Averages in optical coherence: resolving the Magyar and Mandel-Wolf paradox

The ubiquity of optical coherence arising from its importance in everything from astronomy to photovoltaics means that underlying assumptions such as stationarity and ergodicity can become implicit. When these assumptions become implicit, it can appear that two different averages are independent: the finite time averaging of a detector and the ensemble average of the optical field over multiple detections. One of the two types of averaging may even be ignored. We can observe coherence as an interference fringe pattern and learn properties of the field through both methods of averaging but the coherence will not be the same, as demonstrated by the Magyar and Mandel-Wolf paradox.