Development and implementation of efficient noise suppression methods for emission computed tomography

In PET and SPECT imaging, iterative reconstruction is now widely used due to its capability of incorporating into the reconstruction process a physics model and Bayesian statistics involved in photon detection. Iterative reconstruction methods rely on regularization terms to suppress image noise and render radiotracer distribution with good image quality. The choice of regularization method substantially affects the appearances of reconstructed images, and is thus a critical aspect of the reconstruction process. Major contributions of this work include implementation and evaluation of various new regularization methods. Previously, our group developed a preconditioned alternating projection algorithm (PAPA) to optimize the emission computed tomography (ECT) objective function with the non-differentiable total variation (TV) regularizer. The algorithm was modified to optimize the proposed reconstruction objective functions. First, two novel TV-based regularizers—high-order total variation (HOTV) and infimal convolution total variation (ICTV)—were proposed as alternative choices to the customary TV regularizer in SPECT reconstruction, to reduce “staircase” artifacts produced by TV. We have evaluated both proposed reconstruction methods (HOTV-PAPA and ICTV-PAPA), and compared them with the TV regularized reconstruction (TV-PAPA) and the clinical standard, Gaussian post-filtered, expectation-maximization reconstruction method (GPF-EM) using both Monte Carlo-simulated data and anonymized clinical data. Model-observer studies using Monte Carlo-simulated data indicate that ICTV-PAPA is able to reconstruct images with similar or better lesion detectability, compared with clinical standard GPF-EM methods, but at lower detected count levels. This implies that switching from GPF-EM to ICTV-PAPA can reduce patient dose while maintaining image quality for diagnostic use. Second, the 1 norm of discrete cosine transform (DCT)-induced framelet regularization was studied. We decomposed the image into high and low spatial-frequency components, and then preferentially penalized the high spatial-frequency components. The DCT-induced framelet transform of the natural radiotracer distribution image is sparse. By using this property, we were able to effectively suppress image noise without overly compromising spatial resolution or image contrast. Finally, the fractional norm of the first-order spatial gradient was introduced as a regularizer. We implemented 2/3 and 1/2 norms to suppress image spatial variability. Due to the strong penalty of small differences between neighboring pixels, fractional-norm regularizers suffer from similar cartoon-like artifacts as with the TV regularizer. However, when penalty weights are properly selected, fractional-norm regularizers outperform TV in terms of noise suppression and contrast recovery

X-ray scatter tomography using coded apertures

This work proposes and studies a new field of x-ray tomography which combines the principles of scatter imaging and coded apertures, termed coded aperture x-ray scatter imaging (CAXSI). Conventional x-ray tomography reconstructs an object's electron density distribution by measuring a set of line integrals known as the x-ray transform, based physically on the attenuation of incident rays. More recently, scatter imaging has emerged as an alternative to attenuation imaging by measuring radiation from coherent and incoherent scattering. The information-rich scatter signal may be used to infer density as well as molecular structure throughout a volume. Some scatter modalities use collimators at the source and detector, resulting in long scan times due to the low efficiency of scattering mechanisms combined with a high degree of spatial filtering. CAXSI comes to the rescue by employing coded apertures. Coded apertures transmit a larger fraction of the scattered rays than collimators while also imposing structure to the scatter signal. In a coded aperture system each detector is sensitive to multiple ray paths, producing multiplexed measurements. The coding problem is then to design an aperture which enables de-multiplexing to reconstruct the desired physical properties and spatial distribution of the target. In this work, a number of CAXSI systems are proposed, analyzed, and demonstrated. One-dimensional pencil beams, two-dimensional fan beams, and three-dimensional cone beams are considered for the illumination. Pencil beam and fan beam CAXSI systems are demonstrated experimentally. The utility of energy-integrating (scintillation) detectors and energy-sensitive (photon counting) detectors are evaluated theoretically, and new coded aperture designs are presented for each beam geometry. Physical models are developed for each coded aperture system, from which resolution metrics are derived. Systems employing different combinations of beam geometry, coded apertures, and detectors are analyzed by constructing linear measurement operators and comparing their singular value decompositions. Since x-ray measurements are typically dominated by photon shot noise, iterative algorithms based on Poisson statistics are used to perform the reconstructions. This dissertation includes previously published and unpublished co-authored material.Doctor of Philosoph

