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ITS Alignment: Millepede ITS Alignment: Millepede ResultsResults
S. MorettoS. Moretto, ,
C. Bombonati, A. Dainese, M. C. Bombonati, A. Dainese, M. Lunardon, A. RossiLunardon, A. Rossi
S. MorettoS. Moretto Convegno Fisica di Alice Palau, Settembre Convegno Fisica di Alice Palau, Settembre 20082008
Contents:Contents:
Alignment Strategy and Task
Millepede Method:
– Idea of Millepede
– the ITS Millepede Class
Validation of the strategy with simulation:
– tests and results with Millepede
First Cosmic Data:
– Results and Status of the alignment with
Millepede
S. MorettoS. Moretto Convegno Fisica di Alice Palau, Settembre Convegno Fisica di Alice Palau, Settembre 20082008
ITS Alignment TaskITS Alignment Task
Tracking detectors in high-energy physics experiments require an accurate determination of a large number of alignment parameters in order to allow a precise reconstruction of tracks and vertices. In addition to the initial optical survey, the use of tracks in a special software alignment is essential.
As an example, for the pixel detectors, whose position
resolution is about 12 m in the most precise direction, a residual misalignment not larger than 10 m can be tolerated.
The task of aligning the ALICE ITS is particularly challenging also due to the very large number of degrees of freedom, which are about 13,000.
The ITS alignment procedure will use tracks from cosmic-ray muons (data taking started in February 2008), and tracks from pp collisions that will be collected next year.
S. MorettoS. Moretto Convegno Fisica di Alice Palau, Settembre Convegno Fisica di Alice Palau, Settembre 20082008
ITS Alignment StategyITS Alignment Stategy
For the alignment of the ALICE Inner Tracking System two independent methods, based on tracks-to-measured-points residuals minimization, are being prepared.
One method performs a (local) minimization for each single module and accounts for module correlations by iterating the procedure until convergence is reached.
The second method uses the Millepede approach, where a global fit to all residuals is performed, extracting all the misalignment parameters simultaneously.
S. MorettoS. Moretto Convegno Fisica di Alice Palau, Settembre Convegno Fisica di Alice Palau, Settembre 20082008
Millepede Starting PointMillepede Starting Point
The original development of the Millepede method has been done by V. Blobel (http : www.desy.de/blobel/wwwmille).
All LHC experiments make use of Millepede method.
In ALICE framework, in particular, AliRoot, it was first implemented by the MUON spectrometer group (J. Castillo et al.) and now, a dedicated alignment class has been created (AliITSAlignMille) for ITS.
S. MorettoS. Moretto Convegno Fisica di Alice Palau, Settembre Convegno Fisica di Alice Palau, Settembre 20082008
Millepede IdeaMillepede Idea
In an alignment environment, the track data are position measurements of a charged particle track.The position measurement, from several detector planes of the track detector, depend on the position and orientation of certain sensors, and the corresponding coordinates and angles are global parameters
A practical limit for the number of global (alignment) parameters is about ten thousands
Millepede is a method to solve the linear least
squares problem with a simultaneous fit of all global (alignment) and local (track)
parameters, irrespectively of the number of local
parameters.
S. MorettoS. Moretto Convegno Fisica di Alice Palau, Settembre Convegno Fisica di Alice Palau, Settembre 20082008
Millepede StrategyMillepede Strategy
Main requirement of Millepede approach is that the measured value, the residual, i.e. the deviation between the measured and the fitted data, can be well approximated with a linear function of the track (= local, qk) and alignment (= global, pl) parameters.
ll l
jj j
lkiii pp
fq
q
fpqxfyz
1
),,(
For a set of N local measurements one obtains a system of least squares normal equations with large dimensions
S. MorettoS. Moretto Convegno Fisica di Alice Palau, Settembre Convegno Fisica di Alice Palau, Settembre 20082008
Millepede for the ITSMillepede for the ITS
We can summarize the ITS alignment algorithm in the following steps:
1. Initialization from a configuration file (list of modules to be aligned, constraints, starting geometry);
2. Calculation for each track of the local and global derivatives at each hit and filling the corresponding local equations;
3. Local (track) fits;4. Global (alignment parameters) fit.
S. MorettoS. Moretto Convegno Fisica di Alice Palau, Settembre Convegno Fisica di Alice Palau, Settembre 20082008
Millepede Results with MC Millepede Results with MC datadata
Promising results have been obtained with a sample of 50000 simulated cosmic muons crossing both SPD layers.
