High-dynamic-range coherent diffractive imaging: ptychography using the mixed-mode pixel array detector

Recovery of spatial frequencies in coherent diffraction imaging in the presence of a central obscuration

Coherent diffraction imaging (CDI) and its scanning version, ptychography, are lensless imaging approaches used to iteratively retrieve a sample's complex scattering amplitude from its measured diffraction patterns. These imaging methods are most useful in extreme ultraviolet (EUV) and X-ray regions of the electromagnetic spectrum, where efficient imaging optics are difficult to manufacture. CDI relies on high signal-to-noise ratio diffraction data to recover the phase, but increasing the flux can cause saturation effects on the detector. A conventional solution to this problem is to place a beam stop in front of the detector. The pixel masking method is a common solution to the problem of missing frequencies due to a beam stop. This paper describes the information redundancy in the recorded data set and expands on how the reconstruction algorithm can exploit this redundancy to estimate the missing frequencies. Thereafter, we modify the size of the beam stop in experimental and simulation data to assess the impact of the missing frequencies, investigate the extent to which the lost portion of the diffraction spectrum can be recovered, and quantify the effect of the beam stop on the image quality. The experimental findings and simulations conducted for EUV imaging demonstrate that when using a beam stop, the numerical aperture of the condenser is a crucial factor in the recovery of lost frequencies. Our thorough investigation of the reconstructed images provides information on the overall quality of reconstruction and highlights the vulnerable frequencies if the beam stop size is larger than the extent of the illumination NA. The outcome of this study can be applied to other sources of frequency loss, and it will contribute to the improvement of experiments and reconstruction algorithms in CDI.

High-resolution and high-sensitivity X-ray ptychographic coherent diffraction imaging using the CITIUS detector

Ptychographic coherent diffraction imaging (PCDI) is a synchrotron X-ray microscopy technique that provides high spatial resolution and a wide field of view. To improve the performance of PCDI, the performance of the synchrotron radiation source and imaging detector should be improved. In this study, ptychographic diffraction pattern measurements using the CITIUS high-speed X-ray image detector and the corresponding image reconstruction are reported. X-rays with an energy of 6.5 keV were focused by total reflection focusing mirrors, and a flux of ∼2.6 × 1010 photons s-1 was obtained at the sample plane. Diffraction intensity data were collected at up to ∼250 Mcounts s-1 pixel-1 without saturation of the detector. Measurements of tantalum test charts and silica particles and the reconstruction of phase images were performed. A resolution of ∼10 nm and a phase sensitivity of ∼0.01 rad were obtained. The CITIUS detector can be applied to the PCDI observation of various samples using low-emittance synchrotron radiation sources and to the stability evaluation of light sources.

Coherent modulation imaging using unknown modulators

Coherent modulation imaging (CMI) is an effective lensless diffraction imaging method with fast algorithmic convergence and high robustness to data defects. In the reported algorithms for CMI, one important requirement is that the modulator function need to be known a priori; and an additional step for the modulator characterization is required to be carried out in advance by other methods, such as ptychography, which could be cumbersome in practice. Here, we propose an improved algorithm that allows for the transmission function of a completely unknown modulator to be recovered during the same iterative process of image reconstruction. We have verified the method in both simulations and optical experiments. This improvement would turn CMI into a more practical and standalone technique for broader applications in biology and materials science.

Quantitative birefringence distribution measurement using mixed-state ptychography

Determining the complete optical behavior of anisotropic samples using ptychography is always a difficult problem. We propose a novel birefringence measurement method based on mixed-state ptychography that can simultaneously obtain the azimuth angle and retardation of anisotropic samples in a single scan. By using a reference system transformation, the two mutually orthogonal object states are unambiguously retrieved, and their errors are greatly reduced. The normalized root mean square errors of the obtained azimuth angle and retardation are 0.0011 and 0.0041, respectively. This method offers more rapid data acquisition; compared to interferometric based methods, it has the advantages of unlimited field of view and a simpler, more stable setup. Further, it opens a new possibility for investigating anisotropic samples by means of mixed-state ptychography.

Probing Intracellular Element Concentration Changes during Neutrophil Extracellular Trap Formation Using Synchrotron Radiation Based X-Ray Fluorescence

High pressure frozen (HPF), cryo-substituted microtome sections of 2 μm thickness containing human neutrophils (white blood cells) were analyzed using synchrotron radiation based X-ray fluorescence (SR nano-XRF) at a spatial resolution of 50 nm. Besides neutrophils from a control culture, we also analyzed neutrophils stimulated for 1-2 h with phorbol myristate acetate (PMA), a substance inducing the formation of so-called Neutrophil Extracellular Traps (or NETs), a defense system again pathogens possibly involving proteins with metal chelating properties. In order to gain insight in metal transport during this process, precise local evaluation of elemental content was performed reaching limits of detection (LODs) of 1 ppb. Mean weight fractions within entire neutrophils, their nuclei and cytoplasms were determined for the three main elements P, S and Cl, but also for the 12 following trace elements: K, Ca, Mn, Fe, Co, Ni, Cu, Zn, Se, Br, Sr and Pb. Statistical analysis, including linear regression provided objective analysis and a measure for concentration changes. The nearly linear Ca and Cl concentration changes in neutrophils could be explained by already known phenomena such as the induction of Ca channels and the uptake of Cl under activation of NET forming neutrophils. Linear concentration changes were also found for P, S, K, Mn, Fe, Co and Se. The observed linear concentration increase for Mn could be related to scavenging of this metal from the pathogen by means of the neutrophil protein calprotectin, whereas the concentration increase of Se may be related to its antioxidant function protecting neutrophils from the reactive oxygen species they produce against pathogens. We emphasize synchrotron radiation based nanoscopic X-ray fluorescence as an enabling analytical technique to study changing (trace) element concentrations throughout cellular processes, provided accurate sample preparation and data-analysis.

