Hard-X-ray dark-field imaging using a grating interferometer

Dose and spatial resolution analysis of grating-based phase-contrast mammography using an inverse Compton x-ray source

Purpose: Although the mortality rate of breast cancer was reduced with the introduction of screening mammography, many women undergo unnecessary subsequent examinations due to inconclusive diagnoses. Superposition of anatomical structures especially within dense breasts in conjunction with the inherently low soft tissue contrast of absorption images compromises image quality. This can be overcome by phase-contrast imaging. Approach: We analyze the spatial resolution of grating-based multimodal mammography using a mammographic phantom and one freshly dissected mastectomy specimen at an inverse Compton x-ray source. Here, the focus was on estimating the spatial resolution with the sample in the beam path and discussing benefits and drawbacks of the method used and the estimation of the mean glandular dose. Finally, the possibility of improving the spatial resolution is investigated by comparing monochromatic grating-based mammography with the standard one. Results: The spatial resolution is constant or also higher for the image acquired with monochromatic radiation and the contrast-to-noise ratio (CNR) is higher in our approach while the dose can be reduced by up to 20%. Conclusions: In summary, phase-contrast imaging helps to improve tumor detection by advanced diagnostic image quality. We demonstrate a higher spatial resolution for one mastectomy specimen and increased CNR at an equal or lower dose for the monochromatic measurements.

Imaging evaluation of the cartilage in rheumatoid arthritis patients with an x-ray phase imaging apparatus based on Talbot-Lau interferometry

X-ray Talbot-Lau interferometry is one of the x-ray phase imaging methods that has high sensitivity in depicting soft tissues. Unlike earlier x-ray phase imaging methods that required particular types of x-ray sources, such as a synchrotron or a micro-focus x-ray tube, x-ray Talbot-Lau interferometry enables to perform clinical x-ray phase imaging using a conventional x-ray source with a relatively compact configuration. We developed an apparatus to depict cartilage in the metacarpophalangeal joints of the hands. In addition, we examined the apparatus performance by applying it to healthy volunteers and patients with rheumatoid arthritis (RA). Cartilage deformation, which is thought to be a precursor of destruction of the joints, was successfully depicted by the apparatus, suggesting a potential early diagnosis of RA.

Simplified retrieval method for Edge Illumination X-ray phase contrast imaging allowing multi-modal imaging with fewer input frames

We present data from an implementation of Edge Illumination (EI) that uses a detector aperture designed for increasing dynamic range, suitable for clinically relevant X-ray energies and demonstrated here using synchrotron radiation. By utilising a sufficiently large crosstalk between pixels, this implementation enables single-scan imaging for phase and absorption, and double-scan for phase, absorption and dark field imaging. The presence of the detector mask enables a direct comparison between conventional EI and beam tracking (BT), which we conduct through Monte Carlo and analytical modelling in the case of a single-scan being used for the retrieval of all three contrasts. In the present case, where the X-ray beam width is comparable to the pixel size, we provide an analysis on best-positioning of the beam on the detector for accurate signal retrieval. Further, we demonstrate an application of this method by distinguishing different concentrations of microbubbles via their dark field signals at high energy using an EI system.

Dual phase grating based X-ray differential phase contrast imaging with source grating: theory and validation

In this work, we developed a new theoretical framework using wave optics to explain the working mechanism of the grating based X-ray differential phase contrast imaging (XPCI) interferometer systems consist of more than one phase grating. Under the optical reversibility principle, the wave optics interpretation was simplified into the geometrical optics interpretation, in which the phase grating was treated as a thin lens. Moreover, it was derived that the period of an arrayed source, e.g., the period of a source grating, is always equal to the period of the diffraction fringe formed on the source plane. When a source grating is utilized, the theory indicated that it is better to keep the periods of the two phase gratings different to generate large period diffraction fringes. Experiments were performed to validate these theoretical findings.

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.

Intermittent CPAP limits hyperoxia-induced lung damage in a rabbit model of bronchopulmonary dysplasia

A significant proportion of preterm infants develop bronchopulmonary dysplasia (BPD) leading to poor lifelong respiratory health. Limited treatment options exist with continuous positive airway pressure (CPAP) ventilation being one of the few associated with diminished BPD. However, little is known about the effect of the distending pressure of CPAP on the developing lung exposed to hyperoxia. We aimed to identify the functional and structural effects of CPAP in a preterm hyperoxia rabbit model of BPD. Premature rabbit pups were randomized to normoxia, hyperoxia (≥95% O₂), or hyperoxia plus 4 h daily CPAP [fraction of inspired oxygen (Fi_O2) 0.95, 5 cmH₂O]. On day 7 postdelivery we performed invasive pressure-volume- and forced oscillation-based pulmonary function tests, before lung harvest for histological evaluation. Alveolar and vascular morphology, airway smooth muscle content, respiratory epithelium height, extracellular matrix components, and inflammatory cytokine expression were quantified. Hyperoxia-reared pups had restrictive lungs: alveolar walls were thickened, with the lung parenchymal tissue, collagen content, and airway smooth muscle content increased. In addition, peripheral pulmonary artery wall thickness was increased. CPAP increased alveolar recruitment and limited the structural effect of hyperoxia on the respiratory epithelium and pulmonary arteries. Additionally, CPAP improved lung function, mitigating hyperoxia-associated changes to respiratory system resistance, tissue damping, and tissue elastance. Hyperoxia disrupted functional and structural lung development. Daily intermittent CPAP limited hyperoxia-associated decreased lung function and attenuated structural changes to pulmonary arteries and respiratory epithelium while having no structural alveolar consequences. The mechanism by which CPAP has these beneficial effects needs further investigation.

