Three new reconstruction methods for quantitative phase imaging, including two interrelated two-dimensional methods, called multifilter phase imaging with partially coherent light and phase optical transfer function recovery, which lead to a third three-dimensional method, called tomographic deconvolution phase microscopy, were developed in response to a growing need among biomedical end users for solutions which can be integrated on standard microscope platforms. The performance of these new methods were evaluated using modelling and simulation as well as experimentation with known test cases. In addition to the development of new methods, existing methods for quantitative phase imaging were applied to characterize the effects of manufacturing, cleaving, and fusion splicing in large-mode-area erbium- and ytterbium-doped optical fibers.

Quantitative phase imaging (QPI) is a category of imaging techniques that can retrieve the phase information of the sample quantitatively. QPI features label-free contrast and non-contact detection. It has thus gained rapidly growing attention in biomedical imaging. Capable of resolving biological specimens at tissue or cell level, QPI has become a powerful tool to reveal the structural, mechanical, physiological and spectroscopic properties. Over the past two decades, QPI has seen a broad spectrum of evolving implementations. However, only a few have seen successful commercialization. The challenges are manifold. A major problem for many QPI techniques is the necessity of a custom-made system which is hard to interface with existing commercial microscopes. For this type of QPI techniques, the cost is high and the integration of different imaging modes requires nontrivial hardware modifications. Another limiting factor is insufficient sensitivity. In QPI, sensitivity characterizes the system repeatability and determines the quantification resolution of the system. With more emerging applications in cell imaging, the requirement for sensitivity also becomes more stringent. In this work, a category of highly sensitive full-field QPI techniques based on wavelength shifting interferometry (WSI) is proposed. On one hand, the full-field implementations, compared to point-scanning, spectral domain QPI techniques, require no mechanical scanning to form a phase image. On the other, WSI has the advantage of preserving the integrity of the interferometer and compatibility with multi-modal imaging requirement. Therefore, the techniques proposed here have the potential to be readily integrated into the ubiquitous lab microscopes and equip them with quantitative imaging functionality. In WSI, the shifts in wavelength can be applied in fine steps, termed swept source digital holographic phase microscopy (SS-DHPM), or a multi-wavelength-band manner, termed low coherence wavelength shifting interferometry (LC-WSI). SS-DHPM brings in an additional capability to perform spectroscopy, whilst the LC-WSI achieves a faster imaging rate which has been demonstrated with live sperm cell imaging. In an attempt to integrate WSI with the existing commercial microscope, we also discuss the possibility of demodulation for low-cost sources and common path implementation. Besides experimentally demonstrating the high sensitivity (limited by only shot noise) with the proposed techniques, a novel sensitivity evaluation framework is also introduced for the first time in QPI. This framework examines the Cramér-Rao bound (CRB), algorithmic sensitivity and experimental sensitivity, and facilitates the diagnosis of algorithm efficiency and system efficiency. The framework can be applied not only to the WSI techniques we proposed, but also to a broad range of QPI techniques. Several popular phase shifting interferometry techniques as well as off-axis interferometry is studied. The comparisons between them are shown to provide insights into algorithm optimization and energy efficiency of sensitivity. / Doctor of Philosophy / The most common imaging systems nowadays capture the image of an object with the irradiance perceived by the camera. Based on the intensity contrast, morphological features, such as edges, humps, and grooves, can be inferred to qualitatively characterize the object. Nevertheless, in scientific measurements and research applications, a quantitative characterization of the object is desired. Quantitative phase imaging (QPI) is such a category of imaging techniques that can retrieve the phase information of the sample by properly design the irradiance capturing scheme and post-process the data, converting them to quantitative metrics such as surface height, material density and so on. The imaging process of QPI will neither harm the sample nor leave exogenous residuals. As a result, it has thus gained rapidly growing attention in biomedical imaging. Over the past two decades, QPI has seen a broad spectrum of evolving implementations, but only a few have seen successful commercialization. The challenges are manifold whilst one stands out - that they have expensive optical setups that are often incompatible with existing commercial microscope platforms. The setups are also very complicated such that without professionals having solid optics background, it is difficult to operate the system to perform imaging applications. Another limiting factor is the insufficient understanding of sensitivity. In QPI, sensitivity characterizes the system repeatability and determines its quantification resolution. With more emerging applications in cell imaging, the requirement for sensitivity also becomes more stringent. In this work, a category of highly sensitive full-field QPI techniques based on wavelength shifting interferometry (WSI) is proposed. WSI images the full-field of the sample simultaneously, unlike some other techniques requiring scanning one probe point across the sample. It also has the advantage of preserving the integrity of the interferometer, which is the key structure to enable highly sensitive measurement for QPI methods. Therefore, the techniques proposed here have the potential to be readily integrated into the ubiquitous lab microscopes and equip them with quantitative imaging functionality. Differed by implementations, two WSI techniques have been proposed, termed swept source digital holographic phase microscopy (SS-DHPM), and low coherence wavelength shifting interferometry (LC-WSI), respectively. SS-DHPM brings in an additional capability to perform spectroscopy, whilst the LC-WSI achieves a faster imaging rate which has been demonstrated with live sperm cell imaging. In an attempt to integrate WSI with the existing commercial microscope, we also discuss the possibility of demodulation for low-cost sources and common path implementation. Besides experimentally demonstrating the high sensitivity with the proposed techniques, a novel sensitivity evaluation framework is also introduced for the first time in QPI. This framework not only examines the realistic sensitivity obtained in experiments, but also compares it to the theoretical values. The framework can be widely applied to a broad range of QPI techniques, providing insights into algorithm optimization and energy efficiency of sensitivity.

