Analytical evaluation of the signal and noise propagation in x-ray differential phase-contrast computed tomography

Analyzer-free hard x-ray interferometry

Objective. To enable practical interferometry-based phase contrast CT using standard incoherent x-ray sources, we propose an imaging system where the analyzer grating is replaced by a high-resolution detector. Since there is no need to perform multiple exposures (with the analyzer grating at different positions) at each scan angle, this scheme is compatible with continuous-rotation CT apparatus, and has the potential to reduce patient radiation dose and patient motion artifacts.Approach. Grating-based x-ray interferometry is a well-studied technique for imaging soft tissues and highly scattering objects embedded in such tissues. In addition to the traditional x-ray absorption-based image, this technique allows reconstruction of the object phase and small-angle scattering information. When using conventional incoherent, polychromatic, hard x-ray tubes as sources, three gratings are usually employed. To sufficiently resolve the pattern generated in these interferometers with contemporary x-ray detectors, an analyzer grating is used, and consequently multiple images need to be acquired for each view angle. This adds complexity to the imaging system, slows image acquisition and thus increases sensitivity to patient motion, and is not dose efficient. By simulating image formation based on wave propagation, and proposing a novel phase retrieval algorithm based on a virtual grating, we assess the potential of a analyzer-grating-free system to overcome these limitations.Main results. We demonstrate that the removal of the analyzer-grating can produce equal image contrast-to-noise ratio at reduced dose (by a factor of 5), without prolonging scan duration.Significance.By demonstrating that an analyzer-free CT system, in conjuction with an efficient phase retrieval algorithm, can overcome the prohibitive dose and workflow penalties associated grating-stepping, an alternative path towards realizing clinical inteferometric CT appears possible.

Towards clinical-dose grating interferometry breast CT with fused intensity-based iterative reconstruction

X-ray grating interferometry CT (GI-CT) is an emerging imaging modality which provides three complementary contrasts that could increase the diagnostic content of clinical breast CT: absorption, phase, and dark-field. Yet, reconstructing the three image channels under clinically compatible conditions is challenging because of severe ill-conditioning of the tomographic reconstruction problem. In this work we propose to solve this problem with a novel reconstruction algorithm that assumes a fixed relation between the absorption and the phase-contrast channel to reconstruct a single image by automatically fusing the absorption and phase channels. The results on both simulations and real data show that, enabled by the proposed algorithm, GI-CT outperforms conventional CT at a clinical dose.

Experimental demonstration of ultrahigh sensitivity Talbot-Lau interferometer for low dose mammography

Objective. Even though the techniques used for breast cancer identification have advanced over the years, current mammography based on x-rays absorption, the 'gold standard' screening test at present, still has some shortcomings as concerns sensitivity and specificity to early-stage cancers, due to poor differentiation between tumor and normal tissues, especially in the case of the dense breasts. We investigate a possible additional technique for breast cancer detection with higher sensitivity and low dose, x-ray phase-contrast or refraction-based imaging with ultrahigh angular sensitivity grating interferometers, having several meters length.Approach.Towards this goal, we built and tested on a mammography phantom, a table-top laboratory setup based on a 5.7 m long Talbot-Lau interferometer with angular sensitivity better than 1μrad. We used a high-power x-ray tungsten anode tube with a 400μm focal spot, operated at 40 kVp and 15 mA with a 2 mm aluminum filter.Main results.The results reported in our paper confirm the ultrahigh sensitivity and dose economy possible with our setup. The visibility of objects simulating cancerous formations is strongly increased in the refraction images over the attenuation ones, even at a low dose of 0.32 mGy. Notably, the smallest fiber of 400μm diameter and calcifications specs of 160μm in diameter are detected, even though the spatial resolution at the object of our magnification M ∼ 2 setup with a 400μm source spot is only ∼250μm.Significance.Our experiments on a mammography phantom illustrate the capabilities of the proposed technique and can open the way toward low-dose interferometric mammography.

INSIDEnet: Interpretable nonexpansive data-efficient network for denoising in grating interferometry breast CT

PURPOSE

Breast cancer is the most common malignancy in women. Unfortunately, current breast imaging techniques all suffer from certain limitations: they are either not fully three-dimensional, have insufficient resolution or low soft-tissue contrast. Grating Interferometry Breast Computed Tomography (GI-BCT) is a promising X-ray phase contrast modality that could overcome these limitations by offering high soft-tissue contrast and excellent 3D resolution. To enable the transition of this technology to clinical practice, dedicated data processing algorithms must be developed in order to effectively retrieve the signals of interest from the measured raw data.

METHODS

This article proposes a novel denoising algorithm which can cope with the high noise amplitudes and heteroscedasticity which arise in GI-BCT when operated in a low-dose regime to effectively regularize the ill-conditioned GI-BCT inverse problem. We present a data-driven algorithm called INSIDEnet which combines different ideas such as multiscale image processing, transform-domain filtering, transform learning and explicit orthogonality to build an Interpretable NonexpanSIve Data-Efficient network (INSIDEnet).

RESULTS

We apply the method to simulated breast phantom datasets and to real data acquired on a GI-BCT prototype and show that the proposed algorithm outperforms traditional state-of-the-art filters and is competitive with deep neural networks. The strong inductive bias given by the proposed model's architecture allows to reliably train the algorithm with very limited data while providing high model interpretability, thus offering a great advantage over classical convolutional neural networks (CNNs).

CONCLUSIONS

The proposed INSIDEnet is highly data-efficient, interpretable and outperforms state-of-the-art CNNs when trained on very limited training data. We expect the proposed method to become an important tool as part of a dedicated Plug-and-Play GI-BCT reconstruction framework, needed to translate this promising technology to the clinics.

Performance evaluation of dual-energy CT and differential phase contrast CT in quantitative imaging applications

PURPOSE

The purpose of this study is to evaluate and compare the quantitative material decomposition performance of the dual-energy CT (DECT) and differential phase contrast CT (DPCT) via numerical observer studies.

