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In this work, a novel, to the best of our knowledge, approach based on an x-ray thin lens imaging theory is proposed to predict the angular sensitivity responses of dual-phase-grating differential phase contrast (DPC) interferometers. Experimental validations have been performed to demonstrate the high accuracy of theoretical predictions using two different setups: one with real source images and the other with virtual source images. This new sensitivity calculation method is helpful to optimize the DPC imaging performance of a dual-phase-grating system.

Material decomposition (MD) is an important application of computer tomography (CT). For phase contrast imaging, conventional MD methods are categorized into two types with respect to different operation sequences, i.e., “before” or “after” image reconstruction. Both categories come down to two-step methods, which have the problem of noise amplification. In this study, we incorporate both phase and absorption (PA) information into MD process, and correspondingly develop a simultaneous algebraic reconstruction technique (SART). The proposed method is referred to as phase & absorption material decomposition-SART (PAMD-SART). By iteratively solving an optimization problem, material composition and substance quantification are reconstructed directly from absorption and differential phase projections. Comparing with two-step MD, the proposed one-step method is superior in noise suppression and accurate decomposition. Numerical simulations and synchrotron radiation based experiments show that PAMD-SART outperforms the classical MD method (image-based and dual-energy CT iterative method), especially for the quantitative accuracy of material equivalent atomic number.

In this work, we developed a new theoretical framework using wave optics to explain the working mechanism of the grating based X-ray differential phase contrast imaging (XPCI) interferometer systems consist of more than one phase grating. Under the optical reversibility principle, the wave optics interpretation was simplified into the geometrical optics interpretation, in which the phase grating was treated as a thin lens. Moreover, it was derived that the period of an arrayed source, e.g., the period of a source grating, is always equal to the period of the diffraction fringe formed on the source plane. When a source grating is utilized, the theory indicated that it is better to keep the periods of the two phase gratings different to generate large period diffraction fringes. Experiments were performed to validate these theoretical findings.

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.

As one of the HEPS project beamlines, zone plate based full-field transmission x-ray microscopy (TXM) beamline will provide imaging tool with spatial resolution down to 20nm and exposure time of sub-second, along with different imaging mode such as absorption, Zernike phase and XANES. Because HEPS will operate a nearly diffraction-limited storage ring (less than 60pm·rad), how to utilize the feature of low emittance becomes interesting and it is some challenging to satisfy the zone plate imaging with enough illumination angle and field-of-view. Within the optimized conceptual design, beam shaper condenser instead of capillary was selected to focus x-rays to sample and give enough illumination angle to zone plate, and red-shift undulator radiation was used to improve beamline efficiency.

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.

This paper, “New idea for recording x-ray imaging holography," was presented as part of International Conference on Space Optics—ICSO 1997, held in Toulouse, France.

A description of the rocking curve in diffraction enhanced imaging (DEI) is presented in terms of the angular signal response function and a simple multi-information retrieval algorithm based on the cosine function fitting. A comprehensive analysis of noise properties of DEI is also given considering the noise transfer characteristic of the X-ray source. The validation has been performed with synchrotron radiation experimental data and Monte Carlo simulations based on theGeant4toolkit combined with the refractive process of X-rays, which show good agreement with each other. Moreover, results indicate that the signal-to-noise ratios of the refraction and scattering images are about one order of magnitude better than that of the absorption image at the edges of low-Zsamples. The noise penalty is drastically reduced with the increasing photon flux and visibility. Finally, this work demonstrates that the analytical method can build an interesting connection between DEI and GDPCI (grating-based differential phase contrast imaging) and is widely suitable for a variety of measurement noise in the angular signal response imaging prototype. The analysis significantly contributes to the understanding of noise characteristics of DEI images and may allow improvements to the signal-to-noise ratio in biomedical and material science imaging.

Purpose: Grating-based x-ray phase contrast imaging is considered as one of the most promising techniques for future medical imaging. Many different methods have been developed to retrieve phase signal, among which the phase stepping (PS) method is widely used. However, further practical implementations are hindered, due to its complex scanning mode and high radiation dose. In contrast, the reverse projection (RP) method is a novel fast and low dose extraction approach. In this contribution, the authors present a quantitative analysis of the noise properties of the refraction signals retrieved by the two methods and compare their sensitivities. Methods: Using the error propagation formula, the authors analyze theoretically the signal-to-noise ratios (SNRs) of the refraction images retrieved by the two methods. Then, the sensitivities of the two extraction methods are compared under an identical exposure dose. Numerical experiments are performed to validate the theoretical results and provide some quantitative insight. Results: The SNRs of the two methods are both dependent on the system parameters, but in different ways. Comparison between their sensitivities reveals that for the refraction signal, the RP method possesses a higher sensitivity, especially in the case of high visibility and/or at the edge of the object. Conclusions: Compared with the PS method, the RP method has a superior sensitivity and provides refraction images with a higher SNR. Therefore, one can obtain highly sensitive refraction images in grating-based phase contrast imaging. This is very important for future preclinical and clinical implementations. (C) 2015 American Association of Physicists in Medicine.