Spectral Differential Phase Contrast X-Ray Radiography

We investigate the combination of two emerging X-ray imaging technologies, namely spectral imaging and differential phase contrast imaging. By acquiring spatially and temporally registered images with several different X-ray spectra, spectral imaging can exploit differences in the energy-dependent attenuation to generate material selective images. Differential phase contrast imaging uses an entirely different contrast generation mechanism: The phase shift that an X-ray wave exhibits when traversing an object. As both methods can determine the (projected) electron density, we propose a novel material decomposition algorithm that uses the spectral and the phase contrast information simultaneously. Numerical experiments show that the combination of these two imaging techniques benefits from the strengths of the individual methods while the weaknesses are mitigated: Quantitatively accurate basis material images are obtained and the noise level is strongly reduced, compared to conventional spectral X-ray imaging.

Fast diffraction-enhanced imaging using continuous sample rotation and analyzer crystal scanning

Diffraction-enhanced imaging (DEI) has high sensitivity and a wide dynamic range of density and thus can be used for fine imaging of biological and organic samples that include large differences in density. A fast DEI method composed of continuous fast sample rotations and slow analyzer crystal scanning was developed to shorten the measurement period. Fine sectional images of a biological sample were successfully obtained within a half measurement period of the conventional step-scanning method while keeping the same exposure time. In addition, a fine three-dimensional image of a rat tail was obtained with a 375 s measurement period.

Transmission, refraction and dark-field retrieval in hard X-ray grating interferometry

A three-image algorithm is proposed to retrieve the sample's transmission, refraction and dark-field information in hard X-ray grating interferometry. Analytical formulae of the three-image algorithm are theoretically derived and presented, and evaluated by proof-of-principle synchrotron radiation experiments. The results confirm the feasibility of the proposed algorithm. The novelty of the proposed algorithm is that it allows versatile and tunable multimodal X-ray imaging by substantially relaxing the existing limitations on the lateral grating position. Furthermore, this algorithm can also be adapted for samples with negligible refraction, reducing the number of required sample measurements to two. Furthermore, the noise properties of the retrieved images are investigated in terms of the standard deviations. Theoretical models are presented and verified by synchrotron radiation measurements. It is shown that the noise standard deviations exhibit strong dependence on the lateral grating position, especially in the case of refraction and dark-field images. Further noise reduction and dose reduction can thus be possible by optimizing the lateral grating position for a selected region of interest. Those results can serve as general guidelines to optimize the data acquisition scheme for specific applications and problems.

Preterm birth impairs postnatal lung development in the neonatal rabbit model

Background

Bronchopulmonary dysplasia continues to cause important respiratory morbidity throughout life, and new therapies are needed. The common denominator of all BPD cases is preterm birth, however most preclinical research in this area focusses on the effect of hyperoxia or mechanical ventilation. In this study we investigated if and how prematurity affects lung structure and function in neonatal rabbits.

Methods

Pups were delivered on either day 28 or day 31. For each gestational age a group of pups was harvested immediately after birth for lung morphometry and surfactant protein B and C quantification. All other pups were hand raised and harvested on day 4 for the term pups and day 7 for the preterm pups (same corrected age) for lung morphometry, lung function testing and qPCR. A subset of pups underwent microCT and dark field imaging on day 0, 2 and 4 for terms and on day 0, 3, 5 and 7 for preterms.

Results

Preterm pups assessed at birth depicted a more rudimentary lung structure (larger alveoli and thicker septations) and a lower expression of surfactant proteins in comparison to term pups. MicroCT and dark field imaging revealed delayed lung aeration in preterm pups, in comparison to term pups. Preterm birth led to smaller pups, with smaller lungs with a lower alveolar surface area on day 7/day 4. Furthermore, preterm birth affected lung function with increased tissue damping, tissue elastance and resistance and decreased dynamic compliance. Expression of vascular endothelial growth factor (VEGFA) was significantly decreased in preterm pups, however in the absence of structural vascular differences.

Conclusions

Preterm birth affects lung structure and function at birth, but also has persistent effects on the developing lung. This supports the use of a preterm animal model, such as the preterm rabbit, for preclinical research on BPD. Future research that focuses on the identification of pathways that are involved in in-utero lung development and disrupted by pre-term birth, could lead to novel therapeutic strategies for BPD.

Discrimination analysis of breast calcifications using x-ray dark-field radiography

BACKGROUND

X-ray dark-field radiography could enhance mammography by providing more information on imaged tissue and microcalcifications. The dark field signal is a measure of small angle scattering and can thus provide additional information on the imaged materials. This information can be useful for material distinction of calcifications and the diagnosis of breast cancer by classifying benign and malign association of these calcifications.

METHODS

For this study, institutional review board approval was obtained. We present the evaluation of images acquired with interferometric grating-based x-ray imaging of 323 microcalcifications (166 malign and 157 benign associated) in freshly dissected breast tissue and compare the results to the information extracted in follow-up pathological evaluation. The number of imaged calcifications is sufficiently higher than in similar previous studies. Fourteen calcification properties were extracted from the digital images and used as predictors in three different models common in discrimination analysis namely a simple threshold model, a naive Bayes model and a linear regression model, which classify the calcifications as associated with a benign or suspicious finding. Three of these fourteen predictors have been newly defined in this work and are independent from the tissue background surrounding the microcalcifications. Using these predictors no background correction is needed, as in previous works in this field. The new predictors are the length of the first and second principle component of the absorption and dark-field data, as well as the angle between the first principle component and the dark-field axis. We called these predictors data length, data width, and data orientation.

RESULTS

In fourfold cross-validation malignancy of the imaged tissue was predicted. Models that take only classical absorption predictors into account reached a sensitivity of 53.3% at a specificity of 81.1%. For a combination of predictors that also include dark field information, a sensitivity of 63.2% and specificity of 80.8% were obtained. The included dark field information consisted of the newly introduced parameters, data orientation and data width.

CONCLUSIONS

While remaining at a similar specificity, the sensitivity, with which a trained model was able to distinguish malign from benign associated calcifications, was increased by 10% on including dark-field information. This suggests grating-based x-ray imaging as a promising clinical imaging method in the field of mammography.

