Two-color cross-correlation in small-angle static light scattering

We have measured by means of a charge-coupled device sensor the space correlation function between two speckle fields at different wavelengths. The fields are generated from the scattering of a two-color laser beam from a stationary, three-dimensional sample. In general, the speckle fields attain their maximum degree of correlation when the scattering angles are properly scaled according to a grating dispersion rule. The degree of correlation, however, depends both on the thickness of the sample and on its turbidity. At a given angle, the degree of cross-correlation diminishes as the thickness is increased, and it also decreases as the turbidity grows. Working formulas are derived, and we show that the dependence from the sample turbidity is related to the spread in photon paths. A comparison with the photon path spread calculated by means of a multiple-scattering Monte Carlo simulation will be presented. The connection between the present work and studies on polychromatic light diffraction from random two-dimensional transparencies and microwave transmission through thick samples will also be presented.