X-ray Differential Phase Contrast 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.

Phase retrieval for X-ray differential phase contrast radiography with knowledge transfer learning from virtual differential absorption model

Grating-based X-ray phase contrast radiography and computed tomography (CT) are promising modalities for future medical applications. However, the ill-posed phase retrieval problem in X-ray phase contrast imaging has hindered its use for quantitative analysis in biomedical imaging. Deep learning has been proved as an effective tool for image retrieval. However, in practical grating-based X-ray phase contrast imaging system, acquiring the ground truth of phase to form image pairs is challenging, which poses a great obstacle for using deep leaning methods. Transfer learning is widely used to address the problem with knowledge inheritance from similar tasks. In the present research, we propose a virtual differential absorption model and generate a training dataset with differential absorption images and absorption images. The knowledge learned from the training is transferred to phase retrieval with transfer learning techniques. Numerical simulations and experiments both demonstrate its feasibility. Image quality of retrieved phase radiograph and phase CT slices is improved when compared with representative phase retrieval methods. We conclude that this method is helpful in both X-ray 2D and 3D imaging and may find its applications in X-ray phase contrast radiography and X-ray phase CT.

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.

Reweighted L1-norm regularized phase retrieval for x-ray differential phase contrast radiograph.

Talbot-Lau x-ray grating interferometry greatly decreases the requirements on x-ray sources to realize differential phase contrast imaging and has found many applications in industrial and medical imaging. Phase retrieval from the noisy differential signal is crucial for quantitative analysis, comparison, and fusion with other imaging modalities. In this paper, we introduce a reweighted L1-norm based nonlinear regularization method for the phase retrieval problem. Both simulation and experimental results demonstrated that, comparing with the widely used L1-norm based regularization method and Wiener filter method, the proposed method is more effective both in eliminating the strip noises and in preserving the image detail.

Single-shot grating-based X-ray phase contrast imaging via generative adversarial network

Talbot-Lau interferometry obtains X-ray differential phase contrast (DPC) signals of object by subtracting multiple moiré patterns acquired by phase-stepping (PS) procedure. Due to the need of multiple intensity measurements, the long measuring time is inevitable in the conventional DPC imaging, giving rise to X-ray dose and fluctuations. In this paper, we propose a single-shot X-ray phase contrast imaging (XPCI) method based on deep learning. Specifically, in hardware, we propose to replace the analysis absorption grating with the high-resolution X-ray detector system to avoid the illumination flux loss caused by the analysis grating. In software, we employ a U-net based generative adversarial network (GAN) for solving the phase reconstruction problem with single-shot intensity pattern. By examining the performance on a variety of simulated and experimental datasets, we demonstrate that our approach, in spite of only using single intensity pattern, is able to obtain results with high resolution and image contrast which is competitive with the conventional PS approach, while being less time-consuming and low-dose.

High-resolution and sensitivity bi-directional x-ray phase contrast imaging using 2D Talbot array illuminators.

Two-dimensional (2D) Talbot array illuminators (TAIs) were designed, fabricated, and evaluated for high-resolution high-contrast x-ray phase imaging of soft tissue at 10-20 keV. The TAIs create intensity modulations with a high compression ratio on the micrometer scale at short propagation distances. Their performance was compared with various other wavefront markers in terms of period, visibility, flux efficiency, and flexibility to be adapted for limited beam coherence and detector resolution. Differential x-ray phase contrast and dark-field imaging were demonstrated with a one-dimensional, linear phase stepping approach yielding 2D phase sensitivity using unified modulated pattern analysis (UMPA) for phase retrieval. The method was employed for x-ray phase computed tomography reaching a resolution of 3 µm on an unstained murine artery. It opens new possibilities for three-dimensional, non-destructive, and quantitative imaging of soft matter such as virtual histology. The phase modulators can also be used for various other x-ray applications such as dynamic phase imaging, super-resolution structured illumination microscopy, or wavefront sensing.

Ring artifact removal for differential phase-contrast X-ray computed tomography using a conditional generative adversarial network.

The integration process used as a pre-processing step in the reconstruction of differential phase-contrast X-ray CT (d-PCCT) causes the measurement noise to propagate throughout the projection image, which is leading to increased ring artifacts (RA) in the reconstructed image. It is difficult to eliminate the RA using conventional RA removal methods that were developed for the absorption-based CT field. We propose an effective method that can remove RA of d-PCCT images. The proposed method uses Laplacian images reconstructed from second-derivative projections of d-PCCT. This method is based on a conditional generative adversarial network (cGAN), whose loss function is designed by adding the L1- and L2-norm to the original cGAN. The training data were taken from a numerical phantom generated by a d-PCCT imaging simulator. To validate the applicability of the trained network, we tested its RA removal effect on test data from numerical phantoms generated randomly and actual experimental data. The results of numerical validation using numerical phantoms showed that the proposed method improved the RA removal effect compared to conventional methods. In addition, image comparison by visual evaluation showed that only the proposed method was able to remove RA while preserving original structures in the actual biological d-PCCT images. We proposed a cGAN-based method for RA removal that exploits the physical properties of d-PCCT. The proposed method was able to completely remove RA from d-PCCT images on both simulated data and biological data. We believe that this method is useful for the observation of various types of biological soft tissue.

