Degree of First-order Coherence
Where <> denotes an ensemble (statistical) average. For non-stationary states, such as pulses, the ensemble is made up of many pulses. When one deals with stationary states, where the statistical properties do not change with time, one can replace the ensemble average with a time average. If we restrict ourselves to plane parallel waves then . In this case, the result for stationary states will not depend on, but on the time delay (or if ).
This allows us to write a simplified form
- where we now average over t.
In optical interferometers such as the Michelson interferometer, Mach-Zehnder interferometer, or Sagnac interferometer, one splits an electric field into two components, introduces a time delay to one of the components, and then recombines them. The intensity of resulting field is measured as a function of the time delay. The visibility of the resulting interference pattern is given by . More generally, when combining two space-time points from a field
- visibility=
The visibility ranges from zero, for incoherent electric fields, to one, for coherent electric fields. Anything in between is described as partially coherent.
Generally, and .
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