Ever since their discovery, the Trojans have raised many questions among astrophysicists. In 1989 it was found that there were more L4 than L5 Trojans and the current L4:L5 ratio value is estimated to be 1.6. However, this asymmetry could not be explained by Jupiter’s current orbit and must therefore have arisen during the early development of the Solar System. It was suggested that an outward migration as described by the Nice model could cause the asymmetry. To investigate this, we extended a recent research by modelling an outward migration of Jupiter on the actual Trojans and their symmetric copies. In this manner, we had a broad initial Trojan distribution, which allowed us to investigate several effects of initial values like the Trojan inclinations and maximum angular deviations from the Lagrange point. The simulations used a recently found midpoint Yoshida integrator, which allowed fourth order symplectic simulations for our non-separable Hamiltonian problem. From the simulations it followed that the ratio could only be explained if the Trojans initially had large angular deviations from the Lagrange point, which is possible if they later lost energy due to for example mutual collisions. Also the small initial inclinations as predicted for the early Trojans would in general have risen due to the migration, but it could not explain the the inclinations up to 40 degrees for today Trojans, implying that the increase in inclination must have been caused by other reasons. We found that not only the total migration distance and duration are important, but also the function that describes the evolution of Jupiter’s semi-major axis and the eccentricity of Jupiter’s orbit. For further research we suggest to use data sets on those quantities from simulations with the Nice model, to investigate these related problems together. We believe that our model and code is of great advantage for such a research, because of its optimisations and it allows to implement the data on the distance and eccentricity directly into the model without having to alter the equations of motion.

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.

Academic research is inherently cooperative, with researchers exchanging information through formal publications as well as direct messaging. Academia are, however, becoming increasingly competitive: limited financial resources and research spots, among other things, may now affect how researchers cooperate and interact in general. In the current study, the congruence of cooperative and competitive interactions in academia was investigated. To this end, the existing knowledge on the competition and cooperation amalgamation "coopetition", coined for industry relationships, was used. A theoretical framework on coopetition and related theories relavant to academic relationships was constructed. This framework was used to conduct an online survey on academic coopetition among academic microscopy researchers in the Netherlands. The results suggested that competition and cooperation in academia are related yet separate, so that an increase in one does not necessitate a decrease in the other and vice versa. Additionally, the survey responses suggested a discrepancy between the respondents' reported competitive sentiments and those apparent from their other answers. To address this discrepancy, and help academic researchers reflect on what competition and cooperation mean to them, the interactive Guide for Introspection on Competition and Cooperation (GICCo) was developed.

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. @en

Single molecule localization microscopy is a powerful tool that delivers high contrast and imaging specificity at a resolution beyond that of conventional microscopes. To obtain a super-resolved image, one needs to image at least hundred thousand camera frames and estimate the position of millions of molecules with nanometer precision. The tremendous amount of data that needs to be analyzed is one of the challenges scientists face when applying single molecule localization techniques. For this reason, a maximum likelihood estimation method is proposed in this thesis that attains the Cramer-Rao Lower Bound and estimates the position of single molecules in parallel on a GPU to achieve near real-time processing with high precision. A major drawback of current methods that detect single molecules is that the number of false positives is unknown. Therefore, a generalized likelihood ratio test is proposed here, which can control both the number of false positives and true positives withminimal user input. This target is stably achieved in the experiment over a large range of signal to background conditions. A key application of single molecule localization microscopy can be found in in vivo RNA imaging. In this thesis two RNA studies are presented: i) The nuclear pore complex structures and the kinetic interaction with mRNA are investigated, where a point mutation of mex67p triggered the nuclear export efficiency to drop significantly; and ii) A study on the mobility and occupation of mRNA within the nucleus is performed by instantaneously imaging the whole three-dimensional volume ofmRNAs in the nucleus of a living cell. Fromthis study, no evidence was obtained for exclusion or enrichment of the heterochromatin by mRNAs. For the general applicability of singlemolecule localization microscopy, the two-dimensionalmethods will need to be extended to three-dimensions. In threedimensional imaging small aberrations will become significant when imaging away from focus and therefore need to be compensated or calibrated. This thesis shows that one can extend single molecule localization into three-dimensions, or even a fourth-dimension such as color when the point spread function of a microscope is correctly distorted. Additionally, an adaptive optics strategy is presented that can correct for sample induced aberrations, and a method is proposed to encode emission color of the single molecule into the measurement.@en

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.

Gravitational waves predicted by Einstein have been measured in a few observatories worldwide. These detectors are complex interferometers with sizes of kilometers. Misalignments and aberrations in their optical set-up can create higher-order modes in the laser beam. These higher-order mode effects should be compensated to improve the sensitivity of the interferometer. Such a compensating control system requires a real-time wavefront sensor. The phase cameras developed for the Virgo gravitational wave detector can simultaneously create intensity and phase images of the laser wavefront at 11 demodulation frequencies. Currently, the phase images are not used due to difficulties in the interpretation. Therefore, the goal of this research is to improve the understanding of the phase images of a phase camera for the Virgo gravitational wave detector.

A prototype set-up of the phase camera was built at Nikhef. The beam is modulated and sidebands are created such that a beat signal of 80 MHz and the first upper and lower sidebands at 75 and 85 MHz are measured. Images are created by scanning the laser beam across a pinhole diode and digital demodulation. In the chosen optical set-up only one of the two beams that give the measurable beat signal is scanned. This leads to systematic phase effects caused by length differences in the optical path as a function of the scanning angle. To predict the phase images, the interference of two Gaussian beams with a scanning mirror is mathematically derived. Phase images are created with a simulation, which matches within 10 to 20% compared to measurements. To improve the results, the input parameters of the simulation should be measured more accurately and the optical set-up layout should be checked. Also, the phase stability of the prototype set-up is measured. Due to the high sensitivity of the phase camera, very small optical path length differences, for example caused by airflow or temperature differences, lead to significant phase offsets. The long timescale fluctuations in the phase measurements can be reduced by covering the optical set-up. The measured high-frequency phase resolution is Δ𝜙 = 7.1 ± 0.4 mrad and behaves as a function of power as expected.

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.

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.