X-ray Differential Phase Contrast Imaging Research Articles

Transport-of-intensity model for single-mask x-ray differential phase contrast imaging

X-ray phase contrast imaging holds great promise for improving the visibility of light-element materials such as soft tissues and tumors. The single-mask differential phase contrast imaging method stands out as a simple and effective approach to yield differential phase contrast. In this work, we introduce a model for a single-mask phase imaging system based on the transport-of-intensity equation. Our model provides an accessible understanding of signal and contrast formation in single-mask x-ray phase imaging, offering a clear perspective on the image formation process, for example, the origin of alternate bright and dark fringes in phase contrast intensity images. Aided by our model, we present an efficient retrieval method that yields differential phase contrast imagery in a single acquisition step. Our model gives insight into the contrast generation and its dependence on the system geometry and imaging parameters in both the initial intensity image as well as retrieved images. The model validity as well as the proposed retrieval method are demonstrated via both experimental results on a system developed in house as well as Monte Carlo simulations. In conclusion, our work not only provides a model for an intuitive visualization of image formation but also offers a method to optimize differential phase imaging setups, holding tremendous promise for advancing medical diagnostics and other applications.

Theory and verification of moiré fringes for x-ray three-phase grating interferometer

Dual-phase and three-phase grating x-ray interference is a promising new technique for grating-based x-ray differential phase contrast imaging. Dual-phase grating interferometers have been relatively completely studied and discussed. In this paper, the corresponding imaging fringe formula of the three-phase grating interferometer is provided. At the same time, the similarities and differences between the three-phase grating interferometer and the dual-phase grating interferometer are investigated and verified, and that the three-phase grating interferometer can produce large-period moiré fringes without using the analyzing grating is demonstrated experimentally. Finally, a simple method of designing three-phase grating and multi-grating imaging systems from geometric optics based on the thin-lens theory of gratings is presented. These theoretical formulas and experimental results provide optimization tools for designing three-phase grating interferometer systems.

A novel fusion method for X-ray phase contrast imaging based on fast adaptive bidimensional empirical mode decomposition.

X-ray phase contrast imaging (XPCI) can separate the attenuation, refraction, and scattering signals of the object. The application of image fusion enables the concentration of distinctive information into a single image. Some methods have been applied in XPCI field, but wavelet-based decomposition approaches often result in loss of original data. To explore the application value of a novel image fusion method for XPCI system and computed tomography (CT) system. The means of fast adaptive bidimensional empirical mode decomposition (FABEMD) is considered for image decomposition to avoid unnecessary information loss. A parameter δ is proposed to guide the fusion of bidimensional intrinsic mode functions which contain high-frequency information, using a pulse coupled neural network with morphological gradients (MGPCNN). The residual images are fused by the energy attribute fusion strategy. Image preprocessing and enhancement are performed on the result to ensure its quality. The effectiveness of other image fusion methods has been compared, such as discrete wavelet transforms and anisotropic diffusion fusion. The δ-guided FABEMD-MGPCNN method achieved either the first or second position in objective evaluation metrics with biological samples, as compared to other image fusion methods. Moreover, comparisons are made with other fusion methods used for XPCI. Finally, the proposed method applied in CT show expected results to retain the feature information. The proposed δ-guided FABEMD-MGPCNN method shows potential feasibility and superiority over traditional and recent image fusion methods for X-ray differential phase contrast imaging and computed tomography systems.

