Spatial stationarity of statistical optical fields for coherence holography and photon correlation holography

The spatial stationarity of scattered optical fields constitutes a basic premise of coherence holography and photon correlation holography. Nevertheless, spatial stationarity seems to have attracted less attention and still remains a less familiar concept than temporal stationarity because it has been a common practice in statistical optics to assume temporal ergodicity and replace the ensemble average with the time average, rather than the space average. To form the theoretical basis for coherence holography and photon correlation holography, an investigation is made into the spatial stationarity of the statistical optical field, and combinations of a light source and an optical system are identified that can create spatially stationary scattered fields. The result justifies the principles of coherence holography and photon correlation holography, and the previously reported experiments.