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Tracker Alignment with Millepede-II

Ryunosuke O'Neil (@ryuwd)

A Tracker Alignment utility for performing Track-based alignment with the Millepede-II software package. Only no-field cosmic tracks are currently supported.

My thesis on this work: FERMILAB-MASTERS-2020-07.

Alignment set-up

Alignment flow(2)

  • 'Digis' refers to art files containing 'digi' data products. Supported datasets are DS-cosmic-nofield or DS-cosmic-nofield-alignselect. Please see MDC2020Dev on the Mu2e Wiki.
  • Track Reco uses Richie's Time Fit ( Mu2e-doc-33162 )
  • 'MILLE' means to write input files for the 'PEDE' executable. The MILLE stage is implemented by MilleDataWriter.
  • 'Align Tracker' refers to the stage carried out by AlignedTrackerMaker (TrackerConditions). It uses alignment constants provided to the Proditions interface to change tracker straw positions accordingly.
  • 'Track Collection' is where the AlignTrackCollector module selects tracks, calculates the needed quantities for alignment, and writes the data to file using MilleDataWriter.
  • 'PEDE' refers to the millepede executable that performs the alignment fit given the output file(s) produced by the MilleDataWriter class during the AlignTrackCollector job(s).

MC Alignment test

  1. Set up this base release.
source <Offline release>/setup.sh
  1. Set up a TrackerAlignment helper environment. Note that you may also need to install some python packages using pip for the plotting scripts to work.
source ${MU2E_BASE_RELEASE}/TrackerAlignment/scripts/setup.sh

python -m pip install --user -r ${MU2E_BASE_RELEASE}/TrackerAlignment/scripts/requirements.txt
  1. Choose a working directory and setup your starting misalignment
cd /mu2e/data/users/$USER/
mkdir alignment-test
cd alignment-test

mu2ealign new MT_MDC2018_Fix5_30

This command generates job.fcl, alignconstants_in.txt, revision.txt, and sources.txt. This is effectively a working directory for one alignment iteration. This also saves the Mu2e Offline revision at the time of generation.

The Tracker is misaligned according to the 'MT_MDC2018_Fix5_30' configuration. The corresponding DbService text file in ${MU2E_BASE_RELEASE}/TrackerAlignment/test/misalignments/ is copied.

It's important to choose which planes to fix in the alignment, in order to suppress weak modes, such as a stretch or squeeze in z. Fixing planes 5, 30 to zero in all DOFs, for example. This means changing the values accordingly in alignconstants_in.txt for Plane 5 + 30, and ensuring that these parameters are set in job.fcl:

physics.analyzers.AlignTrackCollector.ConstrainStrategy : "Fix"
physics.analyzers.AlignTrackCollector.FixPlane : [ 5, 30 ]

You should also study the other defaults in job.fcl and tune the parameters according to your requirements.

  1. Run Track Collection + PEDE interactively

You can run one process to collect the track data like this:

# running one job only
mu2ealign run

Or, you may run multiple processes:

# running multiple jobs e.g. 4 jobs processing 8 input files, 
# or 8 / 4 = 2 input art files per job
mu2ealign_genparallel 4 8
mu2ealign run

Once the jobs finish, you can run the first alignment fit:

mu2ealign pede

Now you should make a new directory, and import the produced alignment constants:

mkdir iter1 && cd iter1
mu2ealign new ../alignconstants_out.txt

Then return to the beginning of this step.

Or, you can run multiple iterations automatically (easier, recommended)

# 
mu2ealign autorun 3 # for 3 alignment iterations and one nominal run
  1. Examine output
# examine cosmic track diagnostics if needed
aligntrack_display TrackDiag.root < other trackdiag.root files to compare against >


# plot and show shifts and pulls
python ${MU2E_BASE_RELEASE}/TrackerAlignment/scripts/make_shiftplot.py "First Run" alignconstants_out.txt "Second Run" iter1/alignconstants_out.txt

Issues

  • Only the track drift time measurement is included in the chi^2 which is why chi^2/Ndof tends to peak at 0.5, rather than 1 when you plot it. Also Millepede will report a global chi2/ndof of around 0.5.
    • In the actual cosmic fit, there are two terms added to the chi-squared for the track per straw hit (see the definition here)
  • Panel d.o.f.'s not supported yet
    • constraints need to be developed (if you enable the panel DOFs the fit will fail for lack of these)

Alignment Derivatives

Terms

Global degrees of freedom

These are alignment parameters that currently describe a translation or rotation in x, y, z applied to one Plane, and (later) Panel. These are 'global' because their values are common across all input tracks.

Local degrees of freedom

These are the track fit parameters for one track. One set of local parameters describes one track.

Derivatives?

For each global and local degree of freedom, Millepede requires a partial derivative of the track residual with respect to that degree of freedom.

There can be as many as 100 or 1000 global degrees of freedom, however of those Millepede only needs to know what the non-zero derivatives are. In this case, only those DOFs corresponding to the Plane and Panel holding a crossed (or hit) Straw will be nonzero. This sparse storage scheme saves a lot of space.

For the cosmic track time fit, there is a numerical differentiation utility to calculate these quantities. There is also a python utility that constructs the algebraic form of the derivatives. Once calculated, the utility will generate a C++ header and source file (AlignmentDerivatives.hh/AlignmentDerivatives.cc). This is included and implemented in the AlignmentUtilities namespace to provide the required non-zero derivatives given a cosmic track hit for 3 translation and 3 rotational degrees of freedom for Planes, and Panels. Run the generate_derivatives.py script to regenerate these files for the currently sourced Mu2e Offline release, if needed.

Please note: The algebraic derivatives are not used at the moment. Ideally (whether or not this implementation is used), analytical forms of the partial derivatives will be used in the alignment.