X-ray differential phase-contrast imaging simulations with Geant4

The development of accurate simulation tools including x-ray phase-contrast effects is of great use in the design and optimization of x-ray phase-contrast imaging (XPCI) experimental setups. When the lateral coherence of the imaging system is limited, as in most compact laboratory-based XPCI applications, phase-contrast can be effectively described through refraction effects that can be simulated with a ray-tracing approach. This work presents a practical implementation of the x-ray phase-contrast in Geant4 and validates the simulation results against theoretical predictions for the propagation-based (PB) and edge-illumination (EI) imaging configurations. The simulation includes a realistic polychromatic tungsten anode spectrum and an extended x-ray source, a virtual phantom made of plastic wires with a diameter of 1 mm, as well as an accurate description of the absorbing masks and related movement during data acquisition. Results show a good agreement between theory and simulations, with maximum discrepancies below 2% in the intensity of PB images, below 0.3 µrad for EI refraction, and below 0.03 mm for EI projected thickness. Additionally, an often disregarded effect such as the refraction sensitivity inhomogeneity across the field of view (around 20%) was reproduced by the simulation and quantitatively explained through a theoretical model. The presented simulation platform will be extensively used for the design of a novel EI facility that is under construction at the INFN laboratories in Trieste (Italy) in the framework of the Photon-counting Edge-illumination Phase-contrast Imaging (PEPI) project.

Angular sensitivity of an x-ray differential phase contrast imaging system with real and virtual source images.

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.

Enhancing the X-Ray Differential Phase Contrast Image Quality With Deep Learning Technique.

The purpose of this work is to investigate the feasibility of using deep convolutional neural network (CNN) to improve the image quality of a grating-based X-ray differential phase contrast imaging (XPCI) system. In this work, a novel deep CNN based phase signal extraction and image noise suppression algorithm (named as XP-NET) is developed. The numerical phase phantom, the ex vivo biological specimen and the ACR breast phantom are evaluated via the numerical simulations and experimental studies, separately. Moreover, images are also evaluated under different low radiation levels to verify its dose reduction capability. Compared with the conventional analytical method, the novel XP-NET algorithm is able to reduce the bias of large DPC signals and hence increasing the DPC signal accuracy by more than 15%. Additionally, the XP-NET is able to reduce DPC image noise by about 50% for low dose DPC imaging tasks. This proposed novel end-to-end supervised XP-NET has a great potential to improve the DPC signal accuracy, reduce image noise, and preserve object details. We demonstrate that the deep CNN technique provides a promising approach to improve the grating-based XPCI performance and its dose efficiency in future biomedical applications.

8-inch-diameter field of view for X-ray differential phase-contrast imaging

The X-ray differential phase-contrast imaging (DPCI) based on Talbot–Lau​ interferometers (TLIs) is a promising imaging technique for non-destructive testing. The compact imaging configurations that have a large field-of-view (FoV) require the use of bent phase gratings and large-area analyzer gratings. The cascaded TLIs reduce the aspect ratio requirement of large-area analyzer gratings, which facilitates the fabrication of these gratings. However, the bent silicon-based phase gratings are difficult to obtain directly because of the brittleness of silicon wafers. In this work, we present a method to prepare 5-inch cylindrically bent silicon-based phase gratings and 8-inch analyzer gratings. Moreover, we also present their applications in the cascaded TLIs. The mechanical stress that originates from thermal oxidation enables us to cylindrically bend silicon-based phase gratings. Furthermore, as compared to the use of plane phase gratings, the use of cylindrically bent phase gratings allows Moiré fringes to appear in the entire 8-inch FoV. Finally, Moiré fringes and multi-contrast images of the samples (water, liquid soap filled in heat-shrink tubes) demonstrate the effectiveness of the fabrication of the bent silicon-based phase gratings and imaging in the entire 8-inch FoV. The proposed configuration is applicable for attaining multi-contrast images with 8-inch FoV at a low cost.

Hard X-ray omnidirectional differential phase and dark-field imaging

Ever since the discovery of X-rays, tremendous efforts have been made to develop new imaging techniques for unlocking the hidden secrets of our world and enriching our understanding of it. X-ray differential phase contrast imaging, which measures the gradient of a sample's phase shift, can reveal more detail in a weakly absorbing sample than conventional absorption contrast. However, normally only the gradient's component in two mutually orthogonal directions is measurable. In this article, omnidirectional differential phase images, which record the gradient of phase shifts in all directions of the imaging plane, are efficiently generated by scanning an easily obtainable, randomly structured modulator along a spiral path. The retrieved amplitude and main orientation images for differential phase yield more information than the existing imaging methods. Importantly, the omnidirectional dark-field images can be simultaneously extracted to study strongly ordered scattering structures. The proposed method can open up new possibilities for studying a wide range of complicated samples composed of both heavy, strongly scattering atoms and light, weakly scattering atoms.

