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.

For a long time, the resolution of light microscopy was restricted to approximately 200 nm, as described by Abbe’s diffraction limit. Single-Molecule Localization Microscopy (SMLM) overcomes this limit by capturing many frames of a sample labeled with blinking fluorophores, where each frame shows a different subset of molecules. The fluorophores are located by fitting a model of their point spread function (PSF) and these localizations are combined to create an image with 20-50 nm resolution. Localizing a fluorophore is only possible when no other fluorescent molecules are active in the surrounding diffraction-limited area so that its PSF appears as an isolated blob. However, high-density regions unavoidably contain overlapping PSFs, which lead to localization errors as the number of emitters in the region of interest is unknown. To prevent this, the density of active fluorophores is typically kept between 0.01-0.1 μm−2 and data acquisition can take up to days, making dynamic imaging impossible. This theoretical research explores the possibility of enabling high-density SMLM by using Single-Photon Avalanche Diode (SPAD) arrays, detecting every incident photon with picosecond timing precision, instead of capturing the total intensity in a 10-100 ms interval like the conventionally used sCMOS cameras. The photon arrival times from simulated SPAD measurements are used to determine the number of emitters in the field of view, which is directly related to the second-order quantum coherence of the signal. This coherence can be calculated by dividing the arrival times into discrete time bins and convoluting the signal with itself. To correct the number of emitters for the bias that is introduced by the discretization of the data, an analytical expression is derived and validated with simulations. Using this correction, the number of Alexa647 fluorophores can be determined from a 0.1 ms simulated measurement with a relative standard error of 1% independent of emitter count, using a laser intensity of 330 kWcm−2 and 100% detection efficiency. Considering an experimental setting in which 10 kWcm−2 intensity and 10% detection efficiency are more realistic, a 1.5 s measurement is needed to obtain the same accuracy, and a 15 ms interval is required to obtain a standard error of 10%. The newly acquired information about the number of emitters will make it possible to locate fluorophores with overlapping point spread functions for multi-emitter fitting. Consequently, SPAD arrays will provide the ability to image high emitter densities, which enables faster data acquisition and dynamic imaging.

This thesis explores advanced computational techniques in super-resolution microscopy (SRM), with the primary goal of pushing the limits of achievable resolution towards the 1 nm scale. It includes developments in particle fusion algorithms, data analysis of complex biological structures, and exploration of the impact of molecular dipole orientation on MINFLUX localization accuracy and precision.

In the first part, we present a novel fast particle fusion method tailored to single molecule localization microscopy (SMLM). This method first registers particles based on Joint Registration of Multiple Point Clouds (JRMPC) and then classifies and reconnects misaligned locally optimally clustered sets of particles. This approach significantly reduces computational cost compared to earlier template free methods in particular for a large number of particles.. This advancement enables more detailed and accurate reconstructions of super-particles, enhancing the capabilities of SMLM.

The second part of the dissertation deals with a data analysis of nuclear pore complexes (NPCs) reconstructed by the earlier developed particle fusion technique. By fusing thousands of NPCs labeled at nucleoporin Nup96 and analyzing the high-resolution reconstructions, we reveal intricate details of the NPC structure, in particular the unit structure of Nup96. This analysis showcases the potential of SRM in combination with advanced data analysis to contribute to structural biology on the length scale below 10 nm.

The third part focuses on the influence of the dipole orientation on the localization accuracy and precision of MINFLUX. We simulate the imaging process with a physically realistic vector diffraction Point Spread Function (PSF) model and then localize the emitters based on the simplified Gaussian doughnut PSF model used in MINFLUX so far. Our study, including dipoles with free and fixed orientations and key simulation parameters, reveals the need for more refined modeling to overcome the bias, especially for fixed dipole orientations and background fluorescence. This investigation helps to understand the limitations of MINFLUX in its current form and paves the way for future improvements of the technique.

Finally, we discuss potential future directions for improving SRM techniques. These include refining the fast particle fusion method by incorporating localization uncertainties and prior knowledge, optimizing experimental parameters in MINFLUX, and developing advanced localization strategies to improve accuracy and efficiency. By addressing these future challenges, SRM technologies can move closer to the goal of 1 nm resolution in super-resolution imaging.

