Talbot Interferometry Research Articles

Phase contrast laminography based on Talbot interferometry

Synchrotron laminography is combined with Talbot grating interferometry to address weakly absorbing specimens. Integrating both methods into one set-up provides a powerful x-ray diagnostical technique for multiple contrast screening of macroscopically large flat specimen and a subsequent non-destructive three-dimensional (3-D) inspection of regions of interest. The technique simultaneously yields the reconstruction of the 3-D absorption, phase, and the so-called dark-field contrast maps. We report on the theoretical and instrumental implementation of of this novel technique. Its broad application potential is exemplarily demonstrated for the field of cultural heritage, namely study of the historical Dead Sea parchment.

基于Talbot干涉的X射线光栅成像技术研究进展

基于Talbot干涉的X射线光栅成像技术研究进展

Optical Properties of In Situ Eye Lenses Measured with X-Ray Talbot Interferometry: A Novel Measure of Growth Processes

The lens, a major optical component of the eye, has a gradient refractive index, which is required to provide sufficient refractive power and image quality. The refractive index variations across the lens are dependent on the distributions and concentrations of the varying protein classes. In this study, we present the first measurements of the refractive index in the in situ eye lens from five species using a specially constructed X-ray Talbot grating interferometer. The measurements have been conducted in two planes: the one containing the optic axis (the sagittal plane) and the plane orthogonal to this (the equatorial plane). The results show previously undetected discontinuities and fluctuations in the refractive index profile that vary in different species. These may be linked to growth processes and may be the first optical evidence of discrete developmental stages.

Distribution of unresolvable anisotropic microstructures revealed in visibility-contrast images using x-ray Talbot interferometry

X-ray Talbot interferometry has been widely used as a technique for x-ray phase imaging and tomography. We propose a method using this interferometry for mapping distribution of parameters characterizing anisotropic microstructures, which are typically of the order of $\ensuremath{\mu}\mathrm{m}$ in size and cannot be resolved by the imaging system, in a sample. The method uses reduction in fringe visibility, which is caused by such unresolvable microstructures, in moir\'e images obtained using an interferometer. We applied the method to a chloroprene rubber sponge sample, which exhibited uniaxial anisotropy of reduced visibility. We measured the dependencies of reduced visibility on both the Talbot order and the orientation of the sample and obtained maps of three parameters and their anisotropies that characterize the unresolvable anisotropic microstructures in the sample. The maps indicated that the anisotropy of the sample's visibility contrast mainly originated from the anisotropy of the microstructure elements' average size. Our method directly provides structural information on unresolvable microstructures in real space, which is only accessible through the ultra-small-angle x-ray scattering measurements in reciprocal space, and is expected to be broadly applied to material, biological, and medical sciences.

Method for designing phase-calculation algorithms for two-dimensional grating phase-shifting interferometry

We propose a design method of phase-analysis algorithms based on two-dimensional grating phase shifting for Talbot interferometry, Talbot-Lau imaging, or the Ronchi test. These algorithms are designed to separate the two orthogonal shearing wavefronts and eliminate error effects of unwanted diffraction orders, simultaneously. Taking the effect of multidiffraction into account, moving the two-dimensional grating along a certain pass leads to a series of phase-shifted interfrograms, from which two orthogonal shearing wavefronts are derived, for the tested wavefront to be retrieved. The designing process is demonstrated, and the residual errors are analyzed via simulation works and experimental comparison.

Collimation testing using coherent gradient sensing

In the present communication, an application of coherent gradient sensing (CGS) for collimation testing of an optical beam has been proposed. In the path of the beam to be tested, a set of two identical linear Ronchi gratings is introduced. The diffracted orders from the two gratings traveling in the same direction are isolated using spatial filtering arrangement. The resulting laterally sheared wavefronts carry information regarding the defocusing errors. The grating rotation mechanism has been incorporated for collimation setting. The results of experimental investigation are presented. Improved accuracy and precision has been achieved because the requirement of maintaining the grating separation to be equal to self-imaging distance as in Talbot interferometry has been alleviated.

