Rainfall-induced optical phase fluctuations in the atmosphere

Tatarski's spectral expansion technique of optical fields is applied to calculate the phase variance, mutual coherence function, and phase-difference temporal power spectrum of an optical wave propagating through rainfall. The analysis includes the effects of a distribution of rain droplet sizes and their associated terminal velocities. The general features of the associated phase statistics are discussed, and numerical results are presented as a function of the rainfall rate. It is shown that for up to moderate rainfall conditions (i.e., approximately equal to or less than 4 mm/h) the lateral phase coherence of the wave is not significantly degraded for a propagation path of the order of a kilometer. It follows that under these conditions (moderate and less) rainfall will not pose serious limitations to coherent optical systems such as laser radars. In particular, in contrast to clean-air turbulence, rain-induced phase degradations will not limit the aperature size of coherent optical systems in many practical situations. In addition, the theory presented here predicts that for low-cross-wind speed conditions the high-frequency portion of the temporal-phase-difference power spectrum varies as f to the -7th power, where f is the frequency. This behavior has been seen experimentally.