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.

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.

A simple framework that allows a new general diffraction enhanced imaging (DEI) equation to be derived is presented. This latter equation may explain all open problems associated with the equation introduced by Chapman and those not explained by the first DEI equation, such as the noise background due to the small-angle scattering reflected by the analyzer. Combing the DEI equation with computed tomography (CT) theory, we propose a new DEI-CT formula that explains qualitatively the contour contrast caused by extinction of the refraction. Two formulae with a new method to extract the refraction angle are also introduced. Within this new theoretical framework the three components of the gradient of the refractive index can be reconstructed.

Differential phase-contrast (DPC) X-ray imaging has been performed in the Talbot-Lau configuration, in which the X-ray source was a combination of an absorption grating and a laboratory X-ray generator. We report here quantitative analysis of partial coherence effects on the X-ray Talbot-Lau interferometer. Based on the visibility of the self-image, the well-known geometry condition is reproduced. It is shown that effects of partial coherence are determined by the opening ratio of the source grating, and that the effects are independent of the Talbot order and the type of the phase grating, a condition quite different from those in a Talbot interferometer. A possible explanation is discussed from the point of view of the effective spatial coherence length. Taking into account the available X-ray flux and experimental fluctuations, we present the optimum opening ratio. Furthermore, we mention that our results can also be successfully used to discuss the properties of a multiline X-ray source.

A new method to extract the angle of refraction data in diffraction enhanced imaging computed tomography (DEI-CT) is proposed in this paper. In this method the projective data of the refractive angle can be extracted from only one set of projective image data with the sample rotational angle range from 0° to 360°. This method not only much simplifies the process in the experiment of DEI-CT but can also get rid of some misalignments between two sets of projective image data with the sample rotational angle range from 0° to 180°, which are taken at the high angle and the low angle of the analyzer crystal, respectively. Using this method, the refractive index and the two derivatives of the refractive index in the plane perpendicular to the rotational axis of the sample can be reconstructed with higher quality than that done by the former ways. Experimental results confirm the new method.

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.

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.

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.

Based on pinhole imaging and conventional x-ray projection imaging, a more general DEI (diffraction enhanced imaging) equation is derived using simple concepts in this paper. Not only can the new DEI equation explain all the same problems as with the DEI equation proposed by Chapman, but also some problems that cannot be explained with the old DEI equation, such as the noise background caused by small angle scattering diffracted by the analyser.

A comparison between Gabor X-ray holography and lensless Fourier transform X-ray holography is made. Three aspects are considered: recording distance, aberrations in optical reconstructions and digital reconstructions of these two kinds of holograms by theoretical analysis and digital simulations. Some new results are given.

Three-dimensional (3D) topographic structures of acupuncture points were investigated by using synchrotron radiation in-line X-ray phase contrast computerized tomography. Two acupuncture points, named Zhongji (RN3) and Zusanli (ST36), were studied. We found an accumulation of microvessels at each acupuncture point region. Images of the tissues surrounding the acupuncture points do not show such kinds of structure. This is the first time that 3D images have revealed the specific structures of acupuncture points.

An alternative method for quantitative phase retrieval in a transmission X-ray microscope system at sub-50-nm resolution is presented. As an alternative to moving the sample in the beam direction in order to analyze the propagation-introduced phase effect, we have illuminated the TXM using X-rays of different energy without any motor movement in the TXM system. Both theoretical analysis and experimental studies have confirmed the feasibility and the advantage of our method, because energy tuning can be performed with very high energy resolution using a double crystal monochromator at a synchrotron beam line, and there is zero motor error in TXM system in our approach. High-spatial-resolution phase retrieval is accomplished using the proposed method.

A display hologram of an object can be recorded and reconstructed in three primary colors if the angular selectivity of volume recording media is exploited. Three holograms are recorded in the same medium, each at a different primary color. These three holograms are reconstructed by simultaneous illumination of the hologram with the original reference beams. By proper choice of the angles that the reference beams make to the hologram, it is possible to suppress strongly cross talk between the different reconstructions (e.g., the red object reconstruction in green light). The technique exhibits high resolution, high diffraction efficiency, and vivid colors. Through the addition of three holographically recorded volume gratings it is possible to reconstruct the hologram with a beam of white light. The saturation and brightness of each primary color in the reconstruction can be adjusted by selection of an appropriate thickness for the corresponding grating.

Hard X-ray phase-contrast imaging has extremely high sensitivity of weakly absorbing low-Z samples in medical and biological fields. Phase-contrast radiographic images have superposition phenomenon, while phase-contrast computed tomographic images reveal quantitative distribution of refractive index of the samples. But computed tomography requires long exposure time and lots of doses which are likely to damage biological specimens or live samples. We propose differential phase-contrast tomosynthesis based on diffraction enhanced imaging (DEI) to rapidly inspect the samples with a few projections. An experiment on biological samples is performed to prove it can highly enhance the information of detailed structures and mostly remove superposition phenomenon.

