PATH-LENGTH-RESOLVED DYNAMIC LIGHT SCATTERING IN HIGHLY SCATTERING RANDOM MEDIA : THE TRANSITION TO DIFFUSING WAVE SPECTROSCOPY

Dynamic light scattering ~DLS! has been used extensively during the past few decades for characterization of the structural and dynamical properties of materials that weakly scatter light @1,2#. DLS is based on measuring fluctuations in the intensity of the scattered light arising from phase and/or amplitude fluctuations induced by particle dynamics. This technique is applicable to media in which the detected light has scattered no more than once. In highly scattering materials the scattering angle and the polarization of the scattered wave are not well defined due to multiple scattering events and details about the sample properties are lost. However, the intensity of the multiply scattered light is accurately predicted by the photon diffusion equation and therefore the theory of diffusing wave spectroscopy ~DWS! can be applied for quantitative analysis of the angle averaged dynamic properties @3,4#. Although both DLS and DWS provide information about the structural and dynamical properties of the sample, they are only valid in the two extreme cases of single scattered and diffusive light respectively. Durian @5# and Kaplan et al. @6# have studied conditions under which DWS is valid, but still little is known about the intermediate regime between DLS and DWS. Since the detection of multiply scattered light causes degradation of image contrast and resolution in confocal @7# and optical coherence microscopy @8#, a clear understanding of the transition from ballistic to diffusive light will permit a quantitative analysis of scattering media that do not satisfy the single scattering or light diffusion criteria and can lead to the development of new techniques for image quality improvement. In this paper we show how low coherence interferometry ~LCI! can be used to make path-length-resolved measurements of particle Brownian motion within highly scattering media. LCI uses a coherence gate to select light that has traveled a specific path length in the medium. Thus it is possible to detect light that has scattered only once within a turbid medium and to apply DLS for the determination of the sample dynamical properties or to select only diffusive light and apply DWS theory. We experimentally demonstrate these two extremes in highly scattering samples of polystyrene microspheres, as well as the smooth transition between them. We show experimentally that this transition depends on the scattering properties of the medium and the measurement geometry. In particular, we find that the transition to the diffusing light regime occurs at shorter path lengths for either higher scattering anisotropy or a larger numerical aperture ~NA! of the collection optics. A schematic of our LCI system is shown in Fig. 1. The single-mode fiber optic interferometer is illuminated with an 850-nm superluminescent diode ~25-nm spectral bandwidth, 1.2-mW output power!. The optical properties of the sample generate a distribution of optical path lengths in the sample arm, while the path length in the reference arm is determined solely by the position of the retroreflector. Interference is observed only when the optical path-length difference between the reference and the sample arms is within the coherence length of the source. Thus a coherence gate is used to select specific path lengths within the sample. The amplitude of the interference signal is therefore proportional to the path-length-dependent reflection/scattering properties of the sample. In the single scattering regime the axial resolution is determined by the source coherence length, while the lateral resolution depends on the focusing optics. The position of the reference mirror ~retroreflector ! is adjusted in such a way as to align the coherence gate with the beam waist, thus optimizing the rejection of multiply scattered light @8#. As demonstrated in our previous studies @9#, particle dynamics of highly scattering media can be imaged and quantified in the single scattering regime with dynamic LCI by examining the intensity fluctuations of the backscattered light and extracting information from the photocurrent power spectrum. For a fixed position of the reference mirror of the