Workflows For X-ray And Neutron Interferometry/Tomography As Applied To Additive Manufacturing

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.

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).

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.

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 .

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.

Differential phase contrast (DPC) scanning transmission electron microscopy can directly visualize electromagnetic fields inside a specimen. However, their image contrast is not only sensitive to the electromagnetic fields in the sample, but also the changes in diffraction conditions such as sample bends or thickness changes. These additional contrasts are called diffraction contrasts, and sometimes make it difficult to extract pure electromagnetic field information from the experimental DPC images. In this study, we developed a beam scan system that can acquire many DPC images from the same sample region with arbitrarily varying incident beam tilt angles to the sample. Then, these images are precisely averaged to form tilt-scan averaged DPC images. It is shown that the diffraction contrast can be effectively reduced in the tilt-scan averaged DPC images.

Quantitative differential phase-contrast (DPC) imaging is one of the commonly used methods for phase retrieval. However, quantitative DPC imaging requires several pairwise intensity measurements, which makes it difficult to monitor living cells in real-time. In this study, we present a single-shot quantitative DPC imaging method based on the combination of deep learning (DL) and color-encoded illumination. Our goal is to train a model that can generate an isotropic quantitative phase image (i.e., target) directly from a single-shot intensity measurement (i.e., input). The target phase image was reconstructed using a linear-gradient pupil with two-axis measurements, and the model input was the measured color intensities obtained from a radially asymmetric color-encoded illumination pattern. The DL-based model was trained, validated, and tested using thirteen different cell lines. The total number of training, validation, and testing images was 264 (10 cells), 10 (1 cell), and 40 (2 cells), respectively. Our results show that the DL-based phase images are visually similar to the ground-truth phase images and have a high structural similarity index (>0.98). Moreover, the phase difference between the ground-truth and DL-based phase images was smaller than 13%. Our study shows the feasibility of using DL to generate quantitative phase imaging from a single-shot intensity measurement.

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

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.

In scanning transmission electron microscopy (STEM), one can obtain a variety of STEM images such as bright‐field (BF) and annular dark‐field (ADF) STEM images by changing the shape of the scintillator. However, the intensity distribution of convergent beam electron diffraction (CBED) patterns at the detector plane is yet to be fully utilized. Meanwhile, direct electron detectors with fast frame rate have recently been commercialized and used in electron microscopy. Such detectors, when used for recording CBED pattern images for each STEM probe position, are called pixelated STEM detectors. With the obtained 4‐dimensional (4D) dataset, any shape of STEM detector can be synthesized in a post processing by a free selection of the integration area. Therefore, we can synthesize variety of STEM images such as differential phase contrast (DPC) and annular bright field (ABF) images, if we once record the image signal with a pixelated detector. The 4D dataset can also be used for the advanced image processing techniques such as ptychography, which has been shown to provide high efficiency for reconstructing the phase image of an object [1,2]. Using ptychography, not only the phase contrast can be enhanced but also the effect of lens aberrations to the image such as defocus can be corrected by the post processing using the information collected by a pixelated detector. Experiments were performed using an aberration corrected microscope (JEOL JEM‐ARM200F) equipped with a pixelated detector (pnDetector pnCCD), the fast direct electron detector, which can record images at a speed of 1,000 fps in a full frame mode (264 x 264 pixels). Binning or windowing can increase the speed. The camera was placed below the ADF detector to enable simultaneous recording. Figure 1 shows STEM images of a monolayer graphene obtained at 80 kV. Fig. 1a shows an ADF image obtained with the probe current of approximately 0.2 pA and the dwell time for a pixel of 0.5 ms. Because of a combination of low dose and residual uncorrected aberrations, the lattice contrast of graphene is almost buried in the noise originated from 50 Hz commercial frequency. Fig. 1b shows a reconstructed phase image using ptychography. The image contrast is significantly improved compared to the simultaneous ADF image, but the contrast transfer of the image (see the Fourier transform displayed in the inset) is anisotropic, resulting in uncertain positions of carbon atoms. This is because there remains large two‐fold astigmatism and defocus in the image shown in Fig. 1(b), because we could not adjust those by observation of the ADF image due to the weak image signal. Fig. 1c is a phase image in which the aberrations are corrected through post processing using the same 4D dataset by applying correction functions in the spatial frequency domain. The image is no longer anisotropic and the carbon atomic positions can be unambiguously determined. Although the same amount of electron dose is used to form the ADF and the corrected phase images, the result clearly shows the benefit of ptychographic phase reconstruction in improving image signal to noise and being able to correct aberrations through post processing. Figure 2 shows the ptychographic phase maps of the 4D dataset at a certain spatial frequency. With an aberration‐free electron probe, they would be flat phase on the two sidebands, and the phase difference between the bands be π. In Fig. 2a, the map of the original dataset, there is a phase gradient inside each sideband because the aberrations were present in the electron probe. Fig. 2b is the correction function that compensates for the aberration seen in Fig. 2a. Fig. 2c is the corrected phase map and corresponding to the image in Fig. 1c. Here, only defocus and two‐fold astigmatism are corrected but corrections of other higher order aberrations are in principle possible. Figure 3 shows through focus images created in the same way as above. As we know the full information on the electron wave at the condenser aperture plane, we can induce any aberrations such as defocus.

Differential phase contrast (DPC) is a non-interferometric quantitative phase imaging method achieved by using an asymmetric imaging procedure. We report a pupil modulation differential phase contrast (PMDPC) imaging method by filtering a sample's Fourier domain with half-circle pupils. A phase gradient image is captured with each half-circle pupil, and a quantitative high resolution phase image is obtained after a deconvolution process with a minimum of two phase gradient images. Here, we introduce PMDPC quantitative phase image reconstruction algorithm and realize it experimentally in a 4f system with an SLM placed at the pupil plane. In our current experimental setup with the numerical aperture of 0.36, we obtain a quantitative phase image with a resolution of 1.73μm after computationally removing system aberrations and refocusing. We also extend the depth of field digitally by 20 times to ±50μm with a resolution of 1.76μm.

Grating-based X-ray and neutron interferometry tomography using phase-stepping methods generates large data sets. An improved algorithm is presented for solving for the parameters to calculate transmissions, differential phase contrast, and dark-field images. The method takes advantage of the vectorization inherent in high-level languages such as Mathematica and MATLAB and can solve a 16 × 1k × 1k data set in less than a second. In addition, the algorithm can function with partial data sets. This is demonstrated with processing of a 16-step grating data set with partial use of the original data chosen without any restriction. Also, we have calculated the reduced chi-square for the fit and notice the effect of grating support structural elements upon the differential phase contrast image and have explored expanded basis set representations to mitigate the impact.

Differential phase contrast and dark field neutron imaging