Methods For Coherent Lensless Imaging And X Ray Wavefront Measurement
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Lensless Holography Methods for Soft X-ray Resonant Coherent Imaging
The ability to interpret and inverse x-ray diffraction patterns from crystals has largely shaped our understanding of the structure of matter. However, structure determination of noncrystalline objects from their diffraction patterns is a much more difficult task. The dramatic increase in available coherent x-ray photon flux over the past decade has made possible a technique known as lensless coherent diffractive imaging (CDI), that addresses exactly this problem. The central question around CDI is the so-called phase problem: upon detection of the diffraction intensity, the phase information of the diffracted wave is inevitably lost. Generally, the phase problem is approached using iterative phase retrieval algorithms. Holographic methods, through interference with reference diffractions, encode the phase information directly inside the measured x-ray holograms, and are therefore able to avoid the stagnation and uniqueness problems commonly encountered by the iterative algorithms. This dissertation discusses two novel holographic methods for coherent lensless imaging using resonant soft x-rays. The first part focuses on generalizing the multiple-wavelength anomalous diffraction technique, a highly successful method for solving the crystal structures of biomacromolecules, into a multiple-wavelength holography technique for nanoscale resonant x-ray imaging. Using this method I show element specific reconstructions of nanoparticles and magnetization distribution in magnetic thin films with sub 50 nm resolution. The second part discusses progress in X-ray Fourier holography, an ultrafast lensless imaging platform that can be used with the upcoming x-ray free electron lasers. In particular, I will present experiments using two novel types of extended reference structures that bring the resolution beyond the precision of reference fabrication, previously regarded as the resolution limit for x-ray Fourier transform holography. Finally, future applications of holographic methods, especially experimental considerations for time-resolved studies of nanostructures using X-FELs, will be discussed.
Methods for Coherent Lensless Imaging and X-ray Wavefront Measurement
"Advancement and research on phase retrieval techniques are in large part motivated by their application in high resolution lensless laser imaging and x- ray diffractive imaging. In the former a high resolution image can be obtained from measuring the intensity pattern of the propagated field without the use of any imaging optics, thus providing an imaging system that does not increase its thickness along the optical axis as the aperture diameter is increased. For x- ray coherent diffractive imaging, on the other hand, high-resolution conventional imaging is difficult to achieve at these wavelengths because of the difficulty of manufacturing and aligning x-ray focusing elements with sufficient numerical aperture and precision. Thus, in order to achieve resolutions on the order of a nanometer, a coherent x-ray beam is used to illuminate the object of interest and the object is reconstructed from a measurement of its far-field diffraction intensity without any imaging optics. Thus the advancement and application of lensless imaging techniques has become an increasingly important topic of research. X-ray diffractive imaging is set apart from other high-resolution imaging techniques (e.g. scanning electron or atomic force microscopy) for its high penetration depth, which enables tomographic 3D imaging of thick samples and buried structures. Furthermore, using short x-ray pulses, it enables the capability to take ultrafast snapshots, giving a unique opportunity to probe nanoscale dynamics at femtosecond time scales. In this thesis we present improvements to phase retrieval algorithms, assess their performance through numerical simulations, and develop new methods for both imaging and wavefront measurement. Using numerical simulations we identified and explained the origin of the twin-image problem in iterative transform phase retrieval with a centrosymmetric support constraint. We proposed and numerically demonstrated the effectiveness of a modified phase retrieval algorithm that uses Fourier weighted projections to increase the quality and resolution of the reconstructions by mitigating a problem arising from the finite measurement window and finite support constraint. Such an approach is particularly useful when the object presents large phase variations on a length- scale significantly smaller than the resolution, i.e. reconstruction of fully developed speckled images. In order to accurately and efficiently assess phase retrieval algorithm performance, we have developed algorithms for subpixel image registration. Despite being particularly well suited for comparing images from data collected in the Fourier domain (e.g., phase retrieval and holography), these algorithms have al- ready shown a substantial success in other applications as well. Building on the original work by Faulkner and Rodenburg, we developed an improved reconstruction algorithm for phase retrieval with transverse translations of the object relative to the illumination beam. Based on gradient-based non- linear optimization, this algorithm is capable of estimating the object, and at the same time refining the initial knowledge of the incident illumination and the object