A realistic misalignment is applied to the sensors:
for example, SPD: significant misalignments for BARREL for example, SPD: significant misalignments for BARREL (-300 (-300 m, -300 m, -300 m, 500m, 500m, -30mdeg, 40mdeg, -150mdeg), m, -30mdeg, 40mdeg, -150mdeg), HB, Sectors, Half-Staves and LaddersHB, Sectors, Half-Staves and Ladders
The considered modules to be aligned are about 1/3 of the whole ITS and we considered 12 points tracks (two points for each single ITS layer).
655 modules ( 142 + 108 + 405 ) = ( 59%SPD + 41%SDD + 24%SSD)
S. MorettoS. Moretto Convegno Fisica di Alice Palau, Settembre Convegno Fisica di Alice Palau, Settembre 20082008
XXlocloc
YYlocloc
ZZlocloc
MC Results: single module MC Results: single module alignmentalignment
SPDSPD SDDSDD SSDSSD
S. MorettoS. Moretto Convegno Fisica di Alice Palau, Settembre Convegno Fisica di Alice Palau, Settembre 20082008
Summary results for MC Summary results for MC cosmic datacosmic data
All mean values for SPD and SDD ~ 0 m
RMS around 10 micron
(*)values in m or mdeg
PARAM
SPD SDD SSD
mea
nrms
mea
nrms
mea
nrms
X 0 6 0 9 0 16
Y 2 10 17 17 -60 60
Z 0 6 0 11 5 65
Psi 1 19 -2 16 -8164
Theta -2 10 1 6 0 18
Phi 1 71 1 24 -14120
S. MorettoS. Moretto Convegno Fisica di Alice Palau, Settembre Convegno Fisica di Alice Palau, Settembre 20082008
ITS tracking resolutions: dITS tracking resolutions: d00 rr
ITS tracking stand-aloneno misalignmentfull mis + perfect realignfull mis + Millepede realign(all ITS) full mis + Millepede realign(only realigned modules ~500: |/2|<.5 && |-/2|<.5)
S. MorettoS. Moretto Convegno Fisica di Alice Palau, Settembre Convegno Fisica di Alice Palau, Settembre 20082008
Millepede with cosmic dataMillepede with cosmic data
Statistics up Sep. 3rd 2008
58400 total tracks
30300 with 4 pts in SPD (used for Millepede)
24200 with 3 pts in SPD
S. MorettoS. Moretto Convegno Fisica di Alice Palau, Settembre Convegno Fisica di Alice Palau, Settembre 20082008
Millepede Strategy:Millepede Strategy: Hierarchical Alignment Hierarchical Alignment
step 1step 1 HALF BARREL SPDHALF BARREL SPDstep 2step 2 SECTORS SPDSECTORS SPDstep 3step 3 HALF STAVES SPDHALF STAVES SPDstep 4 step 4 LADDERS SPDLADDERS SPD
step 5step 5 SPD position optimized
wrt SSD
step 6step 6 LADDERS SSD LADDERS SSD & SPD FIXED& SPD FIXED
step 7step 7 HALF LADDERS SSD HALF LADDERS SSD & SPD FIXED& SPD FIXED
SPD
SSD
SDD: will be included once calibrated
S. MorettoS. Moretto Convegno Fisica di Alice Palau, Settembre Convegno Fisica di Alice Palau, Settembre 20082008
SPD Alignment Status: SPD Alignment Status: Statistics up Sep. 3rd 2008
= 75% of full SPD(90% of alignable modules)
StavesStaves HalfStavesHalfStaves LadderLadderss
Stat>0Stat>0 53 102102 202202Stat>5Stat>500
5151 9898 180180
Aligned modules Statistics:
StavesStaves HalfStavesHalfStaves LadderLadderss
Stat>0Stat>0 58 111111 220220Stat>5Stat>500
5555 103103 200200
Alignable modules:
S. MorettoS. Moretto Convegno Fisica di Alice Palau, Settembre Convegno Fisica di Alice Palau, Settembre 20082008
Millepede Results: Millepede Results: ResidualsResiduals
Track: 3-points fits on SPD and look at residuals on SSD
S. MorettoS. Moretto Convegno Fisica di Alice Palau, Settembre Convegno Fisica di Alice Palau, Settembre 20082008