In this thesis new dielectric metasurfaces in immersion were explored with a periodic distribution of unit cells with multiple silicon cylinder structures on a reflective gold slab with a fused quartz spacer in between. These new metasurfaces were designed with 60 nm and 130 nm gaps in order to improve manufacturability and enable larger particles to enter the hotspot region while trying to maintain high electric field enhancement and enhancement factors. This was done by simulating the plane wave excitation in a range of 750 nm to 850 nm for a large number of metasurfaces using electromagnetic modelling software Lumerical using its finite difference time domain method. After exploring multiple silicon cylinder structures the focus was put on periodic metasurfaces with unit cells containing single, dimer, and quadrumer positioning of cylinders and enhancement factors of between 500-2000 were found.
Afterwards the found fields for new promising designs were used in an optical trapping algorithm were enhancement factors for 10 nm particles were found between 10^4-10^5 and for 40 nm particles between 10^3-10^4.
The effect of exciting a metasurface with circular polarization for quadrumer structures was thoroughly investigated but yielded no better enhancement factor than previous dimer designs. A new optical trapping scheme where the laser intensity is increased near the end of optical trapping is proposed to give slight improvement of enhancement factors after trapping. Overall, the limitations of the electromagnetic simulations and optical trapping algorithm makes it difficult to assume the enhancement factors found are realizable in experiment. These limitations need to be addressed before any conclusions can be made on whether immersion SERS offers any advantages over dry SERS in the case of dielectric metasurfaces.

As super-resolution methods make it possible to capture images at a resolution beyond the diffraction limit, they have no straightforward measure for optical resolution. Consequently, signal-to-noise ratio-based methods to determine resolution such as Fourier Ring Correlation (FRC) have seen increased
use. We look at a new method, called 1FRC, as it requires only a single image instead of two (2FRC, the original method). It splits each pixel value into two values according to a binomial distribution, producing two images usable in a standard FRC routine. We consider for which noise modalities and conditions
the results are equivalent to using 2FRC. If the image noise is only Poisson-distributed we derive mathematically that 1FRC and 2FRC are equivalent. Using simulations on Siemens star test images we find that the mean squared error between 1FRC and 2FRC curves is small for images containing only Poisson noise and a combination of Poisson and low variance Gaussian noise. However, when
the mean variance ratio 𝜇/𝜎2 (image mean divided by variance of a pixel) is less than one, the 1FRC curve no longer goes to zero at high frequencies, but instead fluctuates at an elevated level. We see that this elevated 1FRC curve level is exactly 1 − 𝜇/𝜎2. For 𝜇/𝜎2 < 0.973 the difference in resolution exceeds one standard deviation of the 1FRC resolution. From this point the Kolmogorov-Smirnov test confidently states that the 1FRC pixel sum distributions are not equal to 2FRC distributions. We also test 1FRC on an experimental dataset made with varying STED intensity. The computed resolution curves fit well to the modified Abbe equation for STED. However, the 1FRC resolutions are up to 30%
better than resolutions obtained using decorrelation analysis.

Localization microscopy has circumvented the diffraction limit by sequentially imaging individual light emitting molecules at a time. The position of these individual molecules can be determined and a super-resolution reconstruction is made with improved resolution. Normally freely rotating emitters are used such that the point spread function (PSF) is rotationally symmetric and only minor errors in the localization process are made by approximating the PSF with a Gaussian. The precision with which the individual emitters can be localized scales with the 1/√N, N the number of detected photons so that more detected photons leads to a better localization precision. However, the emission of fluorescent molecules is limited by photobleaching, a light induced chemical reaction to a permanent non-fluorescent state. In this thesis we investigate the effect of cooling the sample to cryogenic temperatures with liquid nitrogen. This reduces the chemical reaction rates and improves photostability more than 100 fold. To use localization microscopy it is necessary to switch the fluorescent molecules between an on-state and off-state, this turns out to be difficult at cryogenic temperatures. Standard methods used at room temperature in aqueous media do not work. As the molecules are frozen in place at cryogenic temperatures we use polarized light to selectively image molecules with certain orientations at a time. To realize this it is necessary to generate pure linear polarization with an arbitrary orientation in the sample plane. By calibrating the phase difference induced by the dichroic mirrors this can be achieved, effectively modulating the fluorescence of fixed dipole emitters at cryogenic temperatures. The addition of an orthogonal linearly polarized stimulated emission depletion (STED) beam narrows the orientational distribution of fluorescing molecules. This method does induce some degree of sparsity, however, it is not enough for localization microscopy of dense biological samples. Furthermore, the STED process reduces the photon yield of single molecules. This is presumably caused by the long dark-state recovery measured on fluorescent molecules in vacuum and at cryogenic temperatures. Localization microscopy of fixed or orientationally constrained emitters has long been avoided as the orientation of individual molecules leads to bias in the localizations. There are various ways to eliminate this bias but they reduce the amount of information that can be extracted from the sample. By fixing the orientation of fluorescent emitters to biomolecules of interest they become reporters for the orientation of the biomolecules. We have devised the so-called Vortex PSF with which the orientation, 3D position and degree of rotational constraint can be extracted from a single image. Alternatively the orientation of single-molecules can be probed with varying polarization states over multiple frames achieving a better precision with less photons.

