Electron tomography at 2.4 {\AA} resolution

Transmission electron microscopy (TEM) is a powerful imaging tool that has found broad application in materials science, nanoscience and biology(1-3). With the introduction of aberration-corrected electron lenses, both the spatial resolution and image quality in TEM have been significantly improved(4,5) and resolution below 0.5 {\AA} has been demonstrated(6). To reveal the 3D structure of thin samples, electron tomography is the method of choice(7-11), with resolutions of ~1 nm^3 currently achievable(10,11). Recently, discrete tomography has been used to generate a 3D atomic reconstruction of a silver nanoparticle 2-3 nm in diameter(12), but this statistical method assumes prior knowledge of the particle's lattice structure and requires that the atoms fit rigidly on that lattice. Here we report the experimental demonstration of a general electron tomography method that achieves atomic scale resolution without initial assumptions about the sample structure. By combining a novel projection alignment and tomographic reconstruction method with scanning transmission electron microscopy, we have determined the 3D structure of a ~10 nm gold nanoparticle at 2.4 {\AA} resolution. While we cannot definitively locate all of the atoms inside the nanoparticle, individual atoms are observed in some regions of the particle and several grains are identified at three dimensions. The 3D surface morphology and internal lattice structure revealed are consistent with a distorted icosahedral multiply-twinned particle. We anticipate that this general method can be applied not only to determine the 3D structure of nanomaterials at atomic scale resolution(13-15), but also to improve the spatial resolution and image quality in other tomography fields(7,9,16-20).Comment: 27 pages, 17 figure

Compressed sensing for electron cryotomography and high-resolution subtomogram averaging of biological specimens

Cryoelectron tomography (cryo-ET) and subtomogram averaging (STA) allow direct visualization and structural studies of biological macromolecules in their native cellular environment, in situ. Often, low signal-to-noise ratios in tomograms, low particle abundance within the cell, and low throughput in typical cryo-ET workflows severely limit the obtainable structural information. To help mitigate these limitations, here we apply a compressed sensing approach using 3D second-order total variation (CS-TV2) to tomographic reconstruction. We show that CS-TV2 increases the signal-to-noise ratio in tomograms, enhancing direct visualization of macromolecules, while preserving high-resolution information up to the secondary structure level. We show that, particularly with small datasets, CS-TV2 allows improvement of the resolution of STA maps. We further demonstrate that the CS-TV2 algorithm is applicable to cellular specimens, leading to increased visibility of molecular detail within tomograms. This work highlights the potential of compressed sensing-based reconstruction algorithms for cryo-ET and in situ structural biology

Development and Implementation of Fully 3D Statistical Image Reconstruction Algorithms for Helical CT and Half-Ring PET Insert System

X-ray computed tomography: CT) and positron emission tomography: PET) have become widely used imaging modalities for screening, diagnosis, and image-guided treatment planning. Along with the increased clinical use are increased demands for high image quality with reduced ionizing radiation dose to the patient. Despite their significantly high computational cost, statistical iterative reconstruction algorithms are known to reconstruct high-quality images from noisy tomographic datasets. The overall goal of this work is to design statistical reconstruction software for clinical x-ray CT scanners, and for a novel PET system that utilizes high-resolution detectors within the field of view of a whole-body PET scanner. The complex choices involved in the development and implementation of image reconstruction algorithms are fundamentally linked to the ways in which the data is acquired, and they require detailed knowledge of the various sources of signal degradation. Both of the imaging modalities investigated in this work have their own set of challenges. However, by utilizing an underlying statistical model for the measured data, we are able to use a common framework for this class of tomographic problems. We first present the details of a new fully 3D regularized statistical reconstruction algorithm for multislice helical CT. To reduce the computation time, the algorithm was carefully parallelized by identifying and taking advantage of the specific symmetry found in helical CT. Some basic image quality measures were evaluated using measured phantom and clinical datasets, and they indicate that our algorithm achieves comparable or superior performance over the fast analytical methods considered in this work. Next, we present our fully 3D reconstruction efforts for a high-resolution half-ring PET insert. We found that this unusual geometry requires extensive redevelopment of existing reconstruction methods in PET. We redesigned the major components of the data modeling process and incorporated them into our reconstruction algorithms. The algorithms were tested using simulated Monte Carlo data and phantom data acquired by a PET insert prototype system. Overall, we have developed new, computationally efficient methods to perform fully 3D statistical reconstructions on clinically-sized datasets

