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ITS Alignment Meeting CERN, April 13 th 2007 ITS alignment using Millepede: first steps

This document discusses the concept of Millepede alignment and its implementation in the ITS system at CERN. It covers basic concepts, the AliRoot implementation (AliMillepede), and testing of the algorithm. The paper also explores the generation and control of test track sets and correlations and collective modes.

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ITS Alignment Meeting CERN, April 13 th 2007 ITS alignment using Millepede: first steps

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  1. ITS Alignment Meeting CERN, April 13th 2007 ITS alignment using Millepede: first steps M. Lunardon, A. Dainese, S. Moretto, A. Rossi University of Padova INFN of Padova and LNL

  2. Working plan • Understanding Millepede • basic concepts • the AliRoot implementation AliMillepede • the MUON example: AliMUONAlignment • Implementation for ITS • todo list • Testing the algorithm • preparation of test track sets • correlations and collective modes

  3. Understanding Millepede • Starting points • Original development by V. Blobel (http://www.desy.de/~blobel/wwwmille.html) with FORTRAN implementation • C++ translation by S. Viret (LHCb) • AliRoot implementation (AliMillepede) by MUON people (J. Castillo et al.) • Alignment class (AliMUONAlignment) and full test alignment example for MUON ($ALICE_ROOT/MUON/AlirootRun_MUONtestAlign.sh)

  4. Understanding Millepede Millepede: Linear Least Squares Fits with a Large Number of Parameters In certain least squares fit problems with a very large number of parameters the set of parameters can be divided into two classes, global and localparameters. Local parameters are those parameters which are present only in subsets of the data.Detector alignment and calibration is one of the problems, where the interest is only in optimal values of the global parameters. A method to solve the linear least square problem, irrespectively of the number of local parameters, is derived in the paper. A practical limit for the number of global parameters is between one thousand and ten thousand. Main requirement: the measured value (the cluster coordinates in our case) can be expressed as linear function of the global (di) and local (i) parameters

  5. z z x • Understanding Millepede • The simple Blobel’s example : • 2 local track parameters (straight lines) • 10 detector modules • 1 alignment parameter per module (z) • first module is fixed (reference module) For 1000 tracks  1000 x 2 + 9 x 1 ~ 2009 parameters but only 9 are interesting 1) write the measurement z as linear function of local and global parameters In this case: 2) calculate derivatives wrt global and local parameters

  6. Understanding Millepede generation and control plot to be substituted by the cluster coordinate input passing derivatives for each measured points

  7. corrected • Understanding Millepede: the MUON example • For each module j they write a linear function Fj for the residuals(not meas. pts) • The residual function Fj is built using global and local coordinates. • The misalignment parameters are explicitly introduced in the Global-to-Local transformation: yG track point yLreal yL xLreal rL O xL xG

  8. Understanding Millepede: the MUON example Residual function (x and y component) Substitute xtr, ytr with the parameterized value and linearize (1st order exp.) Calculate derivatives ...

  9. Implemetation for ITS • new interface class AliITSAlignment (cut&paste from AliMUONAlignment) • at the moment, use of general class AliMillepede as it is (might need some modifications in the future...) • choice of the input data format: good candidate is AliAlignmentTracks and AliTrackPointArray (evenctually + track parameters) • first attempt with B=0 (straight lines)

  10. Implemetation for ITS • parameterization of the track to get derivatives • - try to use std parameters ytr, ztr, tg , sin , 1/pt • identification of the global constraints: • - global translation • - global rotation • - ... • switch on B field

  11. Testing the algorithm • 1) small and simple test cases for software development • generation of a “special” set of cosmics-like tracks: • a narrow beam of parallel 10 GeV muons along the vertical axis  only ~ 20 modules involved in the whole ITS; • simple misalignment: only translations in the x-z local planes  about 20x2 = 40 alignment parameters; • first test data set of about 800 tracks with null and simple-misalignment (12 points required) ready. • next: generation of collision-like tracks in a small radial cone (6 points required) • next: generation with (partially) correlated misalignment

  12. Testing the algorithm • 2) more realistic simulations • full distribution of cosmic muons (B=0 and B!=0) • pp collisions (B=0 and B!=0) • effect of the collective modes • for SPD: • translation of whole SPD planes • rotation of whole SPD planes • torsion of whole SPD sectors • for SDD, SSD: to see...

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