Modulation of Laser Beams by Atmospheric Turbulence - Depth of Modulation*

We have studied the fluctuations produced in a laser beam by atmospheric turbulence over transmission paths up to 2400 feet long as a function of size of receiving aperture, range, and atmospheric conditions. The depth of modulation decreases rapidly with increasing size of receiving aperture for apertures smaller than the direct beam. It does not go to zero, however, but rather levels off at an approximately constant, finite value for apertures larger than the direct beam. When all of the direct beam is collected, the depth of modulation varies approximately with the 3/2 power of range from about 100 to 2400 feet, the largest range used. At ranges less than about 100 feet, however, the dependence is consistently much less than 3/2. These results are independent of weather conditions, of time of day, of local conditions along the path, of whether the transmitter is inside or outside a building, of a twofold change in diameter of the launched beam, of whether the range is a straight pass or is multiply-folded, and of mirror separation in the multiply-folded arrangement. The 3/2 dependence is consistent with near-field scattering theory and leads to an estimate for the lower bound of the effective scale size of turbulence of 5 centimeters. The depth of modulation, however, depends sensitively on atmospheric conditions; in a time of the order of seconds the value can change as much as an order of magnitude. We have systematically measured depth of modulation of the direct beam simultaneously with wind velocity and variability, temperature gradients, and time of day. No simple dependence on these variables was found.