For decades, the resolution of fluorescent light microscopy has been bounded by Abbe’s diffraction limit to λ/2NA. Super-resolution methods, awarded with the 2014 Nobel Prize in Chemistry, use tricks to overcome this limit. The general idea is to image blinking fluorophores for a multitude of frames, such that each frame only contains a sparse subset of fluorophores. Assuming that single emitters give rise to a sparse subset of diffraction-limited spots, their locations can be determined with nanometer precision. The resolution of the final reconstructed image is limited by the localization precision and incomplete fluorescent labeling. To even further improve the resolution, by increasing the signal-to-noise and overcoming the problem of a low label- ing density, single-particle averaging can be used if multiple copies of the same target particle (e.g. macro- molecular complex) can be imaged. All emerging localization patterns are computationally merged into one super-superresolution image. Despite the increase in resolution, potential structural variation among the particles will blur the particle fusion result and possible (small) subsets of structurally different particles can- not be detected in the reconstruction. We present an a-priori knowledge-free, unsupervised classification method that splits the dataset into conformationally different groups of images prior to the merging process, which can subsequently be fused per class. The implemented algorithms are validated on multiple exper- imental and simulated datasets. We achieved classification performances of 96% on experimental datasets with up to four different DNA origami structures, are able to detect rare classes of mirrored origami’s occur- ring at a rate of 2%, and capture the variation in the ellipticity of nuclear pore complexes. This new classifica- tion tool will allow microscopists to study heterogeneous samples with single-particle averaging techniques and discriminate between different particles, structures or conformations with a high resolution.

In 2019 werd er voor het eerst een foto van een zwart gat gepubliceerd. Het betreffende super zware zwarte gat ligt in het midden van het sterrenstelsel Messier 87. In dit onderzoek willen we simulaties maken van hoe een foto van een zwart gat eruit ziet. Zowel voor een achtergrond (zoals de sterrenhemel) als de accretieschijf die eromheen zit. De vraag is vervolgens welke informatie uit de foto gehaald kan worden. Om de foto te maken, werd een ray-tracer gemaakt. Hierbij kijk je waar een lichtstraal, die op het scherm komt (een oog of camera), vandaan komt. De bewegingsvergelijkingen zijn vereenvoudigd door constantes van de beweging te zoeken om de geodeetvergelijkingen te versimpelen. Vervolgens zijn de bewegingsvergelijkingen numeriek opgelost. Er is gevonden dat lichtstralen van veraf niet in een zwart gat vallen bij $\frac{\sqrt{27}}{2}R_s$. $R_s$ is de Schwarzschild straal. Dit is de straal waarvandaan licht niet meer kan ontsnappen van een zwart gat. De gesimuleerde plaatjes zijn 128x128 pixels. In de gesimuleerde plaatjes had het zwart gat ongeveer $2.5R_s$. Dit komt nauw overeen maar er wordt een aanzienlijke fout gemaakt door de resolutie van de plaatjes. Verder is kwalitatief de oriëntatie en rotatieparameter $a$ goed uit de plaatjes te halen.