Partially coherent nano-focused x-ray radiation characterized by Talbot interferometry

We have studied the spatial coherence properties of a nano-focused x-ray beam by grating (Talbot) interferometry in projection geometry. The beam is focused by a fixed curvature mirror system optimized for high flux density under conditions of partial coherence. The spatial coherence of the divergent exit wave emitted from the mirror focus is measured by Talbot interferometry The results are compared to numerical calculations of coherence propagation. In view of imaging applications, the magnified in-line image of a test pattern formed under conditions of partial coherence is analyzed quantitatively. Finally, additional coherence filtering by use of x-ray waveguides is demonstrated. By insertion of x-ray waveguides, the beam diameter can be reduced from typical values of 200 nm to values below 15 nm. In proportion to the reduction in the focal spot size, the numerical aperture (NA) of the projection imaging system is increased, as well as the coherence length, as quantified by grating interferometry.

Four-dimensional X-ray phase tomography with Talbot interferometry and white synchrotron radiation: dynamic observation of a living worm

X-ray Talbot interferometry is attractive as a method for X-ray phase imaging and phase tomography for objects that weakly absorb X-rays. Because X-ray Talbot interferometry has the advantage that X-rays of a broad energy bandwidth can be used, high-speed X-ray phase imaging is possible with white synchrotron radiation. In this paper, we demonstrate time-resolved three-dimensional observation with X-ray Talbot interferometry (namely, four-dimensional X-ray phase tomography). Differential phase images, from which a phase tomogram was reconstructed, were obtained through the Fourier-transform method, unlike the phase-stepping method that requires several (at least three) moiré images to be measured sequentially in order to generate one differential phase image. We demonstrate dynamic observation of a living worm in three dimensions with a time resolution of 0.5 s, visualizing a drastic change in the respiratory tract.

Automated collimation testing by incorporating the Fourier transform method in Talbot interferometry

In this paper, we report an automated technique for collimation testing by incorporating Fourier fringe analysis of the recorded interferograms in Talbot interferometry. The triangular profile of Talbot interferometric fringes has been recorded using a CCD and computer system. The interferograms corresponding to the in-focus, at-focus, and out-of-focus positions of the collimating lens have been recorded. Direct phase measurement using the Fourier transform method has been used for detection of collimation positions. Good accuracy and precision in measurement have been achieved.

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.

Real-time slope mapping and defect detection in bent plates using Talbot interferometry

We demonstrate a simple method for obtaining slope contours of bent plates using Talbot interferometry. The technique has been used to map slope contours of polymethyl methacrylate specimens of different shapes. The Talbot image of a coarse grating is projected onto a specimen such that the self-image is backreflected onto the same grating again. As a Talbot interferometer is basically a grating shearing interferometer, it results in the generation of characteristic slope maps of the specimen under test. Results of the investigation match well with other slope-mapping techniques. Validation of experimental results with theoretical predictions in the case of a cantilever beam specimen has been undertaken. Accuracy of about 4.7% with respect to theoretical predictions is obtained.

High-speed X-ray phase imaging and X-ray phase tomography with Talbot interferometer and white synchrotron radiation

X-ray Talbot interferometry, which uses two transmission gratings, has the advantage that broad energy bandwidth x-rays can be used. We demonstrate the use of white synchrotron radiation for high-speed X-ray phase imaging and tomography in combination with an X-ray Talbot interferometer. The moiré fringe visibility over 20% was attained, enabling quantitative phase measurement. X-ray phase images with a frame rate of 500 f/s and an X-ray phase tomogram with a scan time of 0.5 s were obtained successfully. This result suggests a breakthrough for time-resolved three-dimensional observation of objects that weakly absorb X-rays, such as soft material and biological objects.

Evaluation of the curvature of an object by Talbot interferometry

In this study a modified method of Talbot interferometry is developed to evaluate the curvature of an object. The tilt angle of moire fringe formed by two gratings is related to the wavelength, the grating periods, the angle between these two gratings, and the object curvature. Therefore, substituting the known experimental parameters into a special derived equation the object curvature can be evaluated. In order to show the validity of this method, stainless steel balls with curvatures of 1.326 and 1.261 mm−1 were measured. The measurement resolution of curvature was about 3.729 × 10−3 mm−1. It is shown that this method is suitable for both transmission and opaque objects with high accuracy.

Automated collimation testing using a temporal phase shifting technique in Talbot interferometry

We propose a quantitative approach toward the detection of collimation of a coherent optical beam. For detection of collimation position of the collimator, a temporal phase shifting technique has been incorporated into Talbot interferometry. The slope of the phase maps depicts the collimation position of the collimator. This technique offers high precision, accuracy, and provides automated output.

