X-ray phase-attenuation duality and phase retrieval

Phase retrieval is the key to quantitative x-ray phase-contrast imaging. To retrieve the phase image of an x-ray wave field, in general one needs multiple phase-contrast images. We have made a new observation of phase-attenuation duality for soft tissues, and we show how only a single phase-contrast image is needed for successful phase retrieval based on this duality. The phase-retrieval formula based on a single phase-contrast image of inhomogeneous soft tissue is derived and presented. We show the striking enhancement of the tissue contrast in simulated phase images that this new approach produces.     

Generalized eikonal of partially coherent beams and its use in quantitative imaging

The generalized eikonal of a partially coherent paraxial wave is introduced via a differential equation describing the evolution of the time-averaged intensity. The theoretical formalism provides an analytical tool for the study of partially coherent imaging systems. It also makes possible quantitative phase retrieval and compositional mapping of weakly absorbing samples using phase-contrast imaging with broadband polychromatic radiation of known spectral distribution. An experimental demonstration is presented of the quantitative reconstruction of the projected thickness of a sample, given a phase-contrast image obtained using a polychromatic microfocus x-ray source.     

Two-dimensional gratings-based phase-contrast imaging using a conventional x-ray tube

A Talbot-Lau interferometer using two-dimensional gratings and a conventional x-ray tube has been used to investigate a phase-contrast imaging technique that is sensitive to phase gradients in two orthogonal directions. Fourier analysis of Moiré fringe patterns was introduced to obtain differential phase images and scattering images from a single exposure. Two-dimensional structures of plastic phantoms and characteristic features of soft tissue were clearly obtained at 17.5 keV. The phase-stepping technique was also examined to investigate the spatial resolution of different phase retrieval methods. In the presented setup we found that the choice of phase retrieval method made little difference in image blur, and a large effective source size was found to give a high intensity in the image plane.     

Instability of Solution of Phase Retrieval in Direct Diffraction Phase-Contrast Imaging with Partially Coherent X-Ray Source

The theoretical model of direct diffraction phase-contrast imaging with partially coherent x-ray source is expressed by an operator of multiple integral. It is presented that the integral operator is linear. The problem of its phase retrieval is described by solving an operator equation of multiple integral. It is demonstrated that the solution of the phase retrieval is unstable. The numerical simulation is performed and the result validates that the solution of the phase retrieval is unstable.     

A variable-wavelength-based approach of phase retrieval for contrast transfer function based methods

X-ray phase-contrast imaging has emerged as an important method for improving contrast and sensitivity in the field of X-ray imaging. This increase in the sensitivity is attributed to the fact that, in the hard X-ray regime, the phase shift is more prominent as compared with the attenuation for materials having a low X-ray absorption coefficient. Among all the methods using the X-ray phase-contrast technique, in-line phase-contrast imaging scores over the other methods in terms of ease of implementation and efficient use of available X-ray flux. In order to retrieve the projected phase map of the object from the recorded intensity pattern, a large number of algorithms have been proposed. These algorithms generally use either the transport of intensity or contrast transfer function based approach for phase retrieval. In this paper it is proposed to use multiple wavelengths for phase retrieval using the contrast transfer function based formalism.     

相移吸收二元性算法用于X射线混合衬度定量显微CT的可行性研究

本文采用相移吸收二元性(PAD)相位恢复算法来实现混合 衬度样品内部不同密度组分的定量成像, 采用数字模拟和实验研究验证该方法的可行性. 模拟结果表明, 对于三种不同材料其重构误差均小于1%, 且误差值随材料折射率的增大而减小. 利用上海光源X射线成像线站开展了实验研究, 结果表明用单距PAD相位恢复算法可获取样品的定量信息. 与模拟结果相比, 实验中的重构精度相对较低, 环状伪影可能是影响精度的主要原因. 模拟和实验研究过程中, 均只采用了一组单距投影数据. 可以认为, 相移吸收二元性算法可用于混合衬度样品的定量信息分析研究. 由于剂量相对较低, 应可适合于软组织和骨骼同时存在时生物医学样品的定量相衬CT研究.     

Simple phase extraction in x-ray differential phase contrast imaging

A fast and simple method to extract phase-contrast images from interferograms is proposed, and its effectiveness is demonstrated through simulation and experiment. For x-ray differential phase contrast imaging, a strong attenuation signal acts as an overwhelming background intensity that obscures the weak phase signal so that no obvious phase-gradient information is detectable in the raw image. By subtracting one interferogram from another, chosen at particular intervals,the phase signal can be isolated and magnified.     

