The results presented in this dissertation concern two different types of tomographic imaging. The first part of the dissertation is devoted to the time reversal method for approximate reconstruction of images in thermoacoustic tomography. A thorough numerical study of the method is presented. Error estimates of the time reversal approximation are provided. In the second part of the dissertation a type of emission tomography, called Compton camera imaging is considered. The mathematical problem arising in Compton camera imaging is the inversion of the cone transform. We present three methods for inversion of this transform in two dimensions. Numerical examples of reconstructions by these methods are also provided. Lastly, we turn to a problem of significance in homeland security, namely the detection of geometrically small, low emission sources in the presence of a large background radiation. We consider the use of Compton type detectors for this purpose and describe an efficient method for detection of such sources. Numerical examples demonstrating this method are also provided.

Experiment 683, at Fermi National Accelerator Laboratory's Wide Band Photon Laboratory, is designed to study photon-hadron collisions at energies up to ~s = 27 GeV. The Wide Band Photon Lab currently the highest energy photon beam in the world. Several processes are to be studied. One such process in the quantum electrodynamic (QED) Compton effect. This paper is concerned with the design and construction of a small electromagnetic calorimeter (with embedded proportional wire chambers) to be used to aid in the study of the QED Compton effect. A theoretical description of the QED Compton effect is given. Basic principles of calorimetry, as it pertains to high energy physics, are discussed. Tests of the components used for construction of this device is discussed and results reviewed. The components include wavelength shifter, scintillator, photomultiplier tubes, and photomultiplier tube bases. Muon testing of this device is discussed also. / Department of Physics and Astronomy

The Q-weak experiment aims to measure the weak charge of proton with a precision of 4.2%. The proposed precision on weak charge required a 2.5% measurement of the parity violating asymmetry in elastic electron - proton scattering. Polarimetry was the largest experimental contribution to this uncertainty and a new Compton polarimeter was installed in Hall C at Jefferson Lab to make the goal achievable. In this polarimeter the electron beam collides with green laser light in a low gain Fabry- Perot Cavity; the scattered electrons are detected in 4 planes of a novel diamond micro strip detector while the back scattered photons are detected in lead tungstate crystals. This diamond micro-strip detector is the first such device to be used as a tracking detector in a nuclear and particle physics experiment. The diamond detectors are read out using custom built electronic modules that include a preamplifier, a pulse shaping amplifier and a discriminator for each detector micro-strip. We use field programmable gate array based general purpose logic modules for event selection and histogramming. Extensive Monte Carlo simulations and data acquisition simulations were performed to estimate the systematic uncertainties. Additionally, the Moller and Compton polarimeters were cross calibrated at low electron beam currents using a series of interleaved measurements. In this dissertation, we describe all the subsystems of the Compton polarimeter with emphasis on the electron detector. We focus on the FPGA based data acquisition system built by the author and the data analysis methods implemented by the author. The simulations of the data acquisition and the polarimeter that helped rigorously establish the systematic uncertainties of the polarimeter are also elaborated, resulting in the first sub 1% measurement of low energy ( 1 GeV) electron beam polarization with a Compton electron detector. We have demonstrated that diamond based micro-strip detectors can be used for tracking in a high radiation environment and it has enabled us to achieve the desired precision in the measurement of the electron beam polarization which in turn has allowed the most precise determination of the weak charge of the proton.