Dark-field X-ray ptychography: Towards high-resolution imaging of thick and unstained biological specimens

The phase shift of light or electrons in objects is now necessary for probing weak-phase objects such as unstained biological specimens. Optical microscopy (OM) and transmission electron microscopy (TEM) have been used to observe weak-phase objects. However, conventional OM has low spatial resolution and TEM is limited to thin specimens. Here, we report on the development of dark-field X-ray ptychography, which combines X-ray ptychography and X-ray in-line holography, to observe weak-phase objects with a phase resolution better than 0.01 rad, a spatial resolution better than 15 nm, and a field of view larger than 5 μm. We apply this method to the observation of both the outline and magnetosomes of the magnetotactic bacteria MO-1. Observation of thick samples with high resolution is expected to find broad applications in not only biology but also materials science.

Tomography of a Cryo-immobilized Yeast Cell Using Ptychographic Coherent X-Ray Diffractive Imaging

The structural investigation of noncrystalline, soft biological matter using x-rays is of rapidly increasing interest. Large-scale x-ray sources, such as synchrotrons and x-ray free electron lasers, are becoming ever brighter and make the study of such weakly scattering materials more feasible. Variants of coherent diffractive imaging (CDI) are particularly attractive, as the absence of an objective lens between sample and detector ensures that no x-ray photons scattered by a sample are lost in a limited-efficiency imaging system. Furthermore, the reconstructed complex image contains quantitative density information, most directly accessible through its phase, which is proportional to the projected electron density of the sample. If applied in three dimensions, CDI can thus recover the sample's electron density distribution. As the extension to three dimensions is accompanied by a considerable dose applied to the sample, cryogenic cooling is necessary to optimize the structural preservation of a unique sample in the beam. This, however, imposes considerable technical challenges on the experimental realization. Here, we show a route toward the solution of these challenges using ptychographic CDI (PCDI), a scanning variant of coherent imaging. We present an experimental demonstration of the combination of three-dimensional structure determination through PCDI with a cryogenically cooled biological sample—a budding yeast cell (Saccharomyces cerevisiae)—using hard (7.9 keV) synchrotron x-rays. This proof-of-principle demonstration in particular illustrates the potential of PCDI for highly sensitive, quantitative three-dimensional density determination of cryogenically cooled, hydrated, and unstained biological matter and paves the way to future studies of unique, nonreproducible biological cells at higher resolution.

Spread spectrum phase modulation for coherent X-ray diffraction imaging

High dynamic range, phase ambiguity and radiation limited resolution are three challenging issues in coherent X-ray diffraction imaging (CXDI), which limit the achievable imaging resolution. This paper proposes a spread spectrum phase modulation (SSPM) method to address the aforementioned problems in a single strobe. The requirements on phase modulator parameters are presented, and a practical implementation of SSPM is discussed via ray optics analysis. Numerical experiments demonstrate the performance of SSPM under the constraint of available X-ray optics fabrication accuracy, showing its potential to real CXDI applications.

Compound focusing mirror and X-ray waveguide optics for coherent imaging and nano-diffraction

A compound optical system for coherent focusing and imaging at the nanoscale is reported, realised by high-gain fixed-curvature elliptical mirrors in combination with X-ray waveguide optics or different cleaning apertures. The key optical concepts are illustrated, as implemented at the Göttingen Instrument for Nano-Imaging with X-rays (GINIX), installed at the P10 coherence beamline of the PETRA III storage ring at DESY, Hamburg, and examples for typical applications in biological imaging are given. Characteristic beam configurations with the recently achieved values are also described, meeting the different requirements of the applications, such as spot size, coherence or bandwidth. The emphasis of this work is on the different beam shaping, filtering and characterization methods.

Dark-field X-ray ptychography

The dynamic range of X-ray detectors is a key factor limiting both the spatial resolution and sensitivity of X-ray ptychography as well as the coherent flux of incident X-rays. Here, we propose a method for high-resolution and high-sensitivity X-ray ptychography named "dark-field X-ray ptychography", which compresses the dynamic range of intensities of diffraction patterns. In this method, a small reference object is aligned upstream of the sample. The scattered X-rays from the object work as a reference beam for in-line holography. Ptychographic diffraction patterns including the in-line hologram are collected, and then the image of the sample is reconstructed by an iterative phasing method. This method allows us to obscure the low-Q region of the diffraction patterns using a beamstop since the in-line hologram complements structural information in the low-Q region, resulting in the compression of the dynamic range of intensities of diffraction patterns. A numerical study shows that the dynamic range of intensities of diffraction patterns is decreased by about three orders of magnitude.