Alignment Strategy from ATLAS Inner Detector Alignment

P. Brückman de RenstromAlignment Strategy from ATLAS

pp11

LHC Detector Alignment WorkshopCERN, 05 September 2006

Alignment Strategy from Alignment Strategy from ATLASATLAS

Inner Detector AlignmentInner Detector Alignment

Pawel BrPawel Brüückman de Renstromckman de [email protected]

On behalf of the ATLAS ID alignment communityOn behalf of the ATLAS ID alignment community

LHC Detector Alignment WorkshopCERN 05/09/06

Optical and mechanical surveys

Summary

The FSI system – a novel stability monitoring for SCT

The track-based algorithms: Robust Alignment of silicon Global 2 Alignment of silicon Local 2 Alignment of silicon TRT alignment

Introduction to the ID alignment challenge


pp22


The alignment strategyThe alignment strategy

PIXEL + SCT: very high granularity silicon system (~6000 modules)TRT: proportional straw tubes – for alignment purpose granularity limited to barrel modules/end-cap disks (96+28)TRT needs intrinsic calibration (RT with some coarse granularity, T0 at single straw level) – see laterCurrent strategy:

Perform full intrinsic alignment of the silicon Align TRT modules using tracks from siliconAlternative (under consideration):Do a combined simultaneous alignment of both subsystems TRT helps to constrain momentum,TRT helps to constrain momentum, alignment algorithms have same problems (convergence, unconstrained degrees of freedom, etc),alignment algorithms have same problems (convergence, unconstrained degrees of freedom, etc), allows for implementing a single pass algorithm - highly recommended for “fast response”.allows for implementing a single pass algorithm - highly recommended for “fast response”.

96 barrel modules

2x14 end-cap disks

TRT

For more details on the ID subsystems see yesterday talk from Florian Bauer


pp33


BarrelBarrel ForwardForward

DetectorDetector PIXPIX SCTSCT PIXPIX SCTSCT

# of layers/disks# of layers/disks 33 44 2x32x3 2x92x9

# of modules# of modules 14561456 21122112 2x1442x144 2x9882x988

sub Totalsub Total 35683568 22642264

TotalTotal 58325832

In total we have to deal with 34,99234,992 DoF’s!

AT

LA

S S

ilic

on

Tra

ckin

g S

yste

m

3 translations& 3 rotationsof each module

Barrel SCT (4 layers) Forward SCT (9 disks)

Barrel PIXels (3 layers)Forward PIXels (3 disks)


pp44


z

yx

Follo

wed b

y

2004 Combined Test Beam2004 Combined Test Beam

6 TRT modules

6 PIXELmodules

8 SCTmodules

• First ever real data from all three subsystems!• Abundant statistics at different beam momenta (2-180 GeV) (O(105) tracks/module/energy),• Magnetic field.

• A very small setup (14+6),• Layout creating ildefined modes (collimated beam through a narrow tower of modules)


pp55


ID is taking shape!ID is taking shape!

Barrel TRT

Barrel SCTservice cages

visible

SR

1 s

urf

ace

build

ing

(sp

ring

20

06)


pp66


June 2006 SR1 Cosmic RunJune 2006 SR1 Cosmic Run((nearly 400k cosmic events recorded)nearly 400k cosmic events recorded)

View from outside towards Side A

SCT:SCT: 468 of 2112 modules ~ 468 of 2112 modules ~

1/4 of SCT barrel1/4 of SCT barrel TRT:TRT:

2X ~6600 Channels ~ 2X ~6600 Channels ~ 1/8 of TRT barrel1/8 of TRT barrel

3 scintilators for trigger3 scintilators for trigger No PIXEL, No B-field!No PIXEL, No B-field! Low p tracks dominate:Low p tracks dominate:

p7LHC Detector Alignment WorkshopCERN, 05 September 2006


Robust Alignment

Responsible: Florian Heinemann ([email protected])

Digits Reconstruction RobustAlignAlg

Alignment Constants

Tracks inStoreGate

Final Alignment Constants

Algorithm uses PIXEL and SCT detector description Mean residuals Mean overlap residuals Alignment of neighbouring modules

Stable, no minimisation required

Covers mainly 2 - 3 out of 6 DoFsfor each module

Iteration until convergence

Slides from Florian Heinemann



CTB Alignment

Before alignment

After alignment

PIXEL

SCT

Iteration

Convergence after 15 iterations

Res

idua

ls &

Ove

rlap

Res

idua

ls -

Mea

n &

RM

S




Cosmics Alignment

After 8 iterations:RMS 61µm → 47µm

After 8 iterations:RMS 81µm → 69µm

Prelim

inary




The method consists of minimizing the giant 2

resulting from a simultaneous fit of all particle trajectories and alignment parameters:

Let us consequently use the linear expansion (we assume all second order derivatives are negligible). The track fit is solved by:

while the alignment parameters are given by:

trac

k

hit

residual Key relation!

