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Inverse geometry for grating-based x-ray phase-contrast imaging
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View: Figures


Image of FIG. 1.
FIG. 1.

Grating interferometer geometries for given phase-grating period . The interferometer consists of source grating (G0), phase grating (G1), and analyzer grating (G2). The total length is the distance between G0 and G2, which is smaller than the distance between source (So) and detector (D). (a) Conventional geometry with and , (b) inverse geometry with and , and (c) symmetric geometry with and (for a -shifting phase grating G1). For given , the symmetric geometry has the shortest possible total length.

Image of FIG. 2.
FIG. 2.

Beam path for calculation of angular sensitivity as a function of object position. The relative sensitivity as a function of object position is derived distinguishing the cases: (a) refracting object between G1 and G2 with and (b) refracting object between source point and G1 with . (c) Plot of , which describes the linear scaling of the sensitivity. SP: source point; Obj: object; G1: phase grating; G2: analyzer grating. The source point can either be the focal spot of a microfocus x-ray tube or a slit in a G0 grating.

Image of FIG. 3.
FIG. 3.

Images of the measured phase shift (gray coded) of a square-shaped aluminum rod. The viewing direction is along one of the diagonals of the square-shaped rod. Images measured in the inverse geometry are shown for a few selected object positions : (a) −250 mm, (b) −120 mm, (c) −10 mm, (d) , (e) , and (f) . The gratings G0, G1, and G2 were positioned at , , and , respectively. The extension of the horizontal diagonal is . From (a) to (f), the source-to-rod distance increases, while the geometric magnification of the rod and thus the size of the projection image decrease. The averaging boxes for the left side (red) and the right side (blue) of the rod are exemplarily shown in (d). The images were cropped to a size of pixels and the color bar gives the measured phase-shift in radians.

Image of FIG. 4.
FIG. 4.

Phase shift measured on a square-shaped aluminum rod at 18 object positions. (a) Conventional geometry with G0 and G2 grating at and and (b) inverse geometry with G0 and G2 grating located at and .


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Inverse geometry for grating-based x-ray phase-contrast imaging