ITS Alignment: Millepede Results S. Moretto, C. Bombonati, A. Dainese, M. Lunardon, A. Rossi.

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


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.


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.


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.


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.


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


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.


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)


XXlocloc

YYlocloc

ZZlocloc

MC Results: single module MC Results: single module alignmentalignment

SPDSPD SDDSDD SSDSSD


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


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)


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


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


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:


Millepede Results: Millepede Results: ResidualsResiduals

Track: 3-points fits on SPD and look at residuals on SSD


Residuals: Raw and Residuals: Raw and MillepedeMillepede

SSD INNER SSD OUTERSSD INNER SSD OUTER


Millepede Results: delta XMillepede Results: delta X

One meaningful observable of the realignment quality is the mismatch in X of the tracks @ Y=0


Millepede Results for SPD Millepede Results for SPD Hierarchical AlignmentHierarchical Alignment

Alignment of SPD in 4 steps:sectors -> staves -> half staves -> ladders


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


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


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)


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


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.


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


more and moremore and more


Residuals: Raw and Residuals: Raw and MillepedeMillepede

SPD INNER SPD OUTERSPD INNER SPD OUTER


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”


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


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


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.

ITS Alignment: Millepede Results S. Moretto, C. Bombonati, A. Dainese, M. Lunardon, A. Rossi.

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