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According to the conclusion of Khelashvili et al. [Phys. Med. Biol. 51, 221 (2006)], the minus logarithm of the visibility ratio fulfills the line integral condition; consequently the scattering information can be reconstructed quantitatively by conventional computed tomography (CT) algorithms. Based on Fresnel diffraction theory, we analyzed the influence of particle-size selectivity on the performance of an X-ray grating interferometer (GI) applied for dark-field CT. The results state the signal-to-noise ratio (SNR) of dark-field imaging is sensitive to the particle size, which demonstrate that the X-ray dark-field CT using a GI can efficiently differentiate materials of identical X-ray absorption and help to choose optimal X-ray energy for known particle size, thus extending the application range of grating interferometer.

Theoretical analysis of the mechanical behavior of an x-ray mirror made from piezoelectric bimorph is presented. A complete two-dimensional relationship between the radius of curvature of the mirror and the applied voltage is derived. The accuracy of this relationship is studied by comparing the figures calculated by the relationship and Finite Element Analysis. The influences of several critical parameters in the relationship on the radius of curvature are analyzed. It is found that piezoelectric coefficient d 31 is the main material property parameter that dominates the radius of curvature, and that the optimal thickness of PZT plate corresponding to largest bending range is 2.5 times of that of faceplate. It is demonstrated that the relationship is helpful for us to complete the primary design of the x-ray mirror made from piezoelectric bimorph.

With the development of full-field transmission X-ray microscopy (TXM) for research in biology, life science, material science and physics, zone plate-based full-field TXM is becoming a powerful tool for obtaining quantitative internal structural and chemical information at the nanoscale when combined with spectroscopic imaging. For the TXM beamline design, the best choice is to match the phase space needed by the zone plate from the source point. However, for the nearly diffraction-limited synchrotron radiation sources, it is not easy to fully match the needed phase space due to its low-emittance. Using redshift radiation from an undulator, under consideration of experimental requirements and the heat load effect, this paper describes the design of TXM beamline at the nearly diffraction-limited High Energy Photon Source (HEPS). In this design, not only sufficient illumination angle can be acquired, but also a nearly annular illumination can be obtained to match the illumination required for zone plate imaging. Furthermore, about two times photon flux can be obtained at source point and the photons can be fully used in this design using redshift undulator radiation. The presented design can also be informative for the same kind of beamline design at other nearly diffraction-limited synchrotron photon sources.

Phase sensitive X-ray imaging methods can provide substantially improved contrast over conventional absorption-based techniques, and therefore new and inaccessible information. Here we propose a dual detector approach for X-ray differential phase contrast imaging, which allows a quantitative retrieval of the object's phase information by a single exposure. The analysis performed in our research shows that compared with the phase-stepping method, the dual detector approach is advantageous in fast imaging speed, reduced radiation dose and alignment errors, and avoiding any problems resulting from motion artifacts and X-ray exposure reproducibility. The approach has a direct extension to single exposure two-dimensional differential phase contrast imaging, as well as the possibility to perform three-dimensional reconstruction of the refractive index and its gradient field. We believe that this approach can find its potential in clinical applications, where imaging speed and radiation dose are critical issues.

One of the main benefits of a fractal plate is the formation of a sequence of subsidiary foci when used as a condenser. In order to further demonstrate the reliable use of a fractal zone plate in transmission X-ray microscopy, we studied how a condenser fractal zone plate produces the focal spot in a transmission X-ray microscope layout. We present and discuss the comparison in the X-ray region with a normal condenser zone plate and a numerical simulation that points out that the efficiency of the condenser depends on the structure and the material of the zone plate, and on the energy. This analysis paves a way for foreseen optical applications of modified zone plates in real microscope layouts.

X-ray phase contrast imaging has been demonstrated to have an improved contrast over conventional absorption imaging for those weakly absorbing objects. However, most of the hard X-ray phase-sensitive imaging has so far been impractical with laboratory available X-ray sources. Grating-based phase imaging approach has the prominent advantage that polychromatic laboratory X-ray generators can be efficiently used in a Talbot–Lau configuration. Through numerical simulations, we demonstrate here the efficient use of polychromatic X-ray laboratory sources for differential phase contrast imaging. The presented results explain why in recently reported experiments, polychromatic X-ray tubes could be efficiently used in a Talbot–Lau interferometer. Furthermore, the results indicate that the fractional Talbot distance is not limited by the polychromaticity of the X-ray source. Since the sensitivity of phase measurements is proportional to the fractional Talbot distance, the image quality for phase measurements can be further improved. Finally, the potential optimizations of the imaging system are discussed from an application perspective, taking into consideration both available X-ray flux and compactness of the system.

