Electrical Impedance Tomography (ElT) is an emerging imaging technique with applications in the medical field and in the field of industrial process tomography (lPT). Until recently, data acquisition and image reconstruction schemes have been constructed with the assumption that the object being imaged is two-dimensional. In recent years, some research groups have started to address the third dimensional aspects of ElT by both building three dimensional enabled data acquisition systems and solving the three dimensional Forward Problem numerically since this allows the possibility of modelling complex shapes. However, solving the Forward Problem analytically is still very attractive as an analytical solution does not depend on the way the domain has been meshed. Furthermore, if dynamic images are reconstructed which are less sensitive to the model of the electrodes employed, the shape of the object being imaged and the position of the electrodes, an analytical solution to the Forward Problem can be used to reconstruct dynamic three dimensional images. This thesis will start by describing how a full analytical solution for a finite right circular cylinder (which approximately models the human thorax) on which two electrodes have been placed, is derived. It will be shown that the analytical solution has two different forms. Results will be presented detailing the convergence performance of the two different forms as well as comparisons between the analytical solution and experimentally obtained data. Finally three dimensional images reconstructed using these methods will be presented. In order to better approximate the shape of the human thorax, the above work has been extended to provide an analytical solution for an elliptical cylinder and this is presented in this thesis for the first time together with some simulation results. Today in Multi-frequency Electrical Impedance Tomography (MEIT), new hardware for recording measurements operating above 1MHz is now available. This high operating frequency raises the question of the validity of the employed quasi-static conditions used in the associated Forward Problem modelling. It is important to be able to determine when the quasi-static conditions fail and to investigate the differences between a solution to the Forward Problem based on quasi-static conditions and the one based on non quasistatic conditions at these frequencies. This thesis details the derivation of a new analytical solution based on non quasi-static conditions for a finite right circular cylinder having two electrodes placed on its boundary. Some comparisons between the new analytical solution and data obtained from in-vitro experiments will be presented in this thesis. A comparison between the new analytical solution and the analytical solution derived earlier in this thesis (which is based on quasi-static conditions) is also conducted. Whilst these results are preliminary results, they reveal that for situations associated with imaging the human thorax the quasi-static assumption appear violated when most modern MEIT systems are employed. This frequency dependent three dimensional analytical Forward Problem work has wide ranging implications for the future of MEIT. The thesis will conclude with some initial thoughts on how to incorporate anisotropy into three dimensional Forward Problem solutions.

A Transparência Eletromagneticamente Induzida tem sido muito usada atualmente para implementação de memórias quânticas. Neste trabalho, estudamos este fenômeno, experimental e teoricamente, utilizando um sistema de dois níveis com degenerescências como modelo para o átomo. Tratamos o campo eletromagnético como quantizado e propomos um modelo linearizado para as flutuações que leva em consideração as forças quânticas de Langevin. Devido ao excesso de ruído de fase presente em nosso laser, a implementeção numérica do modelo levou em consideração apenas a autocorrelação de fase como fonte para o sinal de ruído observado. Este modelo mostrou um bom acordo qualitativo com os dados experimentais observados. Fizemos medidas de ruído de soma e subtração com o esquema de deteção balanceada, calculamos os coeficientes de correlação normalizado e mostramos que há regiões de correlação e anticorrelação que variam com a intensidade do feixe. Observamos também uma inversão de picos no sinal de soma não prevista pelo modelo à medida que diminuimos a intensidade. Esta inversão pode ser causada por contribuições das flutuações de amplitude do laser a baixas intensidades. / Electromagnetically Induced Transparency has attracted much attention recently as a source to implement quantum memories. In this work, we studied this phenomenon, both theoretically and experimentally, using a degenerate two-level system modeling the atoms. We quantize the electromagnetic field and propose a linearized model for fluctuations that takes into account the quantum Langevin forces. Because of the excess noise in the phase of our laser, the numerical implementation of the theoretical model takes into account only the phase autocorrelation term as a source for the observed noise. This model showed a good qualitative agreement with the experimental data. We made sum and subtraction noise measurements using the balanced detection scheme, we calculated the normalized correlation coefficient and we showed that there are regions of correlation and anticorrelation that change with laser intensity. We also observed a peak inversion of the sum signal as laser intensity becames smaller that was not predicted by the model with only phase noise. The cause for this inversion can be the contribution of laser amplitude noise at small intensities.

