Proposal for precise geometry parametrization of planar imaging detectors.
Cartesian coordinate system of setup is defined by three mutually orthogonal right-hand-indexed axes with origin in the interaction point (IP) of the photon beam with sample:
as shown in the plot:
Each photon with sample collision happens in different place... IP is an abstract position of the crossing point of the "beam line" and "target", which both are not well defined... Is it really good definition? |
Detector coordinate system may have a translation and rotation with respect to the setup, which can be defined by the 3 vectors in the setup frame:
ey – unit vector along the detector frame y axis,
as shown in the plot:
Third unit vector ez – is assumed to be right-hand triplet component,
ez=[ex × ey]
.
Components of these three unit vectors form the matrix e
, where indexes "i" and "j" corresponds to the vector components in the setup and detector local coordinate frames, respectively. Within this definition 3-d pixel coordinate "c" from in the detector frame can be easily transformed to the setup coordinate "C":ij
Ci=eij·cj + Pi
.
In this note we assume (although it is not necessary for most of algorithms) that:
It is assumed that each tile is presented in DAQ or offline data by a single block of memory. Uniform matrix-type geometry of pixel array is preferable, but other geometry can be handled, for example like in CSPAD 2x1 sensor. Detector data record consists of consecutive tile-blocks, in accordance with numeration adopted by DAQ. For effective memory management, some of the tile-blocks may be missing due to current detector configuration. Available configuration of the detector tile-blocks should be marked in a bit-mask word in position order (bit position from lower to higher is associated with the tile number in DAQ).
For example, consecutive pixel index in the CSPAD 2x1 tile memory block of size (185,388) is
i = col + row*388.
Optical measurements provide a list of coordinates for all sensor points:
Tile # |
---|
Point # | X[µm] | Y[µm] | Y[µm] |
---|
Quality check of optical measurement may include for each tile:
Detector pixels' geometry in 3-d can be unambiguously derived from
The tile location and orientation can be defined by the table of records
Tile # | Xc[µm] | Yc[µm] | Yc[µm] | Rotation angle [degree] | Tilt in X-Y[degree] | Tilt in Y-Z[degree] | Tilt in X-Z[degree] |
---|
where
Tile center coordinates are defined as an average over 4 corners.
Tilt angles are projected angles of the tile sides on relevant planes. Each angle is evaluated as an averaged angle for 2 sides.
Suggested method for imaging detector geometry description provides simple and unambiguous way of pixel coordinate parametrization. This method utilizes all available information from optical measurement and design of the detector and tiles. All geometry parameters are extracted without fitting technique and presented by natural intuitive way.