METHODS

The electron density (ρ_e ) and the effective atomic number (Z_eff ) are selected as the decomposition bases. The image domain based decomposition algorithms with certain noise suppression are used to extract the ρ_e and Z_eff information under three different spatial resolutions (0.3 mm, 0.1 mm, and 0.03 mm). The contrast-to-noise-ratio (CNR) and the numerical human observer model which is sensitive to the noise textures are investigated to compare the quantitative imaging performance of DECT and DPCT under varied radiation dose levels.

RESULTS

The model observer results show that the DECT is superior to DPCT at 0.3 mm spatial resolution (300 mm object size); the DECT and DPCT show similar quantitative imaging performance at 0.1 mm spatial resolution (100 mm object size); and the DPCT outperforms the DECT by approximately 1.5 times for the 0.3 mm sized imaging target at 0.03 mm spatial resolution (30 mm object size).

CONCLUSIONS

In conclusion, the DECT would be recommended to obtain ρ_e and Z_eff for the low spatial resolution quantitative imaging applications such as the diagnostic CT imaging. Whereas, the DPCT would be recommended for ultra high spatial resolution imaging tasks of small objects such as the micro-CT imaging. This study provides a reference to determine the most appropriate quantitative X-ray CT imaging method for a certain radiation dose level. This article is protected by copyright. All rights reserved.

Optimization of multipoint phase retrieval in edge illumination X-ray imaging: A theoretical and experimental analysis

PURPOSE

In this work, an analytical model describing the noise in the retrieved three contrast channels, transmission, refraction, and ultra small-angle scattering, obtained with edge illumination X-ray phase-based imaging system is presented and compared to experimental data.

METHODS

In EI, images acquired at different displacements of the presample mask (i.e., different illumination levels referred to as points on the "illumination curve"), followed by pixel-wise curve fitting, are exploited to quantitatively retrieve the three contrast channels. Therefore, the noise in the final image will depend on the error associated with the fitting process. We use a model based on the derivation of the standard error on fitted parameters, which relies on the calculation of the covariance matrix, to estimate the noise and the cross-channel correlation as a function of the position of the sampling points. In particular, we investigated the most common cases of 3 and 5 sampling points. In addition, simulations have been used to better understand the role of the integration time for each sampling point. Finally, the model is validated by comparison with the experimental data acquired with an edge illumination setup based on a tungsten rotating anode X-ray source and a photon counting detector.

RESULTS

We found a good match between the predictions of the model and the experimental data. In particular, for the investigated cases, an arrangement of the sampling points leading to minimum noise and cross-channel correlation can be found. Simulations revealed that, given a fixed overall scanning time, its distribution into the smallest possible number of sampling points needed for phase retrieval leads to minimum noise thanks to higher statistics per point.

CONCLUSIONS

This work presents an analytical model describing the noise in the various contrast channels retrieved in edge illumination as a function of the illumination curve sampling. In particular, an optimal sampling scheme leading to minimum noise has been determined for the case where 3 or 5 sampling points are used, which represent two of the most common acquisition schemes. In addition, the correlation between noise in the different channels and the role of the number of points and exposure time have been also investigated. In general, our results suggest a series of procedures that should be followed in order to optimize the experimental acquisitions.

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-Based Techniques to Study the Nano-Bio Interface

X-ray-based analytics are routinely applied in many fields, including physics, chemistry, materials science, and engineering. The full potential of such techniques in the life sciences and medicine, however, has not yet been fully exploited. We highlight current and upcoming advances in this direction. We describe different X-ray-based methodologies (including those performed at synchrotron light sources and X-ray free-electron lasers) and their potentials for application to investigate the nano-bio interface. The discussion is predominantly guided by asking how such methods could better help to understand and to improve nanoparticle-based drug delivery, though the concepts also apply to nano-bio interactions in general. We discuss current limitations and how they might be overcome, particularly for future use in vivo.

Dual-Energy X-Ray Dark-Field Material Decomposition

Dual-energy imaging is a clinically well-established technique that offers several advantages over conventional X-ray imaging. By performing measurements with two distinct X-ray spectra, differences in energy-dependent attenuation are exploited to obtain material-specific information. This information is used in various imaging applications to improve clinical diagnosis. In recent years, grating-based X-ray dark-field imaging has received increasing attention in the imaging community. The X-ray dark-field signal originates from ultra small-angle scattering within an object and thus provides information about the microstructure far below the spatial resolution of the imaging system. This property has led to a number of promising future imaging applications that are currently being investigated. However, different microstructures can hardly be distinguished with current X-ray dark-field imaging techniques, since the detected dark-field signal only represents the total amount of ultra small-angle scattering. To overcome these limitations, we present a novel concept called dual-energy X-ray dark-field material decomposition, which transfers the basic material decomposition approach from attenuation-based dual-energy imaging to the dark-field imaging modality. We develop a physical model and algorithms for dual-energy dark-field material decomposition and evaluate the proposed concept in experimental measurements. Our results suggest that by sampling the energy-dependent dark-field signal with two different X-ray spectra, a decomposition into two different microstructured materials is possible. Similar to dual-energy imaging, the additional microstructure-specific information could be useful for clinical diagnosis.

High sensitivity X-ray phase contrast imaging by laboratory grating-based interferometry at high Talbot order geometry

X-ray phase contrast imaging is a powerful analysis technique for materials science and biomedicine. Here, we report on laboratory grating-based X-ray interferometry employing a microfocus X-ray source and a high Talbot order (35th) asymmetric geometry to achieve high angular sensitivity and high spatial resolution X-ray phase contrast imaging in a compact system (total length <1 m). The detection of very small refractive angles (∼50 nrad) at an interferometer design energy of 19 keV was enabled by combining small period X-ray gratings (1.0, 1.5 and 3.0 µm) and a single-photon counting X-ray detector (75 µm pixel size). The performance of the X-ray interferometer was fully characterized in terms of angular sensitivity and spatial resolution. Finally, the potential of laboratory X-ray phase contrast for biomedical imaging is demonstrated by obtaining high resolution X-ray phase tomographies of a mouse embryo embedded in solid paraffin and a formalin-fixed full-thickness sample of human left ventricle in water with a spatial resolution of 21.5 µm.

