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Tato diplomová práce se zabývá modelováním bodové rozptylové funkce (point spread function, PSF) u skenovacího transmisního elektronového mikroskopu (STEM). Nejprve je provedena teoretická rešerše, kde jsou popsány všechny důležitě aspekty, potřebné k následnému modelování. Je tedy proveden základní popis konstrukce přístroje a určeny jeho klíčové komponenty, které mají hlavní vliv na tvar výsledné PSF. Následně jsou popsány hlavní zobrazovací vady, které ovlivňují výslednou PSF. Ty jsou popsány z hlediska vlnové optiky. Na základě toho je pak navržen a zrealizován poměrně přesný model PSF u mikroskopu STEM. Poté je vytvořeno GUI, které umožňuje plné využití daného vytvořeného modelu. Na závěr je získaný model otestován na modelových a reálných datech, pomocí metody Lucy-Richardson.

Coherence scanning interferometry (CSI) is a non-contacting optical technique which is widely used for the measurement of surface topography. CSI combines the lateral resolution of a high power microscope with the axial resolution of an interferometer. As with any other metrology instrument, CSI is calibrated to define measurement uncertainty. The traditional calibration procedure, as recommended by instrument manufacturers, consists of calibration of the axial and lateral scales of the instrument. Although calibration in this way provides uncertainties for the measurement of rectilinear artefacts, it does not give information about tilt-related uncertainty. If an object with varying slope is measured, significant errors are observed as the surface gradient increases. In this thesis a novel approach of calibration and adjustment for CSI using a spherical object is introduced. This new technique is based on three dimensional linear filtering theory. According to linear theory, smooth surface measurement in CSI can be represented as a linear filtering operation, where the filter is characterised either by point spread function (PSF) in space domain or by transfer function (TF) in spatial frequency domain. The derivation of these characteristics usually involves making the Born approximation, which is strictly only applicable for weakly scattering objects. However, for the case of surface scattering and making use of the Kirchhoff approximation, the system can be considered linear if multiple scattering is assumed to be negligible. In this case, the object is replaced by an infinitely thin foil-like object, which follows the surface topography and, therefore, is called the foil model of the surface. For an ideal aberration free instrument, the linear characteristics are determined by the numerical aperture of the objective lens and the bandwidth of the source. However, it is found that the PSF and TF of a commercial instrument can depart significantly from theory and result in a significant measurement error. A new method, based on modified inverse filter to compensate the phase and amplitude-related errors in the system PSF/TF, is demonstrated. Finally, a method based on de-warping to compensate distortion is discussed. The application of the linear theory as well as modified inverse filter is dependent on the assumption of the shift invariance. As distortion introduces a field dependent magnification, the presence of distortion for CSI with relatively large field of view, restricts the applicability of the linear theory. Along with this restriction, distortion also introduces erroneous height measurement for objects with gradients. This new approach, based on de-warping, resolves the problems associated with distortion.

Traditionally, surface topography measurement was in the domain of quality control of engineering parts. With the advancement of manufacturing technology and affordable computational costs, different types of surfaces are produced with varied shapes and surface textures. These pose significant measurement problems, therefore, surface topography research is gaining momentum to achieve a better control of the surface. Coherence scanning interferometry (CSI) is one of the most common techniques used for measurement of surface topography. It is preferred over tactile and other non-contact techniques since it provides fast and accurate measurement with high vertical (~ 1 nm) and lateral (~1 μm) resolutions over larger areas without any damage to the surface. Essentially, CSI is treated as one dimensional (1D) superposition of the light waves from an object and a reference that generates a three dimensional (3D) interferogram. Secondly, despite the advantages, there is no standard configuration of CSI that can provide absolute surface topography measurement of an engineering part with multiple materials. An effective solution to this problem will be particularly useful in the field of semiconductor and bio-related industries where chips and instruments are made of many materials. In this Thesis, first, the CSI technique is analysed in terms of a wider theoretical framework of 3D linear filtering technique which shows the similarities among other seemingly disparate techniques such as confocal and optical coherence tomography. Due consideration to the spectral characteristic of the source and the effect of numerical aperture are given and important parameters such as vertical and lateral resolutions are computed to compare this theory with standard analysis methods. Additionally, it is shown that the 3D fringe pattern can be considered to be a superposition of a reference field and the scattered field from the top foil-like layer on the top the object. The scattered field from this foil object is dependent on the normal Fresnel reflection coefficients. Therefore, it explains the phase offset and the proportional height offset introduced by different materials, especially, metals. In an object, where multiple materials are present, each material introduces different phase to the fringe pattern and therefore, the surface topography of the entire object is altered. To overcome this problem, the optical polarising properties of the material are exploited. A novel configuration of polarisation sensitive CSI is presented where interferograms with orthogonal circular polarisations are recorded and analysed. The configuration, initially, needs to be calibrated with a material and after that at each point on the object, the refractive index and height offset can be calculated. Therefore, it can be dually used to identify unknown materials present on the object and also to compensate for the height offset introduced by each material to produce absolute surface topography of the entire object. The configuration provides good agreement with ellipsometric results for metals. Additionally, it retains the advantages of high vertical and lateral resolution same as other standard coherence scanning interferometers.