Single-shot, omni-directional x-ray scattering imaging with a laboratory source and single-photon localization

Omni-directional, ultra-small-angle x-ray scattering imaging provides a method to measure the orientation of micro-structures without having to resolve them. In this letter, we use single-photon localization with the Timepix3 chip to demonstrate, to the best of our knowledge, the first laboratory-based implementation of single-shot, omni-directional x-ray scattering imaging using the beam-tracking technique. The setup allows a fast and accurate retrieval of the scattering signal using a simple absorption mask. We suggest that our new approach may enable faster laboratory-based tensor tomography and could be used for energy-resolved x-ray scattering imaging.

Recent Progress in X-ray and Neutron Phase Imaging with Gratings

Under the JST-ERATO project in progress to develop X-ray and neutron phase-imaging methods together, recent achievements have been selected and reviewed after describing the merit and the principle of the phase imaging method. For X-ray phase imaging, recent developments of four-dimensional phase tomography and phase microscopy at SPring-8, Japan are mainly presented. For neutron phase imaging, an approach in combination with the time-of-flight method developed at J-PARC, Japan is described with the description of new Gd grating fabrication.

A high visibility Talbot-Lau neutron grating interferometer to investigate stress-induced magnetic degradation in electrical steel

Neutron grating interferometry (nGI) is a unique technique allowing to probe magnetic and nuclear properties of materials not accessible in standard neutron imaging. The signal-to-noise ratio of an nGI setup is strongly dependent on the achievable visibility. Hence, for analysis of weak signals or short measurement times a high visibility is desired. We developed a new Talbot-Lau interferometer using the third Talbot order with an unprecedented visibility (0.74) over a large field of view. Using the third Talbot order and the resulting decreased asymmetry allows to access a wide correlation length range. Moreover, we have used a novel technique for the production of the absorption gratings which provides nearly binary gratings even for thermal neutrons. The performance of the new interferometer is demonstrated by visualizing the local magnetic domain wall density in electrical steel sheets when influenced by residual stress induced by embossing. We demonstrate that it is possible to affect the density of the magnetic domain walls by embossing and therefore to engineer the guiding of magnetic fields in electrical steel sheets. The excellent performance of our new setup will also facilitate future studies of dynamic effects in electric steels and other systems.

Quantitative analysis of a micro array anode structured target for hard x-ray grating interferometry

Talbot-Lau interferometry (TLI) provides additional contrast modes for x-ray imaging that are complementary to conventional absorption radiography. TLI is particularly interesting because it is one of the few practical methods for realizing phase contrast with x-rays that is compatible with large-spot high power x-ray sources. A novel micro array anode structured target (MAAST) x-ray source offers several advantages for TLI over the conventional combination of an extended x-ray source coupled with an absorption grating including higher flux and larger field of view, and these advantages become more pronounced for x-ray energies in excess of 30 keV. A Monte Carlo simulation was performed to determine the optimal parameters for a MAAST source for use with TLI. It was found that the both spatial distribution of x-ray production and the number of x-ray produced in the MAAST have a strong dependence on the incidence angle of the electron beam.

Talbot-Lau interferometry-based x-ray imaging system with retractable and rotatable gratings for nondestructive testing

We develop an x-ray imaging system based on Talbot-Lau interferometry equipped with a mechanical structure for retracting and rotating gratings from the optical axis, which enables not only x-ray phase contrast imaging but also conventional x-ray imaging with high-magnification such as microcomputed tomography (μCT). We investigate the characterization of carbon fiber reinforced plastic (CFRP) laminates using this apparatus. Microcracks and fiber orientations are visualized in the dark-field images. Compared with the obtained μCT images, the relationship between the CFRP microstructures and the contrasts in the dark-field images are recognizable.

Picosecond-resolution phase-sensitive imaging of transparent objects in a single shot

With the growing interest in the optical imaging of ultrafast phenomena in transparent objects, from shock wave to neuronal action potentials, high contrast imaging at high frame rates has become desirable. While phase sensitivity provides the contrast, the frame rates and sequence depths are highly limited by the detectors. Here, we present phase-sensitive compressed ultrafast photography (pCUP) for single-shot real-time ultrafast imaging of transparent objects by combining the contrast of dark-field imaging with the speed and the sequence depth of CUP. By imaging the optical Kerr effect and shock wave propagation, we demonstrate that pCUP can image light-speed phase signals in a single shot with up to 350 frames captured at up to 1 trillion frames per second. We expect pCUP to be broadly used for a vast range of fundamental and applied sciences.

Advanced X-ray Imaging Technology

Since their discovery by Wilhelm Conrad Röntgen in 1895, X-rays have become the most widely available, typically fastest, and usually most cost-effective medical imaging modality today. From the early radiographic approaches using X-ray films as detectors, the portfolio of medical X-ray imaging devices developed into a large range of dedicated instrumentation for various applications. While X-ray imaging has come a long way, there are some physical properties of X-rays, which have not yet been fully exploited, and which may offer quite some room for further enhancements of current X-ray imaging equipment. Firstly, X-ray imaging today is mainly black and white, despite the fact that X-ray generators actually create a full spectrum of X-ray energies, and that the interactions of X-rays that occur within the human body are not the same for all energies and every material. Exploiting these spectral dependencies allows to not only obtain a black and white CT image, but also to obtain more molecularly specific information, which is relevant particularly in oncological precision radiology. The second aspect of X-rays, and so far in radiology mainly neglected and unused, is the physical fact that X-rays can also be interpreted in the wave picture, and not only as presently been done in the particle picture. If interpreted as waves, X-rays-just like visible light-experience a phase shift in matter, and this-if exploited correctly-can produce a new class of X-ray images, which then depict the wave interactions of X-rays with matter, rather than only the attenuating properties, as done until now.

