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Optical singularities are points in complex scalar and vector fields where a property of the field becomes undefined (singular). In complex scalar fields these are phase singularities and in vector fields they are polarisation singularities. In the former the phase of the field is singular and in the latter it is the polarisation ellipse axes. In three dimensions these singularities are lines and natural light fields are threaded by these lines. The interference between three, four and five waves is investigated and inequalities are given which establish the topology of the singularity lines in fields composed of four plane waves. Beyond several waves, numerical simulations are used, supported by experiments, to establish that optical singularties in speckle fields have the fractal properties of a Brownian random walk. Approximately 73% of singularity lines percolate random optical fields, the remainder forming closed loops. The statistical results are found to be similar to those of vortices in random discrete lattice models of cosmic strings, implying that the statistics of singularities in random optical fields exhibit universal behavior. It is also established that a random superposition of plane-waves, such as optical speckle, form singularities which not only map out fractal lines, but create topological features within them. These topological features are rare and include vortex loops which are threaded by infinitely long lines and pairs of loops that form links. Such structures should be not only limited to optical fields but will be present in all systems that can be modeled as random wave superpositions such as those found in cosmic strings and Bose-Einstein condensates. Also reported are results from experiments that generated compact vortex knots and links in real Gaussian beams. These results were achieved through the use of algebraic knot theory and random search optimisation algorithms. Finally, polarisation singularity densities are measured experimentally which confirm analytic predictions.

Microscopic imaging of rapid biophysical processes often relies on high-contrast, high-resolution, and high-speed acquisition. However, confocal microscopes capable of such imaging lack the capacity to manipulate the sample or its surrounding environment in real-time. As a result, the possibility to non-invasively initiate, alter or halt a biochemical process during imaging is restricted. To overcome this limitation, we have established a sui generis versatile holographic system equipped with diverse photo-perturbation techniques including photo-manipulation, photo-activation, photo-ablation, optical-trapping and optogenetics, combined with the ability for active surveillance and monitoring of biological targets through confocal imaging and potential capacity for super-resolution imaging. This hybrid system is comprised of a spinning disk confocal unit, a spatial light modulator and a digital micromirror device, and is able to elucidate the dynamics of molecules, measure local forces, and re-localise or switch molecular behaviour. Here, we present the first application of this hybrid system to the study of cell shape regulation and the role of effective membrane tension in unionising actomyosin movement to resist external deformational and destabilising forces. We demonstrate that simultaneously trapping and unfolding the cell membrane, quantitatively imaging actin network dynamics and measuring cellular forces, allowing for a multi-level understanding of how the interplay of membrane tension and actin dynamics governs cell shape. Specifically, our results show a link between the movements of myosin that lead to a surge in actin concentration and cause an increase in the effective membrane tension. These results provide direct evidence for the role of physical interactions by plasma membrane in interpreting the environment that surrounds the cell to regulate and control cell dynamics and by extension cell behaviours. Furthermore, the results strongly reiterate the role of the actomyosin cortex in regulating cell shape during the transition phase and maintaining cell shape by resisting deformation during the stationary phase. More generally, our findings have the potential to expand our understanding of how mechanical properties of the cell surface are locally and globally responsible for driving cell shape changes in physiological and disease conditions. Additionally, we demonstrate the possibility of simultaneously holographic-trapping and dynamically exciting multiple independent cellular targets each located in specific areas and having different excitation and emission wavelengths, by custom developed and optimised method which utilises a single modulator to generate multi-chromatic holograms. Our programming code uses an iterative algorithm with only ten iterations to achieve a PSNR of above 35 dB, an efficiency of 96\% and a crosstalk of less than 1\% in the results. The method retains high adaptability and customisability to prioritise the quality of the reconstructed image, or the speed of the hologram generation, or improve both quality and speed at the cost of other variables based on the application specificity.

The regulation of transcription is well understood to be linked to the three-dimensional organisation of the genome within the nucleus, however, the mechanisms through which the different levels of organisation regulate genes are poorly understood. Newly developing super-resolution imaging techniques offer an important new way to investigate structural features of the genome, however, imaging chromatin within the nucleus is traditionally very difficult due to the dense packaging with a small nuclear volume. The nuclei of Drosophila melanogaster primary spermatocytes have unique properties that can circumvent these limitations, with comparatively large nuclei with well-separated chromosome masses, and transcriptionally active Y loops that expand into the nuclear interior as clearly observable individual fibres. Therefore, during this thesis I took advantage of this model system to image both the chromatin of the Y loops and chromosome masses. A single molecule localisation microscopy technique was optimised for imaging within the nucleus, with both 3D and dual-colour capability. Then, the Y loops were imaged at super-resolution, and a specialised clustering protocol was developed for quantification. This showed that the Y loops are organised as a chain of clusters, with an average width of approximately 50 nm, and an average distance apart from each other of roughly 100 nm. The relationship between actively elongating transcription, as well as different phosphorylation states of RNA polymerase II, and the Y loop chromatin was investigated and quantified, revealing that polymerase appears adjacent to the Y loop fibres, attached via a smaller chromatin loop emanating from the clusters. The role of transcription in chromatin organisation was assessed on the Y loops through the use of transcription inhibition, and on the autosomal chromosomes through mutant fly lines, using empty-space statistics to quantify their organisation. This indicated that the Y loop chains of clusters structure was unlikely to be determined by transcription. Active and inactive histone modifications were labelled along the Y loops, which were quantified for comparative analysis, with implications for the link between chromatin state and function. The work conducted during this thesis identified novel architectures of transcriptionallyactive chromatin and so provides a foundation for understanding chromatin organisation within the nucleus, and the relationship between transcription and chromatin state.