Dual Energy Differential Phase Contrast CT (DE-DPC-CT) Imaging

When more than two elemental materials are present in a given object, material quantification may not be robust and accurate when the routine two-material decomposition scheme in current dual energy CT imaging is employed. In this work, we present an innovative scheme to accomplish accurate three-material decomposition with measurements from a dual energy differential phase contrast CT (DE-DPC-CT) acquisition. A DE-DPC-CT system was constructed using a grating interferometer and a photon counting CT imaging system with two energy bins. The DE-DPC-CT system can simultaneously measure both the imaginary and the real part of the complex refractive index to enable a three-material decomposition. Physical phantom with 21 material inserts were constructed and measured using DE-DPC-CT system. Results demonstrated excellent accuracy in elemental material quantification. For example, relative root-mean-square errors of 4.5% for calcium and 5.2% for iodine were achieved using the proposed three-material decomposition scheme. Biological tissues with iodine inserts were used to demonstrate the potential utility of the proposed spectral CT imaging method. Experimental results showed that the proposed method correctly differentiates the bony structure, iodine, and the soft tissue in the biological specimen samples. A triple spectra CT scan was also performed to benchmark the performance of the DE-DPC-CT scan. Results demonstrated that the material decomposition from the DE-DPC-CT has a much lower quantification noise than that from the triple spectra CT scan.

Wave optics simulation of grating-based X-ray phase-contrast imaging using 4D Mouse Whole Body (MOBY) phantom

PURPOSE

Demonstrate realistic simulation of grating-based x-ray phase-contrast imaging (GB-XPCI) using wave optics and the four-dimensional Mouse Whole Body (MOBY) phantom defined with non-uniform rational B-splines (NURBS).

METHODS

We use a full-wave approach, which uses wave optics for x-ray wave propagation from the source to the detector. This forward imaging model can be directly applied to NURBS-defined numerical phantoms such as MOBY. We assign the material properties (attenuation coefficient and electron density) of each model part using the data for adult human tissues. The Poisson noise is added to the simulated images based on the calculated photon flux at each pixel.

RESULTS

We simulate the intensity images of the MOBY phantom for eight different grating positions. From the simulated images, we calculate the absorption, differential phase, and normalized visibility contrast images. We also predict how the image quality is affected by different exposure times.

CONCLUSIONS

GB-XPCI can be simulated with the full-wave approach and a realistic numerical phantom defined with NURBS.

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

OBJECTIVE

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.

METHODS

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.

RESULTS

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.

CONCLUSION

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.

SIGNIFICANCE

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.

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?

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.

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.

Direct information retrieval after 3D reconstruction in grating-based X-ray phase-contrast computed tomography

Grating-based X-ray differential phase-contrast imaging has attracted a great amount of attention and has been considered as a potential imaging method in clinical medicine because of its compatibility with the traditional X-ray tube source and the possibility of a large field of view. Moreover, phase-contrast computed tomography provides three-dimensional phase-contrast visualization. Generally, two-dimensional information retrieval performed on every projection is required prior to three-dimensional reconstruction in phase-contrast computed tomography. In this paper, a three-dimensional information retrieval method to separate absorption and phase information directly from two reconstructed images is derived. Theoretical derivations together with numerical simulations have been performed to confirm the feasibility and veracity of the proposed method. The advantages and limitations compared with the reverse projection method are also discussed. Owing to the reduced data size and the absence of a logarithm operation, the computational time for information retrieval is shortened by the proposed method. In addition, the hybrid three-dimensional images of absorption and phase information were reconstructed using an absorption reconstruction algorithm, hence the existing data pre-processing methods and iterative reconstruction algorithms in absorption reconstruction may be utilized in phase reconstruction immediately.

Choosing sensitivity to reduce X-ray dose in medical phase contrast imaging

In medical X-ray imaging, phase contrast imaging is to measure refraction angles caused by the patient. The X-ray dose for a given image quality depends on the sensitivity of the setup, i.e. on the angular measurement range. Measurement ranges of existing phase contrast setups are either too high or too low for perfectly imaging a human finger in air: There is a gap in available measurement ranges, which prevents a reduction of X-ray dose. To fill the gap, this work proposes a novel variant of a Talbot-Lau interferometer. Instead of a single phase grating, it uses two phase gratings, each consisting of tiny prisms. The height of the prisms is an additional factor in the measurement range, which allows to fill the gap. The potential is a dose-reduction by a factor of 5.4 compared to Talbot-Lau setups of same post-patient length. Simulation results indicate a polychromatic visibility of up to 20%.

Revising the lower statistical limit of x-ray grating-based phase-contrast computed tomography

Phase-contrast x-ray computed tomography (PCCT) is currently investigated as an interesting extension of conventional CT, providing high soft-tissue contrast even if examining weakly absorbing specimen. Until now, the potential for dose reduction was thought to be limited compared to attenuation CT, since meaningful phase retrieval fails for scans with very low photon counts when using the conventional phase retrieval method via phase stepping. In this work, we examine the statistical behaviour of the reverse projection method, an alternative phase retrieval approach and compare the results to the conventional phase retrieval technique. We investigate the noise levels in the projections as well as the image quality and quantitative accuracy of the reconstructed tomographic volumes. The results of our study show that this method performs better in a low-dose scenario than the conventional phase retrieval approach, resulting in lower noise levels, enhanced image quality and more accurate quantitative values. Overall, we demonstrate that the lower statistical limit of the phase stepping procedure as proposed by recent literature does not apply to this alternative phase retrieval technique. However, further development is necessary to overcome experimental challenges posed by this method which would enable mainstream or even clinical application of PCCT.

