Spatial and temporal distribution measurements of atmospheric coherence length by moiré deflectometry with double cross gratings.

The atmospheric coherence length reflects turbulence effects and is a crucial parameter for atmospheric propagation and adaptive optics. In this paper, moiré deflectometry based on double-cross gratings has, for the first time to our knowledge, been implemented to achieve the measurements of the spatial-temporal distribution of atmospheric coherence length. Initially, the theoretical relationship between phase and atmospheric coherence length is established. Subsequently, the phase information is extracted from the grid moiré fringes captured in the experiment. Based on this, the spatial-temporal distribution of atmospheric coherence length can finally be obtained. The results are in good agreement with typical values calculated by other methods, which verify their reliability and superiority. In other words, the related outcomes expand the potential of moiré deflectometry with cross gratings, which opens up new possibilities for its application in the study of atmospheric turbulence properties.