Coherence (physics)
Coherence is a property of waves that measures the ability of the waves to interfere with each other. Two waves that are coherent can be combined to produce constructive and destructive interference (an interference pattern) depending on the relative phase of the waves at their meeting point. Waves that are incoherent, when combined, do not produce an interference pattern.
A wave can also be coherent with itself, a property known as temporal coherence. If a wave is combined with a delayed copy of itself (as in a Michelson interferometer), the duration of the delay over which it produces interference is known as the coherence time of the wave, Δtc. From this, a corresponding coherence length can be calculated:
The temporal coherence of a wave is related to the spectral bandwidth of the source. A truly monochromatic (single frequency) wave would have an infinite coherence time and length. In practice, no wave is truly monochromatic (since this requires a wavetrain of infinite duration), but in general, the coherence time of the source is inversely proportional to its bandwidth.
Waves also have the related property of spatial coherence; this is the ability of any one spatial position of the wavefront to interfer with any other spatial position. Young's double-slit experiment relies on spatial coherence of the beam illuminating the two slits; if the beam was spatially incoherent, no interference pattern would be seen.
Light waves produced by a laser are often highly coherent (though the degree of coherence depends strongly on the exact properties of the laser). For example, a stabilised helium-neon laser can produce light with coherence lengths in excess of 5 m. Light from common sources (such as light bulbs) has a very short coherence length (~1 μm), and can be considered totally incoherent for most purposes. Spatial coherence of laser beams also manifests itself as speckle patterns.