Optimization of grating duty cycle in non-interferometric grating-based X-ray phase contrast imaging

Grating-based X-ray phase contrast imaging technology is one of the most potential imaging methods in real applications. It can be classified into two categories: interferometry and non-interferometric imaging. The non-interferometric grating-based X-ray phase contrast imaging (NIGPCI) instrument has a great advantage in the forthcoming commercial applications for the flexible system design and the use of large periodic gratings. The performance of the NIGPCI instrument depends on its angular sensitivity to a great extent. Therefore, good angular sensitivity is mandatory in order to obtain high quality phase-contrast images. Several parameters, such as the X-ray spectrum, the inter-grating distances, and the parameters of the three gratings, influence the angular sensitivity of the imaging system. However, the quantitative relationship between the angular sensitivity and grating duty cycle is unclear. Therefore, this paper is devoted to revealing their internal relation by theoretical deduction and emulation of the imaging process with the theories of linear system and Fourier optics. Furthermore, a quantitative analysis method to optimize the duty cycles of gratings is proposed and its applicability to a general NIGPCI system is verified.

Studies of signal estimation bias in grating-based x-ray multicontrast imaging

PURPOSE

In grating-based x-ray multi-contrast imaging, signals of three contrast mechanisms-absorption contrast, differential phase contrast (DPC), and dark-field contrast-can be estimated from the same set of acquired data. The estimated signals, N₀ (related to absorption), N₁ (related to dark-field), and φ (related to DPC) may be intrinsically biased. However, it is yet unclear how large these biases are and how the data acquisition parameters affect the biases in the extracted signals. The purpose of this paper was to address these questions.

METHODS

The biases of the extracted signals (i.e., N₀ , N₁ and φ) were theoretically studied for a well-known signal estimation method. Experimental data acquired from a grating-based x-ray multi-contrast benchtop imaging system with a photon counting detector were used to validate the theoretical results for the signal biases of the three contrast mechanisms.

RESULTS

Both theoretical and experimental studies showed the following results: (1) The bias of signal estimation for the absorption contrast signal is zero; (2) The bias of signal estimation for N₁ is inversely proportional to the number of phase steps and to the average fringe visibility of the grating interferometer, but the ratio between the bias and the signal level (i.e., the relative bias) is independent of the number of phase steps; (3) The bias of signal estimation for φ depends on the mean DPC signal level, the total exposure level of the multi-contrast data acquisition, and the mean fringe visibility of the interferometer.

CONCLUSIONS

In grating-based x-ray multi-contrast imaging, the estimated absorption contrast signal is unbiased; the estimated dark-field contrast signal is biased, but the relative bias is only dependent on the mean fringe visibility of the interferometer and the exposure level. The estimated DPC signal may be biased, and the bias level depends on the mean signal level, the exposure level, and the interferometer performance.

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.

Large field-of-view tiled grating structures for X-ray phase-contrast imaging

X-ray grating-based interferometry promises unique new diagnostic possibilities in medical imaging and materials analysis. To transfer this method from scientific laboratories or small-animal applications to clinical radiography applications, compact setups with a large field of view (FoV) are required. Currently the FoV is limited by the grating area, which is restricted due to the complex manufacturing process. One possibility to increase the FoV is tiling individual grating tiles to create one large area grating mounted on a carrier substrate. We investigate theoretically the accuracy needed for a tiling process in all degrees of freedom by applying a simulation approach. We show how the resulting precision requirements can be met using a custom-built frame for exact positioning. Precise alignment is achieved by comparing the fringe patterns of two neighboring grating tiles in a grating interferometer. With this method, the FoV can be extended to practically any desired length in one dimension. First results of a phase-contrast scanning setup with a full FoV of 384 mm × 24 mm show the suitability of this method.

Lens gratings for dose optimization of medical X-ray phase contrast imaging

A novel way to build arrays of X-ray lenslets is proposed for use in medical imaging, in particular for X-ray phase contrast imaging. Focusing on Talbot-Lau interferometers, this work is about patient dose reduction, especially for design energies above 50 keV. A low dose poses a fabrication problem, because it requires an analyzer grating which is both fine and high: It has to be fine for a good angular sensitivity. It has to be high to absorb well. However, gratings can currently be built either fine or high. The proposed solution is to use a fine novel lens grating in front of a high analyzer grating: The lens grating uses lenslets to combine fine fringes into wider strips. This coarser pattern is then analyzed by a high grating. Regular binary production processes are sufficient to build lens gratings. Simulation-based results show that lens gratings can save dose with no impact on reconstructed images.

Improving radiation dose efficiency of X-ray differential phase contrast imaging using an energy-resolving grating interferometer and a novel rank constraint

In this paper, a novel method was developed to improve the radiation dose efficiency, viz., contrast to noise ratio normalized by dose (CNRD), of the grating-based X-ray differential phase contrast (DPC) imaging system that is integrated with an energy-resolving photon counting detector. The method exploits the low-dimensionality of the spatial-spectral DPC image matrix acquired from different energy windows. A low rank approximation of the spatial-spectral image matrix was developed to reduce image noise while retaining the DPC signal accuracy for every energy window. Numerical simulations and experimental phantom studies have been performed to validate the proposed method by showing noise reduction and CNRD improvement for each energy window.

Report of improved performance in Talbot-Lau phase-contrast computed tomography

PURPOSE

Many expectations have been raised since the use of conventional x-ray tubes on grating-based x-ray phase-contrast imaging. Despite a reported increase in contrast-to-noise ratio (CNR) in many publications, there is doubt on whether phase-contrast computed tomography (CT) is advantageous in clinical CT scanners in vivo. The aim of this paper is to contribute to this discussion by analyzing the performance of a phase-contrast CT laboratory setup.