Electron Beam X-Ray Computed Tomography for Multiphase Flows and An Experimental Study of Inter-channel Mixing

This thesis consists of two parts. In the first, a high speed X-ray Computed Tomography (CT) system for multiphase flows is developed. X-ray Computed Tomography (CT) has been employed in the study of multiphase flows. The systems developed to date often have excellent spatial resolution at the expense of poor temporal resolution. Hence, X-ray CT has mostly been employed to examining time averaged phase distributions. In the present work, we report on the development of a Scanning Electron Beam X-ray Tomography (SEBXT) CT system that will allow for much higher time resolution with acceptable spatial resolution. The designed system, however, can have issues such as beam-hardening and limited angle artifacts. In the present study, we developed a high speed, limited angle SEBXT system along with a new CT reconstruction algorithm designed to enhance the CT reconstruction results of such system. To test the performance of the CT system, we produced example CT reconstruction results for two test phantoms based on the actual measured sinograms and the simulated sinograms. The second part examines, the process by which fluid mixes between two parallel flow channels through a narrow gap. This flow is a canonical representation of the mixing and mass transfer processes that often occur in thermo-hydraulic systems. The mixing can be strongly related to the presence of large-scale periodic flow structures that form within the gap. In the present work, we have developed an experimental setup to examine the single-phase mixing through the narrow rectangular gaps connecting two rectangular channels. Our goal is to elucidate the underlying flow processes responsible for inter-channel mixing, and to produce high-fidelity data for validation of computational models. Dye concentration measurements were used to determine the time average rate of mixing. Particle Imaging Velocimetry (PIV) was used to measure the flow fields within the gap. A Proper Orthogonal Decomposition (POD) of the PIV flow fields revealed the presence of coherent flow structure. The decomposed flow fields were then used to predict the time averaged mixing, which closely matched the experimentally measured values.PHDNaval Architecture & Marine EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/138666/1/seongjin_2.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/138666/2/seongjin_1.pd

Doctor of Philosophy

dissertationMicrowave/millimeter-wave imaging systems have become ubiquitous and have found applications in areas like astronomy, bio-medical diagnostics, remote sensing, and security surveillance. These areas have so far relied on conventional imaging devices (empl