Method of single exposure phase contrast imaging without analyser grating

X-ray differential phase contrast imaging technology can reveal the weakly absorbing fine structure which cannot be observed by the conventional X-ray absorption contrast imaging. Hence, it has potential applications in many fields such as medical science, and material science. But in the traditional X-ray grating differential phase contrast imaging system, the analyser grating is used as a spatial filter, and needs to be phase stepped, then multiple exposures are required for information extraction. Thus this leads to high-dose radiation exposure and low efficiency of X-ray utilization. All these disadvantages limit its application in various disciplines. In order to cope with the above issues, a new algorithm based on single-shot grating differential phase contrast imaging system without analyzer grating is proposed. In such a system the absorption, refraction and scattering information can be obtained from one projective image of the sample acquired by a high-resolution detector. The reliability of this new algorithm is confirmed by numerical simulation. Compared with the phase stepping algorithm, the proposed algorithm can provide very accurate and reliable information extraction results without requiring the grating period to match with detector pixel size. It facilitates the reduction of the radiation damage to sample. We emphasize that this method is highly compatible with the future X-ray phase contrast imaging clinical applications.

Model-driven phase retrieval network for single-shot x-ray Talbot-Lau interferometer imaging.

The single-shot x-ray Talbot-Lau interferometer-based differential phase contrast (DPC) imaging is able to accelerate time-consuming data acquisition; however, the extracted phase image suffers from severe image artifacts. Here, we propose to estimate the DPC image via a deep convolutional neural network (CNN) incorporated with the physical imaging model. Instead of training the CNN with thousands of labeled data beforehand, both phantom and biological specimen validation experiments show that high-quality DPC images can be automatically generated from only one single-shot projection image with a certain periodic moiré pattern. This work provides a new, to the best of our knowledge, paradigm for single-shot x-ray DPC imaging.

Sample phase gradient and fringe phase shift in triple phase grating X-ray interferometry.

Triple phase grating X-ray interferometry is a promising new technique of grating based X-ray differential phase contrast imaging. Accurate retrieval of sample phase gradients from measured interference fringe shifts is a key task in X-ray interferometry. To fulfill this task in triple phase grating X-ray interferometry with monochromatic X-ray sources, the authors derived exact formulas relating sample phase gradient to fringe phase shift. These formulas not only provide a design optimization tool for triple phase grating interferometry, but also lay a foundation for quantitative phase contrast imaging.

Dual phase grating based X-ray differential phase contrast imaging with source grating: theory and validation.

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.

A theoretical framework for comparing noise characteristics of spectral, differential phase-contrast and spectral differential phase-contrast x-ray imaging

Spectral and grating-based differential phase-contrast (DPC) x-ray imaging are two emerging technologies that offer additional information compared with conventional attenuation-based x-ray imaging. In the case of spectral imaging, energy-resolved measurements allow the generation of material-specific images by exploiting differences in the energy-dependent attenuation. DPC imaging uses the phase shift that an x-ray wave exhibits when traversing an object as contrast generation mechanism. Recently, we have investigated the combination of these two imaging techniques (spectral DPC imaging) and demonstrated potential advantages compared with spectral imaging. In this work, we present a noise analysis framework that allows the prediction of (co-) variances and noise power spectra for all three imaging methods. Moreover, the optimum acquisition parameters for a particular imaging task can be determined. We use this framework for a performance comparison of all three imaging methods. The comparison is focused on (projected) electron density images since they can be calculated with all three imaging methods. Our study shows that spectral DPC imaging enables the calculation of electron density images with strongly reduced noise levels compared with the other two imaging methods for a large range of clinically relevant pixel sizes. In contrast to conventional DPC imaging, there are no long-range noise correlations for spectral DPC imaging. This means that excessive low frequency noise can be avoided. We confirm the analytical predictions by numerical simulations.

