Simulation study of phase retrieval for hard X-ray in-line phase contrast imaging

Two algorithms for the phase retrieval of hard X-ray in-line phase contrast imaging are presented. One is referred to as Iterative Angular Spectrum Algorithm (IASA) and the other is a hybrid algorithm that combines IASA with TIE (transport of intensity equation). The calculations of the algorithms are based on free space propagation of the angular spectrum. The new approaches are demonstrated with numerical simulations. Comparisons with other phase retrieval algorithms are also performed. It is shown that the phase retrieval method combining the IASA and TIE is a promising technique for the application of hard X-ray phase contrast imaging.

Influence of tube voltage and current on in-line phase contrast imaging using a microfocus x-ray source

In-line x-ray phase contrast imaging has attracted much attention due to two major advantages： its effectiveness in imaging weakly absorbing materials, and the simplicity of its facilities. In this paper a comprehensive theory based on Wigner distribution developed by Wu and Liu [Med. Phys. 31 2378-2384 （2004）] is reviewed. The influence of x-ray source and detector on the image is discussed. Experiments using a microfocus x-ray source and a CCD detector are conducted, which show the role of two key factors on imaging： the tube voltage and tube current. High tube current and moderate tube voltage are suggested for imaging.

A new method for information retrieval in two-dimensional grating-based X-ray phase contrast imaging

Grating-based X-ray phase contrast imaging has been demonstrated to he an extremely powerful phase-sensitive imaging technique. By using two-dimensional （2D） gratings, the observable contrast is extended to two refraction directions. Recently, we have developed a novel reverse-projection （RP） method, which is capable of retrieving the object information efficiently with one-dimensional （1D） grating-based phase contrast imaging. In this contribution, we present its extension to the 2D grating-based X-ray phase contrast imaging, named the two-dimensional reverse- projection （2D-RP） method, for information retrieval. The method takes into account the nonlinear contributions of two refraction directions and allows the retrieval of the absorption, the horizontal and the vertical refraction images. The obtained information can be used for the reconstruction of the three-dimensionak phase gradient field, and for an improved phase map retrieval and reconstruction. Numerical experiments are carried out, and the results confirm the validity of the 2D-RP method.

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.

Single-shot grating-based x-ray differential phase contrast imaging with a modified analyzer grating

X-ray grating interferometer has attracted widely attention in the past years due to its capability in achieving x-ray phase contrast imaging with low brilliance source. However, the widely used phase stepping information extraction method reduces system stability and prolongs data acquisition time by several times compared with conventional x-ray absorption- based imaging. The mechanical stepping can be avoided by using a staggered grating, but at the cost of low vertical spatial resolution. In this paper, employing a modified staggered grating and the angular signal radiography, we proposed a single-shot grating-based x-ray differential phase contrast imaging with decent vertical spatial resolution. The theoretical framework was deduced and proved by numerical experiments. Absorption, phase, and scattering computed tomography can be performed without phase stepping. Therefore, we believe this fast and highly stable imaging method with decent resolution would be widely applied in x-ray grating-based phase contrast imaging.

Shifting curves based on the detector integration effect for x-ray phase contrast imaging

In theory, we find that the actual function of the analyzer grating in the Talbot–Lau interferometer is segmenting the self-images of the phase grating and choosing integral areas, which make sure that each period of self-images in one detector pixel contributes the same signal to the detector. Furthermore, in the case of the lack of an analyzer grating, the shifting curves are still existent in theory as long as the number of fringes is non-integral in a detector pixel, which is a sufficient condition for creating shifting curve. The sufficient condition is available for not only the Talbot–Lau interferometer and the inverse geometry of Talbot–Lau interferometer, but also the x-ray phase contrast imaging system based on geometrical optics. In practical applications, we propose a method to improve the performances of the existing systems by employing the sufficient condition. This method can shorten the system length, is applicable to large period gratings, and can use the detectors with large pixels and large field of view. In addition, the experimental arrangement can be simplified due to the lack of an analyzer grating. In order to improve detection sensitivity and resolution, we also give an optimal fringe period.We believe that the theory and method proposed here is a step forward for x-ray phase contrast imaging.