Neural Networks (NNs) (or 'deep' neural networks (DNNs)) have found great success in many applications across all fields of engineering, and in particular have found recent success in the field of Photonics. In this work we discuss the application of NNs to optical interferometry for the purpose of quantitative phase imaging (QPI). We show that NNs are capable of quantifying the optical pathlength difference in an interferogram with sensitivities that achieve the fundamental limit given by the Cramér-Rao bound (CRB). As an application, we consider a particular QPI technique known as wavelength shifting interferometry (WSI) which obtains the OPL by acquiring multiple interferograms at different, evenly spaced wavenumbers. Traditional phase demodulation algorithms for WSI fail to reach the theoretical OPL sensitivity limit set by the CRB. We have designed NNs which are capable of achieving this bound across a wide range of OPL differences. The NNs are trained on simulated data, and then applied to experimental data. In both simulation and experiment, the NNs outperform the existing analytical demodulation techniques and provide highly sensitive signal demodulation in cases where the analytical approach fails. Thus, NNs provide better performance and more flexibility in the design and use of a WSI system. We expect that the techniques developed in this work can be extended to other two-beam interference based QPI system. / M.S. / Neural Networks (NNs) (or 'deep' neural networks (DNNs)) have found great success in many applications across all fields of engineering, and in particular have found recent success in the field of Photonics. In this work we discuss the application of NNs to making so-called 'phase' images of biological cells and tissues (e.g. red blood cells, sperm cells). This is necessary for many biological samples which are transparent under traditional bright field microscopy. We show that NNs are capable of quantifying the phase of these samples to produce images with higher contrast than possible in a typical microscope image. As an example, we introduce a particular phase microscopy system and study the application of NNs to this system. We show that the NNs are capable of providing solutions for this phase in situations where existing analytical techniques fail. The NNs are also capable of making more precise calculations of the phase than the traditional algorithms in many situations where either technique could be used. Therefore, NNs can provide simultaneously higher performance and more flexibility when designing phase microscopy systems.

