A simple, analytic, geometrical optics expression for the variance of the beam displacements caused by propagation through weak refractive turbulence described by the Kolmogorov spectrum is presented. The analytical formula includes the effect of the divergence or convergence of the initial beam. The formula is compared with numerical results obtained from a more complicated expression including effects of diffraction and strong path-integrated turbulence. The simple geometrical optics expression holds for apertures larger than the Fresnel zone size and larger than the ratio of the square of the Fresnel zone to the phase coherence length.
© 1990 Optical Society of America
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