The statistical model of scattered by flowing Brownian particles coherent radiation is suggested. The model includes the random Doppler shifts caused by particle Brownian motion and the speckle fluctuations caused primarily by the flow motion of particles. Analytical expressions are obtained for the correlation function, power spectrum, and spectral width of scattered radiation in the imaging geometry typically used in optical coherence tomography (OCT). It is shown that the spectral density has the Voigt shape, a well-known spectral profile from atomic and molecular spectroscopy. The approach enables the choice of the experimental regimes for the measurement of Brownian particle motion parameters even in the presence of flow. These regimes are characterized by the dominant contribution of Brownian motion in the spectral width of the flow-caused Doppler shift component. Further, the new formalism suggests that prior attempts to extract transverse flow velocity are only valid at near-perpendicular geometry. The impact of the small scattering volume contributing to the OCT signal is also discussed.

Abstract:The probability density function (PDF) of light scattering intensity can be used to characterize the scattering medium. We have recently shown that in optical coherence tomography (OCT), a PDF formalism can be sensitive to the number of scatterers in the probed scattering volume and can be represented by the K-distribution, a functional descriptor for non-Gaussian scattering statistics. Expanding on this initial finding, here we examine polystyrene microsphere phantoms with different sphere sizes and concentrations, and also human skin and fingernail in vivo. It is demonstrated that the K-distribution offers an accurate representation for the measured OCT PDFs. The behavior of the shape parameter of Kdistribution that best fits the OCT scattering results is investigated in detail, and the applicability of this methodology for biological tissue characterization is demonstrated and discussed.

The distribution of backscattered intensities as described by the probability density function (PDF) of tissue-scattered light contains information that may be useful for tissue assessment and diagnosis, including characterization of its pathology. In this Letter, we examine the PDF description of the light scattering statistics in a well characterized tissue-like particulate medium using optical coherence tomography (OCT). It is shown that for low scatterer density, the governing statistics depart considerably from a Gaussian description and follow the K distribution for both OCT amplitude and intensity. The PDF formalism is shown to be independent of the scatterer flow conditions; this is expected from theory, and suggests robustness and motion independence of the OCT amplitude (and OCT intensity) PDF metrics in the context of potential biomedical applications.

The study of flowing Brownian particles finds numerous biomedical applications, ranging from blood flow analysis to diffusion research. A mathematical model for the correlation function of laser radiation scattered by flowing Brownian particles measured with fiber-based optical coherence tomography (OCT), which accounts for the effects of sample arm optics, is presented. It is shown that the parameters of an OCT optical system of any complexity can be taken into account by using the ABCD ray tracing matrix approach. Specifically, the impact of any optical system can be characterized by the changes in the effective beam radius, which replaces the Gaussian beam radius in the existing mathematical models of scattered radiation. It is shown that the validity of the developed ABCD matrix formalism is governed by the condition that the source coherence length is much smaller than the Rayleigh range in the sample. The predictions of the developed model are compared with previously published theories and with experimental data and agree well with the latter.

Abstract: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.