First and Second Moment of an Optical Wave Propagating in a Random Medium: Equivalence of the Solution of the Dyson and Bethe-Salpeter Equation to That Obtained by the Huygens-Fresnel Principle*

It is demonstrated, through terms of second order in the fluctuating part of the index of refraction, that the first and second statistical moment, as obtained from the Dyson and the Bethe-Salpeter equation, respectively, of an optical wave propagating in a random medium are identical to that obtained directly from the extended Huygens-Fresnel principle.