Quantitative coherence analysis with an X-ray Talbot–Lau interferometer

Objective. X-ray phase contrast imaging is a promising technique for future clinical diagnostic as it can provide enhanced contrast in soft tissues compared to traditional x-ray attenuation-contrast imaging. However, the strict requirements on the x-ray coherence and the precise alignment of optical elements limit its applications towards clinical use. To solve this problem, mesh-based x-ray phase contrast imaging method with one hexagonal mesh is proposed for easy alignment and better image visualization. Approach. The mesh produces structured illuminations and the detector captures its distortions to reconstruct the absorption, differential phase contrast (DPC) and dark-field (DF) images of the sample. In this work, we fabricated a hexagonal mesh to simultaneously retrieve DPC and DF signals in three different directions with single shot. A phase retrieval algorithm to obtain artifacts-free phase from DPC images with three different directions is put forward and false color dark-field image is also reconstructed with tri-directional images. Mesh-shifting method based on this hexagonal mesh modulator is also proposed to reconstruct images with better image quality at the expense of increased dose. Main results. In numerical simulations, the proposed hexagonal mesh outperforms the traditional square mesh in image evaluation metrics performance and false color visualization with the same radiation dose. The experimental results demonstrate its feasiblity in real imaging systems and its advantages in quantitive imaging and better visualization. The proposed hexagonal mesh is easy to fabricate and can be successfully applied to x-ray source with it spot size up to 300 μm. Significance. This work opens new possibilities for quantitative x-ray non-destructive imaging and may also be instructive for research fields such as x-ray structured illumination microscopy (SIM), x-ray spectral imaging and x-ray phase contrast and dark-field computed tomography (CT).

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.

DeepPhase: Learning phase contrast signal from dual energy X-ray absorption images

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.

We analyze the effect of partial spatial coherence on the scattering of light by an arbitrary particle. We extend the definition of the extinction cross section to spatially partially coherent fields. We then discuss the effect of the partial coherence on the extinction scattering cross section by introducing the Wigner transform. It is shown that for rotationally invariant scatterers, the extinction cross section does not depend on the coherence of the incident field. The effect of partial coherence on the angular behavior of the scattered intensity is also discussed in the framework of the Wigner transform. The implications for practical applications are considered.

We report a new preparative method for providing contrast through reduction in electron density that is uniquely suited for propagation-based differential x-ray phase contrast imaging. The method, which results in an air or fluid filled vasculature, makes possible visualization of the smallest microvessels, roughly down to 15 µm, in an excised murine liver, while preserving the tissue for subsequent histological workup. We show the utility of spatial frequency filtering for increasing the visibility of minute features characteristic of phase contrast imaging, and the capability of tomographic reconstruction to reveal microvessel structure and three-dimensional visualization of the sample. The effect of water evaporation from livers during x-ray imaging on the visibility of blood vessels is delineated. The deformed vascular tree in a cancerous murine liver is imaged.

Purpose: The anatomical noise power spectra (NPS) for differential phase contrast (DPC) and dark field (DF) imaging have recently been characterized using a power-law model with two parameters, alpha and beta, an innovative extension to the methodology used in x-ray attenuation based breast imaging such as mammography, DBT, or cone-beam CT. Beta values of 3.6, 2.6, and 1.3 have been measured for absorption, DPC, and DF respectively for cadaver breasts imaged in the coronal plane; these dramatic differences should be reflected in their detection performance. The purpose of this study was to determine the impact of anatomical noise on breast calcification detection and compare the detection performance of the three contrast mechanisms of a multi-contrast x-ray imaging system. Methods: In our studies, a calcification image object was segmented out of the multi-contrast images of a cadaver breast specimen. 50 measured total NPS were measured from breast cadavers directly. The ideal model observer detectability was calculated for a range of doses (5–100%) and a range of calcification sizes (diameter = 0.25–2.5 mm). Results: Overall we found the highest average detectability corresponded to DPC imaging (7.4 for 1 mm calc.), with DF the next highest (3.8 for 1 mm calc.), and absorption the lowest (3.2 for 1 mm calc.). However, absorption imaging also showed the slowest dependence on dose of the three modalities due to the significant anatomical noise. DPC showed a peak detectability for calcifications ∼1.25 mm in diameter, DF showed a peak for calcifications around 0.75 mm in diameter, and absorption imaging had no such peak in the range explored. Conclusion: Understanding imaging performance for DPC and DF is critical to transition these modalities to the clinic. The results presented here offer new insight into how these modalities complement absorption imaging to maximize the likelihood of detecting early breast cancers. J. Garrett, Y. Ge, K. Li: Nothing to disclose. G.-H. Chen: Research funded, GE Healthcare; Research funded, Siemens AX.