The limited spatial resolution in positron emission tomography (PET) images leads to difficulties to measure correct uptake in tumours. This is called partial volume effects (PVE) and can lead to serious bias, especially for small tumours. Correct uptake values are valuable for evaluating therapies and can be used as a tool for treatment planning. The purpose of this project was to evaluate two methods for compensating for PVE. Also, a method for tumour delineation in PET-images was evaluated. The methods were used on images reconstructed with two algorithms, VUE-point HD (VP HD) and VP SharpIR. The evaluation was performed using a phantom including fillable spheres which were used to simulate tumours of different sizes. The first method used for PVE compensation was an iterative deconvolution method which to some degree restores the spatial resolution in the images. The tumour uptake was measured with volumes of interest (VOIs) based on a percentage of the maximum voxel value. The second method was to use recovery coefficients (RCs) as correction factors for the measured activity concentrations. These were calculated by convolving binary images of tumours with the point spread function (PSF). The binary images were achieved both from computed tomography (CT) images and from PET images with a threshold method for tumour delineation. The threshold method was based on both tumour activity and background activity, and was also compared with a conventional threshold technique. The results showed that images reconstructed with VP SharpIR can be used for activity concentration measurements with good precision for tumours larger than 13mm diameter. Smaller tumours benefit from RCs correction. The threshold method for tumour delineation showed substantially better results compared to the conventional threshold method. / Den begränsade spatiella upplösningen i bilder från positronemissions-tomografi (PET) leder till svårigheter i att mäta korrekt upptag i tumörer. Detta kallas partiella volymseffekter (PVE) och kan leda till stora fel, speciellt för små tumörer. Korrekta upptagsvärden är värdefulla vid behandlingsutvärdering och kan användas som ett verktyg för att planera behandlingar. Syftet med detta projekt var att utvärdera två metoder för att kompensera för PVE. Även en metod för tumöravgränsning i PET-bilder utvärderades. Metoderna användes på bilder som rekonstruerats med två olika algoritmer, VUE-point HD (VP HD) och VP SharpIR. Utvärderingen utfördes med ett fantom med sfärer som fylldes med aktivitet och därmed simulerade tumörer av olika storlekar. Den första metoden för PVE-kompensation var en iterativ avfaltningsmetod som, i viss mån, återställer bildernas spatiella upplösning. Upptaget i tumörerna mättes som medelupptaget i s.k. ”volumes of interests” (VOI:ar) som baserades på andelar av maximala voxelvärdet. Den andra metoden byggde på användning av s.k. recovery coefficients (RCs) som korrektionsfaktorer för de uppmätta aktivitetskoncentrationerna. Dessa beräknades genom att falta binära bilder av tumörerna med punktspridningsfunktionen (PSF). De binära bilderna framställdes både från bilder tagna med datortomografi (computed tomography, CT) och från PET-bilder med en tröskelmetod för tumöravgränsning. Tröskelmetoden baserades både på aktiviteten i tumören och på bakgrundsaktiviteten. Den jämfördes också med en konventionell tröskelmetod. Resultaten visade att bilder som rekonstruerats med VP SharpIR kan användas för mätning av aktivitetskoncentration med god precision för tumörer större än 13mm diameter. För mindre tumörer är det bättre att använda RC:s. Tröskelmetoden för tumöravgränsning visade avsevärt bättre resultat jämfört med den traditionella tröskelmetoden.

