Quadriwave lateral shearing interferometry in an achromatic and continuously self-imaging regime for future x-ray phase imaging

Artifacts reduction in high-acutance phase images for X-ray grating interferometry

X-ray grating-based techniques often lead to artifacts in the phase retrieval process of phase objects presenting very fast spatial transitions or sudden jumps, especially in the field of non-destructive testing and evaluation. In this paper, we present a method that prevents the emergence of artifacts by building an interferogram corrected from any variations of the object intensity and given as input in the phase retrieval process. For illustration, this method is applied to a carbon fiber specimen imaged by a microfocus X-ray tube and a single 2D grating. A significant reduction of artifacts has been obtained, by a factor higher than 10. This evaluation has been performed experimentally thanks to the Confidence Map tool, a recently developed method that estimates the error distribution from the phase gradient information.

Compact radial shearing interferometer with a randomly encoded cosinusoidal zone plate for wavefront measurements

A radial shearing interferometer (RSI) using a randomly encoded cosinusoidal zone plate (RECZP) to measure the wavefront is proposed. The RECZP has two foci, i.e., a virtual focus and a real focus, so its Fresnel diffractions contain only two beams. These two beams can be regarded as the extended beam and the contracted beam in the RSI, respectively. This RSI is composed of a RECZP and a charge-coupled device (CCD). The radial shearing rate is continuously adjustable by changing the distance between the CCD and RECZP, which is good for measurement sensitivity and dynamic range for different situation requirements. In the simulation experiment, we analyzed the influence of beam tilt error, distance error of zone plate and CCD, CCD camera nonlinearity, and noise on wavefront reconstruction results. We also analyzed the effects of different fabrication errors (randomly encoded principle error, sidewall angle error, depth error, and alignment error of amplitude zone plate and phase zone plate) on the diffraction intensity distributions, which determine the fabrication tolerance of the RECZP. Experimentally compared with a ZYGO interferometer, the RECZP-RSI optical system can get good results.

Towards X-ray transient grating spectroscopy

The extension of transient grating spectroscopy to the x-ray regime will create numerous opportunities, ranging from the study of thermal transport in the ballistic regime to charge, spin, and energy transfer processes with atomic spatial and femtosecond temporal resolution. Studies involving complicated split-and-delay lines have not yet been successful in achieving this goal. Here we propose a novel, simple method based on the Talbot effect for converging beams, which can easily be implemented at current x-ray free electron lasers. We validate our proposal by analyzing printed interference patterns on polymethyl methacrylate and gold samples using ∼3  keV X-ray pulses.

Beam hardening correction in polychromatic x-ray grating interferometry

The beam hardening is one of the two causes of the fringe shift distortion in polychromatic X-ray grating interferometry. Based on the assumption of the uniform energy dependence, we developed a novel analytic approach to accurately retrieve the monochromatic attenuation function and fringe phase shift from the polychromatic measurement. This approach provides a useful tool for precise measurement of sample electron density distribution in X-ray grating interferometry.

Polychromatic X-ray effects on fringe phase shifts in grating interferometry

In order to quantitatively determine the projected electron densities of a sample, one needs to extract the monochromatic fringe phase shifts from the polychromatic fringe phase shifts measured in the grating interferometry with incoherent X-ray sources. In this work the authors propose a novel analytic approach that allows to directly compute the monochromatic fringe shifts from the polychromatic fringe shifts. This approach is validated with numerical simulations of several grating interferometry setups. This work provides a useful tool in quantitative imaging for biomedical and material science applications.

Predicting visibility of interference fringes in X-ray grating interferometry

The interference fringe visibility is a common figure of merit in designs of x-ray grating-based interferometers. Presently one has to resort to laborious computer simulations to predict fringe visibility values of interferometers with polychromatic x-ray sources. Expanding the authors' previous work on Fourier expansion of the intensity fringe pattern, in this work the authors developed a general quantitative theory to predict the intensity fringe pattern in closed-form formulas, which incorporates the effects of partial spatial coherence, spectral average and detector pixel re-binning. These formulas can be used to predict the fringe visibility of a Talbot-Lau interferometer with any geometry configuration and any source spectrum.

