Grating Interferometer with Redundant Design for Performing Wide-Range Displacement Measurements.

Grating interferometers that use large two-dimensional grating splice modules for performing wide-range measurements have significant advantages for identifying the position of the wafer stage. However, the manufacturing process of large two-dimensional grating splice modules is very difficult. In contrast to existing redundant designs in the grating line dimension, we propose a novel interferometric reading head with a redundant design for obtaining wide-range displacement measurements. This interferometric reading head uses a one-dimensional grating splice module, and it was observed to be compatible with two orthogonal gratings. We designed a grating interferometer system composed of four reading heads to achieve a wide range of measurements and verified it using ZEMAX simulation. By conducting experiments, we were able to verify the compatibility of the reading head with gratings possessing different grating line directions; the measurement noise was found to be less than 0.3 nm.

Quantitative X-ray phase contrast computed tomography with grating interferometry : Biomedical applications of quantitative X-ray grating-based phase contrast computed tomography.

The ability of biomedical imaging data to be of quantitative nature is getting increasingly important with the ongoing developments in data science. In contrast to conventional attenuation-based X-ray imaging, grating-based phase contrast computed tomography (GBPC-CT) is a phase contrast micro-CT imaging technique that can provide high soft tissue contrast at high spatial resolution. While there is a variety of different phase contrast imaging techniques, GBPC-CT can be applied with laboratory X-ray sources and enables quantitative determination of electron density and effective atomic number. In this review article, we present quantitative GBPC-CT with the focus on biomedical applications.

X-Ray Single-Grating Interferometry for Wavefront Measurement and Correction of Hard X-Ray Nanofocusing Mirrors.

X-ray single-grating interferometry was applied to conduct accurate wavefront corrections for hard X-ray nanofocusing mirrors. Systematic errors in the interferometer, originating from a grating, a detector, and alignment errors of the components, were carefully examined. Based on the measured wavefront errors, the mirror shapes were directly corrected using a differential deposition technique. The corrected X-ray focusing mirrors with a numerical aperture of 0.01 attained two-dimensionally diffraction-limited performance. The results of the correction indicate that the uncertainty of the wavefront measurement was less than λ/72 in root-mean-square value.

Ultraprecision Real-Time Displacements Calculation Algorithm for the Grating Interferometer System.

Grating interferometry is an environmentally stable displacement measurement technique that has significant potential for identifying the position of the wafer stage. A fast and precise algorithm is required for real-time calculation of six degrees-of-freedom (DOF) displacement using phase shifts of interference signals. Based on affine transformation, we analyze diffraction spot displacement and changes in the internal and external effective optical paths of the grating interferometer caused by the displacement of the wafer stage (DOWS); then, we establish a phase shift-DOWS model. To solve the DOWS in real time, we present a polynomial approximation algorithm that uses the frequency domain characteristics of nonlinearities to achieve model reduction. The presented algorithm is verified by experiment and ZEMAX simulation.

Two Degree-of-Freedom Fiber-Coupled Heterodyne Grating Interferometer with Milli-Radian Operating Range of Rotation.

In the displacement measurement of the wafer stage in lithography machines, signal quality is affected by the relative angular position between the encoder head and the grating. In this study, a two-degree-of-freedom fiber-coupled heterodyne grating interferometer with large operating range of rotation is presented. Fibers without fiber couplers are utilized to receive the interference beams for high-contrast signals under the circumstances of large angular displacement and ZEMAX ray tracing software simulation and experimental validation have been carried out. Meanwhile, a reference beam generated inside the encoder head is adopted to suppress the thermal drift of the interferometer. Experimental results prove that the proposed grating interferometer could realize sub-nanometer displacement measurement stability in both in-plane and out-of-plane directions, which is 0.246 nm and 0.465 nm of 3σ value respectively within 30 s.

X-ray phase-contrast tomography with a compact laser-driven synchrotron source.

