Hard-X-ray phase-difference microscopy using a fresnel zone plate and a transmission grating

Phase retrieval for X-ray differential phase contrast radiography with knowledge transfer learning from virtual differential absorption model

Grating-based X-ray phase contrast radiography and computed tomography (CT) are promising modalities for future medical applications. However, the ill-posed phase retrieval problem in X-ray phase contrast imaging has hindered its use for quantitative analysis in biomedical imaging. Deep learning has been proved as an effective tool for image retrieval. However, in practical grating-based X-ray phase contrast imaging system, acquiring the ground truth of phase to form image pairs is challenging, which poses a great obstacle for using deep leaning methods. Transfer learning is widely used to address the problem with knowledge inheritance from similar tasks. In the present research, we propose a virtual differential absorption model and generate a training dataset with differential absorption images and absorption images. The knowledge learned from the training is transferred to phase retrieval with transfer learning techniques. Numerical simulations and experiments both demonstrate its feasibility. Image quality of retrieved phase radiograph and phase CT slices is improved when compared with representative phase retrieval methods. We conclude that this method is helpful in both X-ray 2D and 3D imaging and may find its applications in X-ray phase contrast radiography and X-ray phase CT.

Hard X-ray stereographic microscopy for single-shot differential phase imaging

The characterisation of fast phenomena at the microscopic scale is required for the understanding of catastrophic responses of materials to loads and shocks, the processing of materials by optical or mechanical means, the processes involved in many key technologies such as additive manufacturing and microfluidics, and the mixing of fuels in combustion. Such processes are usually stochastic in nature and occur within the opaque interior volumes of materials or samples, with complex dynamics that evolve in all three dimensions at speeds exceeding many meters per second. There is therefore a need for the ability to record three-dimensional X-ray movies of irreversible processes with resolutions of micrometers and frame rates of microseconds. Here we demonstrate a method to achieve this by recording a stereo phase-contrast image pair in a single exposure. The two images are combined computationally to reconstruct a 3D model of the object. The method is extendable to more than two simultaneous views. When combined with megahertz pulse trains of X-ray free-electron lasers (XFELs) it will be possible to create movies able to resolve 3D trajectories with velocities of kilometers per second.

Single-exposure X-ray phase imaging microscopy with a grating interferometer

The advent of hard X-ray free-electron lasers enables nanoscopic X-ray imaging with sub-picosecond temporal resolution. X-ray grating interferometry offers a phase-sensitive full-field imaging technique where the phase retrieval can be carried out from a single exposure alone. Thus, the method is attractive for imaging applications at X-ray free-electron lasers where intrinsic pulse-to-pulse fluctuations pose a major challenge. In this work, the single-exposure phase imaging capabilities of grating interferometry are characterized by an implementation at the I13-1 beamline of Diamond Light Source (Oxfordshire, UK). For comparison purposes, propagation-based phase contrast imaging was also performed at the same instrument. The characterization is carried out in terms of the quantitativeness and the contrast-to-noise ratio of the phase reconstructions as well as via the achievable spatial resolution. By using a statistical image reconstruction scheme, previous limitations of grating interferometry regarding the spatial resolution can be mitigated as well as the experimental applicability of the technique.

Spatio-temporal ultrasound beam modulation to sequentially achieve multiple foci with a single planar monofocal lens

Ultrasound focusing is a hot topic due to its multiple applications in many fields, including biomedical imaging, thermal ablation of cancerous tissues, and non destructive testing in industrial environments. In such applications, the ability to control the focal distance of the ultrasound device in real-time is a key advantage over conventional devices with fixed focal parameters. Here, we present a method to achieve multiple time-modulated ultrasound foci using a single planar monofocal Fresnel Zone Plate. The method takes advantage of the focal distance linear dependence on the operating frequency of this kind of lenses to design a sequence of contiguous modulated rectangular pulses that achieve different focal distances and intensities as a function of time. Both numerical simulations and experimental results are presented, demonstrating the feasibility and potential of this technique.

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

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

Recent progress in synchrotron radiation 3D-4D nano-imaging based on X-ray full-field microscopy

The advent of high-flux, high-brilliance synchrotron radiation (SR) has prompted the development of high-resolution X-ray imaging techniques such as full-field microscopy, holography, coherent diffraction imaging and ptychography. These techniques have strong potential to establish non-destructive three- and four-dimensional nano-imaging when combined with computed tomography (CT), called nano-tomography (nano-CT). X-ray nano-CTs based on full-field microscopy are now routinely available and widely used. Here we discuss the current status and some applications of nano-CT using a Fresnel zone plate as an objective. Optical properties of full-field microscopy, such as spatial resolution and off-axis aberration, which determine the effective field of view, are also discussed, especially in relation to 3D tomographic imaging.

