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Detector coordinate system may have a translation and rotation with respect to the setup, which are defined by the 3 vectors in the setup frame:

• P – translation vector pointing from IP to the detector origin,
• e_x – unit vector along the detector frame x axis,
• e_y – unit vector along the detector frame y axis,

• e_z – is assumed to be right-hand triplet component of  the vector e=(ex, ey, ez)

Within this definition 3-d pixel coordinate "c" from in the detector frame can be easily transformed to the setup coordinate "C":

                              Ci=eij·cj + Pi,

where indexes "i" and "j" corresponds to the vector components in the setup and detector local coordinate frames, respectively.

Tile ideal geometry

• Assume that the detector image is produced by a set of tiles (a.k.a., segment, section, 2x1, sensor, Si-pixel matrix, etc).
• Each tile has well defined by design geometry of pixels, which does not need in separate calibration.
• Pixel (x,y) center coordinate at z=0 for each tile can be defined as a look-up table in its "natural" matrix-style coordinate system.
• For example, CSPAD 2x1 tile pixel geometry is defined as

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