Development of X-ray phase-contrast imaging techniques for medical diagnostics

The X-Ray phase-contrast techniques are innovative imaging methods allowing overtaking the limitations of classic radiology. In addition to the differential X-ray absorption on which standard radiology relies, in phase-contrast imaging the contrast is given by the effects of the refraction of X-rays inside the tissues. The combination of phase-contrast with quantitative computer tomography (CT) allows for a highly accurate reconstruction of the tissues’ index of refraction. Thanks to the high sensitivity of the method, tomographic images can be obtained at clinically compatible dose. For all these reasons phase-contrast imaging is a very promising approach, which can potentially revolutionize diagnostic X-Ray imaging. Several techniques are classified under the name of X-Ray phase-contrast imaging. This Thesis focused on the so-called analyzer-based imaging (ABI) method. ABI uses a perfect crystal, placed between the sample and the detector, to visualize the phase effects occurred within the sample. The quantitative reconstruction of the refraction index from CT data is not trivial and before this Thesis work it was documented only for small size objects. This Thesis has focused on two main scientific problems: (1) the development of theoretical and calculation strategies to determine the quantitative map of the refraction index of large biological tissues/organs (>10 cm) using the ABI technique; and (2) the preparation of accurate and efficient tools to estimate and simulate the dose deposited in CT imaging of large samples. For the determination of the refraction index, two CT geometries were considered and studied: the out-of-plane and the in-plane configurations. The first one, the most used in the works reported in the literature, foresees that the rotation axis of the sample occurs in a plane parallel to that of the sensitivity of the analyzer crystal; while, in the second CT geometry, the rotation axis is perpendicular to that plane. The theoretical study, technical design and experimental implementation of the in-plane geometry have been main tasks of this Thesis. A first experiment has been performed in order to compare the results obtained with in-plane quantitative phase contrast CT with the absorption-based CT ones. An improved accuracy and a better agreement with the theoretical density values have been obtained by exploiting the refraction effect while keeping the dose to sample low. A second campaign of experiments has been performed on large human breasts to investigate the efficiency of the in-plane and out-of-plane CT geometries and the performances of the associated image reconstruction procedures. The same experimental conditions were also studied by numerical simulations and the results were compared. This analysis shows that the in-plane geometry allows producing more accurate quantitative three dimensional maps of the index of refraction, while the out-of-plane case is preferable for qualitative investigations. A study for developing advanced procedures for improving the quality of the obtained CT images has been also conducted. As a result, a two-step procedure has been tested and identified: first the noise level of the experimental images is reduced by applying a wavelet decomposition algorithm and then a deconvolution procedure. The obtained images show an enhanced sharpness of the interfaces and of the object edges and high signal to noise ratio values are preserved. The second problem of this Thesis was to find strategies to calculate, in a fast way, the delivered dose in CT imaging of complex biological samples. For this purpose an acceleration method to speed-up the convergence of Monte Carlo simulations based on the Track Length Estimator method has been computed and included in the open-source software GATE. Results show that this method can lead to the same accuracy of conventional Monte Carlo methods while reducing the required computation time of up to two orders of magnitude, with the respect to the considered geometry. A database of dose curves for the case of monochromatic breast CT has been produced: it allows for a quick estimation of the delivered dose. A way to choose the best energy and the optimal photon flux was also proposed, which leads to a significant reduction of the delivered dose without any loss in terms of image quality. Most of the experimental and data reconstruction methods developed within this Thesis work can be applied also to other phase-contrast techniques. This Thesis shows that high resolution three dimensional diagnostic imaging of large and complex biological organs can, in principle, be performed at clinical compatible doses; this is the most significant contribution of the Thesis towards the clinical implementation of phase-contrast CT.Auf Phasenkontrast basierende Röntgentechniken sind innovative bildgebende Methoden, welche die Limitierungen der klassischen Radiologie überschreiten. Auβer der differentiellen Röntgenabsorption, auf der die herkömmliche Radiologie beruht, ist der Kontrast bei Phasenkontrast-Bildgebung durch die Brechungseffekte der Röntgenstrahlen innerhalb eines Gewebes gegeben. Die Kombination