Appendix A2. Detector Coordinate System¶
Crystal Diffraction simulates a diffraction pattern on a detector. The detector is a finite-sized plane of pixels placed at a fixed distance from the sample, possibly tilted with respect to the incident beam. Accurate simulation requires knowledge of the geometric relationship between detector and sample.
Before rotation (detector normal to beam)¶
Real coordinates (X, Y, Z)¶
3D Cartesian coordinates in mm with the sample as origin. - Z-axis: always parallel to the beam direction (note: differs from Appendix A1 definition). - X-axis: rightward facing Z. - Y-axis: downward.
Detector coordinates (X', Y')¶
2D Cartesian coordinates in mm on the detector plane with the foot as origin. X' and Y' are parallel to X'' and Y''.
Pixel coordinates (X'', Y'')¶
2D coordinates in pixel units with the upper-left corner of the detector as origin.
Key definitions¶
| Term | Definition |
|---|---|
| Foot | The foot of the perpendicular from the sample to the detector plane. If the detector is normal to the beam, the foot coincides with the direct spot |
| Direct spot | Intersection of the incident beam and the detector |
| Camera length 2 (C2) | Distance from sample to foot (mm) |
| Camera length 1 (C1) | Distance from sample to direct spot (mm) |
| Pixel size | Side length of one pixel (mm); square pixels only |
| Detector width/height | Pixel counts horizontally/vertically |
After rotation (tilted detector)¶
Two parameters describe the detector tilt:
| Parameter | Description |
|---|---|
| φ | Direction of the rotation axis (angle from X-axis in the XY plane) |
| τ | Rotation angle around the axis defined by φ (right-hand screw) |
After rotation: - The direct spot and foot are no longer coincident. - C1 = distance from sample to direct spot. - C2 = distance from sample to foot. - The origin of Detector coordinates remains at the foot. - The origin of Pixel coordinates remains at the upper-left corner. - When tilted, X/Y directions do not coincide with X'/Y' directions.