Coherence
The description of diffraction relies on the interference of waves emanating from the same source taking different paths to the same point on a screen. In this description, the difference in phase between waves that took different paths is only dependent on the effective path length. This does not take into account the fact that waves that arrive at the screen at the same time were emitted by the source at different times. The initial phase with which the source emits waves can change over time in an unpredictable way. This means that waves emitted by the source at times that are too far apart can no longer form a constant interference pattern since the relation between their phases is no longer time independent.
The length over which the phase in a beam of light is correlated, is called the coherence length. In order for interference to occur, the path length difference must be smaller than the coherence length. This is sometimes referred to as spectral coherence, as it is related to the presence of different frequency components in the wave. In the case of light emitted by an atomic transition, the coherence length is related to the lifetime of the excited state from which the atom made its transition.
If waves are emitted from an extended source, this can lead to incoherence in the transversal direction. When looking at a cross section of a beam of light, the length over which the phase is correlated is called the transverse coherence length. In the case of Young's double slit experiment, this would mean that if the transverse coherence length is smaller than the spacing between the two slits, the resulting pattern on a screen would look like two single slit diffraction patterns.
In the case of particles like electrons, neutrons and atoms, the coherence length is related to the spatial extent of the wave function that describes the particle.
Read more about this topic: Diffraction
Famous quotes containing the word coherence:
“Twentieth-century art may start with nothing, but it flourishes by virtue of its belief in itself, in the possibility of control over what seems essentially uncontrollable, in the coherence of the inchoate, and in its ability to create its own values.”
—A. Alvarez (b. 1929)
“Art and ideology often interact on each other; but the plain fact is that both spring from a common source. Both draw on human experience to explain mankind to itself; both attempt, in very different ways, to assemble coherence from seemingly unrelated phenomena; both stand guard for us against chaos.”
—Kenneth Tynan (1927–1980)
“When the coherence of the parts of a stone, or even that composition of parts which renders it extended; when these familiar objects, I say, are so inexplicable, and contain circumstances so repugnant and contradictory; with what assurance can we decide concerning the origin of worlds, or trace their history from eternity to eternity?”
—David Hume (1711–1776)