Influence of diffuser grain size on the speckle tracking technique

The speckle-based X-ray imaging technique (SBT), which includes the three imaging modalities of absorption, phase contrast and dark field, is widely used in many fields. However, the influence of the grain size of the diffuser, the coherence of the X-ray source and the pixel size of the detector on the multi-mode imaging quality of SBT is still woefully unclear. In this paper, the whole SBT process is simulated and the influence of these three factors on image quality is discussed. Based on this discussion, the grain size of the diffuser for SBT applications should be limited by the pixel size of the detector and the coherence length of the X-ray source. According to analysis of the noise signal and correlation map, a suitable grain size is an indispensable condition for high-quality SBT images, because an excessively small or large grain size degrades the resolution of the imaging results and generates false signals. In addition, the power spectral density of the measured raw speckle patterns demonstrates that a smaller grain can better retain high-frequency information from an imaged sample. The simulated and experimental results verify these conclusions. The conclusions of this work will be helpful in designing suitable experimental setups for SBT applications and have the potential to promote the performance of SBT in other applications, such as X-ray optics metrology and coherence measurement.

The trigonometric orthogonality of phase-stepping curves in grating-based x-ray phase-contrast imaging: Integral property and its implications for noise optimization

PURPOSE

Grating-based x-ray phase-contrast imaging (GPCI) is a promising technique for clinical applications as it can provide two newly emerging imaging modalities (differential phase-contrast and dark-field contrast) in addition to the conventional absorption contrast. As far, phase-stepping strategy is the most commonly used approach in GPCI to indirectly acquire differential phase-contrast and dark-field contrast. It is known that the obtained phase-stepping curves (PSCs) have the cosine property and the convolution property, leading to two types of information retrieval approaches in literature: the Fourier component analysis and the multi-order moment analysis. The purpose of this paper is to derive a new property of PSCs and apply the property to noise optimization for information retrieval.

METHODS

Based on the cosine expression of the flat PSC without the sample and the well-established convolution relationship between the flat PSC and the sample PSC, we reveal an important integral property of PSCs: the inner product of PSCs and an arbitrary function contains only zero-order and first-order components in the Fourier series. Furthermore, we apply the property to the direct multi-order moment analysis and propose a set of generalized forms including an optimal one in the presence of noise.

RESULTS

To validate the effectiveness of our analysis, we compared the simulated and real experiment results retrieved by the original direct multi-order moment analysis with the ones retrieved by our proposed noise-optimal form. A significant improvement of noise performance by our method is observed and the improvement ratio in differential phase-contrast is consistent with our theoretical calculation (39.2%).

CONCLUSIONS

In this paper, we reveal a new integral property of the acquired PSCs with and without samples in GPCI, which can be applied to information retrieval approaches like the direct multi-order moment analysis. Then we optimize these approaches to improve the noise performance, offering great potentials of dose reduction in practical applications.

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.

High-contrast anisotropic edge enhancement free of shadow effect

We propose a Bessel-like composite vortex filter to perform high-contrast and power-controlled anisotropic edge enhancement with shadow-effect-free and low background noise. The background noise, which is commonly found and strongly decreases the filtered image quality in previous anisotropic vortex filters, is effectively reduced by suppressing the side lobes of the system point spread function, thereby increasing the image edge contrast to 0.98. The shadow effect is totally eliminated by keeping the radial symmetry of the filtering process, which makes edges sharper and improves image resolution. By introducing a weighting factor between two opposite vortex filter components, the power of edge enhancement becomes controllable. Numerical simulations and experimental results prove that the proposed filter achieves higher-contrast edge enhancement for both phase-contrast and amplitude-contrast objects.

X-ray Fokker-Planck equation for paraxial imaging

The Fokker-Planck equation can be used in a partially-coherent imaging context to model the evolution of the intensity of a paraxial x-ray wave field with propagation. This forms a natural generalisation of the transport-of-intensity equation. The x-ray Fokker-Planck equation can simultaneously account for both propagation-based phase contrast, and the diffusive effects of sample-induced small-angle x-ray scattering, when forming an x-ray image of a thin sample. Two derivations are given for the Fokker-Planck equation associated with x-ray imaging, together with a Kramers-Moyal generalisation thereof. Both equations are underpinned by the concept of unresolved speckle due to unresolved sample micro-structure. These equations may be applied to the forward problem of modelling image formation in the presence of both coherent and diffusive energy transport. They may also be used to formulate associated inverse problems of retrieving the phase shifts due to a sample placed in an x-ray beam, together with the diffusive properties of the sample. The domain of applicability for the Fokker-Planck and Kramers-Moyal equations for paraxial imaging is at least as broad as that of the transport-of-intensity equation which they generalise, hence the technique is also expected to be useful for paraxial imaging using visible light, electrons and neutrons.

Applying the Fokker-Planck equation to grating-based x-ray phase and dark-field imaging

X-ray imaging has conventionally relied upon attenuation to provide contrast. In recent years, two complementary modalities have been added; (a) phase contrast, which can capture low-density samples that are difficult to see using attenuation, and (b) dark-field x-ray imaging, which reveals the presence of sub-pixel sample structures. These three modalities can be accessed using a crystal analyser, a grating interferometer or by looking at a directly-resolved grid, grating or speckle pattern. Grating and grid-based methods extract a differential phase signal by measuring how far a feature in the illumination has been shifted transversely due to the presence of a sample. The dark-field signal is extracted by measuring how the visibility of the structured illumination is decreased, typically due to the presence of sub-pixel structures in a sample. The strength of the dark-field signal may depend on the grating period, the pixel size and the set-up distances, and additional dark-field signal contributions may be seen as a result of strong phase effects or other factors. In this paper we show that the finite-difference form of the Fokker-Planck equation can be applied to describe the drift (phase signal) and diffusion (dark-field signal) of the periodic or structured illumination used in phase contrast x-ray imaging with gratings, in order to better understand any cross-talk between attenuation, phase and dark-field x-ray signals. In future work, this mathematical description could be used as a basis for new approaches to the inverse problem of recovering both phase and dark-field information.