Intrinsic measurement error + MCS

Direct Least-Squares solution to the alignment problem

k̂

em

[ATL-INDET-PUB-2005-002]

Equivalent to Millepede approach from V. Blobel



“clocking”R(VTX constraint)

“telescope”z~R

radial distortions(various)

dependent sagittaXabRcR2

dependent sagitta“Global twist”Rcot()

global sagittaR

…

We need extra handles in order to tackle these. Candidates:• Requirement of a common vertex for a group of tracks (VTX constraint),• Constraints on track parameters or vertex position (external tracking (TRT, Muons?), calorimetery, resonant mass, etc.)• Cosmic events,• External constraints on alignment parameters (hardware systems, mechanical constraints, etc).[PHYSTAT’05 proceedings] & talk from Tobi Golling

“Weak modes” - examples



Example “lowest modes” in PIX+SCT as reconstructed by the 2 algorithmGlobal Freedom have been ignored

(only one Z slice shown)

The above “weak modes” contribute to the lowest part of the eigen-spectrum. Consequently they dominate the overall error on the alignment parameters. More importantly, these deformations lead directly to biases on physics (systematic effects).



=10.7 μm

=19.1 μm

PIX

SCT

CTB: convergence of the Global Chi2 algorithm

Before alignment After alignment



SR1 cosmics with Global Chi2 very preliminary (~250k tracks)

TX TY TZ RX RY RZ [mm] [mm] [mm] [mrad] [mrad] [mrad] Barrel3 -0.0044 -0.0162 -0.0169 0.0685 -0.0185 0.0503 Barrel4 0.0061 0.0329 -0.0462 -0.0678 0.0258 0.0527 Barrel5 0.0109 -0.0005 0.0865 0.0318 -0.0134 -0.0947 Barrel6 -0.0126 -0.0162 -0.0234 -0.0200 0.0073 -0.0083

first iteration

Corrections due to modes >1500

Alignment corrections for rigid barrels =32 μm=46 μm

x100

Indication of very good assembly precision!



Full Barrel Geometry with Global Chi2 alignment

Full barrel i.e. 21408 DoF’s (11.5.0, iPatRec, no VTX)

pdsyevd of ScaLAPACK on a ||-cluster AMD Opteron (64-bit).Using 16 CPU grid N=21k system diagonalised within ~1h! [CHEP’06 proceedings]32 nodes should solve the full 35k in <3h.

Pulls of alignment corrections

Nom

inal geom

etr

y -

no m

isalig

nm

ents

:Pulls

of

all

corr

ect

ions

of

~un

it

wid

th a

nd

cen

tred a

t ze

ro

Pulls in diagonal base

Alternative options as suggested by V. Blobel under investigation!

=0.94



• Size of the matrix for full ATLAS 2 problem is 36k x 36k. Reduce this by looking only at 6x6 block matrices at the diagonal of the full size matrix. This neglects all inter-module correlations:

• Approximation is valid if tracking uncertainty is smaller than measurement uncertainty.• No bias corrections. Unbiased residuals and track parameters used.• Diagonal covariance matrix is assumed, i.e. correlated errors from MCS are neglected.• Inter-module correlations are there and cannot simply be ignored. Correlations are

treated by iterating the procedure.

Local 2 alignment - approachSlides from Roland Haertel



Local 2 alignment - functionality

• Algorithm tested with combined testbeam, cosmic test and full ATLAS geometry setup.• Alignment accuracy achievable for the precision coordinate with O(100k) tracks for full

ATLAS setup, starting from nominal alignment: Pixel barrel 10 m, Pixel endcap 2 m, SCT barrel 50 m, SCT endcap 20 m.