zwischen Phasenkontrast und quantitativer Computertomographie (CT) erlaubt eine höchstgenaue Rekonstruktion der Brechzahl der Gewebe. Aufgrund der hohen Empfindlichkeit dieser Methode, können tomographische Bilder mit einer klinisch verträglichen Dosis erzeugt werden. Aus all diesen Gründen, stellt Phasenkontrast-Bildgebung einen vielversprechenden Ansatz dar, welcher die diagnostische Röntgenbildgebung revolutionieren könnte. Verschiedene röntgenbildgebende Techniken werden als Phasenkontrast-Verfahren bezeichnet. Die vorliegende Doktorarbeit befasst sich mit der sogenannten Bildgebungsmethode mithilfe eines Analysatorkristalls (auf englisch: analyser-based imaging (ABI) ). ABI benutzt ein perfektes, zwischen der Probe und dem Detektor angeordnetes Kristall, um in der Probe stattfindenden Phaseneffekte zu veranschaulichen. Die quantitative Rekonstruktion des Brechungsindizes aus den CT-Daten ist jedoch nicht trivial und war vor dieser Arbeit nur für kleine Gegenstände beschrieben. Im Mittelpunkt dieser Dissertation stehen folgende wissenschaftliche Fragestellungen: (1) die Entwicklung theoretischer und rechnerischer Strategien, um die quantitative räumliche Verteilung des Brechungsindizes in größeren Organen aus biologischen Geweben (10 cm) unter Verwendung der ABI-Technik zu bilden und (2) die Vorbereitung von genauen und leistungsfähigen Rechenmitteln zur Abschätzung und Simulation der in größeren Proben bei einem CT-Bildgebungsversuch abgelagerten Strahlendosis zu treffen. Für die Bestimmung des Brechungsindizes wurden zwei geometrische Anordnungen in Betracht gezogen und untersucht, und zwar die Konfiguration auβerhalb (out-of-plane) bzw. in der Ebene (in-plane) der Probe. Erstere wird am häufigsten in der Fachliteratur zitiert und sieht vor, dass die Probe-Drehachse sich in der parallelen Ebene zur Achse des Analysatorkristalls befindet, wobei in der zweiteren Geometrie die Drehachse orthogonal zu jener Ebene ist. Die theoretische Studie, der technische Entwurf und die experimentelle Umsetzung der geometrischen Anordnung in der Probe-Ebene stellen die Hauptaufgaben dieser Arbeit dar. Ein erstes Experiment wurde durchgeführt, um die durch quantitative Phasenkontrast-CT nach in-plane-Modus erlangten Ergebnisse mit entsprechenden, auf Absorption basierenden CT-Versuchen zu vergleichen. Eine höhere Genauigkeit sowie eine bessere Übereinstimmung mit den theoretischen Dichtewerten wurden dadurch erzielt, dass man sich die Brechungseffekte zunutze macht, indem man die an die Probe gelieferte Dosis niedrig hält. Eine zweite Versuchsreihe wurde auβerdem auf menschliche Brüste ausgeführt, um die Effizienz sowohl der in-plane- als auch der out-of-plane-CT-Geometrien sowie die Leistungsfähigeit der entsprechenden Bildrekonstruktionsverfahren zu überprüfen. Die gleichen Experimentalbedingungen wurden auch anhand von numerischen Simulationen untersucht und die Ergebnisse miteinander verglichen. Diese Analyse zeigt, dass die in-plane-Geometrie die Erstellung genauerer dreidimensionaler Verteilungen der Brechzahl ermöglicht, während der out-of-plane-Fall eher für die Zwecke qualitativer Untersuchungen vorzuziehen ist. Fortschrittliche Prozeduren zur Verbesserung der Qualität von aufgezeichneten CT-Bildern wurden im Rahmen dieser Doktorarbeit konzipiert und entwickelt. Das Fazit: eine zweistufige Vorgehensweise wurde ermittelt und geprüft. Zunächst wird der Rauschpegel der Meβdaten über die Anwendung eines Zerlegungsalgorithmus mittels Wavelets gesenkt, anschlieβend gefolgt von einem Entfaltung-Verfahren. Die damit gewonnenen Bilder weisen eine erhöhte Schärfe der Schnittstellen auf. Die Objektkanten und das Signal-zu-Rausch-Verhältnis bleiben damit erhalten. Die zweite Fragestellung dieser Arbeit war es, Lösungansätze zu erarbeiten, um die während CT-Bildgebung-Messungen über complexe biologische Proben abgegebene Dosis möglichst rapide zu berechnen. Zu diesem Zweck wurde ein Verfahren zur Beschleunigung der Konvergenz von Monte-Carlo-Simulationen auf der Grundlage der Track-Length-Estimator-Methode entwickelt und in die Open-Source-Software GATE eingegliedert. Die bisherigen Ergebnisse zeigen, dass dieses Verfahren zur selben Genauigkeit der herkömmlichen Monte-Carlo-Methoden bei gleichzeitiger Minderung bis zu zwei Gröβenordnungen der zur Berechnung einer und der selben Geometrie notwendigen Rechenzeit führt. Eine Datenbank von Dosiskurven für den Fall von monochromatischer Brust-CT ist erzeugt worden, die eine schnelle Schätzung der abgegebenen Dosis erlaubt. Darüber hinaus wurde ein Lösungsweg zur Auswahl der besten Energie und des optimalen Photonenflusses vorgeschlagen, welcher eine bedeutende Abnahme der abgelieferten Dosis zur Folge hat, und zwar ohne Bildqualitätsverluste. Die meisten, im Rahmen dieser Doktorarbeit entwickelten Experimental- und Datenrekonstruktion-Verfahren können freilich auch an andere Phasenkontrast-Techniken angewendet werden. Es wird hiermit gezeigt, dass hochauflösende dreidimensionale bildgebende Verfahren zur Diagnostik gröβerer und komplexer biologischer Gegenstände bei klinisch verträglichen Dosen grundsätzlich eingesetzt werden können. Dies ist der nennenwerteste Beitrag dieser Dissertation zur klinischen Umsetzung der Phasenkontrast-CT

