Two-frequency mutual coherence function, coherence bandwidth, and coherence time of millimeter and optical waves in rain, fog, and turbulence

Propagation characteristics of pulse waves in rain, fog, and turbulence are determined by a two-frequency mutual coherence function. Parabolic differential equations applicable to strong fluctuation cases are derived for the two-frequency mutual coherence function for randomly distributed scatterers and turbulence. These equations are solved for the plane wave case using the eigenfunction-eigenvalue method. Numerical calculations are given for millimeter waves (100 GHz) and optical waves (0.6943 and 10.6 μm) in rain, fog, and turbulence over the distance of 5 km. The coherence bandwidths are found to be in the range of MHz for millimeter waves (100 GHz) in heavy rain (25 mm/hr) and for optical waves in fog, and considerable distortion of pulse shape may result in these situations. For other cases, the effect on pulse shape distortion may be negligibly small.