Multiple scattering effects on coherent bandwidth and pulse distortion of a wave propagating in a random distribution of particles

In this paper, integral and differential equations are derived for the two-frequency mutual coherence function in a random distribution of stationary and moving particles. The differential equation is then solved for a plane wave case, and the coherent bandwidth is obtained for both the weak and strong fluctuation cases. Using the two-frequency correlation function, the output pulse shape is calculated for different particle densities. When the optical distance is small compared with unity, the pulse shape is substantially unchanged, but a long tail develops. When the optical distance is large, the coherent bandwidth is reduced and considerable pulse spread and delay occur. Numerical calculations are given for a nanosecond optical pulse propagating through cloud. It is shown that in dense cloud (density 0.5×10⁹m^-3), the pulse delay and spread are 3 and 1.28 μsec respectively over a distance of 5 km. This agrees with available experimental data.