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. @en

We demonstrate wavenumber-dependent DLS-OCT measurements of collective and self-diffusion coefficients in concentrated silica suspensions across a broad $q$-range, utilizing a custom home-built OCT system. Depending on the sample polydispersity, either the collective or self-diffusion is measured. The measured collective-diffusion coefficient shows excellent agreement with hard-sphere theory and serves as an effective tool for accurately determining particle sizes. We employ the decoupling approximation for simultaneously measuring collective and self-diffusion coefficients, even in sufficiently monodisperse suspensions, using a high-speed Thorlabs OCT system. This enables particle size and volume fraction determination without the necessity of wavenumber-dependent measurements. We derive a relationship between the particle number-based polydispersity index and the ratio of self and collective mode amplitudes in the autocorrelation function and utilize it to measure the particle number-based polydispersity index. Notably, the polydispersity determined in this manner demonstrates improved sensitivity to smaller particle sizes compared to the standard intensity-based DLS cumulant analysis performed on dilute samples.@en

We demonstrate wavenumber-dependent DLS-OCT measurements of collective and self-diffusion coefficients in concentrated silica suspensions across a broad q-range, utilizing a custom home-built OCT system. Depending on the sample polydispersity, either the collective or self-diffusion is measured. The measured collective-diffusion coefficient shows excellent agreement with hard-sphere theory and serves as an effective tool for accurately determining particle sizes. We employ the decoupling approximation for simultaneously measuring collective and self-diffusion coefficients, even in sufficiently monodisperse suspensions, using a high-speed Thorlabs OCT system. This enables particle size and volume fraction determination without the necessity of wavenumber-dependent measurements. We derive a relationship between the particle number-based polydispersity index and the ratio of self and collective mode amplitudes in the autocorrelation function and utilize it to measure the particle number-based polydispersity index. Notably, the polydispersity determined in this manner demonstrates improved sensitivity to smaller particle sizes compared to the standard intensity-based DLS cumulant analysis performed on dilute samples.

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We quantify the precision and bias of dynamic light scattering optical coherence tomography (DLS-OCT) measurements of the diffusion coefficient and flow speed for first and second-order normalized autocovariance functions. For both diffusion and flow, the measurement precision and accuracy are severely limited by correlations between the errors in the normalized autocovariance function. We demonstrate a method of mixing statistically independent normalized autocovariance functions at every time delay for removing these correlations. The mixing method reduces the uncertainty in the obtained parameters by a factor of two but has no effect on the standard error of the mean. We find that the precision in DLS-OCT is identical for different averaging techniques but that the lowest bias is obtained by averaging the measured correlation functions before fitting the model parameters. With our correlation mixing method, it is possible to quantify the precision in DLS-OCT and verify whether the Cramer-Rao bound is reached.

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We show number fluctuations dynamic light scattering optical coherence tomography (OCT) for measuring extremely slow, sub-diffusion flows of dilute particle suspensions. Our method removes the minimum measurable velocity limitation of conventional correlation-based or phase-resolved Doppler OCT, set by flowing particles’ Brownian motion. Our technique works for any Doppler angle, is applicable to 2D flow imaging with scanning OCT systems and can be used to determine concentration of particles under flow.

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We show number fluctuations dynamic light scattering optical coherence tomography (OCT) for measuring extremely slow, sub-diffusion flows of dilute particle suspensions. Our method removes the minimum measurable velocity limitation of conventional correlation-based or phase-resolved Doppler OCT, set by flowing particles’ Brownian motion. Our technique works for any Doppler angle, is applicable to 2D flow imaging with scanning OCT systems and can be used to determine concentration of particles under flow.

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We have implemented number fluctuation dynamic light scattering optical coherence tomography (OCT) for measuring extremely slow, sub-diffusion flows of dilute particle suspensions using the second-order autocovariance function. Our method has a lower minimum measurable velocity than conventional correlation-based OCT or phase-resolved Doppler OCT, as the velocity estimation is not affected by the particle diffusion. Similar to non-dilute correlation-based OCT, our technique works for any Doppler angle. With our analysis we can quantitatively determine the concentration of particles under flow. Finally, we demonstrate 2D sub-diffusion flow imaging with a scanning OCT system at high rate by performing number fluctuation correlation analysis on subsequent B-scans@en

We show scanning dynamic light scattering optical coherence tomography (OCT) omnidirectional flow measurements. Our method improves the velocity measurement limit over conventional correlation-based or phase-resolved Doppler OCT by more than a factor of 2. Our technique is applicable without a-priori knowledge of the flow geometry as our method works both for non-zero Doppler angle and non-ideal scan alignment. In addition, the method improves the particle diffusion coefficient estimation for particles under flow.

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We report on omnidirectional flow measurements using B-scan correlationbased OCT. Our method extends velocity measurement limits of OCT and provides improvements over the conventional correlation-based or phase-resolved Doppler flow measurement techniques.

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We show scanning dynamic light scattering optical coherence tomography (OCT) omnidirectional flow measurements. Our method improves the velocity measurement limit over conventional correlation-based or phase-resolved Doppler OCT by more than a factor of 2. Our technique is applicable without a-priori knowledge of the flow geometry as our method works both for non-zero Doppler angle and non-ideal scan alignment. In addition, the method improves the particle diffusion coefficient estimation for particles under flow.

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