Quantitative phase Imaging(QPI) has emerged as a valuable tool for imaging specimens with weak scattering and absorbing abilities such as cells and tissues. It is complementary to fluorescence microscopy, as such, it can be applied to unlabelled specimens without the need for fluorescent tagging. By quantitatively mapping the phase changes induced in the incident light field by the optical path length delays of the specimen, QPI provides objective measurement of the cellular dynamics and enables imaging the specimen with high contrast. Transport of Intensity Equation(TIE) is a powerful computational tool for QPI because of its experimental and computational simplicity. Using TIE, the phase can be quantitatively retrieved from defocused intensity images. However, the resolution of the phase image computed using TIE is limited by the diffraction limit of the imaging system used to capture the intensity images. In this thesis, we have developed a super resolution phase imaging technique by applying the principles of Structured Illumination Microscopy(SIM) to Transport of Intensity phase retrieval. The modulation from the illumination shifts the high frequency components of the phase object into the system pass-band. This enables phase imaging with resolutions exceeding the diffraction limit. The proposed method is experimentally validated using a custom-made upright microscope. Because of its experimental and computational simplicity, the method in this thesis should find application in biomedical laboratories where super resolution phase imaging is required / Master of Science / Transport of Intensity Equation is a quantitative phase microscopy technique that enables imaging thin transparent specimens with high phase contrast using a through focus intensity stack. It provides speckle free imaging, compatibility with bright field microscopes and valid under partial coherence. However, the Optical Transfer Function(OTF) of the imaging system or the microscope acts a low pass filter, effectively limiting the maximum spatial frequency that can pass through the system. This reduces the spatial resolution of the computed phase image to the spatial diffraction limit. There has been a continuous drive to develop Super resolution techniques that will provide sub-diffraction resolutions because it will provide better insight into the cellular structure, morphology and composition. Structured Illumination Microscopy(SIM) is one such established technique. Existing work in super resolution phase imaging using SIM is exclusively limited to holography and interferometry based techniques. However, such methods require two-beam interference, illumination sources with high coherence, high experimental stability and phase unwrapping in the postprocessing step to retrieve the true object phase. In this work, we demonstrate a single beam propagation based super resolution phase imaging technique by applying structured illumination to Transport of Intensity Equation. It is valid under partial coherence, and does not require interference, simplifying the experimental and computational requirement. We have designed an upright microscope to demonstrate high resolution phase imaging of human cheek cells.

A position-sensitive microchannel plate (MCP) detector has been installed at the Canadian Penning Trap (CPT) mass spectrometer located at the CAlifornium Rare Isotope Breeder Upgrade (CARIBU) facility at Argonne National Laboratory in order to carry out Phase-Imaging Ion Cyclotron Resonance (PI-ICR) measurements. With this new measurement method, proof-of-principle mass measurements of five nuclei were made to a precision of $\delta m/m \approx 10^{-7}$. The PI-ICR results are found to be consistent with previous Time-of-Flight Ion Cyclotron Resonance (ToF-ICR) measurements. The content of this thesis covers the entire mass measurement process beginning with beam production at CARIBU through to ion detection at the CPT and a comparison of the ToF-ICR and PI-ICR measurement methods. The future of mass measurements at the CPT with this new technique will also be discussed. / May 2016

<p>Optical coherence tomography (OCT) is a non-invasive imaging modality that uses low coherence interferometry to generate three-dimensional datasets of a sample's structure. OCT has found tremendous clinical applications in imaging the retina and has demonstrated great utility in the diagnosis of various retinal diseases. However, such diagnoses rely upon the ability to observe abnormalities in the structure of the retina caused by pathology. By the time an ocular disease has progressed to the point of affecting the morphology of the retina, irreversible vision loss in the eye may already occur. Changes in the functionality of the tissue often precede changes to the structure. Thus, if imaging methods are developed to provide additional functional information about the behavior and response of the retinal tissue and vasculature, earlier treatment for disease may be prescribed, thus preserving vision for the patient. </p><p>Within the last decade, significant technological advances in OCT systems have enabled high-speed and high sensitivity image acquisition using either spectral domain OCT (SDOCT) or swept-source OCT (SSOCT) configurations. Such systems use Fourier processing to extract structural information of a sample from interferometric principles. But such systems also have access to the optical phase information, which allows for functional analysis of sample dynamics. This dissertation details the development and application of methods using both intensity and phase information as a tool for studying interesting biological phenomena. The goal of this work is an extension of techniques to image the vasculature in the retina and enhance the clinical utility of OCT.</p><p>I first outline basic theory necessary for understanding the principles of OCT. I then describe OCT phase imaging in cellular applications as a demonstration of the ability of OCT to provide functional information on biological dynamics. Phase imaging methods suffer from an artifact known as phase wrapping, and I have developed a software technique to overcome this problem in OCT, thus extending its usefulness in providing quantitative information. I characterize the limitations in measuring moving scatterers with Doppler OCT in both SDOCT and SSOCT system. I also show the ability to image the vasculature in the retina using variance imaging with a high-speed retinal imaging system and software based methods to correct for patient motion and create a widefield mosaic in an automated manner. Finally, future directions for this work are discussed.</p> / Dissertation