Theory and method of dual-energy x-ray grating phase-contrast imaging

The principle of dual-energy x-ray grating phase-contrast imaging(DEPCI) is clarified by using the theory of x-ray interference and Fresnel diffraction. A new method of retrieving phase from the two interferograms is proposed for DEPCI,and its feasibility is verified via simulation. Finally, the proposed method applied to DEPCI experiment demonstrates the effectiveness of the method. This paper lays the theoretical foundation for performance optimization of DEPCI and the further integration of DEPCI and computed tomography.     

Phase contrast, phase retrieval and aberration balancing in shift-invariant linear imaging systems

We treat the problems of phase-contrast image formation, deterministic phase retrieval and aberration balancing, in the imaging of weak objects using two-dimensional shift-invariant linear imaging systems. Three classes of model sample are considered: weak phase objects, weak phase-amplitude objects and single-material weak phase-amplitude objects. For each class of sample we show how the various aberration coefficients, which characterise a given imaging system, contribute to the structure of the associated phase-contrast image. The corresponding inverse problem, of obtaining a closed-form expression for the input wave-field given one or more aberrated phase-contrast images of the same, is then examined. Two sample applications are considered: analyser-crystal phase-contrast imaging of weak objects using hard X-rays, and Zernike-type phase-contrast imaging. We close with a discussion of how coherent and incoherent aberrations may be “balanced” against one another, briefly mentioning the applications of this idea to both “deblur by defocus” and proximity-corrected X-ray lithography.     

Zernike apodized photon sieves for high-resolution phase-contrast x-ray microscopy

We present a type of diffractive lens, Zernike apodized photon sieves (ZAPS), used as the objective for high spatial resolution and high phase-contrast imaging of weakly absorbing materials in x rays. The structure of ZAPS is based on the combination of two concepts: apodized photon sieves and Zernike phase contrast. The ZAPS is a single optic that integrates the appropriate ±π/2 rad phase shift through selective zone placement shifts in an apodized photon sieve. Analysis of the focusing properties of the apodized photon sieve in terms of point-spread function show that the sidelobes have been significantly suppressed at the expense of slightly widening the width of the main lobe. In combination with synchrotron light sources, ZAPS offers new opportunities for high-resolution phase-contrast x-ray microscopy in the physical and life sciences.     

Hard X ray holographic diffraction imaging

We determine the absolute electron density of a lithographically grown nanostructure with 25 nm resolution by combining hard x-ray Fourier transform holography with iterative phase retrieval methods. While holography immediately reveals an unambiguous image of the object, we deploy in addition iterative phase retrieval algorithms for pushing the resolution close to the diffraction limit. The use of hard (8 keV) x rays eliminates practically all constraints on sample environment and enables a destruction-free investigation of relatively thick or buried samples, making holographic diffraction imaging a very attractive tool for materials science. We note that the technique is ideally suited for subpicosecond imaging that will become possible with the emerging hard x-ray free-electron lasers.     

Optical solitons in 1+2 dimensions with non-Kerr law nonlinearity

The combination of grazing-incidence small-angle x-ray scattering (GISAXS)with tomographic methods and phase retrieval is proposed for thereconstruction of the three-dimensional (3D) electron density of nanometersized objects. In this approach GISAXS data from a small object arecollected successively at different azimuthal angular positions. This 3Dintensity distribution in reciprocal space is used for the phase retrievaland reconstruction of the 3D electron density. The power of our approach isdemonstrated in a series of calculations performed in the frame ofkinematical and distorted-wave Born approximation (DWBA) theories for thecase of GISAXS scattering on a 200?nm island in the form of truncatedpyramid.     

Iterative phase retrieval without support

An iterative phase retrieval method for nonperiodic objects has been developed from the charge-flipping algorithm proposed in crystallography. A combination of the hybrid input-output (HIO) algorithm and the flipping algorithm has greatly improved performance. In this combined algorithm the flipping algorithm serves to find the support (object boundary) dynamically, and the HIO part improves convergence and moves the algorithm out of local minima. It starts with a single intensity measurement in the Fourier domain and does not require a priori knowledge of the support in the image domain. This method is suitable for general image recovery from oversampled diffuse elastic x-ray and electron-diffraction intensities. The relationship between this algorithm and the output-output algorithm is elucidated.     

