Temporal and spatial coherence

The electric field (associated with a wave) at a point changes in phase with time.  Let deltaphi be the phase change in a small interval of time deltat. is directly proportional to deltat, for any value of delta, then the wave is said to have ideal temporal coherence.  In practice, no beam will have ideal temporal coherence.  Instead, this proportionality exists over an interval      , the coherence time (O<Δ<ґ).  If the interval exceeds ґ the proportionality condition will be violated.

Spatial coherence refers to the coherence between the vibrations at different points on a plane    perpendicular to the direction of beam.  The beam is said to have perfect spatial coherence if the phase of vibrations at any two points on such are by a constant value.  In practice, no beam will have perfect spatial coherence.  Then coherence will be seen to exist over a small area around a point.  Such an area can be taken as a measure of the spatial coherence existing in the them.

The waves at two points are space coherent if they preserve a constant phase difference over an interval of time.  This is possible even when two beams are individually time incoherent, as long as any phase change in one of the beams is accompanied by a simultaneous equal phase change in the other beam.  Young's double-slit experiment is example.  With ordinary light sources, space coherence is achieved if the two beams are produced from the same part of the source.

Time coherence is a characteristic of a single beam of light whereas space coherence concerns the relationship between two separate beams of light normally.

Coherent Sources

The sources of light are said to be mutually coherent if they emit light waves of the same wavelength and amplitude with a constant phase difference between them.

Two independent sources can never be mutually coherent.  A source of light consists of a large number of atoms and each atom consists of a central nucleus around which revolve electrons in various definite orbits.  In an excited state an electron occupies a higher energy orbit and so the atom becomes unstable.  The electron spontaneously falls back to the inner orbit within 10 8  s and in doing so will emit light pulses.  The emission of light pulses from various atoms is random and there is an constant phase relationship between two pulses.  So two independent sources or two parts of the same source cannot act as coherent sources.  Two slits illuminated by monochromatic light from a single slit can be used as coherent sources, since any phase change in one of the beams is accompanied by simultaneous equal phase change in the other beam.