In this dissertation we use digital holographic quantitative phase microscopy to observe and measure phase-only structures due to induced photothermal interactions and nanoscopic structures produced by photomechanical interactions. Our use of the angular spectrum method combined with off-axis digital holography allows for the successful hologram acquisition and processing necessary to view these phenomena with nanometric and, in many cases, subnanometric precision. We show through applications that this has significance in metrology of bulk fluid and interfacial properties. Our accurate quantitative phase mapping of the optically induced thermal lens in media leads to improved measurement of the absorption coefficient over existing methods. By combining a mathematical model describing the thermal lens with that describing the surface deformation effect of optical radiation pressure, we simulate the ability to temporally decouple the two phenomena. We then demonstrate this ability experimentally as well as the ability of digital holography to clearly distinguish the phase signatures of the two effects. Finally, we devise a pulsed excitation method to completely isolate the optical pressure effect from the thermal lensing effect. We then develop a noncontact purely optical approach to measuring the localized surface properties of an interface within a system using a single optical pressure pulse and a time-resolved digital holographic quantitative phase imaging technique to track a propagating nanometric capillary disturbance. We demonstrate the method's ability to accurately measure the surface energy of pure media and chemical monolayers formed by surfactants with good agreement to published values. We discuss the possible adaptation of this technique to applications for living biological cell membranes.

abstract: The research of this dissertation has involved the nanoscale quantitative characterization of patterned magnetic nanostructures and devices using off-axis electron holography and Lorentz microscopy. The investigation focused on different materials of interest, including monolayer Co nanorings, multilayer Co/Cu/Py (Permalloy, Ni81Fe19) spin-valve nanorings, and notched Py nanowires, which were fabricated via a standard electron-beam lithography (EBL) and lift-off process. Magnetization configurations and reversal processes of Co nanorings, with and without slots, were observed. Vortex-controlled switching behavior with stepped hysteresis loops was identified, with clearly defined onion states, vortex states, flux-closure (FC) states, and Omega states. Two distinct switching mechanisms for the slotted nanorings, depending on applied field directions relative to the slot orientations, were attributed to the vortex chirality and shape anisotropy. Micromagnetic simulations were in good agreement with electron holography observations of the Co nanorings, also confirming the switching field of 700-800 Oe. Co/Cu/Py spin-valve slotted nanorings exhibited different remanent states and switching behavior as a function of the different directions of the applied field relative to the slots. At remanent state, the magnetizations of Co and Py layers were preferentially aligned in antiparallel coupled configuration, with predominant configurations in FC or onion states. Two-step and three-step hysteresis loops were quantitatively determined for nanorings with slots perpendicular, or parallel to the applied field direction, respectively, due to the intrinsic coercivity difference and interlayer magnetic coupling between Co and Py layers. The field to reverse both layers was on the order of ~800 Oe. Domain-wall (DW) motion within Py nanowires (NWs) driven by an in situ magnetic field was visualized and quantified. Different aspects of DW behavior, including nucleation, injection, pinning, depinning, relaxation, and annihilation, occurred depending on applied field strength. A unique asymmetrical DW pinning behavior was recognized, depending on DW chirality relative to the sense of rotation around the notch. The transverse DWs relaxed into vortex DWs, followed by annihilation in a reversed field, which was in agreement with micromagnetic simulations. Overall, the success of these studies demonstrated the capability of off-axis electron holography to provide valuable insights for understanding magnetic behavior on the nanoscale. / Dissertation/Thesis / Ph.D. Materials Science and Engineering 2010

