Abstract

The variance of the wander of an optical beam in the turbulent atmosphere is calculated using a geometric optics calculation. A uniform beam of diameter D and focal range F is assumed to propagate a distance L through the atmosphere. A geometric optics calculation and several reasonable physical assumptions lead to a simple integral expression for the one-axis wander variance. If turbulence strength ${\text{C}}_n^2$ is constant along the path and the beam does not come to a focus between the transmitter and receiver, the integral can be evaluated to $0.97C_n^2{\text{D}}^{-1/3}{L}^3{}_2{F}_1(1/3,1;4;L/F)$, where ₂f₁ is the hypergeometric function. This expression reduces to the expected results for collimated beams (L/F infinite) and focused beams (L/F unity). The geometric optics expression is shown to be valid for D larger than the Fresnal zone and also larger than the ratio of the square of the Fresnel zone to the lateral coherence length.

© 1989 Optical Society of America