A Transparência Eletromagneticamente Induzida tem sido muito usada atualmente para implementação de memórias quânticas. Neste trabalho, estudamos este fenômeno, experimental e teoricamente, utilizando um sistema de dois níveis com degenerescências como modelo para o átomo. Tratamos o campo eletromagnético como quantizado e propomos um modelo linearizado para as flutuações que leva em consideração as forças quânticas de Langevin. Devido ao excesso de ruído de fase presente em nosso laser, a implementeção numérica do modelo levou em consideração apenas a autocorrelação de fase como fonte para o sinal de ruído observado. Este modelo mostrou um bom acordo qualitativo com os dados experimentais observados. Fizemos medidas de ruído de soma e subtração com o esquema de deteção balanceada, calculamos os coeficientes de correlação normalizado e mostramos que há regiões de correlação e anticorrelação que variam com a intensidade do feixe. Observamos também uma inversão de picos no sinal de soma não prevista pelo modelo à medida que diminuimos a intensidade. Esta inversão pode ser causada por contribuições das flutuações de amplitude do laser a baixas intensidades. / Electromagnetically Induced Transparency has attracted much attention recently as a source to implement quantum memories. In this work, we studied this phenomenon, both theoretically and experimentally, using a degenerate two-level system modeling the atoms. We quantize the electromagnetic field and propose a linearized model for fluctuations that takes into account the quantum Langevin forces. Because of the excess noise in the phase of our laser, the numerical implementation of the theoretical model takes into account only the phase autocorrelation term as a source for the observed noise. This model showed a good qualitative agreement with the experimental data. We made sum and subtraction noise measurements using the balanced detection scheme, we calculated the normalized correlation coefficient and we showed that there are regions of correlation and anticorrelation that change with laser intensity. We also observed a peak inversion of the sum signal as laser intensity becames smaller that was not predicted by the model with only phase noise. The cause for this inversion can be the contribution of laser amplitude noise at small intensities.

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Cone-beam computed tomography (CBCT) is an imaging technique used in conjunction with radiation therapy. CBCT is used to verify the position of tumours just prior to radiation treatment session. The accuracy of the radiation treatment of thoracic and upper abdominal tumours is heavily affected by respiratory movement. Blurring artefacts, due to the movement during a CBCT scanning, cause misregistration between the CBCT image and the planning image. There has been growing interest in the use of motion-compensated CBCT for correcting the breathing-induced artefacts. A wide range of iterative reconstruction methods have been developed for CBCT imaging. The direct motion compensation technique has been applied to algebraic reconstruction technique (ART), simultaneous ART (SART), ordered-subset SART (OS-SART) and conjugate gradient least squares (CGLS). In this thesis a dual modality imaging of electrical impedance tomography (EIT) and CBCT is proposed for the first time. This novel dual modality imaging uses the advantages of high temporal resolution of EIT imaging and high spatial resolution of the CBCT method. The main objective of this study is to combine CBCT with EIT imaging system for motion-compensated CBCT using experimental and computational phantoms. The EIT images were used for extracting motion for a motion-compensated CBCT imaging system. A simple motion extraction technique is used for extracting motion data from the low spatial resolution EIT images. This motion data is suitable for input into the direct motion-compensated CBCT. The performance of iterative algorithms for motion compensation was also studied. The dual modality CBCT-EIT is verified using experimental EIT system and computational CBCT phantom data.

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Por meio da espectroscopia de ruído, estudamos a correlação entre dois feixes de luz com polarizações circulares opostas, acoplando a transição 5S1/2 F=2 à 5P3/2 F1=2 em configuração de Transparência Eletromagneticamente Induzida (EIT sigla em inglês) com átomos frios de Rubídio 85. Observamos a mudança de correlação para anti-correlação entre os feixes de prova e controle fora da ressonância, conforme aumentamos a sua potência. Esta transição é uma consequência da competição que existe entre a absorção de um fóton no sistema , responsável pelo regime de correlação, e as transições Stokes e Anti-Stokes que produzem a anti-correlação dos feixes. A partir dos espectros do sinal médio da intensidade e da correlação de ruído observamos, nesta última, que o pico de EIT é livre de alargamento por potência, o que possibilita que a medida do tempo de coerência entre os níveis fundamentais na condição de EIT seja mais precisa. Usando o modelo de Difusão de Fase para campos em EIT em configuração, observamos que os espectros teóricos de correlação estão de acordo com os dados experimentais. Isto mostra que esta teoria modela um sistema que envolve níveis hipefinos com degenerescência, através de um sistema simples de 3 níveis. O modelo também prevê o não alargamento do pico de correlação e mostramos ser esta uma medida mais fina de caracterização da largura de linha em comparação ao sinal médio da intensidade. / Using noise espectroscopy, we have studied the correlation between two laser beams with opposite circular polarizations, coupling the transition 5S1/2 F=2 to 5P3/2 F1=2 in -type Electromagnetically Induzed Transparency (EIT), using cold atoms of 85Rb. We have observed the transition from correlation to anti-correlation, between the slightly off-resonance probe and control beams, when the intensity of both beams was increased. This transition is a consequence of the competition between the single photon transition in a system, which is responsible for the correlation regime, and the Stoke and Anti-Stoke transitions producing anti-correlation between both beams. Studying the spectra of the intensity mean value and the noise correlation, we observed in the last one that the EIT peak is free of power broadening, which makes it possible to preciselly measure the coherence time between the ground states in EIT condition. Using the Phase Difusion model for the lasers in a EIT system, we show that the theoretical correlation spectra are in good accordance with the experimental data. This theory models a system with degenerate hyperfine levels, using a simple three-level model. Moreover, the model predicts the non-broadening of the correlation peak, showing the correlation as a more accurated measurement than the intensity mean value.

