Speckle patterns in small angle light scattering: The spatial autocorrelation function

Abstract

The study deals with the determination of the spatial autocorrelation function of speckle patterns caused by the small-angle light scattering from polymer films. The autocorrelation function determines the shape, size and anisometry of the speckle. The effect of the inner structure and orientation of samples (polypropylene foil, poly(decamethylene terephthalate) and a sample of polypropylene filaments) is discussed; it is shown that under the usual experimental conditions the spatial autocorrelation function of speckle patterns can be determined on the basis of the van Cittert-Zernike theorem of the classical coherence theory. The good agreement between the theoretical and experimental dependences of anisometry, the angular dependence of speckle size and the dependence of speckle size on the sample thickness confirm the suitability of a uniform description based on the classical theory of coherence. From the standpoint of the theory of speckle effect, the results presented in this study allow us to infer that in the light scattering from polymer films under usual conditions the assumptions of the application of the central limit theorem are fulfilled: in the scattering volume there is a sufficient number of scattering units, and path fluctuations due to the scattering foil exceed the wavelength of light.