Research on photon counting detectors (PCDs) is focused on semiconductor materials, and silicon is a strong candidate to use in PCDs for photon counting computer tomography (CT). In a silicon detector, a significant portion of the counts is due to Compton scattering events. Since only part of the incident photon energy is deposited in a Compton interaction, Compton interactions lead to a loss of spectral information. By using Compton coincidence detection, i.e., combining information from multiple Compton events caused by the same incident photon, it is possible to obtain more spectral information from Compton scattered photons, increasing the energy resolution of the detector. The goal of this thesis is to develop and evaluate a method for Compton coincidence detection for photon counting CT. In this thesis, a method for Compton coincidence detection based on Compton kinematics and a χ2 test is presented and compared to a previously developed method based on maximum likelihood estimation. The χ2 method utilised the connection between the energy before vs after a Compton interaction, and the scattering angle. The possible scattering angles due to deposited energy in each interaction were called the energy angles. The spatial angles between the interaction positions in the detector were calculated and compared to the energy angles through a χ2 test in order to find the correct order of interaction and the incident photon energy. The χ2 method correctly identified the interaction order of 85.8% of simulated interaction chains ending in photoelectric effect and 64.1% of simulated interaction chains containing only Compton interactions. The energy estimation was 100% correct for all chains ending in photoelectric effect, since all of the incident energy was deposited in the detector. For chains of only Comptoninteractions, the energy was estimated with an RMS error of 21.2 keV. Combining the results from chains ending in a photoelectric interaction and chains of only Comptoninteractions, the total RMS error of the energy estimation was 11.5 keV. / Datortomografi (CT) är en viktig del av dagens sjukvård, och fotonräknande detektorer för CT är på väg från forskning till klinisk användning. Forskningen inom fotonräknande detektorer fokuserar på att använda halvledande material, och kisel är en stark kandidat till att användas för fotonräknande detektorer. I en kiseldetektor interagerar en betydande andel av fotonerna genom Compton-spridning. Då endast en del av fotonenergin deponeras i detektorn när en Compton-interaktion sker leder det till en förlust av spektral information. Genom att kombinera information från flera Compton-interaktioner som orsakats av samma infallande foton, så kallad sammanfallsdetektering, är det möjligtatt erhålla en ökad mängd spektral information från Compton-spridna fotoner. Målet med detta examensarbete är att utveckla och utvärdera en metod för sammanfallsdetektering för att erhålla spektral information från Compton-spridda fotoner i en detektortill fotonr¨aknande CT. I detta arbete presenteras en metod baserad på kinematiken bakom en Compton-interaktion och ett χ2-test. Metoden jämförs sedan med en tidigare utvecklad metod baserad på maximum likelihood-uppskattning. χ2-metoden utnyttjade sambandet mellan deponerad energi i en Compton-interaktion och möjliga spridningsvinklar, här kallade energivinklar. De spatiella vinklarna mellan interaktionerna i detektorn mättes och jämfördes genom ett χ2-test för att hitta interaktionsordningen och den infallande energin. χ2-metoden identifierade interaktionsordningen korrekt för 85.5% av alla simulerade interaktionskedjor som slutade i fotoelektrisk effekt och 64.1% av alla simulerade interaktionskedjorsom endast innehöll Compton-interaktioner. Uppskattningen av infallande energi var 100% korrekt för alla interaktionskedjor som slutade med en fotoelektrisk interaktion,eftersom all infallande energi deponerats i detektorn. För kejdor som endast bestod av Compton-interaktioner uppskattades den infallande energin med ett RMS-fel på 21.2 keV. Genom att kombinera resultaten från kedjor som slutade med en fotoelektrisk interaktion och resultaten från kejdor som endast bestod av Compton-interaktioner blev det totala RMS-felet för energi-uppskattningen 11.5 keV.

