Measurement of smoothed Wigner phase-space distributions for small-angle scattering in a turbid medium

We study Wigner phase-space distributions W (x, p) in position (x) and momentum (p) for light undergoing multiple small-angle scattering in a turbid medium. Smoothed Wigner phase-space distributions are measured by using a heterodyne technique that achieves position and momentum resolution determined by the width and the diffraction angle of the local oscillator beam. The sample consists of 5.7-micron-radius polystyrene spheres suspended in a water-glycerol mixture. The momentum distribution of the transmitted light is found to contain a ballistic peak, a narrow diffractive pedestal, and a broad background. The narrow diffractive pedestal is found to decay more slowly than the ballistic peak as the concentration of scatterers is increased. The data are in excellent agreement with a simple theoretical model that explains the behavior of the narrow pedestal by including multiple diffractive scattering and treating large-angle scattering as a loss.