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Following the recent developement of Fourier ptychographic microscopy (FPM) in the visible range by Zheng et al. (2013), we propose an adaptation for hard x-rays. FPM employs ptychographic reconstruction to merge a series of low-resolution, wide field of view images into a high-resolution image. In the x-ray range this opens the possibility to overcome the limited numerical aperture of existing x-ray lenses. Furthermore, digital wave front correction (DWC) may be used to charaterize and correct lens imperfections. Given the diffraction limit achievable with x-ray lenses (below 100 nm), x-ray Fourier ptychographic microscopy (XFPM) should be able to reach resolutions in the 10 nm range.
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Fourier Ptychographic Microscopy (FPM) is a computational imaging method that is able to super-resolve features beyond the diffraction-limit set by the objective lens of a traditional microscope. This is accomplished by using synthetic aperture and phase retrieval algorithms to combine many measurements captured by an LED array microscope with programmable source patterns. FPM provides simultaneous large field-of-view and high resolution imaging, but at the cost of reduced temporal resolution, thereby limiting live cell applications. In this work, we learn LED source pattern designs that compress the many required measurements into only a few, with negligible loss in reconstruction quality or resolution. This is accomplished by recasting the super-resolution reconstruction as a Physics-based Neural Network and learning the experimental design to optimize the networks overall performance. Specifically, we learn LED patterns for different applications (e.g. amplitude contrast and quantitative phase imaging) and show that the designs we learn through simulation generalize well in the experimental setting. Further, we discuss a context-specific loss function, practical memory limitations, and interpretability of our learned designs.
We demonstrate X-ray phase contrast microscopy performed at the European X-ray Free-Electron Laser sampled at 1.128 MHz rate. We have applied this method to image stochastic processes induced by an optical laser incident on water-filled capillaries with micrometer scale spatial resolution. The generated high speed water jet, cavitation formation and annihilation in water and glass, as well as glass explosions are observed. The comparison between XFEL and previous synchrotron MHz microscopy shows the superior contrast and spatial resolution at the XFEL over the synchrotron. This work opens up new possibilities for the characterization of dynamic stochastic systems on nanosecond to microsecond time scales at megahertz rate with object velocities up to few kilometers per second using X-ray Free-Electron Laser sources.
In recent years, x-ray speckle tracking techniques have emerged as viable tools for wavefront metrology and sample imaging applications. These methods are based on the measurement of near-field images. Thanks to the simple experimental set-up, high angular sensitivity and compatibility with low coherence sources these methods have been actively developed for use with synchrotron and laboratory light sources. Not only do speckle-tracking techniques give the potential for high resolution imaging, but they also provide rapid and robust characterisation of aberrations of x-ray optical elements, focal spot profiles and the sample position and transmission properties. In order to realise these capabilities, we require software implementations that are equally rapid and robust. To address this need, a software suite has been developed for the ptychographic x-ray speckle tracking technique -- an x-ray speckle based method suitable for highly divergent wavefields. The software suite is written in Python 3, with an OpenCL back end for GPU and multi-CPU core processing. It is accessible as a Python module, through the command line or through a graphical user interface and is available as source code under version 3 or later of the GNU General Public License.
We present a method for the measurement of the phase gradient of a wavefront by tracking the relative motion of speckles in projection holograms as a sample is scanned across the wavefront. By removing the need to obtain an un-distorted reference image of the sample, this method is suitable for the metrology of highly divergent wavefields. Such wavefields allow for large magnification factors, that, according to current imaging capabilities, will allow for nano-radian angular sensitivity and nano-scale sample projection imaging. Both the reconstruction algorithm and the imaging geometry are nearly identical to that of ptychography, except that the sample is placed downstream of the beam focus and that no coherent propagation is explicitly accounted for. Like other x-ray speckle tracking methods, it is robust to low-coherence x-ray sources making is suitable for lab based x-ray sources. Likewise it is robust to errors in the registered sample positions making it suitable for x-ray free-electron laser facilities, where beam pointing fluctuations can be problematic for wavefront metrology. We also present a modified form of the speckle tracking approximation, based on a second-order local expansion of the Fresnel integral. This result extends the validity of the speckle tracking approximation and may be useful for similar approaches in the field.
Operation of an X-ray spectrometer based on a spherical variable line spacing grating is analyzed using dedicated ray-tracing software allowing fast optimization of the grating parameters and spectrometer geometry. The analysis is illustrated with optical design of a model spectrometer to deliver a resolving power above 20400 at photon energy of 930 eV (Cu L-edge). With this energy taken as reference, the VLS coefficients are optimized to cancel the lineshape asymmetry (mostly from the coma aberrations) as well as minimize the symmetric aberration broadening at large grating illuminations, dramatically increasing the aberration-limited vertical acceptance of the spectrometer. For any energy away from the reference, we evaluate corrections to the entrance arm and light incidence angle on the grating to maintain the exactly symmetric lineshape. Furthermore, we evaluate operational modes when these corrections are coordinated to maintain either energy independent focal curve inclination or maximal aberration-limited spectrometer acceptance. The results are supported by analytical evaluation of the coma term of the optical path function. Our analysis gives thus a recipe to design a high-resolution spherical VLS grating spectrometer operating with negligible aberrations at large acceptance and over extended energy range.
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