Cette thèse porte sur la conception et la réalisation du système optique d'une nouvelle source de rayonnement gamma, ELI-NP-GBS (Extreme Light Infrastructure - Nuclear Physics - Gamma Beam Source), qui utilise des développements récents des technologies des lasers, de l'optique et des accélérateurs. Les caractéristiques finales que devra atteindre cette source sont au moins d'un ordre de grandeur, en intensité, supérieur à la meilleure machine Compton actuelle, HIGS. Un nouveau type de système optique a été conçu pour ELI-NP-GBS. Il s'agit d'un système à 32 passages composé de deux miroirs paraboliques confocaux et d'un ensemble de paires de miroirs. Les miroirs paraboliques permettent la focalisation et la collimation successives d'un faisceau laser de haute intensité (400 mJ par impulsion). La géométrie "dragon-shape" garantie que le croisement du faisceau laser avec le faisceau d'électron se produise avec un angle constant en un point unique. De telles performances sont assurées par un alignement des éléments optiques à mieux que quelques micromètres en position et quelques microradians en orientation et une synchronisation de tous les passages avec les paquets d'électrons à mieux que quelques centaines de femtosecondes. Cet alignement et cette synchronisation est obtenue par l'intermédiaire de procédures et d'algorithmes spécialement développés pour ce système. Les algorithmes ont ainsi été développés et testés sur des simulations numériques dédiées prenant en compte les aspects mécaniques et optiques du système tel que les pré-alignements mécaniques, les états de surfaces des miroirs, la polarisation du faisceau laser, etc. Une première preuve de principe de la méthode de synchronisation a été concluante. / This thesis is about the design and the realization of the optical system of a new gamma-ray source, ELI-NP-GBS (Extreme Light Infrastructure - Nuclear Physics - Gamma Beam Source), which benefits from the recent developments in laser technology, optics and accelerators. The final characteristics that this source aims to reach is one order of magnitude higher in intensity than the actual best Compton machine, HIGS. A new type of optical system has been designed for ELI-NP-GBS. It is a 32 passes system made of two confocal parabolic mirrors and a set of Mirror-Pair Systems. The parabolic reflectors focalize and collimate successively a high intensity laser beam (400 mJ per pulse). The ``dragon-shape'' geometry ensures that the laser beam and electron bunches cross at a constant angle in a unique point. These performances are guaranteed by a few micrometers precision in position alignment, a few microradians precision in orientation alignment and by a few hundreds femtoseconds synchronization between electron bunches and laser pulses for each pass. This alignment and this synchronization is performed by used of dedicated procedures and algorithms. These algorithms have been developed and tested with numerical simulations which take into account the mechanical and optical aspects of the system such as the mechanical pre-alignment, the mirrors' surface deformations, the laser beam polarization, etc. A first proof of principle of the synchronization method has been successful.

Em vista de recentes determinações experimentais do perfil de Compton (Eisenberger, Phys. Rev., A2, 1678(1970); Wellenstein e Bonham, Phys. Rev., A7, 1568(1973}, procuramos efetuar um estudo comparativo de cálculos teóricos do perfil de Compton para o átomo de hélio (1S). Para tal, o conjunto de funções de onda elaboradas por Shull e L6wdin (J.Chem.Phy., 23, 1362(1955); 23, 1565(1955}; 30, 617(1959} mostrou-se bastante adequado, visto que permitiu observar a influência da função de onda no cálculo de perfil de Compton. Nossos resultados mostram em contraste à idéia geralmente aceita, que mesmo funções de onda igualmente boas para o cálculo da energia podem fornecer perfis de Compton com um erro maior que o experimental. Alem disso, apresentamos um conjunto de novos dados para o perfil de Compton e para a distribuição radial de momentum. Procuramos, também explicar essas discrepâncias relacionando-as com a transformada de Fourier da função de onda no espaço de configuração. / In view of the recent experimental determination of the Compton profile (Eisenberger, Phys., Rev., A2,1678(1970); Wellenstein and Bonham, Phys, Rev., A7, 1568(1973), we have performed a comparative study of theoretical calcu1ation of the Compton profile for the helium atom (1S). For such, the set of wave functions elaborated by Shull and Löwdin (J.Chem. Phys., 23, 1362(1955); 23, 1565(1955); 30, 617(1959) show itself specially suftable since it was possible to observe the influence af the wave functions on the calculated profile. Our results show in, contrast to general accepted idea, that even equally good wave functions in the energy sense may give theoretical profiles in error greater than the experimental one. Besides, we have presented a set of new data for the Compton profile and radial momentum distribution. A1so we have tried to explain the source of these discrepancies relating them to the Fourier transformation of the wave function in the configuration space.

Uma simulação baseada em métodos Monte Carlo foi criada com o intuito de avaliar a potencialidade da utilização do espalhamento Compton em altas energias para a obtenção de medidas absolutas e de alta precisão da energia de fótons marcados. Esse método se baseia em medidas angulares dos produtos desse espalhamento para reconstruir a energia dos fótons incidentes, utilizando a cinemática do espalhamento Compton em aproximação de impulso. A simulação inclui vários efeitos relevantes à medida, como espalhamento múltiplo de elétrons, momento interno dos elétrons nos átomos do alvo, resolução do detetor e vários parâmetros geométricos do arranjo experimental. Através da simulação de um experimento que utiliza esse método para a calibração em energia de um feixe de fótons marcados, foi possível identificar duas fontes de erros sistemáticos. Métodos de análise que minimiza um desse erros sistemáticos foram desenvolvidos, bem como métodos para a criação de correções para as medidas de energia. Verificou-se que, pelo menos no arranjo experimental estudado, é possível obter medidas da energia dos fótons incidentes com precisão da ordem de 0.07%. / A simulation based on Monte Carlo methods was created in order to evaluate the potentiality of using Compton scattering at high energies to obtain high precision absolute measurements of tagged photon energies. This method is based on angular measurements of the scattering products to reconstruct the incident photon energy using the kinematics of Compton scattering in impulse approximation. The simulation includes several effects that are relevant to the measurement, such as electron multiple scattering, internal momentum of the electrons in the atoms of the target, detector resolution and several geometrical parameters of the experimental setup. Through simulation of an experiment that uses this method for energy calibration of a tagged photon beam, it was possible to identify two sources of systematic errors. Analysis methods that minimize one of these systematic errors were developed, as well as methods for the creation of corrections to the energy measurements. Our results show that, at least in the studied experimental setup, it is possible to obtain energy measurements with a precision in the order of 0.07%.

