Refraction in a Talbot-Lau setup allows High Energy, Visibility, and Sensitivity

Preusche O, Weber T, Anton G (2015)

Publication Language: English

Publication Type: Conference contribution, Abstract of a poster

Publication year: 2015

Event location: Garmisch-Patenkirchen


Photon energies above 50 keV are rarely used in Talbot-Lau interferometers, because the analyzer grating G2 becomes quite transparent at higher photon energies [1-4]. For medical imaging, this transparency causes an inacceptable increase in radiation dose. To allow higher energies, several proposals exist to allow higher gold gratings: Edge-on illumination [2] strongly reduces the field-of-view, glancing angle geometry [3] may increase setup length, and phase gratings consisting of alternating prisms [4] reduce angular sensitivity. In this work, we present a further new proposal to solve the aspect ratio problem.

Method: The basic idea is to use a refracting lens to combine N>1 fringes into a single fringe (see Fig. 1). An array of such lenses (called 'lens grating') replaces the analyzer grating G2. A new G2 (the period now is N times larger) is put into the focal plane of the lens-array. To this end, several problems have to be solved.

Problem 1 – Refraction strongly depends on photon energy. Since G2 is now coarse, the refraction angle is allowed to change by a factor of 3.

Problem 2 – Production of strong prisms for a fresnel-style lens. [4] inclines the light source during lithography by rotation around a grating bar (around the y-axis), this delivers strong alternating prisms. We incline by rotating within a grating bar (around the x-axis) and use a y-periodic contract in the grating layout to produce differently strong prisms – this allows to encode a complete fresnel lens in a simple binary layout.

Problem 3 – The lenses must analyze the fringe phase. To do so, two arrays of fresnel lenses are interleaved into each other. The even lenses (black) focus on G2 grating bars, the odd lenses (magenta) focus on G2 grating slits.

Problem 4 – This does not work with a regular source grating G0. An additional coherence constraint defines a set of planes in which G2 can be placed. Also required is a grouping: In each group of Q slits, only q < Q/2 slits may stay open – we need hierarchical coherence in the form of a darker G0 (see orange lines in Fig. 1).

The resulting setup allows analyzer grating periods as large as in the source grating G0. A lens grating may consist of very narrow strips, allowing higher angular sensitivities (refraction is proportional to aspect ratio).

Results: We present simulation results of a setup of 180 mm post-patient length for a design energy of 59 keV. The setup uses a modified binary phase grating G1 to operate in second talbot order. This increases sensitivity. The lens grating has a strip width of 0.9 µm ('period' 1.8 µm) and a gold height of 54 µm (aspect ratio 73). It combines 5 fringes to one, resulting in a period of 9.3 µm for G2. The simulation (see Fig. 2) is based on Fresnel-Kirchhoff diffraction. It shows that the lens grating keeps 92% of the visibility created by the first two gratings.

Conclusion: The proposal solves the height-problem in the analyzer grating G2. However, G0 will become the critical component of the setup, because of the additional coherence requirements. One option to solve this might be the combination with the glacing angle [3] approach.


[1] T. Donath, F. Pfeiffer, O. Bunk, W. Groot, M. Bednarzik, C. Grünzweig, E. Hempel, S. Popescu, M. Hoheisel and C. David, "Phase-contrast imaging and tomography at 60 keV using a conventional x-ray tube source", Review of Scientific Instruments 80, 053701 (2009), DOI 10.1063/1.3127712

[2] T. Thüring, M. Abis, Z. Wang, C. David, and M. Stampanoni, "X-ray phase-contrast imaging at 100 keV on a conventional source", Scientific Reports 4 : 5198 (2014), DOI: 10.1038/srep05198

[3] A. Sarapata, J. W. Stayman, M. Finkenthal, J. H. Siewerdsen, F. Pfeiffer, and D. Stutman, "High energy x-ray phase contrast CT using glancing-angle grating interferometers", Med Phys. Feb 2014; 41(2): 021904, Doi: 10.1118/1.4860275

[4] A. Yaroshenko, M. Bech, G. Potdevin, A. Malecki, T. Biernath, J. Wolf, A. Tapfer, M. Schüttler, J. Meiser, D. Kunka, M. Amberger, J. Mohr, and F. Pfeiffer, "Non-binary phase gratings for x-ray imaging with a compact Talbot interferometer," Opt. Express 22, 547-556 (2014), Doi: 10.1364/OE.22.000547

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Preusche, O., Weber, T., & Anton, G. (2015). Refraction in a Talbot-Lau setup allows High Energy, Visibility, and Sensitivity. Poster presentation at International Symposium on BioMedical Applications of X-Ray Phase Contrast Imaging (IMXP 2014), Garmisch-Patenkirchen.


Preusche, Oliver, Thomas Weber, and Gisela Anton. "Refraction in a Talbot-Lau setup allows High Energy, Visibility, and Sensitivity." Presented at International Symposium on BioMedical Applications of X-Ray Phase Contrast Imaging (IMXP 2014), Garmisch-Patenkirchen 2015.

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