Elemental x-ray imaging using Zernike phase contras

We develop an element-specific x-ray microscopy method by using Zernike phase contrast imaging near absorption edges, where a real part of refractive index changes abruptly. In this method two phase contrast images are subtracted to obtain the target element: one is at the absorption edge of the target element and the other is near the absorption edge. The x-ray exposure required by this method is expected to be significantly lower than that of conventional absorption-based x-ray elemental imaging methods. Numerical calculations confirm the advantages of this highly efficient imaging method.

X-ray phase-sensitive microscope imaging with a grating interferometer:Theory and simulation

A general theoretical framework is presented to explain the formation of the phase signal in an x-ray microscope integrated with a grating interferometer,which simultaneously enables the high spatial resolution imaging and the improved image contrast.By using this theory,several key parameters of phase contrast imaging can be predicted,for instance,the fringe visibility and period,and the conversion condition from the differential phase imaging(DPI)to the phase difference imaging(PDI).Additionally,numerical simulations are performed with certain x-ray optical components and imaging geometry.Comparison with the available experimental measurement[Appl.Phys.Lett.113063105(2018)]demonstrates the accuracy of this developed quantitative analysis method of x-ray phase-sensitive microscope imaging.

Methodology development and application of X-ray imaging beamline at SSRF

This paper introduces some latest developments regarding the X-ray imaging methodology and applications of the X-ray imaging and biomedical application beamline(BL13W1)at Shanghai Synchrotron Radiation Facility in the past 5 years.The photon energy range of the beamline is 8–72.5 keV.Several sets of X-ray imaging detectors with different pixel sizes(0.19–24 lm)are used to realize X-ray microcomputed tomography(X-ray micro-CT)and X-ray in-line phase-contrast imaging.To satisfy the requirements of user experiments,new X-ray imaging methods and image processing techniques are developed.In vivo dynamic micro-CT experiments with living insects are performed in 0.5 s(sampling rate of 2 Hz,2 tomograms/s)with a monochromatic beam from a wiggler source and in 40 ms(sampling rate of 25 Hz,25 tomograms/s)with a white beam from a bending magnet source.A new X-ray imaging method known as move contrast X-ray imaging is proposed,with which blood flow and moving tissues in raw images can be distinguished according to their moving frequencies in the time domain.Furthermore,X-ray speckle-tracking imaging with twice exposures to eliminate the edge enhancement effect is developed.A high-precision quantification method is realized to measure complex three-dimensional blood vessels obtained via X-ray micro-CT.X-ray imaging methods such as three-dimensional X-ray diffraction microscopy,small-angle X-ray scattering CT,and X-ray fluorescence CT are developed,in which the X-ray micro-CT imaging method is combined with other contrast mechanisms such as diffraction,scattering,and fluorescence contrasts respectively.Moreover,an X-ray nano-CT experiment is performed with a 100 nm spatial resolution.Typical user experimental results from the fields of material science,biomedicine,paleontology,physics,chemistry,and environmental science obtained on the beamline are provided.

Optimization of the in-line X-ray phase-contrast imaging setup considering edge-contrast enhancement and spatial resolution

Employing the approximation theory based on refraction and the definition of the total pointspread-function of the imaging system, the variation in the edge contrast of simple model samples is discussed with different source-to-sample and sample-to-detector distances, which actually means different spatial resolutions of the imaging system. The experiments were carried out with the Beamline 4W1A imaging setup at the Beijing Synchrotron Radiation Facility for simple model and insect samples. The results show that to obtain clear phase-contrast images of biologic tissues for the X-ray in-line imaging setup, with determined parameters such as the size of the X-ray source, the pixel size of the detector and the fixed source-to-sample distance, there is a range of optimized sample-to-detector distances. The analysis method discussed in this article can be helpful in optimizing the setup of X-ray in-line phase-contrast imaging.

