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

TL;DR

This paper examines the Magyar and Mandel-Wolf paradox in optical coherence, highlighting how different averaging methods can lead to different coherence measurements due to underlying assumptions like stationarity and ergodicity.

Contribution

It clarifies the implications of implicit assumptions in optical coherence measurements and resolves the paradox by analyzing the differences between finite time and ensemble averages.

Findings

Finite time and ensemble averages can yield different coherence values.

The paradox arises from implicit assumptions of stationarity and ergodicity.

Understanding these differences is crucial for accurate optical coherence analysis.

Abstract

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.