Conventional computerized tomography reconstructs the object by using the projection images which are imaged based on the absorption differences of substances to X-ray. In recent years, X-ray phase-contrast CT technique has been developed rapidly. Diffraction enhanced imaging (DEI) method is one of the three phase-sensitive X-ray imaging techniques which can be used for CT. DEI method can provide higher spatial resolution and distinguish more little differences in density by using monochromatic X-ray from synchrotron light sources than conventional absorption method. It can extract sample's refraction, absorption and scattering information by using an analyser crystal in DEI. This paper discusses the CT reconstruction criteria based on DEI and reconstructs two sample's 2D images and their 3D images. The reconstructed result is better than that of the absorption CT, which proves that the DEI-CT can be a powerful method for use in clinical tomography and material science.

Conventional computerized tomography (CT) technique is based on the absorption contrast. In recent years, X-ray phase-contrast CT (PCCT) has been developing rapidly. It uses the phase information to reconstruct the object and provide high contrast and spatial resolution. Diffraction enhanced imaging (DEI) method is one of the three phase-sensitive X-ray imaging techniques. DEI method employs an analyzer crystal to extract the object's refraction information which can be used for CT. However, when DEI refraction CT is combined with the conventional CT algorithm, it should be satisfied that the refraction information of an arbitrary point in the object is invariable at every projection view. In this paper, the invariance condition of refraction information is analyzed and two feasible methods are provided for reconstruction. Using these two methods, two samples of weak absorption are reconstructed with the experimental data obtained at Beijing Synchrotron Radiation Facility (BSRF).

In this paper, a new method for X‐ray spatial coherence measure is suggested by means of a quasi‐equal optical path interference device with a Fresnel zone plate. It is also feasible to take Gabor in‐line holograms of higher resolution using a lower resolution recording medium on this device.

Development state for X‐ray holographic microscopy and holographic tomography is presented in China.

A ne method to record x-ray in-line holograms with quasi- equal-path is proposed in this paper, the key is using a micro zone plate. This method has several advantages over the traditional x-ray in-line holography. First, the requirement of the temporal coherence for the x-ray beam is very low. Second, it reduces the requirement of the resolution of recording media, and last it weakens the disturbance of the twin image. The method can also be used to measure the spatial coherence of x-ray with a single exposure.

Some primary factors having effects on the resolution in x‐ray holography are discussed. The factors in recording x‐ray holograms are the x‐ray coherent scattering by the specimen, the recording method and the coherence of the x‐ray beam. There are two factors in reconstruction of the hologram. One is that the resolution of the detector may be lower than the spatial frequencies of fringes in x‐ray holograms. The other is aberrations. Consequently, some conditions of x‐ray holography with high resolution are given.

We propose a method for reconstructing a complex field from a series of its near-field diffraction patterns. This method is based on the paraxial Fresnel diffraction equation without making further approximations. Numerical simulations are presented showing that a complex field can even be reconstructed with moderate qualities from its two near-field diffraction patterns and almost exact reconstructions can be obtained when three or more diffraction patterns are used. We also show by numerical simulation that the correct diffraction distances can be recovered in case only coarsely measured values are available. This method may be applied to phase imaging of weak-absorption objects.

In this paper, aberrations in reconstruction are analyzed, and aberration elimination method are discussed, and the feasibility of direct reconstruction of lensless Fourier transform x-ray hologram with visible light is investigated.

The requirements for the temporal coherence in x-ray holography are theoretically analyzed. The conclusion is that the temporal coherence length required is a quadratic function of the resolution in x-ray holography.

Computed tomography of diffraction enhanced imaging (DEI-CT) based on synchrotron radiation source has extremely high sensitivity of weakly absorbing low-Z samples in medical and biological fields. The authors propose a modified backprojection filtration(BPF)-type algorithm based on PI-line segments to reconstruct region of interest from truncated refraction-angle projection data in DEI-CT. The distribution of refractive index decrement in the sample can be directly estimated from its reconstruction images, which has been proved by experiments at the Beijing Synchrotron Radiation Facility. The algorithm paves the way for local reconstruction of large-size samples by the use of DEI-CT with small field of view based on synchrotron radiation source.

X-ray diffraction enhanced imaging based on synchrotron radiation has extremely high sensitivity of weakly absorbing low-Z samples in medical and biological fields. This letter is dedicated to a direct reconstruction algorithm for directional-derivative projections of computed tomography of diffraction enhanced imaging. It is a “one-step” algorithm and does not require any restoration processing compared with the current “two-step” methods. The actual values of the sample’s refractive index decrement can be estimated from its reconstruction images directly. The algorithm is proven by the actual experiment at the Beijing Synchrotron Radiation Facility and the reconstructed images are described finally.

A new method of phase retrieval from a single near-field diffraction image with a large Fresnel number is presented and discussed. This method requires only the oversampled diffraction pattern without any other information such as the object envelope. Moreover, we show that the combination with a fast computational method is possible when the linear oversampling ratio is an integer. Numerical simulations are also presented, showing that the method works well with noisy data.