Is high sensitivity always desirable for a grating-based differential phase contrast imaging system?

In grating-based x-ray differential phase contrast (DPC) imaging, the measured signal amplitude of the phase shift induced by an image object is proportional to the so-called system sensitivity. Therefore, to achieve a better signal-to-noise (SNR) for improved imaging performance, it is generally believed that one should increase the system sensitivity by reducing the period of the analyzer grating or increasing the distance between the phase grating and analyzer grating. The purpose of this work is to theoretically and experimentally demonstrate that there is an optimal system sensitivity to attain the highest SNR for a given task provided that the standard phase-stepping acquisition and phase retrieval methods are used. When system sensitivity goes beyond this optimal value, SNR decreases and the imaging performance deteriorates. Due to the fundamental fact that the measured phase signal is a cyclic variable, the phase wrapping effect is inevitable in DPC imaging when the system sensitivity increases. The phase wrapping effect appears in both signal and noise measurements. The effect in the signal measurement is manifested in the so-called signal statistical bias and such effect often impacts the accuracy of the measurement. The phase wrapping effect also appears in the noise variance measurement and impacts the precision of the measurement. A thorough theoretical analysis was performed in this work to demonstrate the quantitative impacts of phase wrapping on both signal bias and noise variance and thus on the actual system SNR. The joint effect of phase wrapping in both the signal bias and noise variance yields an optimal system sensitivity to achieve the highest SNR. Both extensive numerical simulation studies and experimental studies were performed to validate the theoretical analysis. Both theoretical analysis and experimental studies show that the SNR of the DPC signal is not always proportional to the sensitivity due to the cyclic nature of the signal and the phase wrapping effect. For a given refraction angle and exposure level, there exists an optimal sensitivity factor that maximizes the SNR, beyond which, increasing the sensitivity will decrease the SNR. Increase of system sensitivity does not always improve x-ray DPC imaging performance provided that the standard phase-stepping acquisition and phase retrieval methods are used.

An 8-inch absorption grating used in cascaded Talbot-Lau interferometers for X-ray phase-contrast imaging

Cascaded Talbot-Lau interferometers (CTLI) facilitates X-ray differential phase-contrast imaging (DPCI) by using absorption gratings with large periods. Large-area gratings provide a large field of view (FoV), thus they extend applications of DPCI. However, conventional methods for fabricating such gratings are still costly. We report an 8 inch absorption grating that was fabricated by filling tungsten nanoparticles into grating structures. The fabrication process requires readily available equipment, allowing it to be easily implemented. We experimentally tested these absorption gratings with our X-ray CTLI system, yielding Moiré fringes and multi-contrast images, which demonstrates the effectiveness of our proposed method.

Tungsten nanoparticles-based x-ray absorption gratings for cascaded Talbot–Lau interferometers

Absorption gratings play an indispensable role in grating-based x-ray differential phase-contrast imaging (DPCI), however, are generally challenging to fabricate. Even though several fabrication methods exist, they either involve high costs or require special equipment. In this work, we present a low-cost fabrication method for absorption gratings in order to simplify the fabrication process and lower technical threshold. In this method tungsten nanoparticles are used as the absorbing material and carried by a liquid carrier into grating microstructures pre-prepared by deep reactive ion etching (DRIE) with a depth of 150 µm and period of 42 µm. In addition, a vacuum chamber and ultrasonic cleaning machine are used in the filling process. The micrographs by SEM reveal that the filled nanoparticles are arranged densely. Besides, a comparison with the absorption gratings fabricated by micro-casting is provided to show validation of the current method. To test the performance of the fabricated gratings, a cascaded Talbot–Lau interferometer (CTLI) is constructed with one absorption grating as a periodic source and another as the analyzer. The acquired Moiré fringes, phase-contrast and dark-field images demonstrate that the proposed method produces qualified gratings for x-ray DPCI.