METHODS

A phase-contrast CT performance analysis was done. Projection images of a phantom were recorded, and image slices were reconstructed using standard filtered back projection methods. The resulting image slices were analyzed by determining the CNRs in the attenuation and phase image. These results were compared to analytically calculated expectations according to the already published phase-contrast CT performance analysis by Raupach and Flohr [Med. Phys. 39, 4761-4774 (2012)]. There, a severe mistake was found leading to wrong predictions of the performance of phase-contrast CT. The error was corrected and with the new formulae, the experimentally obtained results matched the analytical calculations.

RESULTS

The squared ratios of the phase-contrast CNR and the attenuation CNR obtained in the authors' experiment are five- to ten-fold higher than predicted by Raupach and Flohr [Med. Phys. 39, 4761-4774 (2012)]. The effective lateral spatial coherence length deduced outnumbers the already optimistic assumption of Raupach and Flohr [Med. Phys. 39, 4761-4774 (2012)] by a factor of 3.

CONCLUSIONS

The authors' results indicate that the assumptions made in former performance analyses are pessimistic. The break-even point, when phase-contrast CT outperforms attenuation CT, is within reach even with realistic, nonperfect gratings. Further improvements to state-of-the-art clinical CT scanners, like increasing the spatial resolution, could change the balance in favor of phase-contrast computed tomography even more. This could be done by, e.g., quantum-counting pixel detectors with four-fold smaller pixel pitches.

Experimental Realisation of High-sensitivity Laboratory X-ray Grating-based Phase-contrast Computed Tomography

The possibility to perform high-sensitivity X-ray phase-contrast imaging with laboratory grating-based phase-contrast computed tomography (gbPC-CT) setups is of great interest for a broad range of high-resolution biomedical applications. However, achieving high sensitivity with laboratory gbPC-CT setups still poses a challenge because several factors such as the reduced flux, the polychromaticity of the spectrum, and the limited coherence of the X-ray source reduce the performance of laboratory gbPC-CT in comparison to gbPC-CT at synchrotron facilities. In this work, we present our laboratory X-ray Talbot-Lau interferometry setup operating at 40 kVp and describe how we achieve the high sensitivity yet unrivalled by any other laboratory X-ray phase-contrast technique. We provide the angular sensitivity expressed via the minimum resolvable refraction angle both in theory and experiment, and compare our data with other differential phase-contrast setups. Furthermore, we show that the good stability of our high-sensitivity setup allows for tomographic scans, by which even the electron density can be retrieved quantitatively as has been demonstrated in several preclinical studies.

Contrast-to-noise ratio optimization for a prototype phase-contrast computed tomography scanner

In the field of biomedical X-ray imaging, novel techniques, such as phase-contrast and dark-field imaging, have the potential to enhance the contrast and provide complementary structural information about a specimen. In this paper, a first prototype of a preclinical X-ray phase-contrast CT scanner based on a Talbot-Lau interferometer is characterized. We present a study of the contrast-to-noise ratios for attenuation and phase-contrast images acquired with the prototype scanner. The shown results are based on a series of projection images and tomographic data sets of a plastic phantom in phase and attenuation-contrast recorded with varying acquisition settings. Subsequently, the signal and noise distribution of different regions in the phantom were determined. We present a novel method for estimation of contrast-to-noise ratios for projection images based on the cylindrical geometry of the phantom. Analytical functions, representing the expected signal in phase and attenuation-contrast for a circular object, are fitted to individual line profiles of the projection data. The free parameter of the fit function is used to estimate the contrast and the goodness of the fit is determined to assess the noise in the respective signal. The results depict the dependence of the contrast-to-noise ratios on the applied source voltages, the number of steps of the phase stepping routine, and the exposure times for an individual step. Moreover, the influence of the number of projection angles on the image quality of CT slices is investigated. Finally, the implications for future imaging purposes with the scanner are discussed.

Statistical iterative reconstruction algorithm for X-ray phase-contrast CT

Grating-based phase-contrast computed tomography (PCCT) is a promising imaging tool on the horizon for pre-clinical and clinical applications. Until now PCCT has been plagued by strong artifacts when dense materials like bones are present. In this paper, we present a new statistical iterative reconstruction algorithm which overcomes this limitation. It makes use of the fact that an X-ray interferometer provides a conventional absorption as well as a dark-field signal in addition to the phase-contrast signal. The method is based on a statistical iterative reconstruction algorithm utilizing maximum-a-posteriori principles and integrating the statistical properties of the raw data as well as information of dense objects gained from the absorption signal. Reconstruction of a pre-clinical mouse scan illustrates that artifacts caused by bones are significantly reduced and image quality is improved when employing our approach. Especially small structures, which are usually lost because of streaks, are recovered in our results. In comparison with the current state-of-the-art algorithms our approach provides significantly improved image quality with respect to quantitative and qualitative results. In summary, we expect that our new statistical iterative reconstruction method to increase the general usability of PCCT imaging for medical diagnosis apart from applications focused solely on soft tissue visualization.

High sensitivity phase retrieval method in grating-based x-ray phase contrast imaging

PURPOSE

Grating-based x-ray phase contrast imaging is considered as one of the most promising techniques for future medical imaging. Many different methods have been developed to retrieve phase signal, among which the phase stepping (PS) method is widely used. However, further practical implementations are hindered, due to its complex scanning mode and high radiation dose. In contrast, the reverse projection (RP) method is a novel fast and low dose extraction approach. In this contribution, the authors present a quantitative analysis of the noise properties of the refraction signals retrieved by the two methods and compare their sensitivities.

METHODS

Using the error propagation formula, the authors analyze theoretically the signal-to-noise ratios (SNRs) of the refraction images retrieved by the two methods. Then, the sensitivities of the two extraction methods are compared under an identical exposure dose. Numerical experiments are performed to validate the theoretical results and provide some quantitative insight.