Tungsten tip and atomic site tomography

Atomic electron tomography aims to precisely locate individual atoms of a nanoparticle in three-dimensional space. In this work, a tomography method based on tungsten tips is developed to allow images to be taken over a full angular range by placing a nanoparticle on the apex of an etched tungsten tip. There is no interference of signal from supporting materials with the suspended nanoparticle. A new reconstruction algorithm, atomic site tomography, is developed using the principle of regularisation in multiple linear regression. This algorithm is specifically designed for identifying the precise locations of individual atoms in three-dimensional space, and the algorithm is validated by an experimental dataset. A gold nanoparticle dataset is successfully obtained by tungsten tip tomography, and the dataset is processed to remove scanning artefacts. Selected region of the gold nanoparticle dataset is used to demonstrate the new reconstruction algorithm and the whole gold nanoparticle is then reconstructed. A tuning fork atomic force microscope is developed to provide a more flexible method to prepare samples for tungsten tip tomography and its progress is reported. This work contributes to the field of atomic electron tomography by improving the experimental techniques for acquiring high-quality tomography dataset and proposing a new reconstruction algorithm which aims at locating individual atoms of nanoparticles precisely

Development of temporal phase unwrapping algorithms for depth-resolved measurements using an electronically tuned Ti:Sa laser