Electron Cyclotron Heating and Suprathermal Electron Dynamics in the TCV Tokamak

This thesis is concerned with the physics of suprathermal electrons in thermonuclear, magnetically confined plasmas. Under a variety of conditions, in laboratory as well as space plasmas, the electron velocity distribution function is not in thermodynamic equilibrium owing to internal or external drives. Accordingly, the distribution function departs from the equilibrium Maxwellian, and in particular generally develops a high-energy tail. In tokamak plasmas, this occurs especially as a result of injection of high-power electromagnetic waves, used for heating and current drive, as well as a result of internal magnetohydrodynamic (MHD) instabilities. The physics of these phenomena is intimately tied to the properties and dynamics of this suprathermal electron population. This motivates the development of instrumental apparatus to measure its properties as well as of numerical codes to simulate their dynamics. Both aspects are reflected in this thesis work, which features advanced instrumental development and experimental measurements as well as numerical modeling. The instrumental development consisted of the complete design of a spectroscopic and tomographic system of four multi-detector hard X-ray (HXR) cameras for the TCV tokamak. The goal is to measure bremsstrahlung emission from suprathermal electrons with energies in the 10-300 keV range, with the ultimate aim of providing the first full tomographic reconstruction at these energies in a noncircular plasma. In particular, suprathermal electrons are generated in TCV by a high-power electron cyclotron heating (ECH) system and are also observed in the presence of MHD events, such as sawtooth oscillations and disruptive instabilities. This diagnostic employs state-of-the-art solid-state detectors and is optimized for the tight space requirements of the TCV ports. It features a novel collimator concept that combines compactness and flexibility as well as full digital acquisition of the photon pulses, greatly enhancing its potential for full spectral analysis in high-fluency scenarios. Additional flexibility is afforded by the possibility to rotate the orientation of two of the cameras, permitting the crucial comparison of radiation emitted perpendicular and parallel to the primary magnetic field. The design of the HXR system was optimized through an extensive iterative simulation process with the aid of tomographic reconstruction codes as well as quasilinear Fokker-Planck modeling of ECH-driven TCV plasmas. In parallel, the selection of the detectors for this system was performed through comprehensive laboratory testing of several candidate detectors available on the market. While the design was completed in the course of the thesis work, commissioning of the system has only commenced recently with one of the four cameras installed on TCV. The first preliminary results, discussed in the last part of this thesis, include basic parameter scans of ECH wave-plasma interaction and the investigation of the dynamic response of suprathermal electrons to modulated ECH. In addition, the cameras possess the novel ability to discriminate against very high-energy γ-ray radiation that cannot be collimated and must thus be excluded from spatial distribution analysis. A basic study of the conditions for γ-ray suppression was conducted in preparation for future experiments. The Fokker-Planck modeling tool used in this diagnostic development was acquired through a collaboration with CEA-Cadarache, initially with the primary motivation of studying the simultaneous plasma heating by 2nd and 3rd harmonic electron cyclotron waves that is uniquely possible on TCV. This motivated a dedicated study, both theoretical and experimental, of one particular instance of this combined heating, which became a second primary subject of this thesis work. The particular scenario studied here is one in which a single ECH frequency is resonant at both harmonics in the same plasma. The primary objective of this study was to determine whether a synergy effect existed, permitting an enhancement of the intrinsically weak 3rd harmonic absorption by the suprathermal electrons generated at the 2nd harmonic resonance. An associated question was whether this effect, if it existed, was experimentally measurable or was in fact observed in TCV. The simulations performed in the course of this study indeed predict the existence of such a synergy, although the answer to the second question was ultimately negative, at least within the current technical limitations. This study has proven nevertheless highly valuable in providing new insight into the complex velocity-space dynamics that govern ECH wave-particle interaction and suprathermal electron dynamics

Generation and Manipulation of Higher Order Fractional and Integer Bessel Gaussian Beams

Optical orbital angular momentum (OAM) describes orbiting photons, swirling local wave vectors, or spiraling phase distribution depending on what theory we use to explain light. If we consider light as a propagating electromagnetic wave, then light has the freedoms of frequency, magnitude, phase, and polarization. For a monochromatic light, expanding the later three freedoms spatiotemporally, numerous optical modes are solved from Maxwell’s equations and boundary conditions. OAM mode study starts from integer charge because it is in the integer form of the fundamental phase singularity structure. Fractional OAM mode is the Fourier series of integer OAM modes. The average OAM does not conserve along with propagation for the traditional fractional OAM modes. We propose a new asymmetric fractional Bessel Gaussian mode providing the average OAM conserving along with the propagation. To better understand the fractional OAM mode or integer OAM mode combination, we study the novel concentric vortex optics. The analytical propagation expression of the concentric vortex beam is derived and analyzed. The concentric vortex beam is essentially the OAM spectrum, with only two integer OAM components. The spectrum coefficiencies are real numbers and approximately power equalized in general cases. The concentric vortex beam is the coherent combination of incomplete Kummer beams. As the inner aperture tuning large, the beam evolves into the Kummer beam with the inner charge number. The aperture decreases, the outer charges Kummer beam dominates. The proposed asymmetric fractional Bessel Gaussian beam’s Fourier transform is azimuthal Gaussian perfect vortex. We use log-polar coordinate mapping diffractive optics to transform the elliptical Gaussian beam into the desired azimuthal Gaussian perfect vortex beam. The generated asymmetric fractional Bessel Gaussian beam is systematically compared with Kotlyar’s asymmetric Bessel Gaussian beam. It’s found that the proposed beam has a narrower OAM spectrum, preserving average fractional OAM. Furthermore, the log-polar transform’s inherent output lateral shifting problem is addressed for the first time to our knowledge. An improved log-polar design is proposed, and we use five critical metrics to show the new log-polar generated asymmetric Bessel Gaussian beam’s quality is much improved. The manipulation of the high order asymmetric fractional Bessel Gaussian beam is critical to applications scaling from communication, sensing, filamentation, to micromanipulation. We propose and demonstrate acousto-optical deflector (AOD) HOBBIT (Higher Order Bessel Beams Integrated in Time) system. The system can continuously tune the OAM modes on the order of 400 kHz. This speed beats the fastest spatial light modulator (SLM), and even better, the proposed system could work for high power applications

