Correlation functions of singly and multiply scattered light analysed by the 3-D cross-correlation technique

Abstract

The 3-D cross-correlation method is a light-scattering technique, which allows to separate the singly scattered light from the multiple scattering contributions. The intensities and the time-correlation functions for both, the singly and multiply scattered light, are determined by evaluating the scattering intensity, the auto-correlation function and the 3-D cross-correlation function. The 3-D cross-correlation function is determined by the single scattering only. We report experiments on solutions of Latex (126 nm, transmission 7–99%) at different scattering angles (30–150°) in a cylindrical sample and at various positions in a square sample. The field-correlation function of the multiply scattered light is determined as difference of the auto-correlation function, corrected for the detector deficiencies, and the 3-D cross-correlation function. The cross-correlation function is a single exponential with the angle dependence, characteristic for particle diffusion. The first cumulant of the multiple-scattering correlation function is given by the angle averaged exponent of the single-scattering correlation function multiplied by the average number of the scattering events along the light-path; it is found to be almost independent of the scattering angle and of the position inside the sample, even if double scattering is the major multiple scattering contribution. The spurious dependencies of the diffusion coefficient from concentration, scattering angle and location in the sample obtained from the analysis of the auto-correlation function are explained quantitatively.