Impact of the sensitivity factor on the signal-to-noise ratio in grating-based phase contrast imaging.

The sensitivity factor of a grating-based x-ray differential phase contrast (DPC) imaging system determines how much fringe shift can be observed for a given refraction angle. It is commonly believed that increasing the sensitivity factor will improve the signal-to-noise ratio (SNR) of the phase signal. However, this may not always be the case if the intrinsic phase wrapping effect is taken into consideration. In this work, a theoretical derivation is provided to quantify relationship between the sensitivity and SNR for a given refraction angle, exposure level, and grating based x-ray DPC system. The theoretical derivation shows that the expected phase signal is not always proportional to the sensitivity factor and may even decrease when the sensitivity factor becomes too large. The noise variance of the signal is not always solely dependent on the exposure level and fringe visibility but may become signal-dependent under certain circumstances. As a result, SNR of the phase signal does not always increase with higher sensitivity. Numerical simulation studies were performed to validate the theoretical models. Results show that when the fringe visibility and exposure level are fixed, there exists an optimal sensitivity factor which maximizes the SNR for a given refraction angle; further increase of the sensitivity factor may decrease the SNR.

Fast X-ray Differential Phase Contrast Imaging with One Exposure and without Movements

Grating interferometry X-ray differential phase contrast imaging (GI-XDPCI) has provided enhanced imaging contrast and attracted more and more interests. Currently the low imaging efficiency and increased dose remain to be the bottlenecks in the engineering applications of GI-XDPCI. Different from the widely-used X-ray absorption contrast imaging (XACI) found in hospitals and factories, GI-XDPCI involves a grating stepping procedure that is time-consuming and leads to a significantly increased X-ray exposure time. In this paper, we report a fast GI-XDPCI method without movements by designing a new absorption grating. There is no grating stepping in this approach, and all components remain stationary during the imaging. Three kinds of imaging contrasts are provided with greatly reduced time. This work is comprised of a numerical study of the method and its verification using a sub-set of the dataset measured with a standard GI-XDPCI system at the beam line BL13W1 of the Shanghai Synchrotron Radiation Facility (SSRF). These results have validated the presented method.

Quantitative Nanoscale 3D Imaging of Intergranular Corrosion of 304 Stainless Steel Using Hard X-Ray Nanoprobe

Multi-modal imaging, which visualizes changes in the structure and chemistry of the same region of interest in materials by combining various techniques, is becoming attractive to material scientists. Here, we describe a multi-modal approach to investigate intergranular (IG) corrosion of sensitized stainless steels using synchrotron-based nanoscale X-ray imaging with sensitivity to microstructure and chemical composition. Three-dimensional tomography of 304 stainless steel samples deteriorated by IG corrosion, was carried out using X-ray fluorescence and differential phase contrast imaging. These findings were further supported with surface imaging and chemical analysis using scanning electron microscopy and energy dispersive X-ray spectroscopy. The combined quantitative structural and chemical analysis indicates that chromium segregates along grain boundaries, cracking is due to IG corrosion, and Cr-enrichment occurs on the cracked surfaces. Such quantitative 3D imaging of Cr23C6 nucleation at grain boundaries and Cr enriched oxides at cracked surfaces is a powerful tool to correlate IG corrosion mechanisms at nanoscale with buried grain boundary structure and alloy composition. Such understanding of IG corrosion mechanisms is critical for both the development of predictive multiscale corrosion models, and the engineering of corrosion resistant materials.

Uncertainty quantification in the optimization routine for X-ray differential phase contrast imaging system based on Talbot effect

Uncertainty quantification technique is applied to analyze the influence of the stochastic factors on the performance of X-ray interferometers based on Talbot effect. These factors are shown to play the important role when information is coded in the phase of the X-ray radiation. The grating periods and the source size when considered as expected values of Gaussian distribution with a given standard deviation (∼5%) need to be corrected by more than 10% as compared to their “deterministic” values providing the designed spatial resolution.