Diffractive small angle X-ray scattering imaging for anisotropic structures

Insights into the micro- and nano-architecture of materials is crucial for understanding and predicting their macroscopic behaviour. In particular, for emerging applications such as meta-materials, the micrometer scale becomes highly relevant. The micro-architecture of such materials can be tailored to exhibit specific mechanical, optical or electromagnetic behaviours. Consequently, quality control at micrometer scale must be guaranteed over extended areas. Mesoscale investigations over millimetre sized areas can be performed by scanning small angle X-ray scattering methods (SAXS). However, due to their long measurement times, real time or operando investigations are hindered. Here we present a method based on X-ray diffractive optics that enables the acquisition of SAXS signals in a single shot (few milliseconds) over extended areas. This method is applicable to a wide range of X-ray sources with varying levels of spatial coherence and monochromaticity, as demonstrated from the experimental results. This enables a scalable solution of spatially resolved SAXS.

Mesoscale investigations of material microarchitecture using small angle X-ray scattering (SAXS) methods have been limited by long measurement times. Here, the authors present an X-ray diffractive optics method which enables single shot acquisition of SAXS signals over large areas.

Limited-View X-Ray Tomography Combining Attenuation and Compton Scatter Data: Approach and Experimental Results

X-ray inspection systems are critical in medical, non-destructive testing, and security applications, with systems typically measuring attenuation along straight-line paths connecting sources and detectors. Computed tomography (CT) systems can provide higher-quality images than single- or dual-view systems, but the need to measure many projections leads to greater system cost and complexity. Typically, off-angle Compton scattered photons are treated as noise during tomographic inversion. We seek to maximize the image quality of limited-view systems by combining attenuation data with measurements of Compton-scattered photons, exploiting the fact that the broken-ray paths followed by scattered photons provide additional geometric sampling of the scene. We describe a single-scatter forward model for Compton-scatter data measured with energy-resolving detectors, and demonstrate a reconstruction algorithm for density that combines both attenuation and scatter measurements. The experimental results suggest that including Compton-scattered data in the reconstruction process can improve image quality for density reconstruction using limited-view systems.

Probing Surface Morphology using X-ray Grating Interferometry

X-ray reflectometry (XRR), a surface-sensitive technique widely used for characterizing surfaces, buried interfaces, thin films, and multilayers, enables determination of the electron density distribution perpendicular to a well-defined surface specularly reflecting X-rays. However, the electron density distribution parallel to the surface cannot be determined from an X-ray reflectivity curve. The electron density correlation in the lateral direction is usually probed by measuring the grazing-incidence small-angle X-ray scattering (GISAXS). GISAXS measurement, however, typically requires using a collimated X-ray point beam to distinguish the GISAXS from the specularly reflected X-rays, and so the sample must be scanned in the lateral direction with the point beam to investigate variations in the surface and interface morphology for a region larger than the size of the beam. In this paper, we report a new approach based on X-ray grating interferometry: an X-ray sheet beam is used instead of an X-ray point beam. A method using this approach can simultaneously provide one-dimensional real-space images of X-ray reflectivity, surface curvature, and ‘dark-field’ contrast with a field-of-view of more than a few millimetres. As a demonstration, a sample having a 400 nm line and space SiO₂ pattern with a depth of 10 nm on its surface was used, and the dark-field contrast due to the unresolved line and space structure, creating GISAXS in the lateral direction, was successfully observed. Quantitative analysis of these contrasts provided the real-space distribution of the structural parameters for a simple model of the grating structure. Our study paves the way to a new approach to structure analysis, providing a quantitative way to investigate real-space variations in surface and interface morphology through wavefront analysis.

Quantitative Phase and Intensity Microscopy Using Snapshot White Light Wavefront Sensing

Phase imaging techniques are an invaluable tool in microscopy for quickly examining thin transparent specimens. Existing methods are limited to either simple and inexpensive methods that produce only qualitative phase information (e.g. phase contrast microscopy, DIC), or significantly more elaborate and expensive quantitative methods. Here we demonstrate a low-cost, easy to implement microscopy setup for quantitative imaging of phase and bright field amplitude using collimated white light illumination.

Super-resolution x-ray phase-contrast and dark-field imaging with a single 2D grating and electromagnetic source stepping

Here we report a method for increased resolution of single exposure three modality x-ray images using super-resolution. The three x-ray image modalities are absorption-, differential phase-contrast-, and dark-field-images. To create super-resolution, a non-mechanically movable micro-focus x-ray source is used. A series of almost identical x-ray projection images is obtained while the point source is translated in a two-dimensional grid pattern. The three image modalities are extracted from fourier space using spatial harmonic analysis, also known as the single-shot method. Using super-resolution on the low-resolution series of the three modalities separately results in high-resolution images for the modalities. This approach allows to compensate for the inherent loss in resolution caused by the single-shot method without increasing the need for stability or algorithms accounting for possible motion.

Design optimization of a periodic microstructured array anode for hard x-ray grating interferometry

Talbot-Lau grating interferometer (TLGI) has great advantages in x-ray imaging contrasts, especially for low-Z materials, over conventional absorption contrast. A microstructured array anode target (MAAT) source offers significantly higher imaging throughput than the combination of an extended x-ray source paired with an absorption grating (also known as source grating). The performance of the MAAT source can be optimized with respect to the areal density, dimensions, and choice of material for the microstructured metal inserts (MMI) and the substrate in which they are embedded. In this paper, we analyze the x-ray generation efficiency per incident electron, relative fraction of x-rays generated by MMI and substrate, x-ray spectrum, and angular distribution via Monte Carlo simulation. Based on the simulation results, the optimal parameters are obtained for a MAAT with incident electron energies from 30 keV to 120 keV. The corresponding temperature distribution within the MAAT is also simulated for the optimal set of the parameters via finite element analysis. As demonstrated by the thermal analysis data, the maximum allowable electron-beam power loading was derived that allows a stable operation of the transmission MAAT.

Imaging features in post-mortem x-ray dark-field chest radiographs and correlation with conventional x-ray and CT

Background

Although x-ray dark-field imaging has been intensively investigated for lung imaging in different animal models, there is very limited data about imaging features in the human lungs. Therefore, in this work, a reader study on nine post-mortem human chest x-ray dark-field radiographs was performed to evaluate dark-field signal strength in the lungs, intraobserver and interobserver agreement, and image quality and to correlate with findings of conventional x-ray and CT.

