  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.