General measurement of optical system aberrations with a continuously variable lateral shear ratio by a randomly encoded hybrid grating

A general lateral shearing interferometry method to measure the wavefront aberrations with a continuously variable shear ratio by the randomly encoded hybrid grating (REHG) is proposed. The REHG consists of a randomly encoded binary amplitude grating and a phase chessboard. Its Fraunhofer diffractions contain only four orders which are the ±1 orders in two orthogonal directions due to the combined modulation of the amplitude and phase. As a result, no orders selection mask is needed for the REHG and the shear ratio is continuously variable, which is beneficial to the variation of sensitivity and testing range for different requirements. To determine the fabrication tolerance of this hybrid grating, the analysis of the effects of different errors on the diffraction intensity distributions is carried out. Experiments have shown that the testing method can achieve a continuously variable shear ratio with the same REHG, and the comparison with a ZYGO GPI interferometer exhibits that the aberration testing method by the REHG is highly precise and also has a good repeatability. This testing method by the REHG is available for general use in testing the aberrations of different optical systems in situ.

Quantitative phase imaging in flows with high resolution holographic diffraction grating

This paper proposes quantitative phase imaging by using a high resolution holographic grating for generating a four-wave shearing interferogram. The high-resolution holographic grating is designed in a "kite" configuration so as to avoid parasitic mixing of diffraction orders. The selection of six diffraction orders in the Fourier spectrum of the interferogram allows reconstructing phase gradients along specific directions. The spectral analysis yields the useful parameters of the reconstruction process. The derivative axes are exactly determined whatever the experimental configurations of the holographic grating. The integration of the derivative yields the phase and the optical thickness. Demonstration of the proposed approach is carried out for the case of the analysis of the supersonic flow of a small vertical jet, 5.56mm in diameter. The experimental results compared with those obtained with digital holography exhibit a very good agreement.

Objective shearing digital holography for removing aberration from optical system

We propose a new digital holography based on the lateral shearing interference concept to remove the total aberrations from the reference wave, illumination wave, and the optical elements. It uses three mutually shifted image holograms of the object that are divided from each other to obtain phase differences. The phase aberration can be removed and the original sample phase can be reconstructed by the phase differences. Then, the influence of the stage moving imprecision on the reconstruction quality is analyzed. Optical experiments verified that the proposed method can totally remove the phase aberrations. As a result, the proposed method could be used for ultra-precise optical measurement through eliminating optical phase aberration to increase the measurement accuracy.

A general theory of interference fringes in x-ray phase grating imaging

PURPOSE

The authors note that the concept of the Talbot self-image distance in x-ray phase grating interferometry is indeed not well defined for polychromatic x-rays, because both the grating phase shift and the fractional Talbot distances are all x-ray wavelength-dependent. For x-ray interferometry optimization, there is a need for a quantitative theory that is able to predict if a good intensity modulation is attainable at a given grating-to-detector distance. In this work, the authors set out to meet this need.

METHODS

In order to apply Fourier analysis directly to the intensity fringe patterns of two-dimensional and one-dimensional phase grating interferometers, the authors start their derivation from a general phase space theory of x-ray phase-contrast imaging. Unlike previous Fourier analyses, the authors evolved the Wigner distribution to obtain closed-form expressions of the Fourier coefficients of the intensity fringes for any grating-to-detector distance, even if it is not a fractional Talbot distance.

RESULTS

The developed theory determines the visibility of any diffraction order as a function of the grating-to-detector distance, the phase shift of the grating, and the x-ray spectrum. The authors demonstrate that the visibilities of diffraction orders can serve as the indicators of the underlying interference intensity modulation. Applying the theory to the conventional and inverse geometry configurations of single-grating interferometers, the authors demonstrated that the proposed theory provides a quantitative tool for the grating interferometer optimization with or without the Talbot-distance constraints.

CONCLUSIONS

In this work, the authors developed a novel theory of the interference intensity fringes in phase grating x-ray interferometry. This theory provides a quantitative tool in design optimization of phase grating x-ray interferometers.

Diffraction grating three-beam interferometry without self-imaging regime contrast modulations

Achromatic grating shearing interferometry method for wave front sensing is developed. Two Fresnel diffraction patterns formed by grating three lowest diffraction orders are recorded. The beam-splitter grating is displaced laterally by half its period between exposures. Calculating the sum of two patterns results in a two-beam interferogram free of inherent light propagation direction and observation plane contrast modulations imposed by the self-imaging phenomenon (Talbot effect). Single-frame automatic fringe pattern processing provides the interferogram phase distribution. The technique enables continuous shear variations suitable for dynamic range sensing. Experimental works corroborate enhanced capabilities of the proposed approach.

