This thesis presents an investigation into the application of electrodynamic sensors to a tornographic imaging system. Several sensing mechanisms for measurement using non-intrusive techniques are discussed and their relevance to pneumatic conveying considered. Electrical charge tomography systems are shown to be worthy of investigation. Electrodynamic sensors are inherently low cost and simple in concept. This sensor is used to detect the inherent charge on dry, moving solids. Models are developed to predict the sensitivity of circular and rectangular electrodes. The spatial filtering effect of these sensors is investigated. Cross correlation is briefly reviewed and a software program is presented and tested. For tomographic imaging the forward problem for the individual sensors is modelled, used to solve the inverse problem and derive the linear back projection and filtered back projection algorithms. The design of the electronic circuitry which forms the transducer is presented. The gravity drop flow rig is described and the relationship between sand flow and plastic bead flow relative to the flow indicator setting determined. The dual 16-channel sensor array measurement section is described. Flow models are developed and used to predict the relative output voltage profiles expected from the sensor arrays. The linearity and frequency bandwidth of the sensor electronics is measured. The effect of sensor size on sensitivity and spatial filtering are investigated for circular and rectangular electrodes. Estimates of the solid concentration of flowing particles are made using individual sensors. Concentration profiles are generated and compared with predicted values. Peripheral velocities of the flowing material are determined from transit times calculated by cross correlation of upstream and downstream sensor signals. Concentration profiles are calculated using linear back projection and filtered back projection algorithms from data measured by the sensor arrays. Velocity profiles are obtained by cross correlation of upstream and downstream pixel concentration values. Estimates of the mass flow rate are obtained by combining concentration and velocity profiles. Suggestions for further work on electrodynamic sensors and tomographic measurements are made.

Diss. (sammanfattning) Göteborg : Göteborgs universitet, 2009. / Härtill 5 uppsatser.

Neste trabalho desenvolveu-se desenvolver uma versão sem linearizações do método D-bar para Tomografia por Impedância Elétrica (TIE). O problema inverso de TIE é não-linear e mal-posto. O algoritmo baseia-se na prova de existência e unicidade de Adrian Nachman [Ann. of Math. 143 (1996)] para domínios com distribuição de condutividade duas vezes diferenciáveis. O método faz uso de uma Transformada de Fourier não-linear chamada scattering transform, e o caráter mal-posto do Problema Inverso torna-se evidente no cálculo desta transformada, mais especificamente na determinação das soluções Complex Geometrical Optics (CGO). Atuais implementações práticas do método D-bar para padrões trigonométricos tem aproximado os valores na fronteira das soluções CGO por seu comportamento assintótico no cálculo da scattering transform, o que constitue uma linearização nesta etapa específica do método. Neste trabalho calcula-se a scattering transform a partir das soluções exponencialmente crescentes, o que implica calcular as funções Green de Faddeev, com o objetivo de encontrar imagens com maior resolução espacial e precisão nos valores de condutividade por ter resolvido o problema não-linear de forma completa. Dados de simulação numérica e experimentais usando padrões de injeção pula eletrodos e trigonométricos foram usados na avaliação do método. As imagens obtidas apresentam comportamento diferente em função do padrão de injeção utilizado. Do cálculo completo da transformada scattering resultam imagens com melhor resolução espacial. As imagens reconstruídas a partir de padrões de injeção trigonométricos apresentam também melhor resolução espacial comparadas as imagens reconstruídas a partir de padrões por pares, separados por três eletrodos. / This work proposes to develop a version of the D-bar method linearization for Electrical Impedance Tomography (EIT). The inverse problem of EIT is both nonlinear and very ill-posed. The version of the D-bar method implemented here is based on the existence and uniqueness proof of Adrian Nachman [Ann. of Math. 143 (1996)]. The method relies on the use of a nonlinear Fourier transform called the scattering transform, and the inherent ill-posedness of the inverse conductivity problem becomes evident in the computation of the scattering transform, more specifically in the determination of the Complex Geometrical Optics (CGO) solutions. Current practical implementations of the D-bar method using trigonometric patterns have replaced the boundary values of the CGO solutions by their asymptotic behavior in the calculation of the scattering transform, which is a linearization in this particular step of the overall method. This work proposes to calculate the scattering transform from exponentially growing solutions, which implies the calculation of the Faddeev Greens function, with the goal of obtaining images with higher resolution and accuracy in the conductivity values because the full nonlinear problem is solved. Numerical and experimental data using pairwise and trigonometric current injection patterns were used to evaluate the performance of the method. Better spatial resolution is obtained from the complete computation of the scattering transform. Reconstructed images from trigonometric current patterns also show better spatial resolution compared to pairwise current injection patterns, skipping three electrodes.

