Statistical properties of dynamic speckles from flowing Brownian scatterers in the vicinity of the image plane in optical coherence tomography

A closed-form analytical expression is obtained for the spatio-temporal correlation function of the scattered radiation detected in fiber-based optical coherence tomography (OCT), assuming a clean optical system arrangement in the OCT sample arm. It is shown that the transverse flow component causes purely translational speckle motion with the predicted speckle velocity 2x higher than the velocity of the flowing particles as would be observed in the image plane under incoherent illumination. It is also shown that both speckle velocity and speckle radius do not depend on the position of the scattering volume relative to the focal plane, hence the derived correlation function is independent of the position of the scattering volume relative to the focal plane. Although the analytical results are obtained for a clean optical system arrangement, they can be used with high accuracy in most practical implementations of fiber based OCT. Validation experiments in control scattering phantoms with varying liquid viscosities show excellent agreement with the developed theoretical model, under both no-flow and flow conditions. Accurate viscosity determinations enabled by this methodology may have applications to non-invasive glucose measurements in medicine.