An Improved Phase Retrieval Algorithm for X-ray In-line Phase-Contrast Imaging

Phase contrast imaging technique has been improved promptly in recent years. Among these techniques in-line phase-contrast imaging is widely used. Various algorithms for in-line phase retrieval have been proposed so far such as TIE(transport of intensity equation), CTF(contrast transfer function), first born-approximations, GSF(Gerchberg-Saxton-Fienup), etc. Bronnikov's algorithm(BA) is a type of linear algorithm that is simple and efficient. But it can only be used without absorption situations. In this paper, an improved algorithm based on BA was presented. The approach adds Δφ(x,y) to the phase map φ_b(x,y) retrieved by BA to make the reconstructed phase map more precise. Further, the approach was evaluated on simulated images and confirmed to be accurate at higher absorption rates.

Improvement and error analysis of quantitative information extraction in diffraction-enhanced imaging

Diffraction-enhanced imaging （DEI） is a powerful phase-sensitive technique that provides higher spatial resolution and supercontrast of weakly absorbing objects than conventional radiography. It derives contrast from the X-ray absorption, refraction, and ultra-small-angle X-ray scattering （USAXS） properties of an object. The separation of different-contrast contributions from images is an important issue for the potential application of DEI. In this paper, an improved DEI （IDEI） method is proposed based on the Gaussian curve fitting of the rocking curve （RC）. Utilizing only three input images, the IDEI method can accurately separate the absorption, refraction, and USAXS contrasts produced by the object. The IDEI method can therefore be viewed as an improvement to the extended DEI （EDEI） method. In contrast, the IDEI method can circumvent the limitations of the EDEI method well since it does not impose a Taylor approximation on the RC. Additionally, analysis of the IDEI model errors is performed to further investigate the factors that lead to the image artifacts, and finally validation studies are conducted using computer simulation and synchrotron experimental data.

Quantitative coherence analysis of dual phase grating x-ray interferometry with source grating

Dual phase grating x-ray interferometry is compatible with common imaging detectors,and abandons the use of an absorption analyzer grating to reduce the radiation dose.When using x-ray tubes,an absorbing source grating must be introduced into the dual phase grating interferometer.In order to attain a high fringe visibility,in this work we conduct a quantitative coherence analysis of dual phase grating interferometry to find how the source grating affects the fringe visibility.Theoretical analysis shows that with the generalized Lau condition satisfied,the fringe visibility is influenced by the duty cycle of the source grating and the transmission through the grating bar.And the influence of the source grating profile on the fringe visibility is independent of the phase grating type.Numerical results illustrate that the maximum achievable fringe visibility decreases significantly with increasing transmission in the grating bar.Under a given transmission,one can always find an optimal duty cycle to maximize the fringe visibility.These results can be used as general guidelines for designing and optimizing dual phase grating x-ray interferometers for potential applications.

X-ray volumetric quantitative phase imaging by Foucault differential filtering with linear scanning

Non-interferometric X-ray quantitative phase imaging(XQPI),much simpler than the interferometric scheme,has provided high-resolution and reliable phase-contrast images.We report on implementing the volumetric XQPI images using concurrent-bidirectional scanning of the orthogonal plane on the optical axis of the Foucault differential filter;we then extracted data in conjunction with the transport-intensity equation.The volumetric image of the laminate microstructure of the gills of a fish was successfully reconstructed to demonstrate our XQPI method.The method can perform 3D rendering without any rotational motion for laterally extended objects by manipulating incoherent X-rays using the pinhole array.

Denoising method of X-ray phase contrast DR image for TRISO-coated fuel particles

TRISO （tristructural-isotropic） fuel is a type of micro fuel particles used in high-temperature gas-cooled reactors （HTGRs）. Among the quality evaluation methods for such particles, inqine phase contrast imaging technique （PCI） is more feasible for nondestructive measurement. Due to imaging hardware limitations, high noise level is a distinct feature of PCI images, and as a result, the dimensional measurement accuracy of TRISO-coated fuel particles decreases. Therefore, we propose an improved denoising hybrid model named as NL P-M model which introduces non-local theory and retains the merits of the Perona-Malik （P-M） model. The improved model is applied to numerical simulation and practical PCI images. Quanti- tative analysis proves that this new anisotropic diffusion model can preserve edge or texture information effectively, while ruling out noise and distinctly decreasing staircasing artifacts. Especially during the process of coating layer thickness measurement, the NL P-M model makes it easy to obtain continuous contours without noisy points or fake contour segments, thus enhancing the measurement accuracy. To address calculation complexity, a graphic processing unit （GPU） is adopted to realize the acceleration of the NL P-M denoising.