Propõe-se um novo método D-bar de Tomografia por Impedância Elétrica (TIE) para obter, simultaneamente, a condutividade e a permitividade de um domínio 2-D. O algoritmo direto baseia-se na prova de existência e unicidade do artigo de E. Francini [1]. A caracterização de tecidos biológicos é fortemente facilitada a partir do conhecimento de suas propriedades elétricas. Particularmente, nas aplicações médicas de TIE há grande interesse na permitividade, uma vez que, vários autores tem apresentado critérios para distinguir patologias baseados nesta propriedade, um exemplo constitui a determinação de presença ou ausência de sangue em líquidos acumulados no pulmão. Realizam-se testes com dados simulados numericamente e experimentais com o propósito de verificar e entender as propriedades, capacidades e limitações do algoritmo implementado. No caso dos testes numéricos, é desenvolvido um programa que resolve o problema direto da admitividade, o qual permite calcular conjuntos de dados de voltagem numéricos. São simulados dados aplicando padrões de corrente trigonométricos e por pares. As soluções exponencialmente crescentes do problema inverso são parte essencial do algoritmo e devem ser decompostas nas bases dos padrões de injeção de corrente. A compreensão da natureza destas decomposições para padrões de injeção trigonométricos e por pares, levou ao estabelecimento de especificações no projeto de um sistema de TIE para este algoritmo. Os resultados encorajadores numéricos e experimentais obtidos nas reconstruções de condutividade e permitividade, quanto à resolução espacial e às magnitudes, indicam que o algoritmo é promissor para uso clínico. / This work proposes a new D-bar method of Electrical Impedance Tomography (EIT) for reconstructing the conductivity and permittivity simultaneously in a 2-D domain. The direct algorithm presented is based on the existence and uniqueness proof by E. Francini [1]. Biological tissue characterization is strongly facilitated by the knowledge of its electric properties. In EIT medical applications there is great interest in the permittivity as an additional property for distinguishing pathologies. For instance, the determination of presence or absence of blood in fluid accumulation in the lung. Numerical and experimental data tests are carried out in order to verify and understand the properties, capabilities and limitations of the implemented algorithm. A numerical phantom to solve the forward admittivity problem is developed which allows to simulate voltage data sets. Trigonometric and pairwise injection current patterns are applied. Exponentially growing solutions of the inverse problem are a key part of the algorithm, which have to be expanded in terms of the current patterns. Understanding the nature of these expansions for trigonometric and pairwise injection current patterns leads to a set of specifications in the design of an EIT system for this algorithm. The encouraging numerical and experimental results obtained in conductivity and permittivity reconstructions, regarding the magnitude and spatial resolution, indicate that the algorithm is promising for clinical use.