Maximum likelihood reconstruction for grating-based X-ray microscopy

The combination of grating-based phase-contrast imaging with X-ray microscopy can result in a complicated image formation. Generally, transverse shifts of the interference fringes are nonlinearly dependent on phase differences of the measured wave front. We present an iterative reconstruction scheme based on a regularized maximum likelihood cost function that fully takes this dependency into account. The scheme is validated by numerical simulations. It is particularly advantageous at low photon numbers and when the premises for deconvolution-based reconstructions are not met. Our reconstruction scheme hence enables a broader applicability of X-ray grating interferometry in imaging and wave front sensing.

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.

Wavefront sensing at X-ray free-electron lasers

Here a direct comparison is made between various X-ray wavefront sensing methods with application to optics alignment and focus characterization at X-ray free-electron lasers (XFELs). Focus optimization at XFEL beamlines presents unique challenges due to high peak powers as well as beam pointing instability, meaning that techniques capable of single-shot measurement and that probe the wavefront at an out-of-focus location are desirable. The techniques chosen for the comparison include single-phase-grating Talbot interferometry (shearing interferometry), dual-grating Talbot interferometry (moiré deflectometry) and speckle tracking. All three methods were implemented during a single beam time at the Linac Coherent Light Source, at the X-ray Pump Probe beamline, in order to make a direct comparison. Each method was used to characterize the wavefront resulting from a stack of beryllium compound refractive lenses followed by a corrective phase plate. In addition, difference wavefront measurements with and without the phase plate agreed with its design to within λ/20, which enabled a direct quantitative comparison between methods. Finally, a path toward automated alignment at XFEL beamlines using a wavefront sensor to close the loop is presented.

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.

Effect of insufficient temporal coherence on visibility contrast in X-ray grating interferometry

X-ray grating interferometry, which has been spotlighted in the last decade as a multi-modal X-ray imaging technique, can provide three independent images, i.e., absorption, differential-phase, and visibility-contrast images. We report on a cause of the visibility contrast, an effect of insufficient temporal coherence, that can be observed when continuous-spectrum X-rays are used. This effect occurs even for a sample without unresolvable random structures, which are known as the main causes of visibility contrast. We performed an experiment using an acrylic cylinder and quantitatively explained the visibility contrast due to this effect.

Development toward high-resolution X-ray phase imaging

Since the 1990s, the use of X-ray phase contrast has been extensively studied for imaging weakly absorbing objects consisting of low-Z elements such as biological soft tissues and polymers. The development of X-ray microscopy was also progressing during this time, although absorption contrast was only available. It was straightforward and important to develop phase-contrast X-ray microscopy. One characteristic in the development is that quantitative phase measurement is possible through the acquisition of phase-contrast images under a specific procedure, thanks to digital X-ray image detectors. Therefore, such a technique is called 'phase imaging' rather than phase-contrast imaging in this review. Highly sensitive three-dimensional phase imaging is feasible in combination with tomography. This article reviews the progress in X-ray phase imaging, especially with regards to X-ray microscopy.

Simulation of concave-convex imaging mirror system for development of a compact and achromatic full-field x-ray microscope

We propose the use of two pairs of concave-convex mirrors as imaging optics for the compact full-field x-ray microscope with high resolution and magnification factors. The optics consists of two pairs of hyperbolic convex and elliptical concave mirrors with the principal surface near the object, consequently enabling the focal length to be 10 times shorter than conventional advanced Kirkpatrick-Baez mirror optics. This paper describes characteristics of the optics calculated by ray-tracing and wave-optical simulators. The expected spatial resolution is approximately 40 nm with a wide field of view of more than 10 μm and a total length of about 2 m, which may lead to the possibility of laboratory-sized, achromatic, and high-resolution full-field x-ray microscopes.