RESULTS

The SNRs of the two methods are both dependent on the system parameters, but in different ways. Comparison between their sensitivities reveals that for the refraction signal, the RP method possesses a higher sensitivity, especially in the case of high visibility and/or at the edge of the object.

CONCLUSIONS

Compared with the PS method, the RP method has a superior sensitivity and provides refraction images with a higher SNR. Therefore, one can obtain highly sensitive refraction images in grating-based phase contrast imaging. This is very important for future preclinical and clinical implementations.

Quantitative imaging using high-energy X-ray phase-contrast CT with a 70 kVp polychromatic X-ray spectrum

Imaging of large and dense objects with grating-based X-ray phase-contrast computed tomography requires high X-ray photon energy and large fields of view. It has become increasingly possible due to the improvements in the grating manufacturing processes. Using a high-energy X-ray phase-contrast CT setup with a large (10 cm in diameter) analyzer grating and operated at an acceleration tube voltage of 70 kVp, we investigate the complementarity of both attenuation and phase contrast modalities with materials of various atomic numbers (Z). We confirm experimentally that for low-Z materials, phase contrast yields no additional information content over attenuation images, yet it provides increased contrast-to-noise ratios (CNRs). The complementarity of both signals can be seen again with increasing Z of the materials and a more comprehensive material characterization is thus possible. Imaging of a part of a human cervical spine with intervertebral discs surrounded by bones and various soft tissue types showcases the benefit of high-energy X-ray phase-contrast system. Phase-contrast reconstruction reveals the internal structure of the discs and makes the boundary between the disc annulus and nucleus pulposus visible. Despite the fact that it still remains challenging to develop a high-energy grating interferometer with a broad polychromatic source with satisfactory optical performance, improved image quality for phase contrast as compared to attenuation contrast can be obtained and new exciting applications foreseen.

Regularized iterative integration combined with non-linear diffusion filtering for phase-contrast x-ray computed tomography

Phase-contrast x-ray computed tomography has a high potential to become clinically implemented because of its complementarity to conventional absorption-contrast.In this study, we investigate noise-reducing but resolution-preserving analytical reconstruction methods to improve differential phase-contrast imaging. We apply the non-linear Perona-Malik filter on phase-contrast data prior or post filtered backprojected reconstruction. Secondly, the Hilbert kernel is replaced by regularized iterative integration followed by ramp filtered backprojection as used for absorption-contrast imaging. Combining the Perona-Malik filter with this integration algorithm allows to successfully reveal relevant sample features, quantitatively confirmed by significantly increased structural similarity indices and contrast-to-noise ratios. With this concept, phase-contrast imaging can be performed at considerably lower dose.

Correlation between human observer performance and model observer performance in differential phase contrast CT

PURPOSE

With the recently expanding interest and developments in x-ray differential phase contrast CT (DPC-CT), the evaluation of its task-specific detection performance and comparison with the corresponding absorption CT under a given radiation dose constraint become increasingly important. Mathematical model observers are often used to quantify the performance of imaging systems, but their correlations with actual human observers need to be confirmed for each new imaging method. This work is an investigation of the effects of stochastic DPC-CT noise on the correlation of detection performance between model and human observers with signal-known-exactly (SKE) detection tasks.

METHODS

The detectabilities of different objects (five disks with different diameters and two breast lesion masses) embedded in an experimental DPC-CT noise background were assessed using both model and human observers. The detectability of the disk and lesion signals was then measured using five types of model observers including the prewhitening ideal observer, the nonprewhitening (NPW) observer, the nonprewhitening observer with eye filter and internal noise (NPWEi), the prewhitening observer with eye filter and internal noise (PWEi), and the channelized Hotelling observer (CHO). The same objects were also evaluated by four human observers using the two-alternative forced choice method. The results from the model observer experiment were quantitatively compared to the human observer results to assess the correlation between the two techniques.

RESULTS

The contrast-to-detail (CD) curve generated by the human observers for the disk-detection experiments shows that the required contrast to detect a disk is inversely proportional to the square root of the disk size. Based on the CD curves, the ideal and NPW observers tend to systematically overestimate the performance of the human observers. The NPWEi and PWEi observers did not predict human performance well either, as the slopes of their CD curves tended to be steeper. The CHO generated the best quantitative agreement with human observers with its CD curve overlapping with that of human observer. Statistical equivalence between CHO and humans can be claimed within 11% of the human observer results, including both the disk and lesion detection experiments.

CONCLUSIONS

The model observer method can be used to accurately represent human observer performance with the stochastic DPC-CT noise for SKE tasks with sizes ranging from 8 to 128 pixels. The incorporation of the anatomical noise remains to be studied.

X-ray phase-contrast imaging at 100 keV on a conventional source

X-ray grating interferometry is a promising imaging technique sensitive to attenuation, refraction and scattering of the radiation. Applications of this technique in the energy range between 80 and 150 keV pose severe technical challenges, and are still mostly unexplored. Phase-contrast X-ray imaging at such high energies is of relevant scientific and industrial interest, in particular for the investigation of strongly absorbing or thick materials as well as for medical imaging. Here we show the successful implementation of a Talbot-Lau interferometer operated at 100 keV using a conventional X-ray tube and a compact geometry, with a total length of 54 cm. We present the edge-on illumination of the gratings in order to overcome the current fabrication limits. Finally, the curved structures match the beam divergence and allow a large field of view on a short and efficient setup.

Performance and optimization of X-ray grating interferometry

The monochromatic and polychromatic performance of a grating interferometer is theoretically analysed. The smallest detectable refraction angle is used as a metric for the efficiency in acquiring a differential phase-contrast image. Analytical formulae for the visibility and the smallest detectable refraction angle are derived for Talbot-type and Talbot-Lau-type interferometers, respectively, providing a framework for the optimization of the geometry. The polychromatic performance of a grating interferometer is investigated analytically by calculating the energy-dependent interference fringe visibility, the spectral acceptance and the polychromatic interference fringe visibility. The optimization of grating interferometry is a crucial step for the design of application-specific systems with maximum performance.

