Radiative Transfer Limits of Two-Frequency Wigner Distribution for Random Parabolic Waves

The present note establishes the self-averaging, radiative transfer limit for the two-frequency Wigner distribution for classical waves in random media. Depending on the ratio of the wavelength to the correlation length the limiting equation is either a Boltzmann-like integral equation or a Fokker-Planck-like differential equation in the phase space. The limiting equation is used to estimate three physical parameters: the spatial spread, the coherence length and the coherence bandwidth. In the longitudinal case, the Fokker-Planck-like equation can be solved exactly.