We report here a quantitative analysis of the effect of partial coherence on grating-based phase-contrast X-ray imaging. The self-image intensity has been derived through the phase-space formulation in the framework of the Wigner distribution. Based on the behavior of the self-image visibility, the minimum required spatial coherence length is given for three different types of gratings. Furthermore, we show that the coherence requirement, at different fractional Talbot distances, increases linearly with the Talbot order for the three types of gratings. The approach we presented can also be successfully applied to the Talbot–Lau geometry.

Through real time synchrotron radiation topography observation, dynamical behavior of ferroelectric domains as a function of temperature in unpoled 0.92Pb(Zn1/3Nb2/3)O-3-0.08PbTiO(3) (PZN-8% PT) crystals is investigated. A sequence of temperature-induced monoclinic phase transformations is observed, and verified by combining this method with temperature-dependence Raman scattering, capacitance measurement, and X-ray diffraction. This phase evolution picture seems remarkably unique as the monoclinic phase is able to coexist with the cubic phase well above T-C. (C) 2008 Elsevier Ltd. All rights reserved.

This contribution investigates the effect on the imaging contrast of the small angle scattering and of the rocking curve in the entire angular range. We show that based on the small angle scattering properties, the reflectivity of the crystal analyzer and the rocking curve of the monochromator–analyzer, in a diffraction enhanced imaging (DEI) experimental setup the contrast of the image collected at the top of the rocking curve is always higher than that of the apparent absorption image. Moreover, our experimental data confirm that the quality of a refraction image is superior to a refraction-like image. In order to understand the observed behavior we introduce and discuss the contribution of a new term in the classical DEI equation.

Sample parameters that are involved in the projection data of Computed Tomography reconstruction have to fulfill the rotational invariance, i.e., the contribution to the projection data of a single sample point has to be invariant respect to the illumination direction. In the reconstruction procedure of the Diffraction Enhanced Peak Imaging (DEPI) technique, while the Inverse Radon Transform is fulfilled, the rotation invariance is no longer satisfied because of the contribution induced by refraction at the edge of the sample. However, DEPI experimental results address the question how the edge contrast is generated. In this contribution, theoretical simulations of DEPI have been performed to investigate the edge contrast due to the refraction process and to test the rotation invariance condition of the DEPI-CT reconstruction algorithm.

Hard X-ray Phase-Contrast Imaging (HX-PCI) is a new and valuable method that may provide information of the inner parts of an opaque object. Previous reports demonstrated its applicability in soft and hard tissue imaging. Here we provide further evidence for improved image quality and the effective capability to distinguish inner microstructures in real biomedical systems such as cochlea. Experiments performed both at the 4W1A beamline of the Beijing Synchrotron Radiation Facility (BSRF) and at the Taiwan National Synchrotron Radiation Research Center (NSRRC) clearly show details of samples’ inner microstructure with a resolution of a few microns. The improved spatial resolution is a relevant achievement for future improved understanding and clinical trials.

Small angle scattering plays an important role in diffraction enhanced imaging (DEI). The DEI equation proposed by Chapman is accepted and widely used by many applications in medical, biological and material researches. However, in this framework the contribution of the small angle scattering determined by the crystal analyzer is neglected and the extinction contrast caused by the rejection of the small angle scattering by the analyzer is not explicitly expressed. In this contribution we introduce two additional terms in the DEI equation that describe the additional background introduced by the small angle scattering collected by the analyzer crystal and the extinction contrast associated to the rejection of the small angle scattering by the analyzer crystal, respectively. Four kinds of images of the DEI method were considered by using these revised equations and results were presented and discussed.

Diffraction enhanced imaging (DEI) with two crystals has been performed at the 4W1A beamline at Beijing Synchrotron Radiation Facility (BSRF). Two different crystal geometrical layouts were used to collect images, in the first layout the rotation axis of the crystal has been set perpendicular to the orbital plane while in the second the axis is parallel to the orbital plane. Performance comparison between the two layouts is discussed in terms of thermal expansion of the crystal induced by the heat load, imaging homogeneity, spatial resolution and angular resolution. From both experimental and theoretical data we show that the best images may be obtained with the optical layout in which the rotation axis of the crystals is perpendicular to the orbital plane.

In-line phase contrast imaging has been discussed in both plane wave and point source condition in many works. For source with finite size and non-uniform distribution, however, it is not easy to obtain images with high contrast. In this work, we propose a new theoretical method to improve image contrast on this type of source. For a non-uniformly distributed source based on a simple cylinder model, we discuss the dependence of the contrast on the experimental conditions, i.e., the radius of the cylinder, the distance between the detector and the object, the difference of the refractive index, and the spatial coherence of the source. Optimal parameters for different samples and sources, which are meaningful for a non-uniformly distributed source, are presented and discussed. A series of experimental results are presented to confirm the theoretical framework.