This thesis is concerned with (a) the development of full-field, multi-axis and phase contrast wavelength scanning interferometer, using an electronically tuned CW Ti:Sa laser for the study of depth resolved measurements in composite materials such as GFRPs and (b) the development of temporal phase unwrapping algorithms for depth re-solved measurements. Item (a) was part of the ultimate goal of successfully extracting the 3-D, depth-resolved, constituent parameters (Young s modulus E, Poisson s ratio v etc.) that define the mechanical behaviour of composite materials like GFRPs. Considering the success of OCT as an imaging modality, a wavelength scanning interferometer (WSI) capable of imaging the intensity AND the phase of the interference signal was proposed as the preferred technique to provide the volumetric displacement/strain fields (Note that displacement/strain fields are analogous to phase fields and thus a phase-contrast interferometer is of particular interest in this case). These would then be passed to the VFM and yield the sought parameters provided the loading scheme is known. As a result, a number of key opto-mechanical hardware was developed. First, a multiple channel (x6) tomographic interferometer realised in a Mach-Zehnder arrangement was built. Each of the three channels would provide the necessary information to extract the three orthogonal displacement/strain components while the other three are complementary and were included in the design in order to maximize the penetration depth (sample illuminated from both sides). Second, a miniature uniaxial (tensile and/or compression) loading machine was designed and built for the introduction of controlled and low magnitude displacements. Last, a rotation stage for the experimental determination of the sensitivity vectors and the re-registration of the volumetric data from the six channels was also designed and built. Unfortunately, due to the critical failure of the Ti:Sa laser data collection using the last two items was not possible. However, preliminary results at a single wavelength suggested that the above items work as expected. Item (b) involved the development of an optical sensor for the dynamic monitoring of wavenumber changes during a full 100 nm scan. The sensor is comprised of a set of four wedges in a Fizeau interferometer setup that became part of the multi-axis interferometer (7th channel). Its development became relevant due to the large amount of mode-hops present during a full scan of the Ti:Sa source. These are associated to the physics of the laser and have the undesirable effect of randomising the signal and thus preventing successful depth reconstructions. The multi-wedge sensor was designed so that it provides simultaneously high wavenumber change resolution and immunity to the large wavenumber jumps from the Ti:Sa. The analysis algorithms for the extraction of the sought wavenumber changes were based on 2-D Fourier transform method followed by temporal phase unwrapping. At first, the performance of the sensor was tested against that of a high-end commercial wavemeter for a limited scan of 1nm. A root mean square (rms) difference in measured wavenumber shift between the two of ∼4 m-1 has been achieved, equivalent to an rms wavelength shift error of ∼0.4 pm. Second, by resampling the interference signal and the wavenumber-change axis onto a uniformly sampled k-space, depth resolutions that are close to the theoretical limits were achieved for scans of up to 37 nm. Access of the full 100 nm range that is characterised by wavelength steps down to picometers level was achieved by introducing a number of improvements to the original temporal phase unwrapping algorithm reported in ref [1] tailored to depth resolved measurements. These involved the estimation and suppression of intensity background artefacts, improvements on the 2-D Fourier transform phase detection based on a previously developed algorithm in ref [2] and finally the introduction of two modifications to the original TPU. Both approaches are adaptive and involve signal re-referencing at regular intervals throughout the scan. Their purpose is to compensate for systematic and non-systematic errors owing to a small error in the value of R (a scaling factor applied to the lower sensitivity wedge phase-change signal used to unwrap the higher sensitivity one), or small changes in R with wavelength due to the possibility of a mismatch in the refractive dispersion curves of the wedges and/or a mismatch in the wedge angles. A hybrid approach combining both methods was proposed and used to analyse the data from each of the four wedges. It was found to give the most robust results of all the techniques considered, with a clear Fourier peak at the expected frequency, with significantly reduced spectral artefacts and identical depth resolutions for all four wedges of 2.2 μm measured at FWHM. The ability of the phase unwrapping strategy in resolving the aforementioned issues was demonstrated by successfully measuring the absolute thickness of four fused silica glasses using real experimental data. The results were compared with independent micrometer measurements and showed excellent agreement. Finally, due to the lack of additional experimental data and in an attempt to justify the validity of the proposed temporal phase unwrapping strategy termed as the hybrid approach, a set of simulations that closely matched the parameters characterising the real experimental data set analysed were produced and were subsequently analysed. The results of this final test justify that the various fixes included in the hybrid approach have not evolved to solve the problems of a particular data set but are rather of general nature thereby, highlighting its importance for PC-WSI applications concerning the processing and analysis of large scans