Electrical Impedance Tomography (EIT) is a technique for imaging the spatial distribution of conductivity inside a body using the boundary voltages, in response to applied current patterns, to reconstruct an image. Even though EIT has been proved useful in several medical applications such as mechanical respiration and ventilation monitoring of the lungs, its reported success in localising cerebral conductivity changes due to brain stimulation is very scant. In the case of the human head, the amplitude of the brain response to stimulation is usually very small and gets contaminated with physiological noise initiated from inside the cranium or the scalp. Three types of evoked responses were experimentally investigated: auditory startle response (ASR), CO2 reactivity response, and transient hyperaemic response (THR). ASR is expected to be a result of the brain’s functioning processes. However, the responses to CO2 and THR are expected to be due to cerebral blood volume or flow, due to physiological intervention in blood supply. According to the results, even when the amplitude of EIT measurements shows profound variation as in the case of CO2 reactivation, those could not be physiologically linked to the targeted responses and have been shown to be initiated from the scalp. The consistency of the measurements in the case of CO2 reactivation response was poor (37.50-50%). Meanwhile in the case of THR, although the magnitude of conductivity changes was overall 50% smaller than the previous cases, the subject movement was not necessary. This could be a reason that the consistency of THR case was very good (87%), and this can emphasize the necessity to maintain the changes in the scalp at minimum levels. In the case of ASR the response magnitude was very small (six times smaller than the CO2 reactivity case), and the evoked response can be detected with only 50% consistency. To measure very small EIT signals (such as those expected due to brain function) effectively, one must improve the sensitivity of the measurements to conductivity changes by increasing the excitation current. The functional EIT for Evoked Response (fEITER) system used in our investigations was modified from its initial configuration to increase its excitation current from 1 mApk-pk to 2 mApk-pk or 1 mArms. The bit-truncation in the process of Phase-Sensitive Detection (PSD) has also been improved, to modify the original 16-bit data readout to be 24-bit data readout. These improvements have doubled the instrument’s sensitivity, and have substantially reduced the truncation error to about 183 times. The quality of the physiological waveform was also significantly improved. Therefore, one could study more effectively very fast brain response using the modified system. For example, the latency of responses can be more precisely extracted, or the monitoring of the conductivity change in a period of only a few tens of milliseconds is then possible. The reconstruction of brain images corresponding to these physiologically evoked responses has been the ultimate goal of this thesis. To ensure obtaining the correct images, some crucial issues regarding EIT reconstruction were firstly investigated. One of these issues concerns the modelling error of the numerical head models. The reconstruction requires an accurate model capturing the geometry of the subject’s head with electrodes attached and accurate in-vivo tissue conductivities. However, since it is usually impractical to have a personalised model for each subject, many different head models (including a subject model) were constructed and investigated, to evaluate the possibility of using a generic model for all subjects. The electrode geometry was also carefully included into the models to minimise error. Another issue concerns the appropriate reconstruction algorithm. A novel nonlinear reconstruction method, based on the difference imaging approach and Generalized Minimal Residual method (GMRes) algorithm, with optimal parameters and prior information, was proposed to deal with significant modelling errors. With this algorithm, the experimental results showed that it is possible to use a generic model for reconstructing an impedance change, but the magnitude of the change should be rather small. The last issue tackled was regarding the a priori choice of model parameters, and in particular the tissue conductivities. The tissue conductivities of the scalp and the skull were also estimated by a proposed methodology based on the Gauss-Newton method. The estimation showed that, compared to previous reported values, the conductivity of the scalp was higher, at 0.58 S/m, and that of the skull lower, at 0.008 S/m. Eventually, by exploiting the hardware and firmware advances in the measuring instrument in conjunction with the proposed modelling and reconstruction algorithm, processing our experimental EIT data captured on human heads and a head-like tank confirm that the localisation and imaging of conductivity changes occurring within the head is indeed possible. From the low quality measurements in the case of the CO2 reactivity response, the reconstructed images of this response do not reflect the true conductivity change. The consistency of the images to localise the sources of the changes was very poor (0-50%), i.e. the conductivity changing locations in the images were likely to be random. Our analysis suggests that the changes inside the cranium are likely to be due to the large change in the scalp. In the case of THR, the reconstructed images were able to localise the response in a similar manner to what had been found on the measurements, and the consistency was quite high (76%). Meanwhile, in the case of ASR, surprisingly the consistency of the images was 82%, much higher than the consistency of the measurements, which was only 50%. This was because the changing amplitude of the measurements was too small to be noticed by visualisation, and it was practically cumbersome to investigate all measurements. This statistic confirms that image reconstruction can reveal information that is not directly apparent by observing the measurements. In summary, EIT can be used in brain (function) imaging applications to some extent. The targeted response, which typically originates from inside the cranium is always infused with neurophysiological noise or physical noise at the scalp, and the amplitude of noise determines the possibility to localise the changes. It is also necessary for the desired response to have sufficiently large amplitude. These results show that EIT has been successful in THR and ASR, but for CO2 reactivity response, EIT lacks the necessary sensitivity.