Subnanoradian X-ray phase-contrast imaging using a far-field interferometer of nanometric phase gratings

Hard X-ray phase-contrast imaging characterizes the electron density distribution in an object without the need for radiation absorption. The power of phase contrast to resolve subtle changes, such as those in soft tissue structures, lies in its ability to detect minute refractive bending of X-rays. Here we report a far-field, two-arm interferometer based on the new nanometric phase gratings, which can detect X-ray refraction with subnanoradian sensitivity, and at the same time overcomes the fundamental limitation of ultra-narrow bandwidths (Δλ/λ~10⁻⁴) of the current, most sensitive methods based on crystal interferometers. On a 1.5% bandwidth synchrotron source, we demonstrate clear visualization of blood vessels in unstained mouse organs in simple projection views, with over an order-of-magnitude higher phase contrast than current near-field grating interferometers.

Phase-contrast imaging has become popular for medical diagnostic purposes because of the ability to see transparent structures at relatively small radiation energy dosed to samples. Wen et al. further develop this technique using nanometric phase gratings to achieve subnanoradian sensitivity.

Phase-contrast microscopy at high x-ray energy with a laboratory setup

We report on the design and realization of an x-ray imaging system for quantitative phase-contrast microscopy at high x-ray energy with laboratory-scale instrumentation. Phase and amplitude were separated quantitatively at x-ray energies up to 80 keV with micrometric spatial resolution. The accuracy of the results was tested against numerical simulations, and the spatial resolution was experimentally quantified by measuring a Siemens star phase object. This simple setup should find broad application in those areas of x-ray imaging where high energy and spatial resolution are simultaneously required and in those difficult cases where the sample contains materials with similar x-ray absorption.

Boosting phase contrast with a grating Bonse-Hart interferometer of 200 nanometre grating period

We report on a grating Bonse-Hart interferometer for phase-contrast imaging with hard X-rays. The method overcomes limitations in the level of sensitivity that can be achieved with the well-known Talbot grating interferometer, and without the stringent spectral filtering at any given incident angle imposed by the classic Bonse-Hart interferometer. The device operates in the far-field regime, where an incident beam is split by a diffraction grating into two widely separated beams, which are redirected by a second diffraction grating to merge at a third grating, where they coherently interfere. The wide separation of the interfering beams results in large phase contrast, and in some cases absolute phase images are obtained. Imaging experiments were performed using diffraction gratings of 200 nm period, at 22.5 keV and 1.5% spectral bandwidth on a bending-magnetic beamline. Novel design and fabrication process were used to achieve the small grating period. Using a slitted incident beam, we acquired absolute and differential phase images of lightly absorbing samples. An advantage of this method is that it uses only phase modulating gratings, which are easier to fabricate than absorption gratings of the same periods.

Three-dimensional phase-contrast X-ray microtomography with scanning-imaging X-ray microscope optics

A three-dimensional (3D) X-ray tomographic micro-imaging system has been developed. The optical system is based on a scanning-imaging X-ray microscope (SIXM) optics, which is a hybrid system consisting of a scanning microscope optics with a one-dimensional (1D) focusing (line-focusing) device and an imaging microscope optics with a 1D objective. In the SIXM system, each 1D dataset of a two-dimensional (2D) image is recorded independently. An object is illuminated with a line-focused beam. Positional information of the region illuminated by the line-focused beam is recorded with the 1D imaging microscope optics as line-profile data. By scanning the object with the line focus, 2D image data are obtained. In the same manner as for a scanning microscope optics with a multi-pixel detector, imaging modes such as phase contrast and absorption contrast can be arbitrarily configured after the image data acquisition. By combining a tomographic scan method and the SIXM system, quantitative 3D imaging is performed. Results of a feasibility study of the SIXM for 3D imaging are shown.

Interferometric hard x-ray phase contrast imaging at 204 nm grating period

We report on hard x-ray phase contrast imaging experiments using a grating interferometer of approximately 1/10th the grating period achieved in previous studies. We designed the gratings as a staircase array of multilayer stacks which are fabricated in a single thin film deposition process. We performed the experiments at 19 keV x-ray energy and 0.8 μm pixel resolution. The small grating period resulted in clear separation of different diffraction orders and multiple images on the detector. A slitted beam was used to remove overlap of the images from the different diffraction orders. The phase contrast images showed detailed features as small as 10 μm, and demonstrated the feasibility of high resolution x-ray phase contrast imaging with nanometer scale gratings.