Between X-ray tubes and large-scale synchrotron sources, a large gap in performance exists with respect to the monochromaticity and brilliance of the X-ray beam. However, due to their size and cost, large-scale synchrotrons are not available for more routine applications in small and medium-sized academic or industrial laboratories. This gap could be closed by laser-driven compact synchrotron light sources (CLS), which use an infrared (IR) laser cavity in combination with a small electron storage ring. Hard X-rays are produced through the process of inverse Compton scattering upon the intersection of the electron bunch with the focused laser beam. The produced X-ray beam is intrinsically monochromatic and highly collimated. This makes a CLS well-suited for applications of more advanced--and more challenging--X-ray imaging approaches, such as X-ray multimodal tomography. Here we present, to our knowledge, the first results of a first successful demonstration experiment in which a monochromatic X-ray beam from a CLS was used for multimodal, i.e., phase-, dark-field, and attenuation-contrast, X-ray tomography. We show results from a fluid phantom with different liquids and a biomedical application example in the form of a multimodal CT scan of a small animal (mouse, ex vivo). The results highlight particularly that quantitative multimodal CT has become feasible with laser-driven CLS, and that the results outperform more conventional approaches.

Reconstruction of scalar and vectorial components in X-ray dark-field tomography.

Grating-based X-ray dark-field imaging is a novel technique for obtaining image contrast for object structures at size scales below setup resolution. Such an approach appears particularly beneficial for medical imaging and nondestructive testing. It has already been shown that the dark-field signal depends on the direction of observation. However, up to now, algorithms for fully recovering the orientation dependence in a tomographic volume are still unexplored. In this publication, we propose a reconstruction method for grating-based X-ray dark-field tomography, which models the orientation-dependent signal as an additional observable from a standard tomographic scan. In detail, we extend the tomographic volume to a tensorial set of voxel data, containing the local orientation and contributions to dark-field scattering. In our experiments, we present the first results of several test specimens exhibiting a heterogeneous composition in microstructure, which demonstrates the diagnostic potential of the method.

X-ray phase-contrast computed tomography visualizes the microstructure and degradation profile of implanted biodegradable scaffolds after spinal cord injury.

Tissue engineering strategies for spinal cord repair are a primary focus of translational medicine after spinal cord injury (SCI). Many tissue engineering strategies employ three-dimensional scaffolds, which are made of biodegradable materials and have microstructure incorporated with viable cells and bioactive molecules to promote new tissue generation and functional recovery after SCI. It is therefore important to develop an imaging system that visualizes both the microstructure of three-dimensional scaffolds and their degradation process after SCI. Here, X-ray phase-contrast computed tomography imaging based on the Talbot grating interferometer is described and it is shown how it can visualize the polyglycolic acid scaffold, including its microfibres, after implantation into the injured spinal cord. Furthermore, X-ray phase-contrast computed tomography images revealed that degradation occurred from the end to the centre of the braided scaffold in the 28 days after implantation into the injured spinal cord. The present report provides the first demonstration of an imaging technique that visualizes both the microstructure and degradation of biodegradable scaffolds in SCI research. X-ray phase-contrast imaging based on the Talbot grating interferometer is a versatile technique that can be used for a broad range of preclinical applications in tissue engineering strategies.

Combining Monte Carlo methods with coherent wave optics for the simulation of phase-sensitive X-ray imaging.

Phase-sensitive X-ray imaging shows a high sensitivity towards electron density variations, making it well suited for imaging of soft tissue matter. However, there are still open questions about the details of the image formation process. Here, a framework for numerical simulations of phase-sensitive X-ray imaging is presented, which takes both particle- and wave-like properties of X-rays into consideration. A split approach is presented where we combine a Monte Carlo method (MC) based sample part with a wave optics simulation based propagation part, leading to a framework that takes both particle- and wave-like properties into account. The framework can be adapted to different phase-sensitive imaging methods and has been validated through comparisons with experiments for grating interferometry and propagation-based imaging. The validation of the framework shows that the combination of wave optics and MC has been successfully implemented and yields good agreement between measurements and simulations. This demonstrates that the physical processes relevant for developing a deeper understanding of scattering in the context of phase-sensitive imaging are modelled in a sufficiently accurate manner. The framework can be used for the simulation of phase-sensitive X-ray imaging, for instance for the simulation of grating interferometry or propagation-based imaging.

Development of a High-Sensitivity Acoustic Sensor Based on Grating Interferometer Combined with Glass Diaphragm.