Estimamos os valores das polarizabilidades dipolares elétrica e magnética do próton, levando em conta as contribuições das ressonâncias nucleônicas de menor massa: P33 (1236), P11 (1450), D13 (1525), S11(1550), e da ressonância mesônica &#949 (660). O valor obtido para a soma das polarizabilidades concorda bem com os dados experimentais. Por outro lado, o valor obtido para cada uma delas, que depende do valor não bem determinado da largura do decaimento &#949 &#8594 &#933 &#933, é compatível com os valores experimentais / We have estimated the values of electric and magnetic polarizabilities of the proton, taking into account the contributions of the low masses nucleon ressonances : P33 (1236), P11 (1450), D13 (1525), S11(1550) and the meson ressonance &#949 (660). The obtained value for the sumo f the polarizabilities is in good agreement with the experimental data. On the other hand, the value, of each polarizability, which depends on the not too well determined width decay &#949 &#8594 &#933 &#933, is compatible with experimental values

No último século, houve grande avanço no entendimento das interações das radiações com a matéria. Essa compreensão se faz necessária para diversas aplicações, entre elas o uso de raios X no diagnóstico por imagens. Neste caso, imagens são formadas pelo contraste resultante da diferença na atenuação dos raios X pelos diferentes tecidos do corpo. Entretanto, algumas das interações dos raios X com a matéria podem levar à redução da qualidade destas imagens, como é o caso dos fenômenos de espalhamento. Muitas abordagens foram propostas para estimar a distribuição espectral de fótons espalhados por uma barreira, ou seja, como no caso de um feixe de campo largo, ao atingir um plano detector, tais como modelos que utilizam métodos de Monte Carlo e modelos que utilizam aproximações analíticas. Supondo-se um espectro de um feixe primário que não interage com nenhum objeto após sua emissão pelo tubo de raios X, este espectro é, essencialmente representado pelos modelos propostos anteriormente. Contudo, considerando-se um feixe largo de radiação X, interagindo com um objeto, a radiação a ser detectada por um espectrômetro, passa a ser composta pelo feixe primário, atenuado pelo material adicionado, e uma fração de radiação espalhada. A soma destas duas contribuições passa a compor o feixe resultante. Esta soma do feixe primário atenuado, com o feixe de radiação espalhada, é o que se mede em um detector real na condição de feixe largo. O modelo proposto neste trabalho visa calcular o espectro de um tubo de raios X, em situação de feixe largo, o mais fidedigno possível ao que se medem em condições reais. Neste trabalho se propõe a discretização do volume de interação em pequenos elementos de volume, nos quais se calcula o espalhamento Compton, fazendo uso de um espectro de fótons gerado pelo Modelo de TBC, a equação de Klein-Nishina e considerações geométricas. Por fim, o espectro de fótons espalhados em cada elemento de volume é somado ao espalhamento dos demais elementos de volume, resultando no espectro total espalhado. O modelo proposto foi implementado em ambiente computacional MATLAB® e comparado com medições experimentais para sua validação. O modelo proposto foi capaz de produzir espectros espalhados em diferentes condições, apresentando boa conformidade com os valores medidos, tanto em termos quantitativos, nas quais a diferença entre kerma no ar calculado e kerma no ar medido é menor que 10%, quanto qualitativos, com fatores de mérito superiores a 90%. / The understanding of the interactions between radiation and matter advanced considerably in the last century. This understanding was needed by several applications, such as the use of X-rays in diagnostic imaging. In diagnostic applications, the image is created by the contrast resulting from the X-ray attenuation by the different body tissues. However, some interactions between the X-rays with the matter may reduce the quality of the images obtained in diagnostic imaging, as is the case of the scattering phenomenon. There are several modeling approaches to estimate the spectral distribution of photons scattered through a barrier, as in the case of a broad beam hitting a spectrometer detector. For instance, there are approaches that use Monte Carlo methods and approaches that use analytical approximations. Assuming a primary spectrum that does not interact with any object after its issuance by the X -ray tube, this spectrum is essentially represented by the previously proposed models. However, considering a broad beam of X-rays interacting with an object, the radiation to be detected by a spectrometer is now composed of the primary beam attenuated by the added material, and a scattered radiation fraction. The sum of these two contributions becomes part of the resulting beam. This sum of attenuated primary beam with the scattered radiation beam is what is measured in a real detector in broad beam condition. The model proposed in this work aims to simulate the spectrum of an x-ray tube in wide beam situation, the most reliable possible to what is measured in real conditions. In this work we propose the discretisation of the volume of interaction into small volume elements, which are used to calculate the Compton scattering. The spectrum of the photon spreading in each volume element is added to other volume elements, resulting in the spectrum of the whole barrier. The proposed model was implemented in MATLAB®, a computational environment. We evaluate the model by comparing the computational results with results from physical experiments. The model we propose was capable of creating accurate distribution of the spectrum spreading, under different conditions and in different experiments. The model results were close to the results obtained by experimental evaluation, both quantitatively, such as the difference smaller than 10% between the simulated air kerma and the measured air kerma obtained in the experimental evaluation, and qualitatively.