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.

Removal of artifacts caused by grating imperfections in X-ray phase contrast tomography

Artifact removal algorithms are crucial for image quality in computed tomography. Many ring artifact removal algorithms have been proposed in conventional X-ray absorption computed tomography, but relatively fewer algorithms were suggested for differential X-ray phase contrast imaging. In this paper, a novel method is proposed to eliminate the ring artifacts caused by grating imperfections in X-ray phase contrast tomography. This method requires 360-degree projection data and exploits the anti-symmetry of conjugate rays to locate the artifact regions. Moreover, an interpolation scheme for sinogram-domain is proposed to correct artifacts. Experimental results show that the algorithm performs well in the case of severe artifacts.

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.

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.

Method of reconstructing region of interest for differential phase contrast computed tomography imaging

X-ray differential phase contrast computed tomography imaging based on grating interferometer system can reconstruct not only the linear attenuation coefficient, but also the phase shift coefficient and the linear scattering coefficient of the object. In practical application, it is very difficult to make a large area grating, so the sample is often larger than the grating. When the sample is scanned with a grating smaller than the sample, the part of the sample beyond the field of view of the grating will cause the differential phase projection information to be truncated. In this paper, a method of reconstructing the region of interest for differential phase contrast computed tomography is proposed. The method is based on the approximate linear relation between the phase shift coefficient of the object and the linear attenuation coefficient (i.e. the decrement in the real part of the refractive index and the imaginary part of the refractive index), the phase shift coefficient of the region of interest is approximately reconstructed by the polynomial of Lambda function of the phase shift coefficient and Lambda inverse function of linear attenuation coefficient. In this paper, according to the Fresnel diffraction theory and differential phase grating phase step-by-step method of imaging a simulation experiment is performed. In the experiment, conducted is the approximate reconstruction by using the first order polynomial and quadratic polynomial of Lambda function of the phase shift coefficient and Lambda inverse function of linear attenuation coefficient. The sample size is five times of grating imaging field, and the results show that this method can approximately reconstruct the region of interest for the sample image. We also carry out the actual data experiment. The actual data are obtained by the Talbot grating interferometer system of Shanghai synchrotron radiation BL13W1 station, and the standard model and biological sample are imaged. The method of reconstructing the region of interest is proposed in this paper. This method can be applied to the multi-material samples with a similar relationship between the decrement in the real part of the refractive index and the decrement in the imaginary part of the refractive index, and also to single-material samples. The comparison between the numerical simulations and the actual experimental results verifies the effectiveness of the proposed method.

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.

An experimental approach to optimising refraction sensitivity for lab-based edge illumination phase contrast set-ups

Refraction sensitivity can be optimised for differential x-ray phase contrast (XPC) imaging methods by modifying the set-up. Often, modifications involve changing source/detector parameters, propagation distances, or the design of optical components, i.e. parameters that are not readily changed without non-trivial time investment, replacing components, or performing high-precision recalibrations. The edge illumination (EI) XPC method provides a method of optimising the refraction sensitivity, by exploiting micrometric translations of its periodic masks, that bypasses the constraints listed above. These translations can be performed on-the-fly and allow optimising the refraction signal for specific applications without making significant changes to the set-up. The method can prove advantageous for lab-based systems that make use of larger sources but with limited available set-up space. In this paper, we study how refraction sensitivity varies as a function of illuminated pixel fraction (IPF) under two commonly encountered experimental conditions: (1) at approximately constant detected counts, and (2) at equal exposure time. We compare the standard deviation in the background of reconstructed refraction images at different IPFs and find that refraction sensitivity is optimal at 25% IPF under both conditions. Finally, we demonstrate that refraction sensitivity affects the visibility of weakly refracting features on an insect leg. The results suggest that IPFs lower than 50% can actually be preferable, especially in the case where the statistics is kept constant, and provide experimental validation that phase sensitivity in EI is not fixed once the system parameters are defined.

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.

Holographic fiducial marks: A system for precise alignment of x-ray optics

This Letter covers the design and implementation of a generalizable system for the precise alignment of X-ray gratings. Next-generation high-energy grating-based Differential Phase Contrast (gDPC) X-ray imaging systems require precise alignment of the X-ray gratings as low as 1 mrad in rotation and 0.5 mm in translation. In this work, we designed holographic fiducial marks, consisting of four reflective Fresnel zone plates, each placed in a separate quadrant of the mark. When illuminated with a collimated laser beam, each mark creates a predefined pattern of four points, which changes quantitatively for any misalignment in each of the three translational and three rotational degrees of freedom. We fabricated the designed fiducial marks using photolithography and etching processes. The experimental system is implemented using a HeNe laser and an optical imaging system, which includes a beam expander, a plate beam splitter, and a CMOS camera, suitable for aligning practical gratings in gDPC X-ray imaging systems. Our experimental results demonstrate the rotational precision capabilities of the reported alignment system down to 0.42 mrad around the optical axis and 0.03 mrad around the axes perpendicular to the optical axis. The translational precision of 83.64 μm along the optical axis and 1.22 μm along the axes perpendicular to the optical axis is also demonstrated.