Development of X-ray phase-contrast imaging techniques for medical diagnostics

The X-Ray phase-contrast techniques are innovative imaging methods allowing overtaking the limitations of classic radiology. In addition to the differential X-ray absorption on which standard radiology relies, in phase-contrast imaging the contrast is given by the effects of the refraction of X-rays inside the tissues. The combination of phase-contrast with quantitative computer tomography (CT) allows for a highly accurate reconstruction of the tissues’ index of refraction. Thanks to the high sensitivity of the method, tomographic images can be obtained at clinically compatible dose. For all these reasons phase-contrast imaging is a very promising approach, which can potentially revolutionize diagnostic X-Ray imaging. Several techniques are classified under the name of X-Ray phase-contrast imaging. This Thesis focused on the so-called analyzer-based imaging (ABI) method. ABI uses a perfect crystal, placed between the sample and the detector, to visualize the phase effects occurred within the sample. The quantitative reconstruction of the refraction index from CT data is not trivial and before this Thesis work it was documented only for small size objects. This Thesis has focused on two main scientific problems: (1) the development of theoretical and calculation strategies to determine the quantitative map of the refraction index of large biological tissues/organs (>10 cm) using the ABI technique; and (2) the preparation of accurate and efficient tools to estimate and simulate the dose deposited in CT imaging of large samples. For the determination of the refraction index, two CT geometries were considered and studied: the out-of-plane and the in-plane configurations. The first one, the most used in the works reported in the literature, foresees that the rotation axis of the sample occurs in a plane parallel to that of the sensitivity of the analyzer crystal; while, in the second CT geometry, the rotation axis is perpendicular to that plane. The theoretical study, technical design and experimental implementation of the in-plane geometry have been main tasks of this Thesis. A first experiment has been performed in order to compare the results obtained with in-plane quantitative phase contrast CT with the absorption-based CT ones. An improved accuracy and a better agreement with the theoretical density values have been obtained by exploiting the refraction effect while keeping the dose to sample low. A second campaign of experiments has been performed on large human breasts to investigate the efficiency of the in-plane and out-of-plane CT geometries and the performances of the associated image reconstruction procedures. The same experimental conditions were also studied by numerical simulations and the results were compared. This analysis shows that the in-plane geometry allows producing more accurate quantitative three dimensional maps of the index of refraction, while the out-of-plane case is preferable for qualitative investigations. A study for developing advanced procedures for improving the quality of the obtained CT images has been also conducted. As a result, a two-step procedure has been tested and identified: first the noise level of the experimental images is reduced by applying a wavelet decomposition algorithm and then a deconvolution procedure. The obtained images show an enhanced sharpness of the interfaces and of the object edges and high signal to noise ratio values are preserved. The second problem of this Thesis was to find strategies to calculate, in a fast way, the delivered dose in CT imaging of complex biological samples. For this purpose an acceleration method to speed-up the convergence of Monte Carlo simulations based on the Track Length Estimator method has been computed and included in the open-source software GATE. Results show that this method can lead to the same accuracy of conventional Monte Carlo methods while reducing the required computation time of up to two orders of magnitude, with the respect to the considered geometry. A database of dose curves for the case of monochromatic breast CT has been produced: it allows for a quick estimation of the delivered dose. A way to choose the best energy and the optimal photon flux was also proposed, which leads to a significant reduction of the delivered dose without any loss in terms of image quality. Most of the experimental and data reconstruction methods developed within this Thesis work can be applied also to other phase-contrast techniques. This Thesis shows that high resolution three dimensional diagnostic imaging of large and complex biological organs can, in principle, be performed at clinical compatible doses; this is the most significant contribution of the Thesis towards the clinical implementation of phase-contrast CT.Auf Phasenkontrast basierende Röntgentechniken sind innovative bildgebende Methoden, welche die Limitierungen der klassischen Radiologie überschreiten. Auβer der differentiellen Röntgenabsorption, auf der die herkömmliche Radiologie beruht, ist der Kontrast bei Phasenkontrast-Bildgebung durch die Brechungseffekte der Röntgenstrahlen innerhalb eines Gewebes gegeben. Die Kombination