Este trabalho apresenta um novo tomógrafo de espalhamento de fótons por efeito Compton para estudos de solos agrícolas em ambiente de campo. O seu desenvolvimento está fundamentado na física computacional, em uma instrumentação nuclear avançada e nas técnicas do espalhamento Compton. O posicionamento lado a lado da fonte de raios X e do detector de estado sólido, operando em efeito Compton, viabiliza uma técnica não invasiva para aplicação direta em campo agrícola, não necessitando coleta de amostras e preservando as condições naturais do solo. Este tomógrafo Compton de campo possui um sistema de detecção baseado em fotodiodo de Silício (SDD - Silicon Drift Detector) com eficiência de detecção de 18,9% (@ 35 keV), módulo eletrônico de processamento de sinais de dimensões reduzidas (7,0x10,0x2,5 cm) e baixo consumo de energia elétrica (2,5 W). Outro aspecto relevante é a sua sonda de medida que viabiliza a coleta de projeções tomográficas, bem como o georeferenciamento que permite uma correta identificação da localização das análises. Resultados obtidos diretamente em um campo agrícola viabilizaram a obtenção de imagens tomográficas com resolução espacial 1x1 cm2, faixa de abordagem de 10x10 cm2, medidas densitométricas na faixa de 1,0 a 1,3 g/cm3 e energia de 37,8 keV, o que viabilizou medidas em profundidade de interesse agrícola. / This research presents a new tomograph scattering of photons by the Compton Effect for studies of agricultural soils in a field environment. Its development is based on computational physics, in an advanced nuclear instrumentation and techniques of Compton scattering. The side by side position of X-ray source and solid-state detector, operating in the Compton Effect, enables a noninvasive technique for direct application in the agricultural field, without sampling and preserving the natural soil conditions. This field Compton tomograph has a detection system based on Silicon photodiode (SDD Silicon Drift Detector) with detection efficiency of 18.9% (@ 35keV), electronic module of signal processing with reduced dimensions (7.0 x 10.0 x 2.5 cm) and low power consumption (2.5 W). Another relevant aspect is its measuring probe that enables the acquisition of tomographic projections and its georeferencing that allows a correct identification of the analysis location. Results obtained directly in agricultural field enabled the achievement of tomographic images with spatial resolution of 1x1cm2, range approach of 10x10 cm2, densitometric measurements in the range from 1.0 to 1.3 g/cm3 and energy of 37.8 keV, which enabled in-depth measures of agricultural interest.