A solution to the inversion problem of scattering would offer aberration-free diffraction-limited 3D images without the resolution and depth-of-field limitations of lens-based tomographic systems. Powerful algorithms are increasingly being used to act as lenses to form such images. Current image reconstruction methods, however, require the knowledge of the shape of the object and the low spatial frequencies unavoidably lost in experiments. Diffractive imaging has thus previously been used to increase the resolution of images obtained by other means. We demonstrate experimentally here a new inversion method, which reconstructs the image of the object without the need for any such prior knowledge.Comment: 5 pages, 3 figures, improved figures and captions, changed titl

X-ray diffraction microscopy (XDM) is a new form of x-ray imaging that is being practiced at several third-generation synchrotron-radiation x-ray facilities. Nine years have elapsed since the technique was first introduced and it has made rapid progress in demonstrating high-resolution threedimensional imaging and promises few-nm resolution with much larger samples than can be imaged in the transmission electron microscope. Both life-and materials-science applications of XDM are intended, and it is expected that the principal limitation to resolution will be radiation damage for life science and the coherent power of available x-ray sources for material science. In this paper we address the question of the role of radiation damage. We use a statistical analysis based on the socalled "dose fractionation theorem" of Hegerl and Hoppe to calculate the dose needed to make an image of a single life-science sample by XDM with a given resolution. We find that for simplyshaped objects the needed dose scales with the inverse fourth power of the resolution and present experimental evidence to support this finding. To determine the maximum tolerable dose we have assembled a number of data taken from the literature plus some measurements of our own which cover ranges of resolution that are not well covered otherwise. The conclusion of this study is that, based on the natural contrast between protein and water and "Rose-criterion" image quality, one should be able to image a frozen-hydrated biological sample using XDM at a resolution of about 10 nm.6Corresponding author: mrhowells@lbl.gov, phone 510 486 4949, fax 510 486 7696.

Coherent X-ray diffraction microscopy is a method of imaging non-periodic isolated objects at resolutions only limited, in principle, by the largest scattering angles recorded. We demonstrate X-ray diffraction imaging with high resolution in all three dimensions, as determined by a quantitative analysis of the reconstructed volume images. These images are retrieved from the 3D diffraction data using no a priori knowledge about the shape or composition of the object, which has never before been demonstrated on a non-periodic object. We also construct 2D images of thick objects with infinite depth of focus (without loss of transverse spatial resolution). These methods can be used to image biological and materials science samples at high resolution using X-ray undulator radiation, and establishes the techniques to be used in atomic-resolution ultrafast imaging at X-ray free-electron laser sources.

In this review we propose to address the question: for the life-science researcher, what does X-ray microscopy have to offer that is not otherwise easily available?We will see that the answer depends on a combination of resolution, penetrating power, analytical sensitivity, compatibility with wet specimens, and the ease of image interpretation.

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...

Advances in the development of free-electron lasers offer the realistic prospect of high-resolution imaging to study the nanoworld on the time-scale of atomic motions. We identify X-ray Fourier Transform holography 1,2,3 , (FTH) as a promising but, so far, inefficient scheme to do this. We show that a uniformly redundant array 4 (URA) placed next to the sample, multiplies the efficiency of X-ray FTH by more than one thousand (approaching that of a perfect lens) and provides holographic images with both amplitude-and phase-contrast information. The experiments reported here demonstrate this concept by imaging a nano-fabricated object at a synchrotron source, and a bacterial cell at a soft X-ray free-electron-laser, where illumination by a single 15 fs pulse was successfully used in producing the holographic image. We expect with upcoming hard X-ray lasers to achieve considerably higher spatial resolution and to obtain ultrafast movies of excited states of matter.

Fourier transform x-ray holography has been used to image gold test objects with submicrometer structure, resolving features as small as 60 nanometers. The hologram-recording instrument uses coherent 3.4-nanometer radiation from the soft x-ray undulator beamline X1A at the National Synchrotron Light Source. The specimen to be imaged is placed near the first-order focal spot produced by a Fresnel zone plate; the other orders, chiefly the zeroth, illuminate the specimen. The wave scattered by the specimen interferes with the spherical reference wave from the focal spot, forming a hologram with fringes of low spatial frequency. The hologram is recorded in digital form by a charge-coupled device camera, and the specimen image is obtained by numerical reconstruction.

The inversion of a diffraction pattern offers aberration-free diffraction-limited 3D images without the resolution and depth-of-field limitations of lens-based tomographic systems, the only limitation being radiation damage. We review our experimental results, discuss the fundamental limits of this technique and future plans.