Grating-based interferometry/tomography is being rapidly developed for non-destructive evaluation of additive manufacturing test articles. An application requiring an efficient workflow is extremely necessary for stress and fatigue testing samples. At present, scientific workflows play an important role for computational experiments in additive manufacturing 3D printing and interferometry/tomography imaging analysis. A clear workflow template allows scientists to process experiments easier and faster. Work flow library grows, but to find an appropriate workflow for their task is challenging. In our research, there are mainly three portions in the workflow, interferometry analysis, image reconstruction and 3D visualization. Currently, the hierarchy of workflows in interferom etry/tomography projects is Mathematica, TomoPy/ASTRA/Jupyter notebook, VisTrails and Dragonfly. In general, two methods of interferometry analysis have been used in the first portion of workflow, single-shot interferometry and stepped-grating interferometry. As for the second portion, with a Jupyter notebook, the reconstruction method ’Gridrec’ in TomoPy and ’SIRT’ (Simultaneous Iterative Reconstruction Technique) in ASTRA gener ated a powerful reconstruction volume for absorption projections and dark-field projections separately. For the last portion, Dragonfly developed by ORS (Object Research System) company is a 3D visualization software with powerful scripting capabilities implemented in Python macros. Meanwhile, the VisTrails workflow incorporated both interferometry anal ysis and image reconstruction portions into VisTrails modules. Workflows in VisTrails hide much of the complexity of Mathematica or Python programming from users. Instead, with a simple GUI, it is possible for users to make their interferometry/tomography workflows through VisTrails modules. Especially, for DPC (differential phase contrast) images in grating-based interferome try/tomography, we addressed the phase unwrapping issue with the method of 2D integra tion through generating phase images. With the algorithm, we have demonstrated the 2D integrated phase images denote a clearer contrast than DPC images.

Imaging soft biomaterials in vivo is a significant challenge, as most conventional techniques are limited by biomaterial contrast, penetration depth, or spatial resolution. Exogeneous contrast agents used to increase contrast may also alter material properties or exhibit local toxicity. The capability to observe biomaterial constructs in vivo without introducing exogenous contrast would improve preclinical testing and evaluation. Conventional X-ray Computed Tomography allows fast, high-resolution imaging at high penetration depth, but biomaterial contrast is low. Previous studies employing X-ray phase contrast (XPC) and utilizing a synchrotron source provided support for the significant potential of XPC in imaging biomaterials without contrast agents. In this study, XPC tomography was used to image alginate hydrogel microspheres within a small animal omental pouch model using a commercially available X-ray source. Multilayer microbeads could be identified in the XPC images with volumetric and structural information not possible in histological analysis. The number of microbeads present and microbead volume and diameter could be quantified from the images. The results of this study show that XPC tomography can be a useful tool for monitoring of implanted soft biomaterials in small animal models.

In x-ray differential phase contrast imaging (DPCI), a simple sinusoidal model is used to describe the measured signal intensities. When there is no noise added to the measurements, one is able to estimate the three unknown parameters, absorption contrast, phase-contrast, and small angle scatter, directly from the signal model. However, for x-ray detections, noise is always present and the noise level increases with a decrease in x-ray flux. When noise is involved, an experimental ensemble average is needed to make the above parameter estimation method accurate. Unfortunately, an ensemble average requires a large number of measurements acquired under identical experimental conditions. Such repetition procedures would significantly prolong the data acquisition time and require additional radiation dose to the image object. Therefore, it is desirable to develop a reliable parameter estimation method from a group of single x-ray signal intensity measurements. This paper addresses this concern by proposing a statistical signal estimation method. This method maximizes the joint probability of measurements in a complete phase stepping period and is able to estimate the three unknowns in DPCI simultaneously. Our numerical simulations demonstrate that the statistical signal estimation method outperformed the current blind estimation method by minimizing the noise variance of each parameter. As a result, this method has the potential to further improve the dose efficiency of DPCI.

