, Sound This assumption means that, on the average, δ A( t) and δ B( t) do not change much per period.

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 &ohgr. 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. These expressions as they stand could describe de Broglie waves in quantum mechanics. It is convenient, and no restriction, to choose both A and B real.

Coherence definition