Spatial Stationarity of Statistical Optical Fields for Correlation Holography

Abstract

The concept of the ensemble average plays a key role in coherence theory and statistical optics in general. Since the ensemble average is a conceptual quantity defined mathematically in terms of the probability and the ensemble, it needs be associated with a physical quantity that is observable by experiment. It is common practice to replace the ensemble average with the time average, assuming that the statistical field is stationary and ergodic in time [1]. This assumption is justifiable in many cases of practical interest, such as partially coherent illumination in microscopy and thermal light analyzed by Fourier spectroscopy. Such a system of traditional statistical optics based on temporal stationarity and temporal ergodicity may be called temporal statistical optics to distinguish it from spatial statistical optics to be discussed in this paper.