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

Rizzi, Julien; Weitkamp, Timm; Guérineau, Nicolas; Idir, Mourad; Mercère, Pascal; Druart, Guillaume; Vincent, Grégory; Silva, Paulo da; Primot, Jérôme

doi:10.1364/ol.36.001398

Cited by 35 publications

(19 citation statements)

References 10 publications

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“…20,[22][23][24][25][26] Moreover, the formulas for the 1-D phase grating interferometry can easily be derived from the general twodimensional theory through a dimension reduction. As is shown in Fig.…”

Section: Methodsmentioning

confidence: 99%

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

Yan

Liu

2015

Med. Phys.

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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 twodimensional 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 Talbotdistance 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. C 2015 American Association of Physicists in Medicine.

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Section: Methodsmentioning

confidence: 99%

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

Yan

Liu

2015

Med. Phys.

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“…This is because this technique may provide highly sensitive means for imaging soft tissues and low-Z materials, hence it has many potential applications in medical imaging and material science [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. X-ray grating interferometry is usually implemented as a Talbot-Lau interferometer [4,[15][16][17], which consists of an X-ray source, a source grating G 0 , a phase grating G 1 and an imaging detector, as is schematically shown in Fig.…”

Section: Introductionmentioning

confidence: 99%

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

Yan

Liu

2017

Opt. Express

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Abstract: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. T. Den, "Two-dimensional grating-based x-ray phase-contrast imaging using fourier transform phase retrieval," Opt. Express 19, 3339-3346 (2011). 14. J. Rizzi, P. Mercere, M. Idir, P. D. Silva, G. Vincent, and J. Primot, "X-ray phase contrast imaging and noise evaluation using a single phase grating interferometer," Opt. Express 21, 17340-17351 (2013). 15. A. Bravin, P. Coan, and P. Suortti, "X-ray phase-contrast imaging: from pre-clinical applications towards clinics,"Physics in Medicine and Biology 58, R1-R35 (2013). 16. N. Morimoto, S. Fujino, K. Ohshima, J. Harada, T. Hosoi, H. Watanabe, and T. Shimura, "X-ray phase contrast imaging by compact talbot-lau interferometer with a single transmission grating," Opt. Lett. 39, 4297-4300 (2014). 17. N. Morimoto, S. Fujino, A. Yamazaki, Y. Ito, T. Hosoi, H. Watanabe, and T. Shimura, "Two dimensional x-ray phase imaging using single grating interferometer with embedded x-ray targets," Opt. Express 23, 16582-16588 (2015).

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“…Even though very small grating periods necessitate interferometer designs outside the near field regime, a number of studies showed that far field interferometers can work as well under the right geometric configurations. [10][11][12][13] Another motivation for smaller grating periods is the image resolution. Recently, a number of promising approaches have been developed in x-ray microscopy that utilizes gratings to extract phase contrast.…”

Section: Introductionmentioning

confidence: 99%

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

Wen

Wolfe

Gomella

et al. 2013

Review of Scientific Instruments

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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.

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

Cited by 35 publications

References 10 publications

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

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

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

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

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