Sensitivity of X-ray Phase Imaging Based on Talbot Interferometry

The sensitivity of X-ray phase imaging based on Talbot interferometry is discussed. In order to evaluate the superiority of the technique to the conventional absorption-contrast method, which relies on X-ray absorption, a criterion is proposed. An experimental result of X-ray phase imaging with a Talbot interferometer is compared with the criterion. The criterion is also available for X-ray phase imaging based on Talbot–Lau interferometry. The advantage of X-ray phase imaging based on Talbot(–Lau) interferometry is more prominent when smaller structures are observed with smaller pixels.

Efficiency of capturing a phase image using cone-beam x-ray Talbot interferometry

We assesses the efficiency of x-ray Talbot interferometry (XTI), a technique based on the Talbot effect for measuring a wavefront gradient, in terms of how quickly it can capture a high-quality phase image with a large signal-to-noise ratio for a given incident photon number. Photon statistics cause errors in the phase of the moiré fringes and impose a detection limit on the wavefront gradient. The relation between the incident photon number and the detection limit is determined, and a figure of merit of XTI for a monochromatic cone beam is then defined. The dependence of the figure of merit on optical system parameters, such as grating pitch and position, is then discussed. The effects of varying the pattern height and linewidth of the second grating are shown for rectangular and trapezoidal teeth. Finally, we show how to design a practical cone-beam Talbot interferometer for certain boundary conditions.

On the possibility of controlling the wave front of a wide-aperture HF(DF) laser by the method of Talbot interferometry

The possibility of using the method of Talbot interferometry to control the wave fronts of wide-aperture pulsed HF(DF) lasers is studied experimentally. A search for sensitive screens for visualisation of radiation from a HF(DF) laser and other IR lasers is performed. Screens based on fine graphite powder on a rigid substrate proved to be most convenient for recording Talbot interferograms (talbotgrams). The emission of screens excited by laser pulses was detected with a digital photographic camera and images were processed in a PC. High-contrast talbotgrams of multifrequency radiation of a HF laser were obtained, demonstrating the possibility of controlling the wave fronts of HF(DF) lasers by the method of Talbot interferometry without separating an individual laser line.

Fabrication of Diffraction Grating with High Aspect Ratio Using X-ray Lithography Technique for X-ray Phase Imaging

The use of conventional X-ray radiography is limited due to weak absorption. This problem is resolved by using phase-sensitive imaging methods to improve the contrast, such as X-ray Talbot interferometry. With a spatially coherent light source and two diffraction gratings for Talbot interferometry, we measured the phase change differential. Using this technique, diffraction gratings were designed to have a fine high-accuracy high-aspect-ratio structure. Then, we fabricated a high-aspect-ratio diffraction grating using a deep X-ray lithography technique. A diffraction grating with a period of 8 µm and a height of about 30 µm was fabricated. This diffraction grating can be used for X-ray phase imaging for X-ray Talbot interferometry.

Phase Tomography by X-ray Talbot Interferometry for Biological Imaging

The X-ray phase tomography of biological samples is reported, which is based on X-ray Talbot interferometry. Its imaging principle is described in detail, and imaging results obtained for a cancerous rabbit liver and a mouse tail with synchrotron radiation are presented. Because an amplitude grating is needed to construct an X-ray Talbot interferometer, a high-aspect-ratio grating pattern was fabricated by X-ray lithography and gold electroplating. X-ray Talbot interferometry has an advantage that it functions with polychromatic cone-beam X-rays. Finally, the compatibility with a compact X-ray source is discussed.

X-ray Talbot Interferometry with Capillary Plates

An X-ray Talbot interferometer consisting of two capillary plates, which were used as X-ray amplitude gratings, was evaluated for X-ray phase imaging. A theoretical aspect of capillary X-ray Talbot interferometry is presented with a preliminary operation result using synchrotron radiation. A two-dimensional X-ray Talbot effect, or self-imaging effect, which was the basis of Talbot interferometry, was observed with the capillary plate, and moiré images formed by the X-ray Talbot interferometer exhibited contrasts corresponding to the differential phase shift caused by phase objects placed in front of the interferometer. Finally, the possibility of quantitative phase measurement with a fringe scanning technique is discussed.