zwischen Phasenkontrast und quantitativer Computertomographie (CT) erlaubt eine höchstgenaue Rekonstruktion der Brechzahl der Gewebe. Aufgrund der hohen Empfindlichkeit dieser Methode, können tomographische Bilder mit einer klinisch verträglichen Dosis erzeugt werden. Aus all diesen Gründen, stellt Phasenkontrast-Bildgebung einen vielversprechenden Ansatz dar, welcher die diagnostische Röntgenbildgebung revolutionieren könnte. Verschiedene röntgenbildgebende Techniken werden als Phasenkontrast-Verfahren bezeichnet. Die vorliegende Doktorarbeit befasst sich mit der sogenannten Bildgebungsmethode mithilfe eines Analysatorkristalls (auf englisch: analyser-based imaging (ABI) ). ABI benutzt ein perfektes, zwischen der Probe und dem Detektor angeordnetes Kristall, um in der Probe stattfindenden Phaseneffekte zu veranschaulichen. Die quantitative Rekonstruktion des Brechungsindizes aus den CT-Daten ist jedoch nicht trivial und war vor dieser Arbeit nur für kleine Gegenstände beschrieben. Im Mittelpunkt dieser Dissertation stehen folgende wissenschaftliche Fragestellungen: (1) die Entwicklung theoretischer und rechnerischer Strategien, um die quantitative räumliche Verteilung des Brechungsindizes in größeren Organen aus biologischen Geweben (10 cm) unter Verwendung der ABI-Technik zu bilden und (2) die Vorbereitung von genauen und leistungsfähigen Rechenmitteln zur Abschätzung und Simulation der in größeren Proben bei einem CT-Bildgebungsversuch abgelagerten Strahlendosis zu treffen. Für die Bestimmung des Brechungsindizes wurden zwei geometrische Anordnungen in Betracht gezogen und untersucht, und zwar die Konfiguration auβerhalb (out-of-plane) bzw. in der Ebene (in-plane) der Probe. Erstere wird am häufigsten in der Fachliteratur zitiert und sieht vor, dass die Probe-Drehachse sich in der parallelen Ebene zur Achse des Analysatorkristalls befindet, wobei in der zweiteren Geometrie die Drehachse orthogonal zu jener Ebene ist. Die theoretische Studie, der technische Entwurf und die experimentelle Umsetzung der geometrischen Anordnung in der Probe-Ebene stellen die Hauptaufgaben dieser Arbeit dar. Ein erstes Experiment wurde durchgeführt, um die durch quantitative Phasenkontrast-CT nach in-plane-Modus erlangten Ergebnisse mit entsprechenden, auf Absorption basierenden CT-Versuchen zu vergleichen. Eine höhere Genauigkeit sowie eine bessere Übereinstimmung mit den theoretischen Dichtewerten wurden dadurch erzielt, dass man sich die Brechungseffekte zunutze macht, indem man die an die Probe gelieferte Dosis niedrig hält. Eine zweite Versuchsreihe wurde auβerdem auf menschliche Brüste ausgeführt, um die Effizienz sowohl der in-plane- als auch der out-of-plane-CT-Geometrien sowie die Leistungsfähigeit der entsprechenden Bildrekonstruktionsverfahren zu überprüfen. Die gleichen Experimentalbedingungen wurden auch anhand von numerischen Simulationen untersucht und die Ergebnisse miteinander verglichen. Diese Analyse zeigt, dass die in-plane-Geometrie die Erstellung genauerer dreidimensionaler Verteilungen der Brechzahl ermöglicht, während der out-of-plane-Fall eher für die Zwecke qualitativer Untersuchungen vorzuziehen ist. Fortschrittliche Prozeduren zur Verbesserung der Qualität von aufgezeichneten CT-Bildern wurden im Rahmen dieser Doktorarbeit konzipiert und entwickelt. Das Fazit: eine zweistufige Vorgehensweise wurde ermittelt und geprüft. Zunächst wird der Rauschpegel der Meβdaten über die Anwendung eines Zerlegungsalgorithmus mittels Wavelets gesenkt, anschlieβend gefolgt von einem Entfaltung-Verfahren. Die damit gewonnenen Bilder weisen eine erhöhte Schärfe der Schnittstellen auf. Die Objektkanten und das Signal-zu-Rausch-Verhältnis bleiben damit erhalten. Die zweite Fragestellung dieser Arbeit war es, Lösungansätze zu erarbeiten, um die während CT-Bildgebung-Messungen über complexe biologische Proben abgegebene Dosis möglichst rapide zu berechnen. Zu diesem Zweck wurde ein Verfahren zur Beschleunigung der Konvergenz von Monte-Carlo-Simulationen auf der Grundlage der Track-Length-Estimator-Methode entwickelt und in die Open-Source-Software GATE eingegliedert. Die bisherigen Ergebnisse zeigen, dass dieses Verfahren zur selben Genauigkeit der herkömmlichen Monte-Carlo-Methoden bei gleichzeitiger Minderung bis zu zwei Gröβenordnungen der zur Berechnung einer und der selben Geometrie notwendigen Rechenzeit führt. Eine Datenbank von Dosiskurven für den Fall von monochromatischer Brust-CT ist erzeugt worden, die eine schnelle Schätzung der abgegebenen Dosis erlaubt. Darüber hinaus wurde ein Lösungsweg zur Auswahl der besten Energie und des optimalen Photonenflusses vorgeschlagen, welcher eine bedeutende Abnahme der abgelieferten Dosis zur Folge hat, und zwar ohne Bildqualitätsverluste. Die meisten, im Rahmen dieser Doktorarbeit entwickelten Experimental- und Datenrekonstruktion-Verfahren können freilich auch an andere Phasenkontrast-Techniken angewendet werden. Es wird hiermit gezeigt, dass hochauflösende dreidimensionale bildgebende Verfahren zur Diagnostik gröβerer und komplexer biologischer Gegenstände bei klinisch verträglichen Dosen grundsätzlich eingesetzt werden können. Dies ist der nennenwerteste Beitrag dieser Dissertation zur klinischen Umsetzung der Phasenkontrast-CT