Methods

In this prospective work, chest x-ray dark-field radiography with a tube voltage of 70 kVp was performed post-mortem on nine humans (3 females, 6 males, age range 52–88 years). Visual quantification of dark-field and transmission signals in the lungs was performed by three radiologists. Results were compared to findings on conventional x-rays and 256-slice computed tomography. Image quality was evaluated. For ordinal data, median, range, and dot plots with medians and 95% confidence intervals are presented; intraobserver and interobserver agreement were determined using weighted Cohen κ.

Results

Dark-field signal grading showed significant differences between upper and middle (p = 0.004–0.016, readers 1–3) as well as upper and lower zones (p = 0.004–0.016, readers 1–2). Median transmission grading was indifferent between all lung regions. Intraobserver and interobserver agreements were substantial to almost perfect for grading of both dark-field (κ = 0.793–0.971 and κ = 0.828–0.893) and transmission images (κ = 0.790–0.918 and κ = 0.700–0.772). Pulmonary infiltrates correlated with areas of reduced dark-field signal. Image quality was rated good for dark-field images.

Conclusions

Chest x-ray dark-field images provide information of the lungs complementary to conventional x-ray and allow reliable visual quantification of dark-field signal strength.

Electronic supplementary material

The online version of this article (10.1186/s41747-019-0104-7) contains supplementary material, which is available to authorized users.

A 3-D Projection Model for X-ray Dark-field Imaging

The X-ray dark-field signal can be measured with a grating-based Talbot-Lau interferometer. It measures small angle scattering of micrometer-sized oriented structures. Interestingly, the signal is a function not only of the material, but also of the relative orientation of the sample, the X-ray beam direction, and the direction of the interferometer sensitivity. This property is very interesting for potential tomographically reconstructing structures below the imaging resolution. However, tomographic reconstruction itself is a substantial challenge. A key step of the reconstruction algorithm is the inversion of a forward projection model. In this work, we propose a very general 3-D projection model. We derive the projection model under the assumption that the observed scatter distribution has a Gaussian shape. We theoretically show the consistency of our model with existing, more constrained 2-D models. Furthermore, we experimentally show the compatibility of our model with simulations and real dark-field measurements. We believe that this 3-D projection model is an important step towards more flexible trajectories and, by extension, dark-field imaging protocols that are much better applicable in practice.

Optimization of tube voltage in X-ray dark-field chest radiography

Grating-based X-ray dark-field imaging is a novel imaging modality which has been refined during the last decade. It exploits the wave-like behaviour of X-radiation and can nowadays be implemented with existing X-ray tubes used in clinical applications. The method is based on the detection of small-angle X-ray scattering, which occurs e.g. at air-tissue-interfaces in the lung or bone-fat interfaces in spongy bone. In contrast to attenuation-based chest X-ray imaging, the optimal tube voltage for dark-field imaging of the thorax has not yet been examined. In this work, dark-field scans with tube voltages ranging from 60 to 120 kVp were performed on a deceased human body. We analyzed the resulting images with respect to subjective and objective image quality, and found that the optimum tube voltage for dark-field thorax imaging at the used setup is at rather low energies of around 60 to 70 kVp. Furthermore, we found that at these tube voltages, the transmission radiographs still exhibit sufficient image quality to correlate dark-field information. Therefore, this study may serve as an important guideline for the development of clinical dark-field chest X-ray imaging devices for future routine use.

Ab initio nonrigid X-ray nanotomography

Reaching the full potential of X-ray nanotomography, in particular for biological samples, is limited by many factors, of which one of the most serious is radiation damage. Although sample deformation caused by radiation damage can be partly mitigated by cryogenic protection, it is still present in these conditions and, as we exemplify here using a specimen extracted from scales of the Cyphochilus beetle, it will pose a limit to the achievable imaging resolution. We demonstrate a generalized tomographic model, which optimally follows the sample morphological changes and attempts to recover the original sample structure close to the ideal, damage-free reconstruction. Whereas our demonstration was performed using ptychographic X-ray tomography, the method can be adopted for any tomographic imaging modality. Our application demonstrates improved reconstruction quality of radiation-sensitive samples, which will be of increasing relevance with the higher brightness of 4th generation synchrotron sources.

Radiation induced sample deformation can be a limiting factor for X-ray imaging resolution at the nanoscale. The authors report a tomographic model that estimates and accounts for morphological changes during data acquisition and enables reconstruction of a high-resolution image ab initio.

Full-field structured-illumination super-resolution X-ray transmission microscopy

Modern transmission X-ray microscopy techniques provide very high resolution at low and medium X-ray energies, but suffer from a limited field-of-view. If sub-micrometre resolution is desired, their field-of-view is typically limited to less than one millimetre. Although the field-of-view increases through combining multiple images from adjacent regions of the specimen, so does the required data acquisition time. Here, we present a method for fast full-field super-resolution transmission microscopy by structured illumination of the specimen. This technique is well-suited even for hard X-ray energies above 30 keV, where efficient optics are hard to obtain. Accordingly, investigation of optically thick specimen becomes possible with our method combining a wide field-of-view spanning multiple millimetres, or even centimetres, with sub-micron resolution and hard X-ray energies.

