Tables for
Volume H
Powder diffraction
Edited by C. J. Gilmore, J. A. Kaduk and H. Schenk

International Tables for Crystallography (2018). Vol. H, ch. 2.5, p. 122

Section Pixel position in diffraction space for a curved detector

B. B. Hea*

aBruker AXS Inc., 5465 E. Cheryl Parkway, Madison, WI 53711, USA
Correspondence e-mail: Pixel position in diffraction space for a curved detector

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The conic sections of the diffraction cones with a curved detector depend on the shape of the detector. The most common curved detectors are cylinder-shaped detectors. The diffraction frame measured by a cylindrical detector can be displayed as a flat frame, typically a rectangle. Fig. 2.5.6[link](a) shows a cylindrical detector in the vertical direction and the corresponding laboratory coordinates XL, YL, ZL. The sample is located at the origin of the laboratory coordinates inside the cylinder. The incident X-rays strike the detector at a point O if there is no sample or beam stop to block the direct beam. The radius of the cylinder is R. Fig. 2.5.6[link](b) illustrates the 2D diffraction image collected with the cylindrical detector. We take the point O as the origin of the pixel position (0, 0). The diffraction-space coordinates (2θ, γ) for a pixel at P(x, y) are given by[\eqalignno{2\theta &= \arccos \left [R\cos \left({x\over R}\right) \big/({R^2} + {y^2})^{1/2} \right],&(2.5.8)\cr \gamma &= {x\over |x|}\arccos \left \{ - y\big/\left[ y^2 + R^2 \sin ^2\left({x \over R}\right)\right]^{1/2} \right\}\quad(-\pi \,\lt\, \gamma\leq \pi).&\cr &&(2.5.9)}]The pixel-position-to-(2θ, γ) conversion for detectors of other shapes can also be derived. Once the diffraction-space coordinates (2θ, γ) of each pixel in the curved 2D detector are determined, most data-analysis algorithms developed for flat detectors are applicable to a curved detector as well.

[Figure 2.5.6]

Figure 2.5.6 | top | pdf |

Cylinder-shaped detector in vertical direction: (a) detector position in the laboratory coordinates; (b) pixel position in the flattened image.

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