Mixed transfer function and transport of intensity approach for phase retrieval in the Fresnel region

We present a method for phase retrieval in propagation-based x-ray imaging, based on the contrast transfer and transport of intensity equation approaches. We show that the contrast transfer model does not coincide with the transport of intensity in the limit of small propagation distances, and we derive a new model that alleviates this problem. Using this model, we devise an algorithm to retrieve the phase from slowly varying samples that is valid beyond the limit of small distances. We show its utility by imaging in three dimensions a biological sample that causes both strong absorption and phase shift.     

Phase transformation α → ε in meteoritic Fe–Ni alloy under shock-wave loading

We have studied microstructural deformation-induced changes and phase transformations in the material of the Sikhote-Alin iron meteorite (IIAB) after loading by spherically converging shock waves. The results obtained by the method of electron backscatter diffraction, as well as the data of local chemical analysis unambiguously indicate the presence of regions experiencing polymorphic α → ε and ε → α transitions in the loaded sample.     

Quantitative in-line phase-contrast imaging with multienergy X rays.

We present a new method for quantitative nondestructive characterization of objects by x-ray phase-contrast imaging. Spatial distributions of the projected values of the complex refractive index in the sample are reconstructed by processing near-field images collected at a fixed sample-to-detector distance using a polychromatic incident beam and an energy-sensitive area detector, such as a CCD used in the photon-counting spectroscopy mode. The method has the potential advantages of decreased radiation dose and increased accuracy compared to conventional techniques of x-ray imaging.     

Visibility in differential phase-contrast imaging with partial coherence source

This paper gives theoretical analysis of visibility of fringes, which is influenced by distances, temporal and spatial coherence of source, in hard x-ray differential phase-contrast imaging with microfocus x-ray source. According to the character of longitudinal periodicity of the interferogram, the setup is insensitive to mechanical drift and vibrations. The effect of temporal coherence of x-ray source is investigated and its related bandwidth is derived. Based on the theory of partially coherent light, it shows that the requirement for the spatial coherence of x-ray source is not strict and can be met by the general microfocus x-ray tube for x-ray differential phase-contrast imaging.     

X-ray spatial harmonic imaging of phase objects

Refractive index gradients in materials or at material interfaces lead to x-ray diffraction. Interference of this radiation with adjacent x-ray waves causes phase contrast that can be used for imaging purposes if an x-ray source with sufficient spatial coherence is used. The imaging modality presented here uses hard x radiation diffracted at interfaces, but requires only little spatial coherence. We report experiments showing, first, that image contrast is not diminished by motional blurring, and second, that contrast can be increased by orders of magnitude relative to in-line x-ray phase-contrast imaging. These properties substantially broaden the applicability of phase-sensitive imaging to moving samples and very weak density gradients.     

结合线性回归的离轴数字全息去载波相位恢复算法

为实现仅用一幅离轴数字全息图便能直接恢复相位,提出一种利用空间载波相移技术(spatial carrier phase shift, SCPS)和线性回归相结合的离轴数字全息去载波相位恢复算法.首先,利用SCPS将一幅离轴数字全息图分为四幅含有载波相移的全息图,其中载波相移由沿行、列两个方向的正交载波所引入;然后,将四幅载波相移全息图作为输入,将所求物体相位和两个正交的载波作为未知量,结合最小二乘法和线性回归同时求出载波和相位信息.相较于已有的去载波技术,本算法无需背景全息图作为参考,便可准确地去除载波,实现高质量的相位重建.本文结合数值仿真和具体实验结果验证本算法的有效性和优越性.     

Phase-contrast imaging of nanostructures by soft x rays from a femtosecond-laser plasma

The possibility of phase-contrast imaging of nanostructures has been analyzed with the use of a femtosecond-laser plasma as a spatially coherent soft x-ray source and a LiF crystal as an x-ray detector having both the submicron spatial resolution in a wide field of view and a high contrast. It is demonstrated that the spatial coherence length of radiation in the wavelength range 1–13 nm at a distance of 30 cm from the femtosecond-laser plasma source is ?1.5 μm. The achieved spatial coherence of the source is sufficient to obtain high-quality phase-contrast x-ray images of foils with various chemical compositions and a thickness of ?100 nm.