Dynamic speckle spatial coherence measurements utilizing a single-mode optical-fiber probe

Abstract

The spatial coherence functions for light scattered by a suspension of particles undergoing Brownian motion are interrogated with a single-mode optical-fiber interferometer. The exposed core of a single-mode optical fiber is utilized as a mobile pointlike probe of the scattered optical field. Two such fiber probes, together with a three-coupler heterodyne interferometer, are used to measure the spatial coherence of fluctuations in the scattered light intensity, the heterodyne carrier amplitude, the intensity-weighted phase rate (IWPR), and the phase rate. Spatial coherence measurements for coherent particle motion are also presented for the IWPR and the phase rate. A theoretical analysis of the spatial coherence functions is developed and compared with the experimental results. The coherence function for fluctuations in the intensity and the IWPR that is due to Brownian particle motion exhibits a Gaussian functional form with a coherence lengths ξc of ~2 ± 1.2 μm at 1.0 kHz. This result is in good agreement with the theoretical result of 1.5 ± 0.9 μm based on the scattering volume dimensions and scattering geometry. Measurements of the phase-rate spatial coherence function for Brownian motion were inaccessible because of signal-to-noise-ratio limitations associated with the signal-processing electronics. The IWPR measurements for coherent particle motion exhibit a bandwidth-dependent coherence function, having a background level of 0.74 and a coherence length ξc of 4.5 μm at 1.8 kHz. The phase-rate coherence function for coherent particle motion was constant with a value of 0.5.