Correlation between the phase and the log-amplitude of a wave through the vertical atmospheric propagation
I present expressions of the correlation between the log-amplitude and the phase of a wavefront propagating through the atmospheric turbulence. The properties of the angular correlation functions are discussed using usual synthetic turbulence profiles. The theoretical study is completed by practical implementations that can be envisioned to determine and eventually compensate the effects of the fluctuations of the intensity during the astronomical observations. The close formulation between the phase and the log-amplitude allows an analytic formulation in the Rytov approximation. Equations contain the product of an arbitrary number of hypergeometric functions that are evaluated using the Mellin transforms integration method.