Snapshot Three-Dimensional Surface Imaging With Multispectral Fringe Projection Profilometry

Fringe Projection Profilometry (FPP) is a popular method for non-contact optical surface measurements, including motion tracking. The technique derives 3D surface maps from phase maps estimated from the distortions of fringe patterns projected onto the surface of an object. Estimation of phase maps is commonly performed with spatial phase retrieval algorithms that use a series of complex data processing stages. Researchers must have advanced data analysis skills to process FPP data due to a lack of availability of simple research-oriented software tools. Chapter 2 describes a comprehensive FPP software tool called PhaseWareTM that allows novice to experienced users to perform pre-processing of fringe patterns, phase retrieval, phase unwrapping, and finally post-processing. The sequential process of acquiring fringe patterns from an object is necessary to sample the surface densely enough to accurately estimate surface profiles. Sequential fringe acquisition performs poorly if the object is in motion between fringe projections. To overcome this limitation, we developed a novel method of FPP called multispectral fringe projection profilometry (MFPP), where multiple fringe patterns are composited into a multispectral illumination pattern and a single multispectral camera is used to capture the frame. Chapter 3 introduces this new technique and shows how it can be used to perform 3D profilometry at video frame rates. Although the first attempt at MFPP significantly improved acquisition speed, it did not fully satisfy the condition for temporal phase retrieval, which requires at least three phase-shifted fringe patterns to characterize a surface. To overcome this limitation, Chapter 4 introduces an enhanced version of MFPP that utilized a specially designed multispectral illuminator to simultaneously project four p/2 phase-shifted fringe patterns onto an object. Combined with spectrally matched multispectral imaging, the refined MFPP method resulted in complete data for temporal phase retrieval using only a single camera exposure, thereby maintaining the high sampling speed for profilometry of moving objects. In conclusion, MFPP overcomes the limitations of sequential sampling imposed by FPP with temporal phase extraction without sacrificing data quality or accuracy of the reconstructed surface profiles. Since MFPP utilizes no moving parts and is based on MEMS technology, it is applicable to miniaturization for use in mobile devices and may be useful for space-constrained applications such as robotic surgery. Fringe Projection Profilometry (FPP) is a popular method for non-contact optical surface measurements such as motion tracking. The technique derives 3D surface maps from phase maps estimated from the distortions of fringe patterns projected onto the surface of the object. To estimate surface profiles accurately, sequential acquisition of fringe patterns is required; however, sequential fringe projection and acquisition perform poorly if the object is in motion during the projection. To overcome this limitation, we developed a novel method of FPP maned multispectral fringe projection profilometry (MFPP). The proposed method provides multispectral illumination patterns using a multispectral filter array (MFA) to generate multiple fringe patterns from a single illumination and capture the composite pattern using a single multispectral camera. Therefore, a single camera acquisition can provide multiple fringe patterns, and this directly increases the speed of imaging by a factor equal to the number of fringe patterns included in the composite pattern. Chapter 3 introduces this new technique and shows how it can be used to perform 3D profilometry at video frame rates. The first attempt at MFPP significantly improved acquisition speed by a factor of eight by providing eight different fringe patterns in four different directions, which permits the system to detect more morphological details. However, the phase retrieval algorithm used in this method was based on the spatial phase stepping process that had a few limitations, including high sensitive to the quality of the fringe patterns and being a global process, as it spreads the effect of the noisy pixels across the entire result. To overcome this limitation, Chapter 4 introduces an enhanced version of MFPP that utilized a specially designed multispectral illuminator to simultaneously project four p/2 phase-shifted fringe patterns onto an object. Combined with a spectrally matched multispectral camera, the refined MFPP method provided the needed data for the temporal phase retrieval algorithm using only a single camera exposure. Thus, it delivers high accuracy and pixel-wise measurement (thanks to the temporal phase stepping algorithms) while maintaining a high sampling rate for profilometry of moving objects. In conclusion, MFPP overcomes the limitations of sequential sampling imposed by FPP with temporal phase extraction without sacrificing data quality or accuracy of the reconstructed surface profiles. Since MFPP utilizes no moving parts and is based on MEMS technology, it is applicable to miniaturization for use in mobile devices and may be useful for space-constrained applications such as robotic surgery