Coherent diffractive imaging (CDI) and scanning transmission x-ray microscopy (STXM) are two popular microscopy techniques that have evolved quite independently. CDI promises to reach resolutions below 10 nanometers, but the reconstruction procedures put stringent requirements on data quality and sample preparation. In contrast, STXM features straightforward data analysis, but its resolution is limited by the spot size on the specimen. We demonstrate a ptychographic imaging method that bridges the gap between CDI and STXM by measuring complete diffraction patterns at each point of a STXM scan. The high penetration power of x-rays in combination with the high spatial resolution will allow investigation of a wide range of complex mesoscopic life and material science specimens, such as embedded semiconductor devices or cellular networks.

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Progress in imaging and metrology depends on exquisite control over and comprehensive characterization of wave fields. As reflected in its name, coherent diffractive imaging relies on high coherence when reconstructing highly resolved images from diffraction intensities alone without the need for image-forming lenses. Fully coherent light can be described adequately by a single pure state. Yet partial coherence and imperfect detection often need to be accounted for, requiring statistical optics or the superposition of states. Furthermore, the dynamics of samples are increasingly the very objectives of experiments. Here we provide a general analytic approach to the characterization of diffractive imaging systems that can be described as low-rank mixed states. We use experimental data and simulations to show how the reconstruction technique compensates for and characterizes various sources of decoherence quantitatively. Based on ptychography, the procedure is closely related to quantum state tomography and is equally applicable to high-resolution microscopy, wave sensing and fluctuation measurements. As a result, some of the most stringent experimental conditions in ptychography can be relaxed, and susceptibility to imaging artefacts is reduced. Furthermore, the method yields high-resolution images of mixed states within the sample, which may include quantum mixtures or fast stationary stochastic processes such as vibrations, switching or steady flows.

We have used the method of x-ray diffraction microscopy to image the complex-valued exit wave of an intact and unstained yeast cell. The images of the freeze-dried cell, obtained by using 750-eV x-rays from different angular orientations, portray several of the cell's major internal components to 30-nm resolution. The good agreement among the independently recovered structures demonstrates the accuracy of the imaging technique. To obtain the best possible reconstructions, we have implemented procedures for handling noisy and incomplete diffraction data, and we propose a method for determining the reconstructed resolution. This work represents a previously uncharacterized application of x-ray diffraction microscopy to a specimen of this complexity and provides confidence in the feasibility of the ultimate goal of imaging biological specimens at 10-nm resolution in three dimensions. coherent x-ray diffraction imaging ͉ x-ray microscopy X -ray diffraction microscopy is a recently developed method in which only the coherent diffraction pattern of the sample is measured. It provides a path to high resolution without the limitations imposed by an x-ray optical system. The idea to image a noncrystalline object by phasing and inverting its diffraction pattern goes back to a suggestion by Sayre (1, 2) and was first demonstrated with x-rays by Miao et al. (3). In this article, we report the imaging of the complex-valued exit wavefront (both phase and magnitude) of a whole freeze-dried and unstained yeast cell. The images, at 30-nm resolution from multiple angular orientations of the cell, required an exposure of approximately one minute each using 750-eV x-rays (1 eV ϭ 1.602 ϫ 10 Ϫ19 J). This demonstration paves the way for the application of 3D x-ray diffraction microscopy (XDM) (4, 5) to frozen-hydrated samples in the future.High-resolution 3D images of biological samples are currently made by at least three methods: zone-plate x-ray microscopy (6-9), transmission electron microscopy (10, 11), and x-ray crystallography. All three have particular strengths and limitations. Both water-window (7-9) and multi-keV (12) zone-plate microscopes are currently limited to Ϸ60-nm 3D resolution by details of zone-plate resolution, depth of field, and operation. On the other hand, high-resolution transmission electron microscopes, although capable of extraordinary resolution, are limited by multiple electron scattering to specimens thinner than 0.5-1 m (10, 13). The third method, x-ray crystallography, traditionally yields the highest resolution structures and is the structural technique of choice, but it is limited to specimens that can be crystallized. In summary, the traditional structural techniques do not provide a capability for 3D imaging of an intact eukaryotic cell with resolution around 10 nm, and it is toward this end that our present efforts are directed.Since its introduction, XDM has been demonstrated with metal test objects in two dimensions (3, 14) and three dimensions (4) and with stained biological specimens (15) an...

We introduce the application of maximum-likelihood (ML) principles to the image reconstruction problem in coherent diffractive imaging. We describe an implementation of the optimization procedure for ptychography, using conjugate gradients and including preconditioning strategies, regularization and typical modifications of the statistical noise model. The optimization principle is compared to a difference map reconstruction algorithm. With simulated data important improvements are observed, as measured by a strong increase in the signal-to-noise ratio. Significant gains in resolution and sensitivity are also demonstrated in the ML refinement of a reconstruction from experimental x-ray data. The immediate consequence of our results is the possible reduction of exposure, or dose, by up to an order of magnitude for a reconstruction quality similar to iterative algorithms currently in use.

Recent advances in coherent x-ray diffractive imaging have paved the way to reliable and quantitative imaging of noncompact specimens at the nanometer scale. Introduced a year ago, an advanced implementation of ptychographic coherent diffractive imaging has removed much of the previous limitations regarding sample preparation and illumination conditions. Here, we apply this recent approach toward structure determination at the nanoscale to biological microscopy. We show that the projected electron density of unstained and unsliced freeze-dried cells of the bacterium Deinococcus radiodurans can be derived from the reconstructed phase in a straightforward and reproducible way, with quantified and small errors. Thus, the approach may contribute in the future to the understanding of the highly disputed nucleoid structure of bacterial cells. In the present study, the estimated resolution for the cells was 85 nm (half-period length), whereas 50-nm resolution was demonstrated for lithographic test structures. With respect to the diameter of the pinhole used to illuminate the samples, a superresolution of about 15 was achieved for the cells and 30 for the test structures, respectively. These values should be assessed in view of the low dose applied on the order of ≃1.3 · 10 5 Gy, and were shown to scale with photon fluence.bacterial nucleoid | cellular imaging | coherent x-ray diffractive imaging | x-ray microscopy

Inline holography is a common phase-contrast imaging method which uses free-space propagation to encode the phase signal into measured intensities. However, quantitative retrieval of the sample's image remains challenging, imposing constraints on the nature of the sample or on the propagation distance. Here, we present a way of simultaneously retrieving the sample's complex-valued transmission function and the incident illumination function from near-field diffraction patterns. The procedure relies on the measurement diversity created by lateral translations of the sample with respect to a structured illumination. The reconstruction approach, in essence identical to that employed in ptychography, is applied to hard X-ray synchrotron measurements and to simulations. Compared to other inline holography techniques, we expect near-field ptychography to reduce reconstruction artefacts by factoring out wavefront imperfections and relaxing constraints on the sample's scattering properties, thus ultimately improving the robustness of propagation-based X-ray phase tomography.