Cette thèse présente les travaux de recherche effectués dans le but de concevoir et optimiser un instrument de métrologie du front d’onde et d’imagerie de phase sur faisceau synchrotron dans la gamme des rayonnements X durs. L’étude s’est focalisée sur la conception d’un interféromètre à réseau unique dont l’extraction des informations associées à l’analyse du front d’onde s’effectue par démodulation Fourier. Ces choix ont été déterminés par la volonté de concevoir un instrument robuste pouvant fonctionner sur une large gamme de conditions expérimentales sans avoir à modifier et accorder les paramètres et éléments constitutifs fondamentaux de l’instrument à chaque expérience. Ceci se résume par la contrainte forte de pouvoir réaliser une calibration absolue du système de façon à garantir la prise de mesure ultérieure par acquisition d’un interférogramme unique tout en s’affranchissant des erreurs de mesure déterministes de l’instrument.La variable expérimentale la plus importante correspond à l’énergie de travail; par conséquent la conception de l’interféromètre s’est organisée autour de la recherche de performances constantes sur une large bande spectrale pour des énergies entre 10 à 30keV, et a conduit à l’étude et à la mise en œuvre d’une configuration interférométrique innovante. Celle-ci exploite un régime diffractif particulier du réseau permettant d’accéder à la propriété d’achromaticité (non rigoureuse) par repliement des performances de mesure sur cette bande spectrale, et ce, pour un instrument reposant pourtant sur un composant diffractif fondamentalement chromatique.D’autre part, afin de garantir l’analyse quantitative de l’information portée par les modulations interférométriques générées par le réseau, nous avons également optimisé les traitements numériques et abouti au développement d’un algorithme de pré-traitement des interférogrammes permettant de s’affranchir des effets de bord lors de l’analyse d’images à support fini. Les artefacts rencontrés sont connus sous le nom de phénomènes de Gibbs et apparaissent dans le cas général de la transformée de Fourier d’un signal discontinu. Ainsi, annuler ces effets de bord permet également de gérer les problèmes d’éclairement partiel de la pupille de l’analyseur dont la gestion est essentielle en métrologie de front d’onde.Enfin nous présenterons les résultats expérimentaux de validation du concept interférométrique et de mesures applicatives en métrologie optique et en imagerie de phase sur des échantillons d’intérêt issus de domaines variés, de la biologie à la paléontologie. / This PhD dissertation presents the optimization and design of a wavefront analyzer dedicated to optical metrology and phase imaging on synchrotron sources in the hard X-ray regime. We chose to develop a single grating interferometer combined with a phase retrieval algorithm based on Fourier analysis. The main purpose here is to conceive a bulk instrument able to work in a great variety of experimental conditions without having to tune the parameters of the instrument in between experiments. This is thus related to the key constraint that is to calibrate the wavefront analyzer so that any further measurements could be corrected from any deterministic errors and allow single shot measurements of any sample.The key varying parameter in synchrotron experiments is the radiation energy (or wavelength). Therefore, the design of the interferometer aimed at minimizing the discrepancies of its performances over a broad spectral range from 10 to 30keV . This research lead in one hand to the description and implementation of an innovative interferometric configuration based on the achromatization of the instrument performances over this spectral range, despite the chromatic nature of the grating.On the other hand, in order to guaranty the quantitative analysis of interferograms, we also optimized the numerical approach to extract and treat the information they contain. This lead to the development of a conditioning procedure for a subsequent phase retrieval by Fourier demodulation. It fulfills the classical boundary conditions imposed by Fourier transform techniques and allows a nearly artifact-free extraction of the information.At last, experimental results demonstrate first, the viability of the grating achromatization concept, and then, the possibility to realize the metrology of grazing incidence optics at different wavelengths. The instrument was then used for phase imaging purposes of biological and archaeological samples.

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