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, pp. 121-122

Section Pixel position in diffraction space for a flat 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 flat detector

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The values of 2θ and γ can be calculated for each pixel in the frame. The calculation is based on the detector-space parameters and the pixel position in the detector. Fig. 2.5.5[link] shows the relationship of a pixel P(x, y) to the laboratory coordinates XL, YL, ZL. The position of a pixel in the detector is defined by the (x, y) coordinates, where the detector centre is defined as x = y = 0. The diffraction-space coordinates (2θ, γ) for a pixel at P(x, y) are given by[\eqalignno{2\theta &= \arccos {{x\sin \alpha + D\cos \alpha } \over {( {{D^2} + {x^2} + {y^2}})^{1/2}}}\quad(0 \,\lt\, 2\theta \,\lt\, \pi), &(2.5.6)\cr \gamma &= {{x\cos \alpha - D\sin \alpha } \over {\left| {x\cos \alpha - D\sin \alpha } \right|}}\arccos {{ - y} \over {[{{y^2} + {{(x\cos \alpha - D\sin \alpha)}^2}})]^{1/2} }}&\cr &\quad\quad(- \pi \,\lt\, \gamma \le \pi). &(2.5.7)}]

[Figure 2.5.5]

Figure 2.5.5 | top | pdf |

Relationship between a pixel P and detector position in the laboratory coordinates.

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