Reconstruction algorithms for multispectral diffraction imaging

Thesis (Ph.D.)--Boston UniversityIn conventional Computed Tomography (CT) systems, a single X-ray source spectrum is used to radiate an object and the total transmitted intensity is measured to construct the spatial linear attenuation coefficient (LAC) distribution. Such scalar information is adequate for visualization of interior physical structures, but additional dimensions would be useful to characterize the nature of the structures. By imaging using broadband radiation and collecting energy-sensitive measurement information, one can generate images of additional energy-dependent properties that can be used to characterize the nature of specific areas in the object of interest. In this thesis, we explore novel imaging modalities that use broadband sources and energy-sensitive detection to generate images of energy-dependent properties of a region, with the objective of providing high quality information for material component identification. We explore two classes of imaging problems: 1) excitation using broad spectrum sub-millimeter radiation in the Terahertz regime and measure- ment of the diffracted Terahertz (THz) field to construct the spatial distribution of complex refractive index at multiple frequencies; 2) excitation using broad spectrum X-ray sources and measurement of coherent scatter radiation to image the spatial distribution of coherent-scatter form factors. For these modalities, we extend approaches developed for multimodal imaging and propose new reconstruction algorithms that impose regularization structure such as common object boundaries across reconstructed regions at different frequencies. We also explore reconstruction techniques that incorporate prior knowledge in the form of spectral parametrization, sparse representations over redundant dictionaries and explore the advantage and disadvantages of these techniques in terms of image quality and potential for accurate material characterization. We use the proposed reconstruction techniques to explore alternative architectures with reduced scanning time and increased signal-to-noise ratio, including THz diffraction tomography, limited angle X-ray diffraction tomography and the use of coded aperture masks. Numerical experiments and Monte Carlo simulations were conducted to compare performances of the developed methods, and validate the studied architectures as viable options for imaging of energy-dependent properties

Holographic optical elements in dichromated gelatin

Abstract unavailable please refer to PDF

Laser absorption spectroscopic tomography with a customised spatial resolution for combustion diagnosis

