Non-binary phase gratings for x-ray imaging with a compact Talbot interferometer

Technical Design Considerations of a Human-Scale Talbot-Lau Interferometer for Dark-Field CT

Computed tomography (CT) as an important clinical diagnostics method can profit from extension with dark-field imaging, as it is currently restricted to X-rays' attenuation contrast only. Dark-field imaging allows access to more tissue properties, such as micro-structural texture or porosity. The up-scaling process to clinical scale is complex because several design constraints must be considered. The two most important ones are that the finest grating is limited by current manufacturing technology to a [Formula: see text] period and that the interferometer should fit into the CT gantry with minimal modifications only. In this work we discuss why an inverse interferometer and a triangular G1 profile are advantageous and make a compact and sensitive interferometer implementation feasible. Our evaluation of the triangular grating profile reveals a deviation in the interference pattern compared to standard grating profiles, which must be considered in the subsequent data processing. An analysis of the grating orientation demonstrates that currently only a vertical layout can be combined with cylindrical bending of the gratings. We also provide an in-depth discussion, including a new simulation approach, of the impact of the extended X-ray source spot which can lead to large performance loss and present supporting experimental results. This analysis reveals a vastly increased sensitivity to geometry and grating period deviations, which must be considered early in the system design process.

Dark-field computed tomography reaches the human scale

X-ray computed tomography (CT) is one of the most commonly used diagnostic three-dimensional imaging modalities today. Conventionally, this noninvasive technique generates contrast by measuring the X-ray attenuation properties of different tissues. Considering the wave nature of X-rays, complementary contrast can be achieved by further measuring their small-angle scattering (dark-field) properties. This provides additional valuable diagnostic information on otherwise unresolved tissue microstructure. In our work, we have translated this wave-optical mechanism from the optical bench to a human-sized prototype CT system. This involved the integration of an interferometer into a clinical CT gantry and overcoming several associated challenges regarding vibrations, continuous gantry rotation, and large field of view. This development puts complementary X-ray contrast within reach for real-word medical applications.

X-ray computed tomography (CT) is one of the most commonly used three-dimensional medical imaging modalities today. It has been refined over several decades, with the most recent innovations including dual-energy and spectral photon-counting technologies. Nevertheless, it has been discovered that wave-optical contrast mechanisms—beyond the presently used X-ray attenuation—offer the potential of complementary information, particularly on otherwise unresolved tissue microstructure. One such approach is dark-field imaging, which has recently been introduced and already demonstrated significantly improved radiological benefit in small-animal models, especially for lung diseases. Until now, however, dark-field CT could not yet be translated to the human scale and has been restricted to benchtop and small-animal systems, with scan durations of several minutes or more. This is mainly because the adaption and upscaling to the mechanical complexity, speed, and size of a human CT scanner so far remained an unsolved challenge. Here, we now report the successful integration of a Talbot–Lau interferometer into a clinical CT gantry and present dark-field CT results of a human-sized anthropomorphic body phantom, reconstructed from a single rotation scan performed in 1 s. Moreover, we present our key hardware and software solutions to the previously unsolved roadblocks, which so far have kept dark-field CT from being translated from the optical bench into a rapidly rotating CT gantry, with all its associated challenges like vibrations, continuous rotation, and large field of view. This development enables clinical dark-field CT studies with human patients in the near future.

High-resolution and sensitivity bi-directional x-ray phase contrast imaging using 2D Talbot array illuminators

Two-dimensional (2D) Talbot array illuminators (TAIs) were designed, fabricated, and evaluated for high-resolution high-contrast x-ray phase imaging of soft tissue at 10-20 keV. The TAIs create intensity modulations with a high compression ratio on the micrometer scale at short propagation distances. Their performance was compared with various other wavefront markers in terms of period, visibility, flux efficiency, and flexibility to be adapted for limited beam coherence and detector resolution. Differential x-ray phase contrast and dark-field imaging were demonstrated with a one-dimensional, linear phase stepping approach yielding 2D phase sensitivity using unified modulated pattern analysis (UMPA) for phase retrieval. The method was employed for x-ray phase computed tomography reaching a resolution of 3 µm on an unstained murine artery. It opens new possibilities for three-dimensional, non-destructive, and quantitative imaging of soft matter such as virtual histology. The phase modulators can also be used for various other x-ray applications such as dynamic phase imaging, super-resolution structured illumination microscopy, or wavefront sensing.

Signal Retrieval from Non-Sinusoidal Intensity Modulations in X-ray and Neutron Interferometry Using Piecewise-Defined Polynomial Function

Grating-based phase-contrast and dark-field imaging systems create intensity modulations that are usually modeled with sinusoidal functions to extract transmission, differential-phase shift, and scatter information. Under certain system-related conditions, the modulations become non-sinusoidal and cause artifacts in conventional processing. To account for that, we introduce a piecewise-defined periodic polynomial function that resembles the physical signal formation process, modeling convolutions of binary periodic functions. Additionally, we extend the model with an iterative expectation-maximization algorithm that can account for imprecise grating positions during phase-stepping. We show that this approach can process a higher variety of simulated and experimentally acquired data, avoiding most artifacts.

X-ray bi-prism interferometry-A design study of proposed novel hardware

PURPOSE

Advances in X-ray phase-contrast imaging can obtain excellent soft-tissue contrast of phase-shift, attenuation, and small-angle scatter. Here, we present fringe patterns for different design parameters of X-ray bi-prism interferometry imaging systems. Our aim is to develop bi-prism interferometry imaging systems with excellent polychromatic performance that produce high-contrast fringes with spatially incoherent X-ray illumination. We also introduce a novel X-ray tube design that uses temporal multiplexing to provide simultaneous virtual "electronic phase stepping" that replace "mechanical phase stepping" popular with grating-based interferometry setups.