Contrast-to-noise ratios and thickness-normalized, ventilation-dependent signal levels in dark-field and conventional in vivo thorax radiographs of two pigs

Lung tissue causes significant small-angle X-ray scattering, which can be visualized with grating-based X-ray dark-field imaging. Structural lung diseases alter alveolar microstructure, which often causes a dark-field signal decrease. The imaging method provides benefits for diagnosis of such diseases in small-animal models, and was successfully used on porcine and human lungs in a fringe-scanning setup. Micro- and macroscopic changes occur in the lung during breathing, but their individual effects on the dark-field signal are unknown. However, this information is important for quantitative medical evaluation of dark-field thorax radiographs. To estimate the effect of these changes on the dark-field signal during a clinical examination, we acquired in vivo dark-field chest radiographs of two pigs at three ventilation pressures. Pigs were used due to the high degree of similarity between porcine and human lungs. To analyze lung expansion separately, we acquired CT scans of both pigs at comparable posture and ventilation pressures. Segmentation, masking, and forward-projection of the CT datasets yielded maps of lung thickness and logarithmic lung attenuation signal in registration with the dark-field radiographs. Upon correlating this data, we discovered approximately linear relationships between the logarithmic dark-field signal and both projected quantities for all scans. Increasing ventilation pressure strongly decreased dark-field extinction coefficients, whereas the ratio of lung dark-field and attenuation signal changed only slightly. Furthermore, we investigated ratios of dark-field and attenuation noise levels at realistic signal levels via calculations and phantom measurements. Dark-field contrast-to-noise ratio (CNR) per lung height was 5 to 10% of the same quantity in attenuation. We conclude that better CNR performance in the dark-field modality is typically due to greater anatomical noise in the conventional radiograph. Given the high physiological similarity of human and porcine lungs, the presented thickness-normalized, ventilation-dependent values allow estimation of dark-field activity of human lungs of variable size and inspiration, which facilitates the design of suitable clinical imaging setups.

Quality and parameter control of X-ray absorption gratings by angular X-ray transmission

Here we report on a non-destructive, spatially resolving and easy to implement quality and parameter control method for high aspect ratio X-ray absorption gratings. Based on angular X-ray transmission measurements, our proposed technique allows to determine the duty cycle, the transmittance, the height, as well as the local inclination of the absorbing grating structures. A key advantage of the presented method is a fast and extensive grating quality evaluation without the need of implementing an entire grating interferometer. In addition to the local and surface-based analysis using a scanning electron microscope, our non-destructive method provides global averaged macroscopic and spatially resolved grating structure information without the requirement of resolving individual grating lines.

Contrast enhancement for visualizing neuronal cytoarchitecture by propagation-based x-ray phase-contrast tomography

Knowledge of the three-dimensional (3d) neuronal cytoarchitecture is an important factor in order to understand the connection between tissue structure and function or to visualize pathological changes in neurodegenerative diseases or tumor development. The gold standard in neuropathology is histology, a technique which provides insights into the cellular organization based on sectioning of the sample. Conventional histology, however, misses the complete 3d information as only individual two-dimensional slices through the object are available. In this work, we use propagation-based phase-contrast x-ray tomography to perform 3d virtual histology on cerebellar tissue from mice. This technique enables us to non-invasively visualize the entire 3d density distribution of the examined samples at isotropic (sub-)cellular resolution. One central challenge, however, of the technique is the fact that contrast for important structural features can be easily lost due to small electron density differences, notably between the cells and surrounding tissue. Here, we evaluate the influence of different embedding media, which are intermediate steps in sample preparation for classical histology, on contrast formation and examine the applicability of the different sample preparations both at a synchrotron-based holotomography setup as well as a laboratory source.

Exploration of different x-ray Talbot-Lau setups for dark-field lung imaging examined in a porcine lung

X-ray dark-field imaging is a promising technique for lung diagnosis. Due to the alveolar structure of lung tissue, a higher contrast is obtained by the dark-field image compared to the attenuation image. Animal studies indicate an enhancement regarding the detection of lung diseases in early stages. In this publication, we focus on the influence of different Talbot-Lau interferometer specifications while maintaining the x-ray source, sample magnification and detector system. By imaging the same porcine lung with three different grating sets, we analyze the contrast-to-noise ratio of the obtained dark-field images with respect to visibility and correlation length. We demonstrate that relatively large grating periods of the phase and of the analyzer grating are sufficient for high quality lung imaging at reasonable dose levels.

Novel Detection Scheme for X-ray Small-Angle Scattering

X-ray imaging techniques, including x-ray radiography and computed tomography, have been in use for decades and proven effective and indispensable in diagnosis and therapy due to their fine resolution and fast acquisition speed. However, the innate disadvantage of x-ray is the poor soft tissue contrast. Small-angle scattering signals were shown to provide unique information about the abnormality of soft tissues that is complementary to the traditional attenuation image. Currently, there is no effective small-angle scattering detection system. In this paper, we propose a new "collimation" design dedicated to capture a small-angle scattering radiographic image directly, which carries critical pathological information for differentiation between normal and abnormal tissues. Our design consists of two interlaced gratings so that both the primary flux and Compton scattering photons are effectively blocked to leave the apertures mainly open to small-angle scattering photons. Theoretical analysis and Monte Carlo simulations demonstrate that small-angle scattering radiography is feasible with our proposed technology.

Talbot-Lau x-ray phase-contrast setup for fast scanning of large samples

Compared to conventional attenuation x-ray radiographic imaging, the x-ray Talbot-Lau technique provides further information about the scattering and the refractive properties of the object in the beam path. Hence, this additional information should improve the diagnostic process concerning medical applications and non-destructive testing. Nevertheless, until now, due to grating fabrication process, Talbot-Lau imaging suffers from small grating sizes (70 mm diameter). This leads to long acquisition times for imaging large objects. Stitching the gratings is one solution. Another one consists of scanning Talbot-Lau setups. In this publication, we present a compact and very fast scanning setup which enables imaging of large samples. With this setup a maximal scanning velocity of 71.7 mm/s is possible. A resolution of 4.1 lines/mm can be achieved. No complex alignment procedures are necessary while the field of view comprises 17.5 × 150 cm². An improved reconstruction algorithm concerning the scanning approach, which increases robustness with respect to mechanical instabilities, has been developed and is presented. The resolution of the setup in dependence of the scanning velocity is evaluated. The setup imaging qualities are demonstrated using a human knee ex-vivo as an example for a high absorbing human sample.

