  Expressions of the correlation between the log-amplitude and the phase of a
wavefront propagating through the atmospheric turbulence are presented. These
expressions are useful to evaluate the feasibility of proposed methods to
increase the confidence level of the detection of faint transient astronomical
objects. The properties of the derived angular correlation functions are
discussed using usual synthetic turbulence profiles. 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.