High energy x-ray phase contrast CT using glancing-angle grating interferometers

PURPOSE

The authors present initial progress toward a clinically compatible x-ray phase contrast CT system, using glancing-angle x-ray grating interferometry to provide high contrast soft tissue images at estimated by computer simulation dose levels comparable to conventional absorption based CT.

METHODS

DPC-CT scans of a joint phantom and of soft tissues were performed in order to answer several important questions from a clinical setup point of view. A comparison between high and low fringe visibility systems is presented. The standard phase stepping method was compared with sliding window interlaced scanning. Using estimated dose values obtained with a Monte-Carlo code the authors studied the dependence of the phase image contrast on exposure time and dose.

RESULTS

Using a glancing angle interferometer at high x-ray energy (∼ 45 keV mean value) in combination with a conventional x-ray tube the authors achieved fringe visibility values of nearly 50%, never reported before. High fringe visibility is shown to be an indispensable parameter for a potential clinical scanner. Sliding window interlaced scanning proved to have higher SNRs and CNRs in a region of interest and to also be a crucial part of a low dose CT system. DPC-CT images of a soft tissue phantom at exposures in the range typical for absorption based CT of musculoskeletal extremities were obtained. Assuming a human knee as the CT target, good soft tissue phase contrast could be obtained at an estimated absorbed dose level around 8 mGy, similar to conventional CT.

CONCLUSIONS

DPC-CT with glancing-angle interferometers provides improved soft tissue contrast over absorption CT even at clinically compatible dose levels (estimated by a Monte-Carlo computer simulation). Further steps in image processing, data reconstruction, and spectral matching could make the technique fully clinically compatible. Nevertheless, due to its increased scan time and complexity the technique should be thought of not as replacing, but as complimentary to conventional CT, to be used in specific applications.

Comparison of two x-ray phase-contrast imaging methods with a microfocus source

We present a comparison for high-resolution imaging with a laboratory source between grating-based (GBI) and propagation-based (PBI) x-ray phase-contrast imaging. The comparison is done through simulations and experiments using a liquid-metal-jet x-ray microfocus source. Radiation doses required for detection in projection images are simulated as a function of the diameter of a cylindrical sample. Using monochromatic radiation, simulations show a lower dose requirement for PBI for small object features and a lower dose for GBI for larger object features. Using polychromatic radiation, such as that from a laboratory microfocus source, experiments and simulations show a lower dose requirement for PBI for a large range of feature sizes. Tested on a biological sample, GBI shows higher noise levels than PBI, but its advantage of quantitative refractive index reconstruction for multi-material samples becomes apparent.

Grating-based x-ray phase-contrast imaging with a multi energy-channel photon-counting pixel detector

We have carried out grating-based x-ray differential phase-contrast measurements with a hybrid pixel detector in 16 energy channels simultaneously. A method for combining the energy resolved phase-contrast images based on energy weighting is presented. An improvement in contrast-to-noise ratio by 58.2% with respect to an emulated integrating detector could be observed in the final image. The same image quality could thus be achieved with this detector and with energy weighting at 60.0% reduced dose compared to an integrating detector. The benefit of the method depends on the object, spectrum, interferometer design and the detector efficiency.

Fundamental relationship between the noise properties of grating-based differential phase contrast CT and absorption CT: theoretical framework using a cascaded system model and experimental validation

PURPOSE

Using a grating interferometer, a conventional x-ray cone beam computed tomography (CT) data acquisition system can be used to simultaneously generate both conventional absorption CT (ACT) and differential phase contrast CT (DPC-CT) images from a single data acquisition. Since the two CT images were extracted from the same set of x-ray projections, it is expected that intrinsic relationships exist between the noise properties of the two contrast mechanisms. The purpose of this paper is to investigate these relationships.

METHODS

First, a theoretical framework was developed using a cascaded system model analysis to investigate the relationship between the noise power spectra (NPS) of DPC-CT and ACT. Based on the derived analytical expressions of the NPS, the relationship between the spatial-frequency-dependent noise equivalent quanta (NEQ) of DPC-CT and ACT was derived. From these fundamental relationships, the NPS and NEQ of the DPC-CT system can be derived from the corresponding ACT system or vice versa. To validate these theoretical relationships, a benchtop cone beam DPC-CT/ACT system was used to experimentally measure the modulation transfer function (MTF) and NPS of both DPC-CT and ACT. The measured three-dimensional (3D) MTF and NPS were then combined to generate the corresponding 3D NEQ.

RESULTS

Two fundamental relationships have been theoretically derived and experimentally validated for the NPS and NEQ of DPC-CT and ACT: (1) the 3D NPS of DPC-CT is quantitatively related to the corresponding 3D NPS of ACT by an inplane-only spatial-frequency-dependent factor 1∕f (2), the ratio of window functions applied to DPC-CT and ACT, and a numerical factor C(g) determined by the geometry and efficiency of the grating interferometer. Note that the frequency-dependent factor is independent of the frequency component f(z) perpendicular to the axial plane. (2) The 3D NEQ of DPC-CT is related to the corresponding 3D NEQ of ACT by an f (2) scaling factor and numerical factors that depend on both the attenuation and refraction properties of the image object, as well as C(g) and the MTF of the grating interferometer.

CONCLUSIONS

The performance of a DPC-CT system is intrinsically related to the corresponding ACT system. As long as the NPS and NEQ of an ACT system is known, the corresponding NPS and NEQ of the DPC-CT system can be readily estimated using additional characteristics of the grating interferometer.