A model is designed for solving gravitational profiles of self-gravitating and rotating planets via the use of Poisson's equation for total gravity, i.e., the sum of the gravitational and rotational potential. Poisson's equation is a partial differential equation that is solved with the usage of Green's functions. This is a major advantage because Earth's surface is an equipotential, which leads to a Dirichlett boundary condition. We apply this methodology to a spherical Earth, where the Green's function is closed. It is demonstrated that, when this Green’s functions based methodology is applied to a homogeneous density, a linear spherical density and the PREM density profiles (where all density profiles are spherically symmetric), then discontinuities occur in the accelerationof gravitation across the surface of the Earth, in the range of 0.01 %- 0.13 %. Such an effect is a symptom of incompatibility with the laws of physics for geostaticalequilibrium, and it is certainly significant as compared to the numerical accuracy of the solution. Moreover, the discrepancy is dependent on geographical latitude, as was to be expected, because it somehow reflects the centrifugal effect. The conclusion is made that this method is indeed capable of detecting, and even quantifying, the incompatibility of spherically symmetric mass distributions with the fundamental laws of physics for self-gravitating and rotating planets. This opens a way -and this is one of the main results- to computing corrections to spherically symmetric mass distributions, such as the PREM model. Based on this method, a further way forward to this end is suggested.

Electron tomography is a powerful tool in materials science to characterize nanostructures in three dimensions (3D). In scanning transmission electron microscopy (STEM), the sample under study is exposed to a focused electron beam and tilted to obtain twodimensional (2D) projections at different angles; many imaging modes are available such as high-angle annular dark-field (HAADF). In tomography, the collection of projections is called a tilt-series, from which we can reconstruct a 3D image that represents the sample. While HAADF tomography can clearly reveal the inner structure of the sample, it cannot directly provide compositional information. To better understand nanomaterials with more types of elements, spectral imaging techniques like energy dispersive X-ray spectroscopy (EDS) must be pursued. EDS tomography, however, is currently hampered by slow data acquisition, resulting in a small number of elemental maps with low signalto- noise ratio (SNR). Electron tomography, especially EDS tomography, is an ill-posed inverse problem whose solution is not stable and unique. Although advanced reconstruction techniques may yield a more accurate result by incorporating prior knowledge, they also involve fine-tuning parameters that highly influence the reconstruction quality. Furthermore, while great efforts have been dedicated to developing tomography techniques for image enhancement, directly combining reconstruction volumes at hand has still not been widely considered to the best of our knowledge.

Single molecule localization microscopy (SMLM) shows promise for quantitative structural analysis of subcellular complexes and organelles with a resolution well below the diffraction limit. This superresolution microscopy technique relies on the blinking events of fluorescent molecules that labeled the structure of interest and are spatiotemporally spread over the entire field of view and time. Once hundred thousands frames of these sparse events are recorded, single molecule positions are localized with nanometer precision to form a 2D/3D point set of coordinates. Therefore, SMLM images are not conventional pixelated images but rather spatial point patterns. Photon scarcity and incomplete labeling of the imaged structure, however, limit the resolution that can possibly be achieved by means of SMLM. Moreover, due to experimental limitations the axial resolution is typically ~2-3 times worse than the lateral resolution in conventional setups. Inspired by single particle analysis (SPA) in cryo-electron microscopy (cryo-EM), proper alignment of repeated structures ("particle fusion") in a 2D/3D SMLM measurement can overcome these limiting factors and so push for isotropic resolution. The existing approaches for particle fusion in SMLM can be classified into customized routines that are borrowed from SPA in EM or methods that use strong prior knowledge about the structure to be reconstructed. While the first approaches are completely ignoring the differences in image formation model between EM and SMLM, the second ones are highly prone to the template-bias problem. In this thesis, a dedicated particle fusion pipeline for 2D/3D SMLM data is proposed. The approach properly considers the pointillistic nature of the SMLM modality and takes into account the localization uncertainties. Furthermore, while it does not require any prior knowledge about the underlying structure of the particles, it can incorporate certain features such as symmetry into the fusion process. Owing to the novel all-to-all registration scheme, the application of the devised pipeline on experimental data with very poor labeling density has been successfully demonstrated. The requirements for successful particle fusion for different SMLM modalities, namely PAINT and STORM, have been characterized through extensive study on 2D and 3D experimental and simulation data. In 2D, an FRC resolution of 3.3 nm on DNA-origami nanostructures has been achieved, and, in 3D, it was demonstrated how the combination of SMLM as a light microscopy technique and a computational approach enables structural analysis of the Nuclear Pore Complex. Future advances of SMLM rely highly on computational routines after data acquisition. Advanced data analysis techniques such as particle fusion can help pushing the boundaries of structural biology using light microscopy.