Because the refractive index for hard x rays is slightly different from unity, the optical phase of a beam is affected by transmission through an object. Phase images can be obtained with extreme instrumental simplicity by simple propagation provided the beam is coherent. But, unlike absorption, the phase is not simply related to image brightness. A holographic reconstruction procedure combining images taken at different distances from the specimen was developed. It results in quantitative phase mapping and, through association with three-dimensional reconstruction, in holotomography, the complete three-dimensional mapping of the density in a sample. This tool in the characterization of materials at the micrometer scale is uniquely suited to samples with low absorption contrast and radiation-sensitive systems.

Phase objects are readily imaged through Fresnel diffraction in the hard x-ray beams of third-generation synchrotron radiation sources such as the ESRF, due essentially to the very small angular size of the source. Phase objects can lead to spurious contrast in x-ray diffraction images (topographs) of crystals. It is shown that this contrast can be eliminated through random phase plates, which provide an effective way of tailoring the angular size of the source. The possibilities of this very simple technique for imaging phase objects in the hard x-ray range are explored experimentally and discussed. They appear very promising, as shown in particular by the example of a piece of human vertebra, and could be extended to phase tomography.

The novel possibilities of phase feature detection in radiography at a third generation synchrotron radiation source are used to image, both in projection and in computed tomography, a cracked silicon single crystal and metal matrix composites strained in tension. Through an instrumentally very simple technique, based on Fresnel diffraction, phase jumps related to the interface between the matrix and the reinforcing phases of the composites are detected even when these phases show very similar x-ray attenuation. Strain-induced cracks with openings below the micrometer range are also visible through the phase modulation they introduce, illustrating the potential of the technique for assessing damage in materials with improved resolution and sensitivity.

We used quantitative phase tomography with synchrotron radiation to elucidate the 3D structure of Arabidopsis seeds in their native state. The cells are clearly distinguished, and their internal structure is revealed through local variations in electron density. We visualized a 3D network of intercellular air space that might allow immediate gas exchange for energy supply during germination and͞or serve for rapid water uptake and distribution during imbibition.mature seed structure ͉ synchrotron radiation ͉ x-ray imaging ͉ embryo organs ͉ cell components O ur understanding of seed structure and germination depends critically on insights about the structural arrangement of organs and tissues within the seed. Germination starts with water uptake by the dry seed and is complete when the elongating radicle traverses the seed coat. One of the first changes during imbibition is reestablishment of respiration in mitochondria. This activity is connected to a remarkable initial rise in oxygen consumption that declines afterward until germination is complete; i.e., the radicle traverses the seed coat, and atmospheric oxygen can enter the seed and reach the young growing plantlet (1-3). In seeds, limited seed coat permeability is a strong obstacle to gas exchange (4, 5). Consequently, the oxygen needed for germination to start should be rapidly available within the seed. Oxygen might originate from inside the seed and͞or from water entering the seed at the beginning of imbibition. At present, no data are available concerning the internal oxygen content in mature seeds because the rigidity of the seed coat at that stage precludes measuring this content. However, stored internal oxygen should exist and be important for germination because oxygen production by endogenous photosynthesis is known to influence seed viability and germination. Unlike animals, plants lack specialized circulation systems for oxygen transport, and the question arises whether air (and oxygen) is stored in seeds and by which means it circulates.To answer these questions it is important to know the fine structure of the mature seeds. Histology of seeds is usually based on optical or electron microscopy of slices, the results from adjacent sections being then combined. The cutting and fixation steps alter the tissues, and only one-directional (i.e., 2D) processing is possible. Thus, methods based on slicing and fixation procedures cannot give reliable visualization of small cellular interspaces or indicate the existence of networks of spaces. We therefore looked for noninvasive tomographic techniques that could improve the visualization of cell-to-cell organization in the seed tissues. The tomographic approach consists of acquiring projections of an object along different directions and combining them computationally to obtain a 3D reconstruction of the object. This approach has been successfully used in soft x-ray microscopy, with Fresnel zone plates as objective lenses, providing unique visualization of a whole cell at 60-nm resolution (6, 7). The emer...

X ray radiography and tomography are important tools in medicine as well as in life science and materials science. Not long ago an approach called in-line holography based on simple propagation became possible using partially coherent synchrotron beams like the ones available at the European Synchrotron Radiation Facility (ESRF). Theoretical and experimental work by Cloetens et al. [Appl. Phys. Lett 75, 2912 (1999)] have shown that quantitative retrieval of the optical phase, from a set of radiographs taken at different sample-to-detector distances, is feasible. Mathematically speaking we are dealing with a direct method based on linearization in order to solve an inverse nonlinear problem. The phase retrieval can be combined with classical tomography in order to obtain a three-dimensional representation of the object’s electron density (holotomography). In order to optimize the image contrast for the numerical phase retrieval process, we have carried out calculations resulting in an optimized choice of value and number of the sample-to-detector distances as well as of the photon energy. These results were then confirmed by experiments on the ESRF long beamline ID19.

Fractional Talbot images of optical gratings acting as periodic phase objects have been obtained by use of x rays of 0.069-nm wavelength from a third-generation synchrotron radiation source. Quantitative evaluation of the data obtained as a function of defocusing distance provides information on the lateral coherence of the beam as well as on the phase modulation in the object.

Particularly high coherence of the x-ray beam is associated, on the ID19 beamline at ESRF, with the small angular size of the source as seen from a point of the sample (0.1-1 µrad). This feature makes the imaging of phase objects extremely simple, by using a `propagation' technique. The physical principle involved is Fresnel diffraction. Phase imaging is being simultaneously developed as a technique and used as a tool to investigate light natural or artificial materials introducing phase variations across the transmitted x-ray beam. They include polymers, wood, crystals, alloys, composites or ceramics, exhibiting inclusions, holes, cracks, ... . `Tomographic' three-dimensional reconstruction can be performed with a filtered back-projection algorithm either on the images processed as in attenuation tomography, or on the phase maps retrieved from the images with a reconstruction procedure similar to that used for electron microscopy. The combination of diffraction (`topography') and Fresnel (`phase') imaging leads to new results.

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