Ce travail de thèse porte sur la caractérisation et l'optimisation du spot de focalisation d'un objectif de microscope de grande ouverture numérique pour des applications d'imagerie super-résolue et de nanofabrication.Dans la première partie, nous avons systématiquement étudié les distributions de polarisation et d'intensité du faisceau laser dans la région du point focal en fonction de différents paramètres du faisceau incident tels que la phase, la polarisation, l’amplitude ainsi que l'influence du milieu de propagation, tel que l’indice de réfraction. Nous avons mis en oeuvre différentes méthodes théoriques pour contrôler et manipuler les distributions de polarisation et d'intensité du spot de focalisation. Ces prédictions théoriques sont vérifiées expérimentalement via un système optique confocal en mesurant l’image de fluorescence d’une nanoparticule d’or pour différentes caractéristiques.Dans la seconde partie de ce travail, une nouvelle microscopie basée sur le mécanisme d'absorption ultra-faible à un photon a été démontré théoriquement et expérimentalement. Le calcul théorique basé sur l'approche vectorielle de Debye, qui prend en compte l'effet d'absorption du matériau, montre qu'il est possible de focaliser le faisceau lumineux en profondeur à l'intérieur d'un matériau si celui-ci présente une absorption linéaire ultra-faible à la longueur d'onde d'excitation. Cette méthode, dite (LOPA), a ensuite permis de fabriquer des structures 2D et 3D submicrométriques, similaires à celles obtenues par la méthode utilisant l’absorption à deux photons. / Nowadays, far field optical microscopy is widely used in many fields, for fundamental research and applications. The low cost, simple operation, high flexibility are its main advantages. The key parameter of an optical microscope is the objective lens.This thesis's work focuses mainly on the characterization and optimization of the point spread function (PSF) of a high numerical aperture (NA) objective lens (OL) for applications of high resolution imaging and nano-fabrication.In the first part of the thesis, we have systematically investigated the dependency of polarization and intensity distributions of the focusing spot on numerous parameters, such as the phase, the polarization, and the beam mode of incident beam, as well as the refractive index mismatch. Then, we demonstrated theoretically different methods for manipulation of the polarization and intensity distributions of the focusing spot, which can have desired shapes and are useful for different applications. By using a home-made confocal microscope, we have experimentally verified some of the theoretical predictions, for example, vector properties of light beam under a tight focusing condition. In the second part of dissertation work, a new, simple and inexpensive method based on the one-photon absorption mechanism has been demonstrated theoretically and experimentally for 3D sub-micrometer imaging and fabrication applications. The theoretical calculation based on vectorial Debye approximation and taken into account the absorption effect of material shows that it is possible to focus the light tightly and deeply inside the material if the material presents a very low one-photon absorption (LOPA) at the excitation wavelength. We have then demonstrated experimentally that the LOPA microscopy allows to achieve 3D imaging and 3D fabrication with submicrometer resolution, similar to those obtained by two-photon absorption microscopy.

Esta tese propõe um método de avaliação de sistemas de obtenção de imagem radiológica através das Funções de Transferência simuladas para qualquer região do campo de radiação. Esse processo de simulação reflete as mudanças sofridas pelo ponto focal e, portanto, pela Função de Espalhamento de Ponto (FEP) ao longo do campo. A avaliação utiliza informações obtidas de Funções de Transferência ótica bi-dimensionais calculadas através da aplicação de Transformadas de Fourier sobre as Funções de Espalhamento de Ponto simuladas. O método permite realizar um mapeamento da resposta em freqüências espaciais dos sistemas radio1ógicos para todo o campo de radiação, comparar a nitidez da imagem de sistemas distintos com relação a regiões equivalentes e estudar uma região especifica para prever as distorções que serão inseridas na imagem. / In this work a method of evaluation for the radiological imaging systems performance by simulated transfer functions for any X-ray field region is proposed. The simulation procedures provide information of the changes of the focal spot sizes and, therefore, of the Point Spread Function (PSF) along the field. The evaluation yields the bi-dimensional optical Transfer Functions calculated from Fourier Transformation of the simulated PSFs. This method provides: the spatial frequency response for the entire radiation field of the radiological systems; comparisons of the image sharpness relative to equivalent field regions for different systems; and the study of a singular region in order to predict image distortions.

The Singular Value Decomposition (SVD) has many applications in image processing. The SVD can be used to restore a corrupted image by separating significant information from the noise in the image data set. This thesis outlines broad applications that address current problems in digital image processing. In conjunction with SVD filtering, image compression using the SVD is discussed, including the process of reconstructing or estimating a rank reduced matrix representing the compressed image. Numerical plots and error measurement calculations are used to compare results of the two SVD image restoration techniques, as well as SVD image compression. The filtering methods assume that the images have been degraded by the application of a blurring function and the addition of noise. Finally, we present numerical experiments for the SVD restoration and compression to evaluate our computation.