Fabrication of 200 nanometer period centimeter area hard x-ray absorption gratings by multilayer deposition

We describe the design and fabrication trials of x-ray absorption gratings of 200 nm period and up to 100:1 depth-to-period ratios for full-field hard x-ray imaging applications. Hard x-ray phase-contrast imaging relies on gratings of ultra-small periods and sufficient depth to achieve high sensitivity. Current grating designs utilize lithographic processes to produce periodic vertical structures, where grating periods below 2.0 μm are difficult due to the extreme aspect ratios of the structures. In our design, multiple bilayers of x-ray transparent and opaque materials are deposited on a staircase substrate, and mostly on the floor surfaces of the steps only. When illuminated by an x-ray beam horizontally, the multilayer stack on each step functions as a micro-grating whose grating period is the thickness of a bilayer. The array of micro-gratings over the length of the staircase works as a single grating over a large area when continuity conditions are met. Since the layers can be nanometers thick and many microns wide, this design allows sub-micron grating periods and sufficient grating depth to modulate hard x-rays. We present the details of the fabrication process and diffraction profiles and contact radiography images showing successful intensity modulation of a 25 keV x-ray beam.

Differential phase contrast x-ray microimaging with scanning-imaging x-ray microscope optics

A novel x-ray microimaging system that consists of a scanning microscope optics with a one-dimensional focusing (line-focusing) device and an imaging microscope optics with a one-dimensional objective is developed. These two optical systems are set normal to each other regarding the optical axis. A two-dimensional image is obtained with one-dimensional translation scan of the line probe. During scans, positional data in the normal to the scanning direction are obtained simultaneously with the imaging microscope optics. Differential phase contrast (DPC) image and absorption contrast (AC) image can be arbitrarily obtained by image processing after data acquisition. Preliminary experiment has been carried out by using a couple of one-dimensional Fresnel zone plate as the linear-focusing device and the one-dimensional objective. Two-dimensional DPC and AC images of test sample have been successfully obtained with 8 keV x-rays.

Development of x-ray laminography under an x-ray microscopic condition

An x-ray laminography system under an x-ray microscopic condition was developed to obtain a three-dimensional structure of laterally-extended planar objects which were difficult to observe by x-ray tomography. An x-ray laminography technique was introduced to an x-ray transmission microscope with zone plate optics. Three prototype sample holders were evaluated for x-ray imaging laminography. Layered copper grid sheets were imaged as a laminated sample. Diatomite powder on a silicon nitride membrane was measured to confirm the applicability of this method to non-planar micro-specimens placed on the membrane. The three-dimensional information of diatom shells on the membrane was obtained at a spatial resolution of sub-micron. Images of biological cells on the membrane were also obtained by using a Zernike phase contrast technique.

Quantitative x-ray phase-contrast imaging using a single grating of comparable pitch to sample feature size

The ability to quantitatively retrieve transverse phase maps during imaging by using coherent x rays often requires a precise grating or analyzer-crystal-based setup. Imaging of live animals presents further challenges when these methods require multiple exposures for image reconstruction. We present a simple method of single-exposure, single-grating quantitative phase contrast for a regime in which the grating period is much greater than the effective pixel size. A grating is used to create a high-visibility reference pattern incident on the sample, which is distorted according to the complex refractive index and thickness of the sample. The resolution, along a line parallel to the grating, is not restricted by the grating spacing, and the detector resolution becomes the primary determinant of the spatial resolution. We present a method of analysis that maps the displacement of interrogation windows in order to retrieve a quantitative phase map. Application of this analysis to the imaging of known phantoms shows excellent correspondence.

Observation of the Talbot effect using broadband hard x-ray beam

We demonstrated the Talbot effect using a broadband hard x-ray beam (Δλ/λ ~1). The exit wave-field of the x-ray beam passing through a grating with a sub micro-meter scale period was successfully replicated and recorded at effective Talbot distance, Z(T). The period was reduced to half at Z(T)/4 and 3/4Z(T), and the phase reversal was observed at Z(T)/2. The propagating wave-field recorded on photoresists was consistent with a simulated result.

On the origin of visibility contrast in x-ray Talbot interferometry

The reduction in visibility in x-ray grating interferometry based on the Talbot effect is formulated by the autocorrelation function of spatial fluctuations of a wavefront due to unresolved micron-size structures in samples. The experimental results for microspheres and melamine sponge were successfully explained by this formula with three parameters characterizing the wavefront fluctuations: variance, correlation length, and the Hurst exponent. The ultra-small-angle x-ray scattering of these samples was measured, and the scattering profiles were consistent with the formulation. Furthermore, we discuss the relation between the three parameters and the features of the micron-sized structures. The visibility-reduction contrast observed by x-ray grating interferometry can thus be understood in relation to the structural parameters of the microstructures.