Multiple-scattering suppression by cross correlation

Abstract

We describe a new method for characterizing particles in turbid media by cross correlating the scattered intensity fluctuations at two nearby points in the far field. The cross-correlation function selectively emphasizes single scattering over multiple scattering. The usual dynamic light-scattering capability of inferring particle size from decay rate is thus extended to samples that are so turbid as to be visually opaque. The method relies on single-scattering speckle being physically larger than multiple-scattering speckle. With a suitable optical geometry to select nearby points in the far field or equivalently slightly different scattering wave vectors ͑of the same magnitude͒, the multiple-scattering contribution to the cross-correlation function may be reduced and in some cases rendered insignificant. Experimental results demonstrating the feasibility of this approach are presented.

Multiple-scattering suppression in dynamic light scattering based on a digital camera detection scheme

“…Such an approach has already been successfully demonstrated by Meyer et al 14 with the scheme based on cross-correlation of scattered intensities detected by two spatially separated fibers.…”

“…The techniques are called two color DLS (TCDLS) 11,12 and three dimensional DLS (3DDLS) 3,12 respectively and the latter one is available commercially 13 . Another cross-correlation approach uses a single-beam two-detector configuration 14,15 . Suppression of multiple scattering is based on a consequence of the van CittertZernike theorem 16 , which states that intensity correlations in an observation region are closely related to the Fourier transform of the intensity distribution across the source.…”

Electric field autocorrelation functions for beginning multiple Rayleigh scattering

“…For a typical dynamic light-scattering experiment 30 with ϭ 0.5145 m, a ϭ 0.05 m, R ave Ϸ 2 mm, m ϭ 1.333, and n ϭ 1.2 corresponding to polystyrene latex ͑PSL͒ spheres in water, Eq. ͑34͒ becomes Q Ϸ 860f.…”

Role of multiple scattering in cross-correlated light scattering with a single laser beam

“…Such detectors have not often been considered because of concerns that they record a large range of values, causing instrumental broadening. Only a singlescattered momentum transfer is recorded, and instrumental broadening is thereby avoided, however, if either bare-end monomode optical fibers coupled to detectors are placed on the paraxial focal line of the index-matching vat 27,28 or if gradient-index lenses are cemented onto the end of the monomode fibers placed far from the vat. 29 For these two geometries, all singly scattered light reaching the detectors has the same scattering angle ͑i.e., ϭ 90°͒ and thus the same scattered momentum transfer.…”

“…The system that we study here consists of a single laser beam and two closely spaced detectors with wide fields of view. [27][28][29] It is shown that multiply scattered light should cease being cross correlated for small detector spacings, whereas singly scattered light ceases being cross correlated for larger detector spacings. Thus if two monomode optical fibers coupled to detectors are positioned beyond the multiple-scattering threshold separation but lie within the single-scattering threshold separation, the multiple-scattering contribution to the cross-correlation function should be strongly suppressed with respect to the singlescattering contribution.…”