Time and Mechanism of Nanoparticle Functionalization by Macromolecular Ligands during Pulsed Laser Ablation in Liquids

Laser ablation of gold in liquids with nanosecond laser pulses in aqueous solutions of inorganic electrolytes and macromolecular ligands for gold nanoparticle size quenching is probed inside the laser-induced cavitation bubble by in situ X-ray multicontrast imaging with a Hartmann mask (XHI). It is found that (i) the in situ size quenching power of sodium chloride (NaCl) in comparison to the ablation in pure water can be observed by the scattering contrast from XHI already inside the cavitation bubble, while (ii) for polyvinylpyrrolidone (PVP) as a macromolecular model ligand an in situ size quenching cannot be observed. Complementary ex situ characterization confirms the overall size quenching ability of both additive types NaCl and PVP. The macromolecular ligand as well as its monomer N-vinylpyrrolidone (NVP) are mainly effective for growth quenching of larger nanoparticles on later time scales, leading to the conclusion of an alternative interaction mechanism with ablated nanoparticles compared to the electrolyte NaCl, probably outside of the cavitation bubble, in the surrounding liquid phase. While monomer and polymer have similar effects on the particle properties, with the polymer being slightly more efficient, only the polymer is effective against hydrodynamic aggregation.

Virtual cleaning and unwrapping of non-invasively digitized soiled bamboo scrolls

In ancient China, symbols and drawings captured on bamboo and wooden slips were used as main communication media. Those documents are very precious for cultural heritage and research, but due to aging processes, the discovered pieces are sometimes in a poor condition and contaminated by soil. Manual cleaning of excavated slips is a demanding and time-consuming task in which writings can be accidentally deleted. To counter this, we propose a novel approach based on conventional 3-D X-ray computed tomography to digitize such historical documents without before manual cleaning. By applying a virtual cleaning and unwrapping algorithm, the entire scroll surface is remapped into 2-D such that the hidden content becomes readable. We show that the technique also works for heavily soiled scrolls, enabling an investigation of the content by the naked eye without the need for manual labor. This digitization also allows for recovery of potentially erased writings and reconstruction of the original spatial information.

Human-Compatible Multi-Contrast Mammographic Prototype System

In the past decade, grating-based x-ray multi-contrast imaging has demonstrated potential advantages for breast imaging, including reduced anatomical noise, sharper tumor boundary and improved visibility of microcalcifications. However, most of the studies have been performed on benchtop-based systems. The experimental conditions including the dose, scanning time and system geometry may not meet clinical standards. Therefore, to evaluate true clinical benefits of grating-based multi-contrast breast imaging, in-vivo imaging should be performed, which requires a human-compatible system. The purpose of this paper is to report the development of a human-compatible prototype multi-contrast imaging system. In particular, this work focuses on several key challenges in building the prototype system. Regarding the challenge of patient safety, the mean glandular dose (MGD) and the scatter radiation were evaluated for the prototype system. Regarding the challenge of the limited field-of-view (FOV), the origin of the problem and corresponding technical solutions are presented. Finally, imaging results of several test phantoms are presented and strategies to improve the image quality are discussed.

Integer and fractional electromagnetically induced Talbot effects in a ladder-type coherent atomic system

Both integer and fractional electromagnetically induced Talbot effects are experimentally investigated in a coherent rubidium 5S_1/2 - 5P_3/2 - 5D_5/2 ladder-type system. By launching a probe laser into a periodically modulated lattice constructed by two crossed coupling fields with a small angle inside the rubidium vapor, a high-resolution diffraction pattern is obtained. The diffraction pattern is reproduced completely at detection positions of an integer multiple of twice the Talbot lengths. Meanwhile, the fractional Talbot effect, presented as complicated subimages at special positions, is also clearly observed. Furthermore, the theoretical simulations are conducted and agree well with the experimental results. These results pave the way for studying the control of light dynamics based on the periodically modulated medium.

Quantitative characterization of ex vivo breast tissue via x-ray phase-contrast tomography

BACKGROUND

Grating-based X-ray phase-contrast imaging (GPCI) has received growing interests in recent years due to its high capability of visualizing soft tissue. Breast imaging is one of the most promising candidates for the first clinical application of this imaging modality.

OBJECTIVE

In this work, quantitative breast tissue characterization based on GPCI computed tomography (CT) is investigated with a laboratory X-ray tube through a comparison between attenuation-based CT images and phase-contrast CT images.

METHODS

The Hounsfield units (HU) scale was introduced to phase-contrast images due to its wide application in clinical medicine. In this work, instead of water, plastic cylinders composed of polyethylene terephthalate (PET) was treated as the calibration material. An alternative test-retest reliability (TRR) was presented to evaluate the repeatability of GPCI. Comparison between attenuation-based CT imaging and GPCI CT imaging was operated with the use of statistical analysis methods like histograms and receiver operating characteristic (ROC) curves.

RESULTS

The determined mean TRR related to cylinders is slightly larger in phase-contrast imaging (0.93) than that in attenuation-based imaging (0.89). With respect to distinguishing breast tissues, the AUC (area under curve) values of ROC curves of phase-contrast images are higher than that of attenuation-based images.

CONCLUSIONS

An ex vivo study of GPCI shows that it is a stable imaging modality for visualizing the breast tissue with good repeatability, and that it could be of potential for the diagnosis of breast cancer as well.

Hard X-ray imaging microscopy with self-imaging phenomenon

The self-imaging phenomenon referred to as the Talbot effect in the field of optics was discovered by H.F. Talbot in the 1830s, and is now widely used for imaging using not only visible light but also X-rays, electrons, neutrons, and matter waves. In this review, the author introduces the current progress being made in hard-X-ray imaging microscopy based on the self-imaging phenomenon. Hard-X-ray imaging microscopy is a promising technique for non-destructively visualizing internal structures in specimens with a spatial resolution up to a few tens of nanometers. The use of the self-imaging phenomenon makes it possible to realize highly sensitive phase-contrast X-ray imaging microscopes. These approaches have several advantages over conventional X-ray imaging microscopes, including the widely used Zernike X-ray phase-contrast microscopes, and can provide a powerful way of quantitative visualization with a high spatial resolution and a high sensitivity even for thick specimens.