Spatial resolution characterization of differential phase contrast CT systems via modulation transfer function (MTF) measurements

By adding a Talbot-Lau interferometer to a conventional x-ray absorption computed tomography (CT) imaging system, both differential phase contrast (DPC) signal and absorption contrast signal can be simultaneously measured from the same set of CT measurements. The imaging performance of such multi-contrast x-ray CT imaging systems can be characterized with standard metrics such as noise variance, noise power spectrum, contrast-to-noise ratio, modulation transfer function (MTF), and task-based detectability index. Among these metrics, the measurement of the MTF can be challenging in DPC-CT systems due to several confounding factors such as phase wrapping and the difficulty of using fine wires as probes. To address these technical challenges, this paper discusses a viable and reliable method to experimentally measure the MTF of DPC-CT. It has been found that the spatial resolution of DPC-CT is degraded, when compared to that of the corresponding absorption CT, due to the presence of a source grating G0 in the Talbot-Lau interferometer. An effective MTF was introduced and experimentally estimated to describe the impact of the Talbot-Lau interferometer on the system MTF.

X-ray phase-contrast imaging: from pre-clinical applications towards clinics

Phase-contrast x-ray imaging (PCI) is an innovative method that is sensitive to the refraction of the x-rays in matter. PCI is particularly adapted to visualize weakly absorbing details like those often encountered in biology and medicine. In past years, PCI has become one of the most used imaging methods in laboratory and preclinical studies: its unique characteristics allow high contrast 3D visualization of thick and complex samples even at high spatial resolution. Applications have covered a wide range of pathologies and organs, and are more and more often performed in vivo. Several techniques are now available to exploit and visualize the phase-contrast: propagation- and analyzer-based, crystal and grating interferometry and non-interferometric methods like the coded aperture. In this review, covering the last five years, we will give an overview of the main theoretical and experimental developments and of the important steps performed towards the clinical implementation of PCI.

Characterization of imaging performance in differential phase contrast CT compared with the conventional CT: spectrum of noise equivalent quanta NEQ(k)

PURPOSE

Differential phase contrast CT (DPC-CT) is emerging as a new technology to improve the contrast sensitivity of conventional attenuation-based CT. The noise equivalent quanta as a function over spatial frequency, i.e., the spectrum of noise equivalent quanta NEQ(k), is a decisive indicator of the signal and noise transfer properties of an imaging system. In this work, we derive the functional form of NEQ(k) in DPC-CT. Via system modeling, analysis, and computer simulation, we evaluate and verify the derived NEQ(k) and compare it with that of the conventional attenuation-based CT.

METHODS

The DPC-CT is implemented with x-ray tube and gratings. The x-ray propagation and data acquisition are modeled and simulated through Fresnel and Fourier analysis. A monochromatic x-ray source (30 keV) is assumed to exclude any system imperfection and interference caused by scatter and beam hardening, while a 360° full scan is carried out in data acquisition to avoid any weighting scheme that may disrupt noise randomness. Adequate upsampling is implemented to simulate the x-ray beam's propagation through the gratings G(1) and G(2) with periods 8 and 4 μm, respectively, while the intergrating distance is 193.6 mm (1∕16 of the Talbot distance). The dimensions of the detector cell for data acquisition are 32 × 32, 64 × 64, 96 × 96, and 128 × 128 μm(2), respectively, corresponding to a 40.96 × 40.96 mm(2) field of view in data acquisition. An air phantom is employed to obtain the noise power spectrum NPS(k), spectrum of noise equivalent quanta NEQ(k), and detective quantum efficiency DQE(k). A cylindrical water phantom at 5.1 mm diameter and complex refraction coefficient n = 1 - δ + iβ = 1 -2.5604 × 10(-7) + i1.2353 × 10(-10) is placed in air to measure the edge transfer function, line spread function and then modulation transfer function MTF(k), of both DPC-CT and the conventional attenuation-based CT. The x-ray flux is set at 5 × 10(6) photon∕cm(2) per projection and observes the Poisson distribution, which is consistent with that of a micro-CT for preclinical applications. Approximately 360 regions, each at 128 × 128 matrix, are used to calculate the NPS(k) via 2D Fourier transform, in which adequate zero padding is carried out to avoid aliasing in noise.

RESULTS

The preliminary data show that the DPC-CT possesses a signal transfer property [MTF(k)] comparable to that of the conventional attenuation-based CT. Meanwhile, though there exists a radical difference in their noise power spectrum NPS(k) (trait 1∕|k| in DPC-CT but |k| in the conventional attenuation-based CT) the NEQ(k) and DQE(k) of DPC-CT and the conventional attenuation-based CT are in principle identical.

CONCLUSIONS

Under the framework of ideal observer study, the joint signal and noise transfer property NEQ(k) and detective quantum efficiency DQE(k) of DPC-CT are essentially the same as those of the conventional attenuation-based CT. The findings reported in this paper may provide insightful guidelines on the research, development, and performance optimization of DPC-CT for extensive preclinical and clinical applications in the future.

Glancing angle Talbot-Lau grating interferometers for phase contrast imaging at high x-ray energy

A Talbot-Lau interferometer is demonstrated using micro-periodic gratings inclined at a glancing angle along the light propagation direction. Due to the increase in the effective thickness of the absorption gratings, the device enables differential phase contrast imaging at high x-ray energy, with improved fringe visibility (contrast). For instance, at 28° glancing angle, we obtain up to ∼35% overall interferometer contrast with a spectrum having ∼43 keV mean energy, suitable for medical applications. In addition, glancing angle interferometers could provide high contrast at energies above 100 keV, enabling industrial and security applications of phase contrast imaging.

Sensitivity of X-ray grating interferometry

It is known that the sensitivity of X-ray phase-contrast grating interferometry with regard to electron density variations present in the sample is related to the minimum detectable refraction angle. In this article a numerical framework is developed that allows for a realistic and quantitative determination of the sensitivity. The framework is validated by comparisons with experimental results and then used for the quantification of several influences on the sensitivity, such as spatial coherence or the number of phase step images. In particular, we identify the ideal inter-grating distance with respect to the highest sensitivity for parallel beam geometry. This knowledge will help to optimize existing synchrotron-based grating interferometry setups.