Introducing a non-pixelated and fast centre of mass detector for differential phase contrast microscopy

In this paper, we have included the effects of initial partial coherence in the quantum theory of a non-degenerate inversionless laser. A three-level atomic system in open A-configuration is considered. The atoms are initially prepared in the partial coherent superposition of the lower two atomic levels with some incoherent population in the excited state. The master equation for the cavity field modes is derived and converted into a Fokker-Planck equation to determine the phase locking and stability conditions. The effects of initial partial coherence on the gain of two modes are studied under these conditions. The range of values of the initial partial coherence for which the action of lasing without inversion can take place are shown. Our results show that under certain conditions the two modes can amplify with equal gain below threshold.

Optical diffraction tomography (ODT) is a promising label-free imaging method capable of quantitatively measuring the three-dimensional (3D) refractive index distribution of transparent samples. In recent years, partially coherent ODT (PC-ODT) has attracted increasing attention due to its system simplicity and absence of laser speckle noise. Quantitative phase imaging (QPI) technologies represented by Fourier ptychographic microscopy (FPM), differential phase contrast (DPC) imaging and intensity diffraction tomography (IDT) need to collect several or hundreds of intensity images, which usually introduce motion artifacts when shooting fast-moving targets, leading to a decrease in image quality. Hence, a quantitative real-time phase microscopy (qRPM) for extended depth of field (DOF) imaging based on 3D single-shot differential phase contrast (ssDPC) imaging method is proposed in this research study. qRPM incorporates a microlens array (MLA) to simultaneously collect spatial information and angular information. In subsequent optical information processing, a deconvolution method is used to obtain intensity stacks under different illumination angles in a raw light field image. Importing the obtained intensity stack into the 3D DPC imaging model is able to finally obtain the 3D refractive index distribution. The captured four-dimensional light field information enables the reconstruction of 3D information in a single snapshot and extending the DOF of qRPM. The imaging capability of the proposed qRPM system is experimental verified on different samples, achieve single-exposure 3D label-free imaging with an extended DOF for 160 µm which is nearly 30 times higher than the traditional microscope system.

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

Quantitative differential phase contrast (qDPC) microscopy enables high‐resolution, label‐free imaging of weakly absorbing samples by combining asymmetrical illumination with phase transfer function (PTF) deconvolution. However, conventional methods are limited by the ill‐posed nature of deconvolution and the band‐limited characteristics of the PTF, leading to poor robustness against noise and background fluctuations, particularly in thick or complex samples. To overcome these challenges, we propose a pupil‐driven differential phase contrast (PD‐DPC) framework that integrates system PTFs into both the data fidelity and regularization terms of the reconstruction model. The proposed model incorporates an edge‐sparsity‐promoting regularization to preserve structural detail and suppress noise, along with a Retinex‐inspired fidelity formulation to mitigate background fluctuations. The resulting non‐convex optimization problem is solved via an efficient Split Bregman algorithm with iterative reweighted soft‐thresholding. Simulations and experiments demonstrate that PD‐DPC outperforms L2‐DPC, Iso‐DPC, TV‐DPC, and Retinex‐DPC in terms of background suppression, phase fidelity, and edge preservation. The framework is compatible with diverse DPC modalities and enables automatic cell contour segmentation as well as high‐resolution imaging of absorbing tissues beyond the weak‐object approximation. By combining physics‐informed priors with a data‐adaptive reconstruction strategy, PD‐DPC offers a robust, broadly applicable solution that substantially enhances the accuracy and applicability of qDPC for biomedical imaging. The MATLAB code is available on GitHub .