Residuals: Raw and Residuals: Raw and MillepedeMillepede
SSD INNER SSD OUTERSSD INNER SSD OUTER
S. MorettoS. Moretto Convegno Fisica di Alice Palau, Settembre Convegno Fisica di Alice Palau, Settembre 20082008
Millepede Results: delta XMillepede Results: delta X
One meaningful observable of the realignment quality is the mismatch in X of the tracks @ Y=0
S. MorettoS. Moretto Convegno Fisica di Alice Palau, Settembre Convegno Fisica di Alice Palau, Settembre 20082008
Millepede Results for SPD Millepede Results for SPD Hierarchical AlignmentHierarchical Alignment
Alignment of SPD in 4 steps:sectors -> staves -> half staves -> ladders
S. MorettoS. Moretto Convegno Fisica di Alice Palau, Settembre Convegno Fisica di Alice Palau, Settembre 20082008
SPD alignment status: delta X final result
Using the full sample of tracks to realign and to check the results
MEAN= 0.9 m
SIGMA= 55 m
Compatible with a spatial resolution of ~ 15 m
S. MorettoS. Moretto Convegno Fisica di Alice Palau, Settembre Convegno Fisica di Alice Palau, Settembre 20082008
Millepede: Extra ClustersMillepede: Extra Clusters
TRACK-EXTRA CLUSTER DISTANCE IN THETRANSVERSE PLANE
Realignment of data with overlapping clusters:
overlapping clusters not used in the alignment gaussian peak (small tails)
sigma ~ 20-22 m
spatial resolution ~ 14-16 m
S. MorettoS. Moretto Convegno Fisica di Alice Palau, Settembre Convegno Fisica di Alice Palau, Settembre 20082008
SSD Alignment StatusSSD Alignment Status
To recall the alignment of SSD procedure: alignment of SSD with the SPD already aligned
– SPD position optimized wrt SSD (raw data)– SPD fixed and Ladders SSD– SPD fixed and Half Ladders SSD
meanX sigmaXmean
Zsigma
Z
raw 1 47 87 326
ladders
-2 36 -10 262
HL -1 36* -3 214
Results for the Delta X (Z) @ Y=0 [abs(X0)<1 cm]
(*) Fitting the peak in [-0.060, 0.060] => sigma = 28 m, to be compared with perfect simulation (17 m)
S. MorettoS. Moretto Convegno Fisica di Alice Palau, Settembre Convegno Fisica di Alice Palau, Settembre 20082008
Stability Test for Millepede Stability Test for Millepede resultsresults
Stability test with 10k-tracks samplesStability test with 10k-tracks samples
DeltaX @ Y=0 plots with same alignment file
From Track
Mean Sigma
0 -10 54.2
10000 -2 53.1
20000 0.9 52.5
30000 2.1 54.3
40000 2.1 53.6
50000 1.3 51.7
Very small differences along the whole cosmic data sample
S. MorettoS. Moretto Convegno Fisica di Alice Palau, Settembre Convegno Fisica di Alice Palau, Settembre 20082008
Millepede Code: StatusMillepede Code: Status
The development and debugging of the The development and debugging of the code is almost completedcode is almost completed
Possible improvements might be Possible improvements might be obtained with further analysis of the dataobtained with further analysis of the data
Hierarchical realignment (ITS Layers, HB, Hierarchical realignment (ITS Layers, HB, sectors, ..) already validated sectors, ..) already validated
The Millepede code for B>0 (helix tracks) has The Millepede code for B>0 (helix tracks) has been already implemented.been already implemented.The code has been verified with simulation The code has been verified with simulation data: similar results wrt B=0 case with NULL data: similar results wrt B=0 case with NULL misalignment.misalignment.