Propõe-se um novo método D-bar de Tomografia por Impedância Elétrica (TIE) para obter, simultaneamente, a condutividade e a permitividade de um domínio 2-D. O algoritmo direto baseia-se na prova de existência e unicidade do artigo de E. Francini [1]. A caracterização de tecidos biológicos é fortemente facilitada a partir do conhecimento de suas propriedades elétricas. Particularmente, nas aplicações médicas de TIE há grande interesse na permitividade, uma vez que, vários autores tem apresentado critérios para distinguir patologias baseados nesta propriedade, um exemplo constitui a determinação de presença ou ausência de sangue em líquidos acumulados no pulmão. Realizam-se testes com dados simulados numericamente e experimentais com o propósito de verificar e entender as propriedades, capacidades e limitações do algoritmo implementado. No caso dos testes numéricos, é desenvolvido um programa que resolve o problema direto da admitividade, o qual permite calcular conjuntos de dados de voltagem numéricos. São simulados dados aplicando padrões de corrente trigonométricos e por pares. As soluções exponencialmente crescentes do problema inverso são parte essencial do algoritmo e devem ser decompostas nas bases dos padrões de injeção de corrente. A compreensão da natureza destas decomposições para padrões de injeção trigonométricos e por pares, levou ao estabelecimento de especificações no projeto de um sistema de TIE para este algoritmo. Os resultados encorajadores numéricos e experimentais obtidos nas reconstruções de condutividade e permitividade, quanto à resolução espacial e às magnitudes, indicam que o algoritmo é promissor para uso clínico. / This work proposes a new D-bar method of Electrical Impedance Tomography (EIT) for reconstructing the conductivity and permittivity simultaneously in a 2-D domain. The direct algorithm presented is based on the existence and uniqueness proof by E. Francini [1]. Biological tissue characterization is strongly facilitated by the knowledge of its electric properties. In EIT medical applications there is great interest in the permittivity as an additional property for distinguishing pathologies. For instance, the determination of presence or absence of blood in fluid accumulation in the lung. Numerical and experimental data tests are carried out in order to verify and understand the properties, capabilities and limitations of the implemented algorithm. A numerical phantom to solve the forward admittivity problem is developed which allows to simulate voltage data sets. Trigonometric and pairwise injection current patterns are applied. Exponentially growing solutions of the inverse problem are a key part of the algorithm, which have to be expanded in terms of the current patterns. Understanding the nature of these expansions for trigonometric and pairwise injection current patterns leads to a set of specifications in the design of an EIT system for this algorithm. The encouraging numerical and experimental results obtained in conductivity and permittivity reconstructions, regarding the magnitude and spatial resolution, indicate that the algorithm is promising for clinical use.

Neste trabalho desenvolveu-se desenvolver uma versão sem linearizações do método D-bar para Tomografia por Impedância Elétrica (TIE). O problema inverso de TIE é não-linear e mal-posto. O algoritmo baseia-se na prova de existência e unicidade de Adrian Nachman [Ann. of Math. 143 (1996)] para domínios com distribuição de condutividade duas vezes diferenciáveis. O método faz uso de uma Transformada de Fourier não-linear chamada scattering transform, e o caráter mal-posto do Problema Inverso torna-se evidente no cálculo desta transformada, mais especificamente na determinação das soluções Complex Geometrical Optics (CGO). Atuais implementações práticas do método D-bar para padrões trigonométricos tem aproximado os valores na fronteira das soluções CGO por seu comportamento assintótico no cálculo da scattering transform, o que constitue uma linearização nesta etapa específica do método. Neste trabalho calcula-se a scattering transform a partir das soluções exponencialmente crescentes, o que implica calcular as funções Green de Faddeev, com o objetivo de encontrar imagens com maior resolução espacial e precisão nos valores de condutividade por ter resolvido o problema não-linear de forma completa. Dados de simulação numérica e experimentais usando padrões de injeção pula eletrodos e trigonométricos foram usados na avaliação do método. As imagens obtidas apresentam comportamento diferente em função do padrão de injeção utilizado. Do cálculo completo da transformada scattering resultam imagens com melhor resolução espacial. As imagens reconstruídas a partir de padrões de injeção trigonométricos apresentam também melhor resolução espacial comparadas as imagens reconstruídas a partir de padrões por pares, separados por três eletrodos. / This work proposes to develop a version of the D-bar method linearization for Electrical Impedance Tomography (EIT). The inverse problem of EIT is both nonlinear and very ill-posed. The version of the D-bar method implemented here is based on the existence and uniqueness proof of Adrian Nachman [Ann. of Math. 143 (1996)]. The method relies on the use of a nonlinear Fourier transform called the scattering transform, and the inherent ill-posedness of the inverse conductivity problem becomes evident in the computation of the scattering transform, more specifically in the determination of the Complex Geometrical Optics (CGO) solutions. Current practical implementations of the D-bar method using trigonometric patterns have replaced the boundary values of the CGO solutions by their asymptotic behavior in the calculation of the scattering transform, which is a linearization in this particular step of the overall method. This work proposes to calculate the scattering transform from exponentially growing solutions, which implies the calculation of the Faddeev Greens function, with the goal of obtaining images with higher resolution and accuracy in the conductivity values because the full nonlinear problem is solved. Numerical and experimental data using pairwise and trigonometric current injection patterns were used to evaluate the performance of the method. Better spatial resolution is obtained from the complete computation of the scattering transform. Reconstructed images from trigonometric current patterns also show better spatial resolution compared to pairwise current injection patterns, skipping three electrodes.

