Optical pulses in atmospheric turbulence

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Abstract
Rytov’s method is generalized so that it can be applied to the time-dependent wave equation. The method is used to obtain an expression for a pulsed spherical wave that has propagated through atmospheric turbulence. The expression contains two terms. One term represents scattering by refractive-index inhomogeneities located on a direct line between the transmitter and receiver. The other term arises from the time-varying dimensions of the scattering volume of the pulsed wave and represents scattering by inhomogencities located on the surface of a prolate spheroid. Under appropriate conditions, the surface scattering can be neglected, so that if the pulse shape does not change significantly over times on the order of the period of the carrier frequency, the pulse shape will be preserved after transmission through the turbulence. In this case, the fluctuations depend upon only the carrier frequency. The statistics of the direct-line term are shown to be identical to the statistics for the monochromatic spherical wave. The surface and direct-line terms remain correlated for only a very short period during the beginning of the pulse.

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