Advancements in dynamic light scattering optical coherence tomography particle sizing and flowmetry

This thesis explores the application of dynamic light scattering optical coherence tomography (DLS-OCT) for in-line particle sizing and flow measurements in particle suspensions. DLS-OCT is capable of measuring the depth-resolved particle diffusion coefficient, which can then be converted into particle size. This capability is particularly advantageous for in-line particle sizing scenarios, where the suspension is under flow, and the depth-resolved particle diffusion coefficient can be separated from the flow contribution. However, there are several other challenges associated with DLS-OCT, such as measuring: at high particle concentrations, in fast and slow flows, in multiple scattering media, and quantifying the measurement uncertainty. These challenges are addressed in this thesis.

In concentrated suspensions, the relationship between particle size and the diffusion coefficient is not well described by the simple Stokes-Einstein equation and the diffusion becomes dependent on multiple factors. Accurate determination of particle size necessitates diffusion coefficient measurements across a wide range of wavenumbers and the application of sophisticated rheological models. In Chapter 2, we address this issue with a broadband DLS-OCT system covering the wavelength range of 350–1000 nm. By inverting hard-sphere rheological models, we successfully measured the particle size and polydispersity in very dense nanoparticle suspensions. Furthermore, we demonstrated the applicability to particle sizing in suspensions that are not suitable for standard DLS-OCT measurements and showed how measurements of different diffusion modes can assess the number-based particle size polydispersity in concentrated suspensions.

DLS-OCT measurement of high flow speeds and small particle sizes in fastflowing suspensions is problematic due to detector sampling limitations, as the rapid decay of the autocorrelation function prevents the extraction of flow speed and particle size information. To address this, in Chapter 3, we showed the incorporation of beam scanning—a standard feature in many OCT systems—to extend the capabilities of DLS-OCT flow imaging beyond its current limitations and improve particle sizing in flowing suspensions. This approach allowed us to demonstrate a two-fold improvement in the flow velocity dynamic measurement range and more accurate particle size measurement deeper within the flow channel, away from the edges. These advancements are beneficial for in-line pharmaceutical and process industry particle sizing applications, where diffusion and mixing near the edges are slower, leading to overestimation of particle size.

Particle Brownian motion imposes limitations on the minimum flow speeds measurable in particle suspensions using DLS-OCT. In Chapter 4, we address this challenge by introducing the concept of number fluctuations to DLS-OCT. This innovation enabled the successful measurement of sub-diffusion flow speeds and particle concentrations in dilute particle suspensions, both in 1D and 2D. By extending the capability of DLS-OCT, this development also facilitates the measurement of the beam shape within the particle suspension, a task traditionally requiring complex calibration in conventional OCT systems.

In Chapter 5, we demonstrate the application of number-fluctuation DLS-OCT for measuring simultaneous 2D flow profiles in organ-on-chip (OoC) devices, overcoming limitations of conventional Doppler OCT and DLS-OCT in low-flow environments. A numerical method was employed to equalize axial and transverse OCT resolutions, eliminating the dependence on Doppler angles in the autocorrelation function and enabling accurate measurement of absolute flow velocities. Additionally, we implemented particle image velocimetry (PIV) on the OCT data to complement numberfluctuation measurements with precise in-plane velocity vector maps. This chapter underscores the effectiveness of number-fluctuation DLS-OCT in biomedical imaging, particularly for measuring extremely small flow speeds and addressing flow direction variability within OoC devices.

The lack of readily available theoretical models for estimating the uncertainty in DLS-OCT measurements of diffusion and flow is a challenge addressed in Chapter 6. We conducted a detailed assessment of precision and bias in DLS-OCT measurements, revealing that errors in autocorrelation coefficients are strongly correlated over time, which complicates accurate quantification of uncertainty in particle size and flow speed measurements. To address this challenge, we introduced a novel method of mixing different autocorrelation functions at the same time delay. This approach effectively eliminates error correlations and enables us to achieve precision levels approaching the Cramer-Rao lower bound. This advancement allows for reliable quantification of particle size and flow speed uncertainties using DLS-OCT, which is crucial for applications in the process industry where maximizing precision is essential.

Multiple scattering in DLS-OCT complicates accurate particle sizing as the models assume single backscattering. In Chapter 7, we propose a simple method to simulate multiple scattering effects on particles undergoing Brownian motion. Through simulations and experimental measurements, we demonstrated that the autocorrelation functions exhibit double-exponential decay in the multiple scattering regime. We employed a double-exponential autocorrelation fit model for all depths, significantly enhancing both the depth range of reliable particle sizing using the singlescattering model. In addition, we can perform particle sizing in the diffusing-wave spectroscopy (DWS) limit of the decorrelation rate.

The final Chapter 8 summarizes the key contributions of this thesis to particle sizing and flow measurements using DLS-OCT. It also discusses potential future research directions aimed at improving the accuracy and expanding the applicability of DLS-OCT across various sectors of the process industry.