Coordinate systems used in the reconstruction Global System

Coordinate systems used in the reconstruction • Global System : event display, calibration, alignment, … • Local Systems : cluster/track finding, alignment, … • “Detector Coordinate System” • “Tracking Coordinate System” I. Belikov ALICE PPR meeting 07 Feb 03 1

Importance of the right choice of the coordinate system • Explicit view (simplicity) of the underlying reconstruction mathematics. • Efficiency (speed) of the transformations Local <-> Local’ and Local <-> Global. • It’s a strategic choice, when designing new • components of the reconstruction software (now: alignment, beam tests data analysis) If agreement on the CS is achieved, then The code is more logical and easier to understand Matching between the detectors is faster The detectors can share more common code • • • I. Belikov PWG 1 meeting, CERN, 31 May 2005 2

Detector Coordinate System (DCS) Definition: the origin is at the center of a detector, the axises are parallel to the faces. (used by Ali. ITSRec. Points) Advantages : n Y The most naïve local CS. Disadvantages: Y Not optimal for the tracking; n Not optimal of the transformations L <-> L’; n Not optimal for the transformations L <-> G. n X Z (Both translations and rotations are needed) I. Belikov ALICE PPR meeting 07 Feb 03 3

Tracking Coordinate System (TCS) Definition: the origin and the Z-axis coincide with the ones of the Global CS, X-axis goes perpendicular to a detector face. (used by Ali. ITScluster. V 2, Ali. TPCcluster, Ali. TDRcluster) Disadvantages : n X’ Less naïve than the DCS. Advantages: Optimal for the tracking (equations, cluster offsets); n Transformations L <-> L’ are a single rotation by 20°… around Z-axis; n Transformations L <-> G are a single rotation by 10°, 30°, 50°… around Z-axis. n Y’ Right angle I. Belikov ALICE PPR meeting 07 Feb 03 4

TCS case 1: X-axis goes via the center of a sub-detector The Y-coordinate in the local DCS and TCS may coincide, but the Z-coordinate does not. X’ Examples: - SSD and SDD layers of the ITS; - TPC/TRD sectors; Y’ - TOF/PHOS/EMCAL modules; Right angle I. Belikov - 3 (out of 7) HMPID modules. ALICE PPR meeting 07 Feb 03 5

TCS case 2: X-axis does not go via the center of a sub-detector Neither Y- nor Z-coordinate in the DCS and TCS coincide ! X’ Example: - The inner SPD layer of the ITS. Y’ Right angle I. Belikov ALICE PPR meeting 07 Feb 03 6

TCS case 2’: X-axis does not go via the center of a sub-detector (y=0 is out of the sub-detector) Neither Y- nor Z-coordinate in the local DCS and TCS coincide ! Example: X’ Y’ - The outer SPD layer of the ITS. Right angle I. Belikov ALICE PPR meeting 07 Feb 03 7

Choice DCS <-> TCS • • The choice DCS (“ITSRec. Point”) – TCS (“ITScluster. V 2”) has very little to do with the cluster finding. Any cluster finder would do : Calculations in “pad/time bin space” Multiplication by pad/time bin width (to go to the “normal space”) Addition of some offset constants (to get the right origin of the coordinates/to compensate for time delays etc). Only the offset constants are different in the DCS and TCS. Each cluster is offset only once. • • • The choice DCS (“ITSRec. Point”) – TCS (“ITScluster. V 2”) has more to do with the track finding : If the choice of the offsets are not optimal, then each cluster has to be offset as many times as it gets used. (The same may be true for any other then tracking procedures that deal with the same cluster several times : event display ? alignment ? ) • I. Belikov PWG 1 meeting, CERN, 31 May 2005 8

Conclusions • • • We have to deal with (at least) two coordinate system : Global Coord. System and Local Coord. System. Choice for the GCS: ALICE Master Coord. System. Choice for the LCS: Tracking Coord. System ? Advantages: • • Simplicity of the tracking equations • The fastest possible transformations L <-> L’ and G <-> L • Suitable for (almost) all the detectors and “non tracking operations”: Cluster finding, beam test data analysis (coincides with DCS, or has a fixed offset at worst) The same software to process the beam test and MC data ! • • Disadvantages: I. Belikov Are there any ? PWG 1 meeting, CERN, 31 May 2005 9