Theory of Remote Sensing of Clear-Air Turbulence Profiles*

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Abstract
A method is presented for determining the profile of atmospheric turbulence along the line of sight to a star or other plane-wave light source. The spectral density of the refractive-index fluctuations is assumed to be a product of a known function of the turbulent wavenumber, Φn(0) (K), and an unknown function of position along the line of sight, Cn2(z). We demonstrate that Tatarski’s formula for calculating the correlation function of the fluctuations of the logarithmic amplitude of a plane electromagnetic wave, Bx(ρ), from Cn2(z) is actually an integral equation for Cn2(z) with a unique solution. Consequently, the turbulence profile, Cn2(z), may be calculated by taking an integro-differential transform of the correlation function, Bx(ρ). For Kolmogorov turbulence the kernel of the transform contains a confluent hypergeometric function. This result suggests that it may be possible to determine the magnitude and position of distant turbulence from a measurement of the correlation function of light which has passed through the turbulence.

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