The 4W1A beamline at the Beijing Synchrotron Radiation Facility (BSRF) had been dedicated to researches in the field of X-ray phase contrast imaging. In both available layouts, e.g., in-line imaging and diffraction enhanced imaging, a spatial resolution better than 10 μm has been achieved and an X-ray phase contrast CT system has been installed and tested on the beamline. With or without analyzer, it can work either in in-line or the diffraction enhanced mode.

A new diffraction-enhanced imaging (DEI) set-up was designed and constructed at Beijing Synchrotron Radiation Facility. The size of imaging beam cross section is the same as that of incident “white” X-ray beam in the new set-up. While in the original set-up, the size is always limited in one direction. Thus, larger samples can be imaging in a single exposure without need for scanning of the sample and detector in the new set-up. Choosing a fly as sample, DEI and DEI-computed-tomography (CT) experiments were carried out using the new set-up. Experimental results show that the spatial resolution of the CT image is in the tens of microns.

Diffraction-enhanced imaging computer tomography (DEI-CT) is a new method to provide the object's inner information. Previous reports demonstrated its applicability in soft and hard tissue imaging. Here, we provide further evidence for the improved overall image quality and for the option to distinguish the inner microstructures of the guinea pig's cochlea. Data has shown the details of the cochlea's inner microstructure such as vestibular membrane which only have 6 μm. A better knowledge of these microstructures may be relevant to achieve progress in the otology of clinical anatomization.

Diffraction enhanced imaging (DEI) is one of the phase contrast imaging methods using the monochromatic X-ray from synchrotron, which provides information on the out-of-plane angular deviation of X-ray. DEI allows the investigation of micro-structures inside weakly absorbing samples at high spatial resolution without serious radiation exposure. Tomographic techniques can be applied readily to phase contrast images. The combination of DEI and tomography allows for a reconstruction of refractive index gradient distribution inside weakly absorbing samples with micrometer resolution, particularly suited for the 3D observation of micro-organisms and tissues. The existing phase contrast tomography methods based on DEI use phase contrast images as projections, such images contain not only the phase information, but also the absorption information. A novel method (DEI in the tomography mode) was developed to greatly increase the proportion of refraction information in phase contrast images by computing the difference between the two sets of images acquired at different angles of the rocking curve to adopt the projections with a complete set (2 π ) for reconstruction. The reconstructed images of cochlea of a guinea pig showed the spatial structures and the micro-features inside the samples. The new method reveals higher spatial resolution compared to the conventional phase contrast tomography methods and is more suitable to the investigation of micro-structures of micro-organisms and tissue materials.

In this paper we reported the fabrication of the ultra-thin freestanding diamond windows for soft X-ray optics using hotfilament CVD method. The diamond film of the window is totally freestanding in a central aperture of 4–8 mm. Raman spectra,XRD and SEM show the deposited diamond films in our laboratory are high quality polycrystalline diamond films. The absolutetransmissions of the diamond windows of 0.4–1.0 mm thickness were measured in the energy range between 75 and 1600 eV.For a freestanding diamond window of 0.4 mm thickness the absolute transmission of carbon fluorescence ( E s284 eV ) is ashigh as 0.59. It will have a variety of applications as an X-ray window for submicron lithography of integrated circuits and X-ray spectroscopy, particularly, for characteristic soft X-ray detection of light elements. 2003 Elsevier Science B.V. All rights reserved. Keywords: Diamond film; Optical properties; X-Ray; Window 1. IntroductionChemical Vapor Deposition (CVD ) diamond possess-es a number of interesting physical and chemical prop-erties that make it has been considered as an idealmaterial in the field of optics w1–3 x. Its superior strength,extremely transparent, high thermal stability and con-ductivity, as well as high radiation tolerant and corrosionresistant make it a best candidate for the traditionalberyllium (Be ) window in a variety of soft X-ray opticalapplications. The atomic number Z of Beryllium issmaller than that of carbon. The soft X-ray transmissionof a Be window should be higher than that of a diamondwindow with equal thickness. But the Be window couldnot be too thin because of its relative weak mechanicalproperties. The normal thickness of the Be windowshould be at least several micrometers. It reduces thesoft X-ray transmission of Be window, therefor prohib-iting the transmission of characteristic soft X-ray fromlight elements such as boron, carbon, nitrogen andfluorine.On the other hand, the CVD diamond freestandingwindow can be fabricated very thin to several hundrednanometers. Recently, the researches on the study of

Aberrations in the reconstruction of images are analysed, aberration elimination methods are discussed and the feasibility of direct image reconstruction from a lensless Fourier transform X-ray hologram with visible light is investigated.