S. MorettoS. Moretto Convegno Fisica di Alice Palau, Settembre Convegno Fisica di Alice Palau, Settembre 20082008
ConclusionsConclusions
Millepede with MonteCarlo simulation has been crucial: to optimize the code to understand the strategy to validate the results
Millepede RESULTS with first cosmics data: hierarchical realignment
ready and validated useful to get information with medium-low statistics
Overall performance of alignment quite stable SPD Alignment:
from width of track-to-track distance plot and overlapping cluster distance, a spatial resolution of about 14-16 micron is extracted;
SSD Alignment: alignment performed at the level of Half-Ladder
SDD Alignment: ready to be included as soon as the calibration has been
done
S. MorettoS. Moretto Convegno Fisica di Alice Palau, Settembre Convegno Fisica di Alice Palau, Settembre 20082008
more and moremore and more
S. MorettoS. Moretto Convegno Fisica di Alice Palau, Settembre Convegno Fisica di Alice Palau, Settembre 20082008
Residuals: Raw and Residuals: Raw and MillepedeMillepede
SPD INNER SPD OUTERSPD INNER SPD OUTER
S. MorettoS. Moretto Convegno Fisica di Alice Palau, Settembre Convegno Fisica di Alice Palau, Settembre 20082008
Millepede: aligned modulesMillepede: aligned modules
Configuration with 500 modulesConfiguration with 500 modules ||/2|<.5 && |/2|<.5 && |/2|<.5)/2|<.5)
vs of realignedmodules:
“alignedsolid angle”
S. MorettoS. Moretto Convegno Fisica di Alice Palau, Settembre Convegno Fisica di Alice Palau, Settembre 20082008
M. Lunardon - ITS Alignment Meeting – CERN – 5.08.2008
Alignment with even tracks (15k used) Check with odd tracks
All odd tracks: sigma = 55 muarea 3 sigma = 89%
SPD alignment status
Stability test with even/odd tracks
S. MorettoS. Moretto Convegno Fisica di Alice Palau, Settembre Convegno Fisica di Alice Palau, Settembre 20082008
Realignment of data with overlapping clusters
orthogonal distanceorthogonal distance number of pairsnumber of pairs meanmean distancedistance
all tracksall tracks 25502550 0.20.2 22.5 +- 0.422.5 +- 0.4
abs(x0)<1cmabs(x0)<1cm 850850 0.10.1 21.4 +- 0.621.4 +- 0.6
SPD1SPD1 && abs(x0)<1cm && abs(x0)<1cm 440440 -1.0-1.0 22.2 +- 0.922.2 +- 0.9
SPD0SPD0 && abs(x0)<1cm && abs(x0)<1cm 410410 1.11.1 19.6 +- 0.819.6 +- 0.8
- overlapping clusters not used in the alignment
- gaussian peak (small tails)
- sigma ~ 20-22 micron => spatial resolution ~ 14-16 micron
SPD alignment status
S. MorettoS. Moretto Convegno Fisica di Alice Palau, Settembre Convegno Fisica di Alice Palau, Settembre 20082008
The matrix on the left side of equation (12) has, from eachlocal measurement, three types of contributions. The first part is a contribution of a symmetric matrix C1j , of dimension n (number of global parameters), and is calculated from the (global) derivatives. The second contribution is the symmetric matrix j, which gives a contribution to the big matrix on the diagonal and is depending only on the j-th local measurementand the (local) derivatives. The third (mixed) contribution is a rectangular matrix Gj , with a row number of n (global) and a column number of (local). There are two contributions to the vector of the normal equations (gradient), g1j for the global and j for the local parameters.