Over the last 30 years, Particle Image Velocimetry (PIV) has become the most powerful tool to study velocity fields in fluid mechanics. This technique is non-intrusive requiring seeding the flow with small tracer particles. The hardware required for these sophisticated PIV methods is very expensive (CCD or CMOS high-speed cameras and lasers), and the present dissertation aims to develop novel and inexpensive alternatives. The first part of this work investigates the use of multiple smartphones as a lower-cost Tomographic-PIV system for reconstructing 3D-3C velocity fields. We use colored shadows to imprint two or three different time-steps on the same image in a RGB-backlit configuration. We use commercially available Tomo-PIV software for the calibration, 3-D particle reconstruction, and particle-field correlations, to obtain three velocity components in a volume. The proposed system is tested with a vortex ring and the results are compared to stereoscopic-PIV for error estimations. We expand this work to a high-speed time-resolved setup to obtain 3D-3C velocity fields in time. This improvement is possible using newer smartphones capable of recording high-speed video at HD resolution. The challenges of using such cameras are presented and tackled. The illumination system, testing flow and image processing is similar to the one presented in the first section. A benchmark of the smartphone system is carried out comparing it to a Tomo-PIV system capable of recording 4K video resolution. A different approach is proposed to reconstruct a 3D-3C velocity field using a single color video camera. This technique uses chromatic structured light with color-gradients projected perpendicularly with respect to the color camera. Thus, we encode the depth position of the particles with a different wavelength of light. Different light sources are used to produce such color gradients. Finally, a variation of the previous technique is tested using a single monochromatic camera and structured volumetric illumination with spatially varying intensity profiles. This technique enables us to encode the depth position of every particle in their intrinsic brightness. The proposed system can achieve a depth resolution of 200 levels, i.e., an order of magnitude higher than previously proposed systems.

A methodology is presented for creating tomographic reconstructions from various projection data, and the relevance of the results to applications in atmospheric science and biomedical imaging is analyzed. The fundamental differences between transform and iterative methods are described and the properties of the imaging configurations are addressed. The presented results are particularly suited for highly ill-conditioned inverse problems in which the imaging data are restricted as a result of poor angular coverage, limited detector arrays, or insufficient access to an imaging region. The class of reconstruction algorithms commonly used in sparse tomography, the algebraic reconstruction techniques, is presented, analyzed, and compared. These algorithms are iterative in nature and their accuracy depends significantly on the initialization of the algorithm, the so-called initial guess. A considerable amount of research was conducted into novel initialization techniques as a means of improving the accuracy. The main body of this paper is comprised of three smaller papers, which describe the application of the presented methods to atmospheric and medical imaging modalities. The first paper details the measurement of mesospheric airglow emissions at two camera sites operated by Utah State University. Reconstructions of vertical airglow emission profiles are presented, including three-dimensional models of the layer formed using a novel fanning technique. The second paper describes the application of the method to the imaging of polar mesospheric clouds (PMCs) by NASA’s Aeronomy of Ice in the Mesosphere (AIM) satellite. The contrasting elements of straight-line and diffusive tomography are also discussed in the context of ill-conditioned imaging problems. A number of developing modalities in medical tomography use near-infrared light, which interacts strongly with biological tissue and results in significant optical scattering. In order to perform tomography on the diffused signal, simulations must be incorporated into the algorithm, which describe the sporadic photon migration. The third paper presents a novel Monte Carlo technique derived from the optical scattering solution for spheroidal particles designed to mimic mitochondria and deformed cell nuclei. Simulated results of optical diffusion are presented. The potential for improving existing imaging modalities through continual development of sparse tomography and optical scattering methods is discussed.

