On the two-scale expansion of the fourth moment of a wave propagating in a random medium

A comprehensive and rigorous analysis of the prevalent version of the two-scale expansion used to solve the fourth-moment equation shows that it is not an asymptotic technique. The correct asymptotic version is derived and found to be analytically non-tractable. An elaborated interpretation to the correction terms used before is established and shows that an additional term of the same order was overlooked. The new expression which will improve the result in the scintillation peak is offered. The role of the small parameter of the problem is discussed.