• Simulation samples with systematically deformed detector geometry are being produced. Validation test with these samples will follow

• Simple implementation, additional features are already implemented (survey constraints, global alignment) or will be implemented soon (Kalman style approach, overlap constraint, vertex constraint).

Pixel barrel alignment parameter ax distribution and flow for full ATLAS setup:

Slides from Roland Haertel



Local 2 alignment – cosmic performance

development of width and mean of residual distributions through the iterations

• Alignment of SCT barrel cosmic test setup with 24k tracks. No B-field and no momentum selection.

• Alignment correction scaling parameter (0.5) used to dampen oscillations.

flow of alignment parameter ax for all modules of barrel layer 2 through the iterations

Slides from Roland Haertel


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TRT alignmentTRT alignment Based on local chi2 principle using reference tracks from the silicon Can determine up to 5 DoF per individual module (two translations and three rotations) TRT is an assembly of gas chambers – internal calibration needed (RT, T0)

cosmics run 2267

>10nscosmics

run 2267worst

module


pp2020


TRT alignment - CTBTRT alignment - CTB Followed the alignment of silicon Could accurately detect time dependent movements of TRT vs silicon:

Relative TRT shift in sensitive direction (left) and rotation (right) as a function of the run number (time):


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TRT alignment – SR1 CosmicsTRT alignment – SR1 Cosmics(preliminary study)(preliminary study)

Intrinsic residuals for TRT-only tracks indicates very good assembly precision Matching between track segments from SCT and TRT provides a measure of the global misalignment between the two systems:

no large global rotation in XY plane (error large: MS can hide no large global rotation in XY plane (error large: MS can hide effect)effect) large (~0.5mm) misalignment in Rphilarge (~0.5mm) misalignment in Rphi about 0.2 mrad rotation in the XZ plane.about 0.2 mrad rotation in the XZ plane.

Δphi0 Δrphi


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SCT photogrammetry in SCT photogrammetry in SR1SR1

SCT Barrel photogrammetry survey in SR1 has been completed early this year.SCT-TRT relative position survey also performed.

Slides from Muge Unel


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Interlinks: Deformations?

Circles (colored) are fits, black curves are guidelines for ellipses using the scaled up differences of data points (col) to the circles

B3 B4

B5 B6

• Measurements performed before and after insertion into TRT. Detailed measurements exist before the insertion O(20μm) in XY.

• After insertion only coordinate system transfer was measured.

• The individual cylinder interlink data showed deformations consistent with tilted ellipses.

• Face A and face C appear to be rotated in opposite directions, hinting at twists of the complete barrel.

• Relative clocking of barrels preliminarily confirmed with cosmics!

Slides from Muge Unel


pp2424


Mean: -2.5 µmSigma: 2.7 µm

Mean: -0.2 µmSigma: 2.6 µm

Survey constraint based on:

● CMM survey of Pixel and SCT prior to installation

● Estimated uncertainties Systematics (thermal expansion, moisture) dominate.

Survey Constraint on Alignment

ATL-INDET-PUB-2006-001

Module survey inPixel Endcap

Delta X = Xmeasured - Xnominal

Delta Y = Ymeasured - Ynominal

Slides from Tobi Golling


pp2525


Survey Constraint on Alignment● Survey data describes test module's position wrt reference modules● No constraint on modules' absolute positions is imposed

Step 1:● Find global transformation of reference modules from survey alignment to current alignment, in other words: Minimize the distance between the survey measurement points (unbiased) ⇒ Prediction of test module's position

Step 2:Transformation of test module from current position to predictedposition from survey represents alignment correction

Reference modules

Reference modules

Test

Test

Test

Test Reference modules(Current alignment)

(Survey alignment)

Step 1 Step 2

Slides from Tobi Golling



Frequency Scanning Interferometry

842 simultaneous lengthmeasurements in SCT! Barrel SCT

End-cap SCT

End-cap SCT

165

165

80+(3x[80+16])+(2x72)=512

B3 B4,5,6 END FLANGES

• Runtime alignment system monitors shape changes of the SCT.• Provides access to short-timescale and low spatial frequency modes of

tracker distortion (e.g. sagitta).• On-detector system forms a geodetic grid of length measurements

between nodes attached to the SCT support structure.• All 842 grid line lengths are measured simultaneously to a precision of

<1micron.• Entire Grid shape can be determined to better than 10m in 3D.

