… subjects that often appear to be well understood and perhaps even a little old-fashioned have frequently some surprises in store for us.

—E. Wolf [249]

The *mutual coherence* of the optical field is

where *E*(**r**, *t*) is the electric field at spatial position **r** and time *t*. For simplicity, we ignore the polarization of the field, which could be accounted for by a tensor-valued mutual coherence. The angular brackets signify the expected value of the terms contained over an ensemble of identical physical systems. The mutual coherence and related functions described in this section are of interest because

- Mutual coherence, like the irradiance but unlike the electric field, is observable. The mutual coherence can be completely described by measuring the irradiance at a suitable range of sampling points.
- Mutual coherence, like the electric field but unlike the irradiance, can be calculated over a volume given its value on a boundary. The mutual coherence at the input to an optical system uniquely determines the mutual coherence at the output. In Chapter 4 we derived input/output transformations for the electric field in imaging systems. In ...

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