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Geometrické struktury založené na kvaternionech.
Floderová, Hana ; Vašík, Petr (oponent) ; Hrdina, Jaroslav (vedoucí práce)
Geometrickou strukturou nazýváme dvojici (V, G), kde V je vektorový prostor a G je podgrupa GL(V), což je množina všech matic přechodu. V této práci klasifikujeme ty struktury, které jsou založeny na vlastnostech kvaternionů. Geometrické struktury založené na kvaternionech nazýváme trojné struktury. Jsou to čtyři struktury s vlastnostmi podobnými kvaternionům. Kvaterniony jsou vytvořeny z reálných čísel přidáním tří komplexních jednotek. Kvaterniony zapisujeme ve tvaru a+bi+cj+dk.
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In vivo application of holographic endoscopy
Tučková, Tereza ; Brzobohatý,, Oto (oponent) ; Bouchal, Petr (oponent) ; Uhlířová, Hana (vedoucí práce)
The progress in understanding of complex brain function is conditioned by the ability to optically access any chosen structure and area in the living brain with minimal tissue damage and with sub-cellular resolution, The progress in accessing deeper into the light-scattering tissue stands nowadays largely on the development of optical endoscopic probes such as microendoscopes with incorporated graded index (GRIN) lenses and fibre-optic bundles. Due to recent advancements in holographic light shaping methodology, using multimode optical fibres (MMF) as imaging elements has become promising for high resolution imaging deep in the tissue. In comparison to GRIN-based endoscopes and fibre bundles endoscopes, MMFs provide the highest ratio of image resolution and probe thickness causing minimal tissue damage. This thesis first provides an overview of the current state-of-the-art in vivo deep brain imaging technology, multi-mode fibre-based endoscopy and its principles to introduce the related technology. The main technological focus of the thesis stands on using a digital micro-mirror device (DMD) to modulate light through the MMF probes. This enables fast raster scanning of the fluorescent sample at the imaging plane of the fibre distal facet. An optical setup exploiting this principle has been built, its imaging properties carefully evaluated, and high stability reached. Its imaging abilities have been demonstrated on 2D and 3D fluorescent phantom samples. Consequently, we have developed an image post-processing procedure to enhance the detected image and reach the full diffraction-limited resolution potential. Using algorithms, one based on a regularised iterative inversion and second on regularised direct pseudo-inversion, lead to enhancement of the image contrast and resolution. Further, we used genetically modified mice to move towards ex vivo and in vivo imaging. Suitable mouse models were identified and its ex vivo brain imaging showed that the images suffer from strong background fluorescent signal from out-of-focus planes. Therefore, further work focused on technological development for light attenuation based on the confocal principle. An optical setup for confocal “pinhole” filtration has been built using a custom-made probe consisting of graded-index MMF spliced at the tip of the step-index MMF and a second DMD. The fluorescent signal collected by the GRIN-SI-MMF was filtered in the probe far field where for every scanning focal point it forms an annular ring. This ring-signal, and thus also the out-of-focus signal, was then separated using a mask on DMD2. On a set of experiments using phantom sample of fluorescent microspheres and fixed brain tissue it has been demonstrated that this confocal filtering leads to attenuation of the background signal, the signal from the out-of-focus planes thus enhancing the images contrast and resolution. This principle of confocal filtering in the holographic endoscope has been also demonstrated using a novel side-view MMF probe. This work shows a piece of a puzzle in a long-term complex development of an optimal tool for deep-tissue and high-resolution imaging. The MMF-based holographic endoscope has been advanced to routine imaging of biological tissue in range of hours with the feature of out-of-focus light attenuation. The endoscope has been tested on imaging of phantom samples as well as fixed mouse brain slices and in vivo vasculature down to depth of 5 mm.
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Geometrické struktury založené na kvaternionech.
Floderová, Hana ; Vašík, Petr (oponent) ; Hrdina, Jaroslav (vedoucí práce)
Geometrickou strukturou nazýváme dvojici (V, G), kde V je vektorový prostor a G je podgrupa GL(V), což je množina všech matic přechodu. V této práci klasifikujeme ty struktury, které jsou založeny na vlastnostech kvaternionů. Geometrické struktury založené na kvaternionech nazýváme trojné struktury. Jsou to čtyři struktury s vlastnostmi podobnými kvaternionům. Kvaterniony jsou vytvořeny z reálných čísel přidáním tří komplexních jednotek. Kvaterniony zapisujeme ve tvaru a+bi+cj+dk.
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