Slides from Stephen Gibson



FSI grid nodes attached to inner surface of SCT carbon-fibre cylinder

Barrel FSISlides from Stephen Gibson



Distance measurements between grid nodes precise to <1 micron

Barrel FSISlides from Stephen Gibson



End-cap FSI (1/18)Slides from Stephen Gibson



• Time + spatial frequency sensitivity of FSI complements track based alignment:

Track alignment seeks average alignment over interval t0-t1 = 24hrs+. Good for high spatial frequency eigenmodes, “long” timescales.

FSI provides “short” timescale (~10minutes) movement field for low spatial frequency eigenmodes.

• Need both to achieve best alignment.

• How to include time dependency?1. FSI provides low spatial frequency module corrections at time ti , t0<ti<t1

2. Track recorded at time ti is reconstructed using FSI module correction at time ti .

3. Offline alignment uses FSI corrected tracks to solve for high spatial frequency modes, averaged over t0<ti<t1, low frequency modes frozen.

4. Subsequent reconstruction of track at time tj uses average alignment from a track-based algorithm + time dependent FSI module correction, tj, t0<tj<t1

Spatial frequencyeigenmode

FSI

Time

seconds

minutes

hours

days

monthsTracks

FSI: integration with track alignment



pp3131


SummarySummary ID of ATLAS adopted variety of techniques in order to assure ID of ATLAS adopted variety of techniques in order to assure

optimal alignment of its precision tracking devices.optimal alignment of its precision tracking devices. There are three independent track-based alignment algorithms There are three independent track-based alignment algorithms

for silicon, a complementary TRT alignment, a common approach for silicon, a complementary TRT alignment, a common approach to survey constraints and a novel Frequency Scanning to survey constraints and a novel Frequency Scanning Interferometry system in the SCT.Interferometry system in the SCT.

All track-based algorithms have provided convincing proof of All track-based algorithms have provided convincing proof of principle. Full-scale tests using large simulation samples are due principle. Full-scale tests using large simulation samples are due later this year.later this year.

Preliminary burn-in of the algorithms assure by the 2004 CTB.Preliminary burn-in of the algorithms assure by the 2004 CTB. Alignment of the real detector is already a reality! We have Alignment of the real detector is already a reality! We have

collected ~400k cosmic events in the SR1 building with SCT+TRT collected ~400k cosmic events in the SR1 building with SCT+TRT detectors. Very high assembly precision has been confirmed. detectors. Very high assembly precision has been confirmed. PIXEL detector will take surface cosmics separately and will be PIXEL detector will take surface cosmics separately and will be inserted into the ID in the pit.inserted into the ID in the pit.

FSI is getting ready to monitor SCT distortions during the PIXEL FSI is getting ready to monitor SCT distortions during the PIXEL insertion process (detect shape difference before and after insertion process (detect shape difference before and after insertion). insertion).

This will be followed by pit cosmics and ultimately accelerator This will be followed by pit cosmics and ultimately accelerator events.events.


pp3232


BACKUPBACKUP



Alignment Constants

residual overlap Rmean residual, overlap mean Z residual,mean i y;x, a ,/1

/2

2

i

iiaa

Sum over neighbours, take correlations into

account

Correct for change in radius

2

residual overlap Rmean z

Sum over all modules in a ring

module / Hits

(cosmics) m100or energy)(high m20~

/1

1 ~Shift

2

i

For a perfect detector:




We follow the same principle but now we haveIndividual track parameters are reduced to while tracks from the same vertex share the same set of three parameters describing the common vertex position.

Using the new form of the full derivative we obtain solution for the alignment parameters:

Direct Least-Squares solution to the alignment problem (2)Fitting a common vertex for a group of tracks

( , , )TQ p

where

New key relations!

were we have defined:



Frequency Scanning Interferometry

The basic principleThe basic principle

Laser

I REF

REFERENCE INTERFEROMETER

I

INTERFEROMETERTO BE MEASURED

Ratio of phase change = Ratio of lengths

/c]D

/c]L




Fused SilicaBeam-splitterDelivery

Fibre

Return Fibre

Quill

Retroreflector

Distance measuredcomponents

FSI – Grid Line Interferometer




FSI barrel-flange component (1/48)


Alignment Strategy from ATLAS Inner Detector Alignment

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