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Proposal for precise geometry parametrization of planar imaging detectors.
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Coordinate system for setup
Axes definition
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 target:
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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 position
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:
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Components of these three unit vectors form the rotation 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" in the detector frame can be transformed to the setup coordinate "C" using equationij
Ci=eij·cj + Pi.
Coordinate system of the detector
In this note we assume that:
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These assumptions are not necessary for most of algorithms. But, in many cases it may be convenient to use small angle approximation or ignore angular misalignment for image mapping between tiles and and 2-d image array.
Tile ideal geometry
- Each tile has well defined by design geometry of pixels, which does not need in separate calibration.
- Pixel center (x,y) coordinates 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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- Regular pixels have size is 109.92 x 109.92 µm2,
- Pixel size in two middle columns 193 and 194 is 274.80 x 109.92 µm2.
Memory model
It is assumed that each tile is presented in DAQ or offline data by a single consecutive block of memory. Uniform matrix-type geometry of pixel array is preferable, but other geometry can be handled. For example, for example like in CSPAD 2x1 sensor pixel index in the tile memory block of size (185,388) can be evaluated as
i = column + row*388.
Detector data record consists of consecutive tile-blocks, in accordance with numeration adopted by in 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
- Optical measurements provide 3-d coordinates of 4 corners for all tiles in the detector in some arbitrary microscope plane which coincides with detector imaging array (tiles) plane within precision of installation.
- Tile corner coordinates do not necessarily coincide with corner pixel centers or edges.
- Numeration of tiles should not necessarily coincide with their numeration in DAQ, but it should be done in fixed order or with indication of tile numbers:
Optical measurements provide a list of coordinates for all sensor points:
Tile # Point # X[µm] Y[µm] Y[µm]
Quality check
Quality check of optical measurement may include for each tile:
- equity of opposite sides
- equity of diagonals
- equity of tilt angles for all sides
- tile flatness in 3-d
Position of tiles in the detector
Detector pixels' geometry in 3-d can be unambiguously derived from
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