Multiple Light Scattering using 3rd Order Correlations Functions

Multiple light scattering provides a non-invasive method for probing the structure of optically opaque materials such as aqueous foam, colloids and sand. Diffusion-wave spectroscopy (DWS) examines the intensity fluctuations of the speckle pattern to extract dynamical information about the scattering sites. When many, uncorrelated scattering sites are present, the electric field is a random Gaussian variable, and the dynamics are easily determined from the second order intensity correlation function g². g²)(tau = 1 + beta(absolute value of ((E less than (0)E*(tau)greater than)²)/ (absolute value of (less than EE*greater than)²)g²)(tau = 1 + beta(absolute value of (gamma(tau))²) This crucial relation relates the measured g² with the electric field auto-correlation function gamma(tau), which can then be expressed in terms of the scattering site dynamics. It is not possible, however, to tell whether the Gaussian approximation is valid by inspection of g² alone. Recently, a method has been developed to test whether the scattering is Gaussian by measuring higher order intensity correlation functions. In this experiment we measured the third order intensity correlation function g³ for aqueous foam (Gillette Foamy Regular) and compared it with the Gaussian prediction for g³. g(3) (tau₁, tau₂) = 1 + beta₁ (absolute value of (gamma₀₁)² absolute value of ((gamma₀₂² absolute value of ((gamma₁₂)² + 2beta₂ Re(gamma₀₁)(gamma₁₂)(gamma₂₀). Preliminary data indicate that the scattering is Gaussian to sixth order in the electric field.