At-wavelength metrology of hard X-ray mirror using near field speckle

We present a method to measure the surface profile of hard X-ray reflective optics with nanometer height accuracy and sub-millimetre lateral resolution. The technique uses X-ray near-field speckle, generated by a scattering membrane translated using a piezo motor, to infer the deflection of X-rays from the surface. The method provides a nano-radian order accuracy on the mirror slopes in both the tangential and sagittal directions. As a demonstration, a pair of focusing mirrors mounted in a Kirkpatrick-Baez (KB) configuration were characterized and the results were in good agreement with offline metrology data. It is hoped that the new technique will provide feedback to optic manufacturers to improve mirror fabrication and be useful for the online optimization of active, nano-focusing mirrors on modern synchrotron beamlines.

Single-shot x-ray phase imaging with grating interferometry and photon-counting detectors

In this Letter, we present a single-shot approach to quantitatively retrieve x-ray absorption and phase shift in grating interferometry. The proposed approach makes use of the energy-resolving capability of x-ray photon-counting detectors. The retrieval method is derived and presented and is tested based on numerical simulations, including photon shot noise. The good agreement between retrieval results and theoretical values confirms the feasibility of the presented approach.

X-ray phase contrast imaging and noise evaluation using a single phase grating interferometer

In this paper we present some quantitative measurements of X-ray phase contrast images and noise evaluation obtained with a recent grating based X-ray phase contrast interferometer. This device is built using a single phase grating and a large broadband X-ray source. It was calibrated using a reference sample and finally used to perform measurements of a biological fossil: a mosquito trapped in amber. As phase images, noise was evaluated from the measured interferograms.

Regularized image reconstruction for continuously self-imaging gratings

In this paper, we demonstrate two image reconstruction schemes for continuously self-imaging gratings (CSIGs). CSIGs are diffractive optical elements that generate a depth-invariant propagation pattern and sample objects with a sparse spatial frequency spectrum. To compensate for the sparse sampling, we apply two methods with different regularizations for CSIG imaging. The first method employs continuity of the spatial frequency spectrum, and the second one uses sparsity of the intensity pattern. The two methods are demonstrated with simulations and experiments.

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.

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

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

Two-dimensional wavefront reconstruction from lateral multi-shear interferograms

We propose and demonstrate multiple shearing interferometry for measuring two-dimensional phase object. Multi-shear interference can effectively eliminate the problem of spectral leakage that results from the single-shear interference. The Fourier coefficients of a two-dimensional wavefront are computed from phase differences obtained from multiple shearing interferograms, which are acquired by a shearing interferometer, and the desired phase is then reconstructed. Numerical and optical tests have confirmed that the multiple shearing interferometry has a higher recovery accuracy than single-shear interferometry and the reconstruction precision increases as the number of shear steps increases.

Trimodal low-dose X-ray tomography

X-ray grating interferometry is a coherent imaging technique that bears tremendous potential for three-dimensional tomographic imaging of soft biological tissue and other specimens whose details exhibit very weak absorption contrast. It is intrinsically trimodal, delivering phase contrast, absorption contrast, and scattering ("dark-field") contrast. Recently reported acquisition strategies for grating-interferometric phase tomography constitute a major improvement of dose efficiency and speed. In particular, some of these techniques eliminate the need for scanning of one of the gratings ("phase stepping"). This advantage, however, comes at the cost of other limitations. These can be a loss in spatial resolution, or the inability to fully separate the three imaging modalities. In the present paper we report a data acquisition and processing method that optimizes dose efficiency but does not share the main limitations of other recently reported methods. Although our method still relies on phase stepping, it effectively uses only down to a single detector frame per projection angle and yields images corresponding to all three contrast modalities. In particular, this means that dark-field imaging remains accessible. The method is also compliant with data acquisition over an angular range of only 180° and with a continuous rotation of the specimen.

Theory of oblique and grazing incidence Talbot‑Lau interferometers and demonstration in a compact source x‑ray reflective interferometer

With the advent of Talbot-Lau interferometers for x-ray phase-contrast imaging, oblique and grazing incidence configurations are now used in the pursuit of sub-micron grating periods and high sensitivity. Here we address the question whether interferometers having oblique incident beams behave in the same way as the well-understood normal incidence ones, particularly when the grating planes are non-parallel. We derive the normal incidence equivalence of oblique incidence geometries from wave propagation modeling. Based on the theory, we propose a practical method to correct for non-parallelism of the grating planes, and demonstrate its effectiveness with a polychromatic hard x-ray reflective interferometer.