Abstract

Laser beam propagation through fog or cloud is a problem of considerable interest. Although numerical solutions of the radiative transfer equation are available for the case of plane wave incidence, only very few numerical solutions are calculated for the beam wave case because of the formidable amount of computation time required. The small-angle approximation has been shown to be useful for lightwave propagation in turbulent media where the variance of index of refraction fluctuations is small. However, its applicability to turbid media with discrete scatterers is not clear because of the much larger contrast in the index of refraction. The small-angle approximation is used to calculate the beam wave solution through foggy atmospheres at visible wavelengths. The Henyey-Greenstein phase function is used to describe the scattering characteristics of the particles. The mutual coherence function is first calculated and then the intensity and the specific intensities are calculated. Numerical results are illustrated as a function of optical thickness and the mean cosine of scattering angles. They are compared with available exact numerical solutions of the transport equations and are also used to explain the results observed in laboratory experimental data.

© 1986 Optical Society of America