Combustion is a widely used energy conversion technology. However, post-combustion gas emissions have adverse effects on climate change. To address the urgent need for carbon neutrality, efforts are being made to develop cleaner fuels and improve combustion efficiency. Accurate in situ measurements of temperature and species concentration are crucial for analysing and diagnosing the combustion process. In industrial applications, probed-based measurement methods are commonly used to detect temperature and species concentration in the combustion, favoured by their simplicity. However, the probe-based techniques are limited in their spatial resolution, as only point-wise measurements can be provided by them. Additionally, their principle often restricts their temporal resolution, which limits their ability to capture the dynamics of the combustion process. To overcome these limitations, researchers are actively working on developing rapid and multi-dimensional in situ techniques for temperature and species concentration monitoring. Laser Absorption Spectroscopy (LAS) has gained significant attention for its non-intrusive nature and fast response in combustion diagnostics. LAS techniques use an emitter-receiver configuration to measure the line-of-sight light intensity absorbed by species in the gaseous medium. By collecting multiple line-of-sight measurements from different angles, LAS enables tomographic measurement of the combustion process. However, implementations of LAS tomography face challenges due to the physical dimensions of the emitter and receiver and the optical access to industrial combustors. These limitations lead to incomplete measurements, which are key factors of ill-posed problems and artefacts in the reconstructed images. The artefacts lead to inaccuracy and unreliability of the diagnostic results. Increasing physical sampling density is one of the most straightforward ways to alleviate the ill-posed problem caused by inadequate line-of-sight measurements. Improvements in sensors have been demonstrated in previous research, such as optimising laser beam arrangement and reducing the spacing of neighbouring laser beams. In this work, a novel design of a miniature and modular sensor is firstly introduced. It reduces the beam spacing between adjacent laser beams, allowing for a more precise and detailed reconstruction of temperature and species concentration distributions. Meanwhile, modular design allows for customisation and adaptation to various measurement requirements. This flexibility in deployment reduces the cost of the LAS technique. The application of small beam spacing in characterising the non-uniformity of the combustion process has also been demonstrated in this thesis. A multi-channel LAS sensor is developed and applied to exhaust measurements of a commercial auxiliary power unit. The results show that the small beam spacing allows a detailed understanding of the exhaust plume at the mixing zone between the exhaust gas and surrounding air. This spatial information can be used to improve the accuracy of temperature and species concentration measurements. On the other hand, prior knowledge, such as smoothness and sparsity of the measurement target and beam arrangement of the LAS tomographic sensor is used to provide extra physical information to the ill-posed inverse problem. To incorporate the beam arrangement information into the reconstruction process, a new meshing scheme is proposed in this thesis. The scheme dynamically allocates smaller meshes in the beam-dense regions and coarser meshes in the beam-loose regions. This adaptive meshing scheme ensures a finer resolution in detailing the combustion zone where the beams are closely spaced while maintaining the integrity of the physical model by using less resolved reconstruction in the bypass flows or regions where the beams are further apart. As a result, the proposed meshing scheme improves the reconstruction accuracy of the combustion zone. Overall, this PhD project designed and developed LAS tomographic sensors and methods that enable accurate and fast measurement of gas temperature and species concentration in combustion processes with a customised spatial resolution. The main contributions of this thesis include the design and prototyping of a miniature and modular optical sensor for flexible LAS tomography; the development of a multi-channel LAS sensor for simultaneously monitoring exhaust gas temperature and water vapour concentration in gas turbine engines; and the development of a size-adaptive hybrid meshing scheme to improve the reconstruction of target flow fields

Metasurfaces for ultrathin optical devices with unusual functionalities

Metamaterials are artificial materials that are made from periodically arranged structures, showing properties that cannot be found in nature. The response of a metamaterial to the external field is defined by the geometry, orientation, and distribution of the artificial structures. Many groundbreaking discoveries, such as negative refraction, and super image resolution has been demonstrated based on metamaterials. Nevertheless, the difficulty in three-dimensional fabrication, especially when the operating band is located in the optical range, hinders their practical applications. As a two-dimensional counterpart, a metasurface consists of an array of planar optical antennas, which locally modify the properties of the scattered light. Metasurfaces do not require complicated three-dimensional nanofabrication techniques, and the complexity of the fabrication is greatly reduced. Also, the thickness of a metasurface can be deep subwavelength, making it possible to realize ultrathin devices. In this thesis, geometric metasurfaces are utilized to realize a series of optical devices with unusual functionalities. Phase gradient metasurface is used to split the incident light into left-handed polarized (LCP) and right-handed polarized (RCP) components, whose intensities can be used to determine the polarization state of the incident light. Then we propose a method to integrate two optical elements with different functionalities into a single metasurface device, and its overall performance is determined by the polarization of the incident light. After that, a helicity multiplexed metasurface hologram is demonstrated to reconstruct two images with high efficiency and broadband. The two images swap their positions with the helicity reversion of the incident light. Finally, a polarization rotator is presented, which can rotate the incident light to arbitrary polarization direction by using the non-chiral metasurface. The proposed metasurface devices may inspire the development of new optical devices, and expand the applications of metasurfaces in integrated optical systems