METHODS

In our investigation, we develop expressions for the irradiance distribution pattern of a bi-prism interferometer composed of multiple point sources and multiple bi-prisms. These expressions are used to plot fringe patterns for X-ray design parameters, including size of point source, number of point sources, and point source separation, and bi-prism design parameters including material, angle, number of bi-prisms, period, and bi-prism array to X-ray source and detector distances.

RESULTS

Results show that the fringe patterns for a bi-prism interferometry system are not longitudinally periodic as with grating interferometers that produce a Talbot-Lau carpet. It is also shown that at 59 keV X-rays the bi-prism material should be something comparable to nickel to obtain reasonable fringe visibility.

CONCLUSION

The irradiance distribution pattern demonstrates that bi-prism interferometry may provide comparable or improved fringe visibility to that of gratings. Special care is given to present our findings within the context of previous advancements. A single-shot image acquisition approach using a temporal multiplexed, high-power X-ray source provides virtual electronic phase stepping without focal spot sweeping. This provides multiple images, each at the same exposure and the same projection view, from different fringe locations that allow one to derive the attenuation, phase, and dark-field images of the sample without mechanical phase stepping of a grating.

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.

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.

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%.

Talbot effect in optical lattices with topological charge

We studied the interference resulting from the superposition of optical lattices, which are non-diffracting fields propagating in free space, and showed a Talbot self-imaging effect. These lattices are formed by spatially Fourier transforming a "quasi"-orbital angular momentum (OAM) state. We experimentally observed that although the Talbot images change, the Talbot length is insensitive to the topological charge of the "quasi"-OAM state. Our findings can be useful for laser-written photonic lattices.

X-ray Dark-field Radiography - In-Vivo Diagnosis of Lung Cancer in Mice

Accounting for about 1.5 million deaths annually, lung cancer is the prevailing cause of cancer deaths worldwide, mostly associated with long-term smoking effects. Numerous small-animal studies are performed currently in order to better understand the pathogenesis of the disease and to develop treatment strategies. Within this letter, we propose to exploit X-ray dark-field imaging as a novel diagnostic tool for the detection of lung cancer on projection radiographs. Here, we demonstrate in living mice bearing lung tumors, that X-ray dark-field radiography provides significantly improved lung tumor detection rates without increasing the number of false-positives, especially in the case of small and superimposed nodules, when compared to conventional absorption-based imaging. While this method still needs to be adapted to larger mammals and finally humans, the technique presented here can already serve as a valuable tool in evaluating novel lung cancer therapies, tested in mice and other small animal models.

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.

Technical Note: spektr 3.0-A computational tool for x-ray spectrum modeling and analysis

PURPOSE

A computational toolkit (spektr 3.0) has been developed to calculate x-ray spectra based on the tungsten anode spectral model using interpolating cubic splines (TASMICS) algorithm, updating previous work based on the tungsten anode spectral model using interpolating polynomials (TASMIP) spectral model. The toolkit includes a matlab (The Mathworks, Natick, MA) function library and improved user interface (UI) along with an optimization algorithm to match calculated beam quality with measurements.

METHODS

The spektr code generates x-ray spectra (photons/mm(2)/mAs at 100 cm from the source) using TASMICS as default (with TASMIP as an option) in 1 keV energy bins over beam energies 20-150 kV, extensible to 640 kV using the TASMICS spectra. An optimization tool was implemented to compute the added filtration (Al and W) that provides a best match between calculated and measured x-ray tube output (mGy/mAs or mR/mAs) for individual x-ray tubes that may differ from that assumed in TASMICS or TASMIP and to account for factors such as anode angle.

RESULTS

The median percent difference in photon counts for a TASMICS and TASMIP spectrum was 4.15% for tube potentials in the range 30-140 kV with the largest percentage difference arising in the low and high energy bins due to measurement errors in the empirically based TASMIP model and inaccurate polynomial fitting. The optimization tool reported a close agreement between measured and calculated spectra with a Pearson coefficient of 0.98.

CONCLUSIONS

The computational toolkit, spektr, has been updated to version 3.0, validated against measurements and existing models, and made available as open source code. Video tutorials for the spektr function library, UI, and optimization tool are available.

Multiple scattering tomography

Multiple scattering represents a challenge for numerous modern tomographic imaging techniques. In this Letter, we derive an appropriate line integral that allows for the tomographic reconstruction of angular resolved scattering distributions, even in the presence of multiple scattering. The line integral is applicable to a wide range of imaging techniques utilizing various kinds of probes. Here, we use x-ray grating interferometry to experimentally validate the framework and to demonstrate additional structural sensitivity, which exemplifies the impact of multiple scattering tomography.

A robust tool for photon source geometry measurements using the fractional Talbot effect

A reliable measurement of beam coherence is important for optimal performance of a number of coherence methods being utilized at third-generation synchrotrons and free-electron lasers. Various approaches have been proposed in the past for determining the source size, and hence the degree of coherence; however they often require complex setups with perfect optics and suffer from undefined uncertainties. We present a robust tool for X-ray source characterization with a full quantitative uncertainty analysis for fast on-the-fly coherence measurements. The influence of three multilayer monochromator crystals on the apparent source size is evaluated using the proposed method.