Simulation study on characteristics of information extraction in multiple-image radiography

Simulation experiments were performed to investigate the characteristics of information extraction in multiple-image radiography(MIR) based on geometrical optics approximation. Different Poisson noise levels were added to the simulation, and the results show that Poisson noise deteriorates the extraction results, with the degree of refraction > USAXS > absorption. The effects of Poisson noise are negligible when the detector's photon counts are about 1000 ph/pixel. A wider sampling range allows more accurate extraction results, but a narrower sampling range has a better signal-to-noise ratio for high Poisson noise levels, e.g., PN(10). The sampling interval can be suitably increased with a minor impact on the extraction results for low Poisson noise levels(PN(10000)). The extraction results are incomplete because a portion of the samplerocking curve is beyond the sampling range. This induces artifacts in the images, especially for strong refraction and USAXS signals. The artifacts are not obvious when the refraction angle and standard deviation of the USAXS are smaller than the sampling range by an order of magnitude.In general, the absorption barely affects the extraction results. However, additional Poisson noise will be generated when the sample is made of high-Z elements or has a large size due to the strong absorption. Here, the extraction results will deteriorate, and additional exposure time is required. This simulation provides important details on practical applications of MIR, with improvements in information extraction.

Non-Linear Phase Tomography Based on Fréchet Derivative

Phase imaging coupled to micro-tomography acquisition has emerged as a powerful tool to investigate specimens in a non-destructive manner. While the intensity data can be acquired and recorded, the phase information of the signal has to be “retrieved” from the data modulus only. Phase retrieval is an ill-posed non-linear problem and regularization techniques including a priori knowledge are necessary to obtain stable solutions. Several linear phase recovery methods have been proposed and it is expected that some limitations resulting from the linearization of the direct problem will be overcome by taking into account the non-linearity of the phase problem. To achieve this goal, we propose and evaluate a non-linear algorithm for in-line phase micro-tomography based on an iterative Landweber method with an analytic calculation of the Fréchet derivative of the phase-intensity relationship and of its adjoint. The algorithm was applied in the projection space using as initialization the linear mixed solution. The efficacy of the regularization scheme was evaluated on simulated objects with a slowly and a strongly varying phase. Experimental data were also acquired at ESRF using a propagation-based X-ray imaging technique for the given pixel size 0.68 μm. Two regularization scheme were considered: first the initialization was obtained without any prior on the ratio of the real and imaginary parts of the complex refractive index and secondly a constant a priori value was assumed on ?. The tomographic central slices of the refractive index decrement were compared and numerical evaluation was performed. The non-linear method globally decreases the reconstruction errors compared to the linear algorithm and is achieving better reconstruction results if no prior is introduced in the initialization solution. For in-line phase micro-tomography, this non-linear approach is a new and interesting method in biomedical studies where the exact value of the a priori ratio is not known.

Cosine fitting radiography and computed tomography

A new method in diffraction-enhanced imaging computed tomography （DEI-CT） that follows the idea developed by Chapman et al. [Chapman D, Thomlinson W, Johnston R E, Washburn D, Pisano E, Gmur N, Zhong Z, Menk R, Arfelli F and Sayers D 1997 Phys. Med. BioL 42 2015] in 1997 is proposed in this paper. Merged with a ＂reverse projections＂ algorithm, only two sets of projection datasets at two defined orientations of the analyzer crystal are needed to reconstruct the linear absorption coefficient, the decrement of the real part of the refractive index and the linear scattering coefficient of the sample. Not only does this method reduce the delivered dose to the sample without degrading the image quality, but, compared with the existing DEI-CT approaches, it simplifies data-acquisition procedures. Experimental results confirm the reliability of this new method for DEI-CT applications.

X-ray computed tomography of adhesive wicking into carbon foam

Laser target components consist of multicomponent porous and nonporous materials that are adhesively bonded together.In order to assess the extent and quantity of adhesive wicking into porous foam, micro X-ray computed tomography(CT)and image processing software have been utilized. Two different laser target configurations have been assessed in situ and volume rendered images of the distribution and quantities of adhesive have been determined for each.