A temporally and spatially non-scanning imaging spectrometer covering two separate spectral bands in the visible region using computed tomographic imaging techniques is described. The computed tomographic techniques allow for the construction of a three-dimensional hyperspectral data cube (x, y, λ) from the two-dimensional input in a single frame time. A computer generated holographic dispersive grating is used to disperse the incoming light into several diffraction orders on a focal plane composed of interwoven pixels independently sensitive to the two bands of interest. Separating the input of the two spectral pixel types gives co-registered output between the two bands and overcomes the limitation of overlapping orders. The proof of concept in the visible is presented using a commercially available camera.The lessons learned from the visible system are applied to a dual infrared band imaging spectrometer. Utilizing recent developments in dual band infrared focal planes a dual band imaging spectrometer is designed covering portions of the MWIR and LWIR atmospheric transmission windows. The system design includes the evaluation of recent developments in dual band infrared focal planes, the design and evaluation of the computer generated holographic disperser, and the optical elements in the system.

<p>'Image volumes' refer to realizations of images in other dimensions such as time, spectrum, and focus. Recent advances in scientific, medical, and consumer applications demand improvements in image volume capture. Though image volume acquisition continues to advance, it maintains the same sampling mechanisms that have been used for decades; every voxel must be scanned and is presumed independent of its neighbors. Under these conditions, improving performance comes at the cost of increased system complexity, data rates, and power consumption. </p><p>This dissertation explores systems and methods capable of efficiently improving sensitivity and performance for image volume cameras, and specifically proposes several sampling strategies that utilize temporal coding to improve imaging system performance and enhance our awareness for a variety of dynamic applications. </p><p>Video cameras and camcorders sample the video volume (x,y,t) at fixed intervals to gain understanding of the volume's temporal evolution. Conventionally, one must reduce the spatial resolution to increase the framerate of such cameras. Using temporal coding via physical translation of an optical element known as a coded aperture, the compressive temporal imaging (CACTI) camera emonstrates a method which which to embed the temporal dimension of the video volume into spatial (x,y) measurements, thereby greatly improving temporal resolution with minimal loss of spatial resolution. This technique, which is among a family of compressive sampling strategies developed at Duke University, temporally codes the exposure readout functions at the pixel level.</p><p>Since video cameras nominally integrate the remaining image volume dimensions (e.g. spectrum and focus) at capture time, spectral (x,y,t,\lambda) and focal (x,y,t,z) image volumes are traditionally captured via sequential changes to the spectral and focal state of the system, respectively. The CACTI camera's ability to embed video volumes into images leads to exploration of other information within that video; namely, focal and spectral information. The next part of the thesis demonstrates derivative works of CACTI: compressive extended depth of field and compressive spectral-temporal imaging. These works successfully show the technique's extension of temporal coding to improve sensing performance in these other dimensions.</p><p>Geometrical optics-related tradeoffs, such as the classic challenges of wide-field-of-view and high resolution photography, have motivated the development of mulitscale camera arrays. The advent of such designs less than a decade ago heralds a new era of research- and engineering-related challenges. One significant challenge is that of managing the focal volume (x,y,z) over wide fields of view and resolutions. The fourth chapter shows advances on focus and image quality assessment for a class of multiscale gigapixel cameras developed at Duke.</p><p>Along the same line of work, we have explored methods for dynamic and adaptive addressing of focus via point spread function engineering. We demonstrate another form of temporal coding in the form of physical translation of the image plane from its nominal focal position. We demonstrate this technique's capability to generate arbitrary point spread functions.</p> / Dissertation