Dynamic light scattering arising from flowing Brownian particles: analytical model in optical coherence tomography conditions

Abstract

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.

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

“…(11) of Ref [12]. In Ref [12], this expression for τ t was derived analytically at only the position of the scattering volume at the Gaussian beam waist; and in Ref [13], using numerical methods, the same expression was shown to be valid not only at the beam waist but also within several Rayleigh ranges of it. The present paper uses a purely analytical approach, and the derived expression for τ t is valid for any displacement from the beam waist.…”

“…The familiar Gaussian form of this term is an approximation, and can be viewed as a zeroth-order term of the Hermite functions expansion [15] of the Fourier transform of the source laser spectral density. As shown in [12] , in the single scattering regime, the spatio-temporal correlation function C s of radiation scattered from flowing Brownian particles (point scatterer model) can be represented as the product of the contributions of Brownian motion C sb and translational motion due to flow C st (provided that l c /2, w 0 >> λ/(2π)):…”

“…in the centre of the fiber end face, Eqs. (11), (12), and (13) yield the following for the temporal correlation function of Eq. (2):…”

“…(4), the resulting combination of the Gaussian beam radius and wavefront curvature cancels out the dependence on z 1 . Therefore, in this singlescattering point scatterer model [12], the correlation properties of the spatio-temporal correlation function (the second exponential term in Eq. (11)) do not depend on the position of the scattering volume relative to the beam waist.…”

“…Since OCT yields depth resolved measurements, it is important to get the solution of the scattering problem not only for the exact focal plane of the optical system used, but also in its vicinity, specifically within several Rayleigh ranges of it. In our recent efforts, an ABCD ray tracing matrix methodology was introduced to obtain numerical solutions of the scattering problem for a number of frequently used optical imaging geometries in the OCT sample arm [12,13]. However, it is preferable to have a closed-form analytical expression for the spatio-temporal correlation function of the scattered radiation.…”