In this study, based on the principle of grating interferometer-based acoustic sensors, design guidelines for the grating interferometric module were obtained and analyzed considering various factors in order to obtain high sensitivity, and a glass-based grating interference component and its acoustic sensor device were developed. The key parameters of the grating interference structure were extracted, and their effects on the acoustic response sensitivity were quantified for multiple mechanisms. For the development of the acoustic sensor, the grating-on-convex-platform structure and the micromachining processes of the glass-based components were designed and developed. The developed acoustic sensor samples achieved high sensitivity. In particular, the sample suitable for low-frequency application obtained a sensitivity of 0.776 V/Pa @ 1 kHz, and the spectrum of its sensitivity was flat from 50 Hz to 8 Hz with a deviation less than 1.5 dB and a sensitivity of 0.408 V/Pa @ 20 Hz.

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

PURPOSE: 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. METHODS: 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. RESULTS: 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. CONCLUSIONS: 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.

Talbot-Lau X-ray phase contrast for tiling-based acquisitions without reference scanning.

PURPOSE: Grating-based Talbot-Lau interferometers are a popular choice for phase-contrast X-ray acquisitions. Here, an air reference scan has to be acquired prior to an object scan. This particularly complicates acquisition of large objects: large objects are tiled into multiple scans due to the small field of view of current gratings. However, phase reference drifts occurring between these scans may require to repeatedly move the object in and out of the X-ray beam to update the reference information. METHODS: We developed an image processing technique that completely removes the need for phase reference scans in tiled acquisitions. We estimate the reference from object scans using a tailored iterated robust regression, using a novel efficient optimizer. RESULTS: Our evaluation indicates that the estimated reference is not only close to the acquired reference but also improves the final image quality. We hypothesize that this is because we mitigate errors that are introduced when actually acquiring the reference phase. CONCLUSION: Phase-contrast imaging of larger objects may benefit from computational estimation of phase reference data due to reduced scanning complexity and improved image quality.

X-ray phase-contrast tomosynthesis for improved breast tissue discrimination.

PURPOSE: Attenuation-based tomosynthesis has proven to successfully resolve the glandular tissue overlap present in mammography. However, the ability of tomosynthesis to differentiate tumorous and glandular tissue remains limited, due to the small differences in X-ray attenuation in breast tissue. One possibility to overcome this limitation and to further increase the diagnostic value of tomosynthesis exams, is the application of recently developed grating-based phase-contrast methods, which provide complementary information on the phase shift and the local scattering power of the sample. In this study, we report on first phase-contrast breast tomosynthesis results of a mastectomy sample slice with an invasive ductal carcinoma. MATERIAL AND METHODS: A slice of a mastectomy sample with histologically proven invasive ductal cancer was imaged at the synchrotron radiation source ESRF (Grenoble, France). We used a two-grating interferometer setup at the ninth fractional Talbot distance and with an X-ray energy of 23 keV. In grating interferometry absorption, differential phase, and scattering images are recorded simultaneously. The tomosynthesis scan comprises 61 projections. Multimodal tomosynthesis results were reconstructed using a standard filtered back-projection approach. Our findings are supported by a comparison of tomographic views to histopathology. RESULTS: Phase-contrast tomosynthesis combines the advantage of improved soft-tissue discrimination in phase-contrast imaging with the ability of tomosynthesis to provide a third dimension so that improved feature visibility is not hampered by superposition artifacts. Our results indicate superior diagnostic value due to the depth resolution supplied in tomosynthesis imaging; a region of necrotic tissue that is obscured in a projection image can clearly be depicted in one single tomosynthesis slice. Compared to absorption tomosynthesis alone, soft tissue contrast is significantly enhanced in phase-contrast tomosynthesis views, where fibrous structures are clearly visible. CONCLUSION: In this article we present the first proof-of-principle grating-based phase-contrast tomosynthesis of a mastectomy sample section. A comparison of conventional attenuation with phase-contrast and dark-field tomosynthesis indicates that complementary information from three signals yields an increase in diagnostic value, which is verified in a comparison of our results to histological sections of the sample. As grating-based phase-contrast mammography efficiently works with conventional lab sources, our benchmark results indicate the potential benefit of translating phase-contrast tomosynthesis into a clinical setting.