Sébastien Harasse

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.

Hard-X-ray Phase-Difference Microscopy with a Low-Brilliance Laboratory X-ray Source

We have developed a hard-X-ray phase-imaging microscopy method using a low-brilliance X-ray source. The microscope consists of a sample, a Fresnel zone plate, a transmission grating, and a source grating creating an array of mutually incoherent X-ray sources. The microscope generates an image exhibiting twin features of the sample with opposite signs separated by a distance, which is processed to generate a phase image. The method is quantitative even for non-weak-phase objects that are difficult to be quantitatively examined by the widely used Zernike phase-contrast microscopy, and it has potentially broad applications in the material and biological science fields.

Iterative reconstruction in x-ray computed laminography from differential phase measurements

Phase-contrast X-ray computed laminography is demonstrated for the volume reconstruction of extended flat objects, not suitable to the usual tomographic scan. Using a Talbot interferometer, differential phase measurements are obtained and used to reconstruct the real part of the complex refractive index. The specific geometry of laminography leads to unsampled frequencies in a double cone in the reciprocal space, which degrades the spatial resolution in the direction normal to the object plane. First, the filtered backprojection formula from differential measurements is derived. Then, reconstruction is improved by the use of prior information of compact support and limited range, included in an iterative filtered backprojection algorithm. An implementation on GPU hardware was required to handle the reconstruction of volumes within a reasonable time. A synchrotron radiation experiment on polymer meshes is reported and results of the iterative reconstruction are compared with the simpler filtered backprojection.

X-ray phase laminography with Talbot interferometer

Laminography is a technique for 3D volume reconstruction, extending the classical tomography to the estimation of local areas in lamellar objects. We demonstrate X-ray phase laminography by using an X-ray Talbot interferometer consisting of two transmission gratings, which has been used only for X-ray phase tomography. In this presentation, experiments using 17.7 keV synchrotron radiation through a double-crystal monochromator are reported. The X-rays passed through the sample placed in front of the first phase grating. The rotation axis of the sample was set almost parallel to the sample plane normal, and inclined from the X-ray beam. Behind the second amplitude grating, moiré fringe patterns were measured by displacing one of the gratings in the direction parallel to its diffraction vector. Differential phase information were extracted through the fringe-scanning method. For the reconstruction of the three-dimensional volume from the differential phase information, the filtered back projection method was used with a specific filtering function. Promising results of phase laminography reconstruction are obtained for simulation data as well as weakly absorbing lamellar objects such as a polymer meshes and other samples. This advancement extends experiments with X-ray Talbot volume reconstruction to a larger variety of samples.

Four-dimensional X-ray phase tomography with Talbot interferometer and white synchrotron light

Taking advantage of the fact that an X-ray Talbot interferometer functions with X-rays of a broad energy bandwidth, high-speed X-ray phase tomography has been demonstrated by using white synchrotron light. Time resolution in addition to three-dimensional spatial resolution has been attained, and we report this achievement as the first four-dimensional (4D) X-ray phase tomography. Moire image movies of samples rotating at a speed of 1 or 2 rps generated by a Talbot interferometer were recorded at a frame rate of up to 1 kf/s, and differential phase image movies of the same frame rate were created by the Fourier-transform method. Consequently, a sub-second time resolution was achieved in the 4D phase tomography, while the spatial resolution was below 0.1 mm and 0.05 mm in axial and in-plane directions, respectively. An X-ray Talbot interferometer generates visibility images in addition to differential phase images, showing the distribution of microstructures, which cause ultra-small angle scattering but cannot be resolved individually with system spatial resolution. Tomographic image reconstruction from the visibility images was also demonstrated.

X-ray Talbot-Lau interferometer for high-speed phase imaging and tomography using white synchrotron radiation

The Talbot interferometer using white synchrotron radiation has already been demonstrated for high-speed X-ray phase imaging and tomography as well as four-dimensional phase tomography for an observation of a dynamic specimen. In those previous experiments, the grating lines were oriented horizontally because the synchrotron radiation source size is large in the horizontal direction, and only the vertical spatial coherence satisfies the requirement for the operation of the Talbot interferometer given its distance from the source. For non-rigid samples, the horizontal axis of rotation causes unwanted motion of the sample due to gravity which results to artifact in the tomography reconstruction. For fluid samples, a vertical rotation axis is certainly necessary. While it is possible to orient the sample rotation axis perpendicular to the grating lines of the Talbot interferometer, solving the definite integral of the differential phase images to obtain the phase shift for x-ray phase tomography proves to be...

X-ray phase laminography with a grating interferometer using iterative reconstruction

X-ray phase computed laminography is performed using a Talbot interferometer and synchrotron radiation. An iterative reconstruction algorithm which includes prior information about limited support, range of values and sparsity of the imaged object has been developped. It allows the reconstruction of objects with an improved resolution of the unsampled frequencies, compared to the classical filtered backprojection. The imaging method, demonstrated for a nylon mesh sample and a leaf sample, shows promising results for the imaging of flat, laterally extended objects made of low absorbing elements.

Quantitative visibility-contrast tomography in the X-ray Talbot interferometry

We propose a tomographic method using X-ray Talbot interferometry for mapping three-dimensional distribution of parameters characterizing microstructures, which are typically of the order of μm in size and cannot be resolved by the imaging system, in a sample. In the method we use reduction in fringe visibility, which is due to such unresolvable microstructures, of moire images obtained in the interferometry. We applied this method to a sample of melamine sponge containing chloroprene rubber. We performed tomographies at several Talbot orders and obtained the dependencies of the reconstructed values on the Talbot order for voxels. The parameters obtained by the least-squares fitting to the dependencies were consistent with those previously obtained from projection images for each material. Our approach provides three-dimensional structural information on unresolvable microstructures in real space, which is only accessible through the ultra-small-angle X-ray scattering (USAXS) in reciprocal space, and is e...

Solving Ill-Posed Linear Systems With Constraints on Statistical Moments

Abstract-The problem of finding a solution to an ill-posed linear problem Ax = b, with specific statistical properties is addressed, constraining the statistical moments of the N elements in x up to a given order d. It is reformulated as a higher dimension minimization problem with Nd variables, whose objective function is the composition of a convex function and a projection. Although convergence to a local minima is possible in rare cases, simulations show that in the vast majority of the cases, global convergence is attained with a standard descent algorithm. By extension, this opens the possibility to efficiently solve a larger class of problems that are linear in the powers of x. The tomographic reconstruction from a limited number of projection angles, constrained by centered moments, is considered as an example.

Hard-x-ray phase-imaging microscopy using the self-imaging phenomenon of a transmission grating

We report on a hard-x-ray imaging microscope consisting of a lens, a sample, and a transmission grating. After the theoretical framework of self-imaging phenomenon by the grating in the system is presented, equations for the electric field on the image plane are derived for ideal and real lenses and an equation for the intensity on the image plane for partially coherent illumination is derived. The equations are simple and similar to those applying to a projection microscope consisting of a transmission grating except that there is no defocusing effect, regardless of whether the grating is in front of or behind the lens. This means that x-ray phase-imaging microscopy can be done without the defocusing effect. It is also shown that, by resolving the self-image on the image plane, high-sensitive x-ray phase-imaging microscopy can be attained without degradation in the spatial resolution due to diffraction by the grating. Experimental results obtained using partially coherent illumination from a synchrotron x-ray source confirm that hard-x-ray phase-imaging microscopy can be quantitatively performed with high sensitivity and without the spatial resolution degradation.