Coherence is the degree to which the difference in phase between two or more waves is constant over some region of time or space.

Beams of wave radiation from two sources are said to be mutually coherent when the difference between the phases of the two waves is constant. Coherence is necessary for the observation of interference, as in Thomas Young's slit experiment. In an interference experiment, the signal power (square of the wave amplitude) will be constant provided the phase difference between interfering waves does not change.

Perfect self-coherence describes the case when the phase difference of all waves in some beam of radiation is constant over all time and space. Maximally incoherent radiation is the superposition of waves such that the phase difference between interfering waves is random. Then the phase of the entire signal, the superposition of waves, is ill-defined. Most natural radiation has intermediate coherence.

Very coherent and very incoherent signals are commonly obtained in the laboratory. Sources of thermal noise commonly produce very incoherent radiation. For example, blackbodies emit incoherent light; similarly, a source of acoustic white noise radiates incoherent sound waves, and the Johnson noise in a resistor produces incoherent electrical signals. On the other hand, slitted screens and beam splitters are used to produce multiple beams that are mutually coherent. Highly coherent (i.e. self-coherent) light is most often obtained from lasing devices (lasers, masers, etc.). Stimulated emission, the process by which lasers amplify a given light frequency, duplicates the phase and frequency of an incoming photon in two outgoing photons. All photons produced then share a common phase, together comprising a very coherent laser beam.

Coherence length and coherence time are quantities which describe the interval of length or time for which the coherence of a beam of waves is acceptably high for a given purpose. The coherence time of a beam with a bandwidth of frequencies [b.delta ] is approximately equal to 1/[b.delta ]ƒ.