Theoretical properties of the autocovariance of wavefront curvature induced by atmospheric turbulence and their potential for Cn2 profiling

Abstract

ABSTRACT Remote measurements of optical turbulence profiles $C_\mathrm{ \mathit{ n}}^2(h)$ in the Earth atmosphere are nowadays performed from the spatial autocovariance of either scintillation or the wavefront slope. Here, I theoretically study the properties of the spatio-angular autocovariance of the wavefront curvature induced by optical turbulence, assuming the von Kármán model for the complex amplitude fluctuations. The width of the curvature autocovariance function is approximately 10 times smaller than that of the scintillation and 1000 times smaller than that of the wavefront slope. Thus, a significant enhancement of the attainable altitude resolution of turbulence profiles is expected from the spatio-angular autocovariance of the curvature. The curvature autocovariance amplitude is proportional to $C_\mathrm{ \mathit{ n}}^2(h)$ and also depends on the turbulence altitude h and on the turbulence inner scale l0. A simple procedure disentangles those dependencies and leads to $C_\mathrm{ \mathit{ n}}^2(h)$ and also to the inner scale profile l0(h).