translations. The advantages of this algorithm over the original iterative transform approach are shown through numerical simulations. Phase retrieval has already shown substantial success in wavefront sensing at optical wavelengths. Although in principle the algorithms can be used at any wavelength, in practice the focus-diversity mechanism that makes optical phase retrieval robust is not practical to implement for x-rays. In this thesis we also describe the novel application of phase retrieval with transverse translations to the problem of x-ray wavefront sensing. This approach allows the characterization of the complex-valued x-ray field in-situ and at-wavelength and has several practical and algorithmic advantages over conventional focused beam measurement techniques. A few of these advantages include improved robustness through diverse measurements, reconstruction from far-field intensity measurements only, and significant relaxation of experimental requirements over other beam characterization approaches. Furthermore, we show that a one-dimensional version of this technique can be used to characterize an x-ray line focus produced by a cylindrical focusing element. We provide experimental demonstrations of the latter at hard x-ray wavelengths, where we have characterized the beams focused by a kinoform lens and an elliptical mirror. In both experiments the reconstructions exhibited good agreement with independent measurements, and in the latter a small mirror misalignment was inferred from the phase retrieval reconstruction. These experiments pave the way for the application of robust phase retrieval algorithms for in-situ alignment and performance characterization of x-ray optics for nanofocusing. We also present a study on how transverse translations help with the well-known uniqueness problem of one-dimensional phase retrieval. We also present a novel method for x-ray holography that is capable of reconstructing an image using an off-axis extended reference in a non-iterative computation, greatly generalizing an earlier approach by Podorov et.al. The approach, based on the numerical application of derivatives on the field autocorrelation, was developed from first mathematical principles. We conducted a thorough theoret- ical study to develop technical and intuitive understanding of this technique and derived sufficient separation conditions required for an artifact-free reconstruction. We studied the effects of missing information in the Fourier domain, and of an im- perfect reference, and we provide a signal-to-noise ratio comparison with the more traditional approach of Fourier transform holography. We demonstrated this new holographic approach through proof-of-principle optical experiments and later ex- perimentally at soft x-ray wavelengths, where we compared its performance to Fourier transform holography, iterative phase retrieval and state-of-the-art zone-plate x-ray imaging techniques (scanning and full-field). Finally, we present a demonstration of the technique using a single 20 fs pulse from a high-harmonic table-top source. Holography with an extended reference is shown to provide fast, good quality images that are robust to noise and artifacts that arise from missing information due to a beam stop."--Leaves viii-xi.
Coherent X-ray diffractive imaging on the single-cell-level of microbial samples
Author: Robin Niklas Wilke
language: en
Publisher: Göttingen University Press
Release Date: 2015
Since its first experimental demonstration in 1999, Coherent X-Ray Diffractive Imaging has become one of the most promising high resolution X-Ray imaging techniques using coherent radiation produced by brilliant synchrotron storage rings. The ability to directly invert diffraction data with the help of advanced algorithms has paved the way for microscopic investigations and wave-field analyses on the spatial scale of nanometres without the need for inefficient imaging lenses. X-Ray phase contrast which is a measure of the electron density is an important contrast mode of soft biological specimens. For the case of many dominant elements of soft biological matter, the electron density can be converted into an effective mass density offering a unique quantitative information channel which may shed light on important questions such as DNA compaction in the bacterial nucleoid through ‚weighing with light‘. In this work X-Ray phase contrast maps have been obtained from different biological samples by exploring different methods. In particular, the techniques Ptychography and Waveguide-Holographic-Imaging have been used to obtain twodimensional and three-dimensional mass density maps on the single-cell-level of freeze-dried cells of the bacteria Deinococcus radiodurans, Bacillus subtilis and Bacillus thuringiensis allowing, for instance, to estimate the dry weight of the bacterial genome in a near native state. On top of this, reciprocal space information from coherent small angle X-Ray scattering (cellular Nano-Diffraction) of the fine structure of the bacterial cells has been recorded in a synergistic manner and has been analysed down to a resolution of about 2.3/nm exceeding current limits of direct imaging approaches. Furthermore, the dynamic range of present detector technology being one of the major limiting factors of ptychographic phasing of farfield diffraction data has been significantly increased. Overcoming this problem for the case of the very intense X-Ray beam produced by Kirkpatrick-Baez mirrors has been explored by using semi-transparent central stops.