P. Brückman de Renstrom Alignment Strategy for ATLAS Vertex 2006 Perugia, September 2006 p1p1 Alignment Strategy for the ATLAS Tracker Pawel Brückman de Renstrom On behalf of the ATLAS ID alignment community Pawel Brückman de Renstrom On behalf of the ATLAS ID alignment community VERTEX th International Workshop on Vertex Detectors Perugia September 2006 Optical and mechanical surveys Summary The FSI system – a novel stability monitoring for SCT The track-based algorithms:  Robust Alignment  Global  2 Alignment  Local  2 Alignment Introduction to the ID alignment challenge

P. Brückman de Renstrom Alignment Strategy for ATLAS Vertex 2006 Perugia, September 2006 p2p2 The 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) Current strategy:  Perform full intrinsic alignment of the silicon  Align TRT modules using tracks from silicon (TRT can help to constrain momentum – eliminate sagitta). Alternative (under consideration): Do a combined simultaneous alignment of both subsystems (TRT can help to constrain momentum – eliminate sagitta). IN THE FOLLOWING I WILL DISCUSS ALIGNMENT OF THE SILICON SYSTEM ONLY 96 barrel modules 2x14 end-cap disks TRT For more details on the PIXEL and the SCT see yesterday talks from Markus and Janet

P. Brückman de Renstrom Alignment Strategy for ATLAS Vertex 2006 Perugia, September 2006 p3p3 BarrelForward DetectorPIXSCTPIXSCT # of layers/disks 342x32x9 # of modules x1442x988 sub Total Total ,992 In total we have to deal with 34,992 DoF’s! ATLAS Silicon Tracking System 3 translations & 3 rotations of each module Barrel SCT (4 layers)Forward SCT (9 disks) Barrel PIXels (3 layers) Forward PIXels (3 disks)

P. Brückman de Renstrom Alignment Strategy for ATLAS Vertex 2006 Perugia, September 2006 p4p4 z y x Followed by 2004 Combined Test Beam 6 TRT modules 6 PIXEL modules 8 SCT modules First ever real data from all three subsystems! Abundant statistics at different beam momenta ( GeV) (O(10 5 ) tracks/module/energy), Magnetic field. A very small setup (14+6), Layout creating ill-defined modes (collimated beam through a narrow tower of modules)

P. Brückman de Renstrom Alignment Strategy for ATLAS Vertex 2006 Perugia, September 2006 p5p5 ID is taking shape! Barrel TRT Barrel SCT service cages visible SR1 surface building (spring 2006) Installation to ATLAS (24 August 2006)

P. Brückman de Renstrom Alignment Strategy for ATLAS Vertex 2006 Perugia, September 2006 p6p6 SCT: SCT: 468 of 2112 modules ~ 1/4 of SCT barrel 468 of 2112 modules ~ 1/4 of SCT barrel TRT: TRT: 2X ~6600 Channels ~ 1/8 of TRT barrel 2X ~6600 Channels ~ 1/8 of TRT barrel 3 scintillators for trigger 3 scintillators for trigger No PIXEL, No B-field! No PIXEL, No B-field! Low p tracks dominate: Low p tracks dominate: June 2006 SR1 Cosmic Run ( over 400k cosmic events recorded) View from outside towards Side A SCT TRT

Vertex 2006 Perugia, September 2006 P. Brückman de Renstrom Alignment Strategy for ATLAS p7 Robust Alignment Responsible: Florian Heinemann DigitsReconstruction RobustAlignAlg Alignment Constants Tracks in StoreGate 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 out of 6 DoFs for each module Iteration until convergence Slides from Florian Heinemann

Vertex 2006 Perugia, September 2006 P. Brückman de Renstrom Alignment Strategy for ATLAS p8 CTB Alignment Before alignment After alignment PIXEL SCT Iteration Convergence after 15 iterations Residuals & Overlap Residuals - Mean & RMS Slides from Florian Heinemann

Vertex 2006 Perugia, September 2006 P. Brückman de Renstrom Alignment Strategy for ATLAS p9 Cosmics Alignment After 8 iterations: RMS 61µm → 47µm After 8 iterations: RMS 81µm → 69µm Preliminary Slides from Florian Heinemann

Vertex 2006 Perugia, September 2006 P. Brückman de Renstrom Alignment Strategy for ATLAS p10 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: track hit residual Key relation! Intrinsic measurement error + MCS Global  2 algorithm: the principles [ATL-INDET-PUB ] Equivalent to Millepede approach from V. Blobel

Vertex 2006 Perugia, September 2006 P. Brückman de Renstrom Alignment Strategy for ATLAS p11 “clocking”  R (VTX constraint) “telescope”  z~R radial distortions (various)  dependent sagitta  X  a  bR  cR 2  dependent sagitta “Global twist”  Rcot(  ) global sagitta  R … 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] “Weak modes” - examples

Vertex 2006 Perugia, September 2006 P. Brückman de Renstrom Alignment Strategy for ATLAS p12 Example “lowest modes” in PIX+SCT as reconstructed by the Global  2 algorithm Singular modes 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).

Vertex 2006 Perugia, September 2006 P. Brückman de Renstrom Alignment Strategy for ATLAS p13  =10.7 μm  =19.1 μm PIX SCT CTB: convergence of the Global  2 algorithm Before alignment After alignment

Vertex 2006 Perugia, September 2006 P. Brückman de Renstrom Alignment Strategy for ATLAS p14 SR1 cosmics with Global  2 preliminary (~250k tracks) TX TY TZ RX RY RZ [mm] [mm] [mm] [mrad] [mrad] [mrad] Barrel Barrel Barrel Barrel first iteration Corrections due to modes >1500 Alignment corrections for rigid barrels  =31.9 μm  =46 μm Corrections x100 Indication of very good assembly precision! 2808 DoF’s Before alignmentAfter alignment

Vertex 2006 Perugia, September 2006 P. Brückman de Renstrom Alignment Strategy for ATLAS p15  =31.2 μm Cosmics with Global  2 Crosscheck with Fully Simulated MC (~260k tracks) Perfectly aligned detector Traces of systematics??? Beware: Alignment is ultimately sensitive to own bugs and approximations but also to slightest upstream imperfections. Sometimes hard to tell apart!

Vertex 2006 Perugia, September 2006 P. Brückman de Renstrom Alignment Strategy for ATLAS p16 Full Barrel Geometry with Global  2 alignment Full barrel i.e DoF’s. 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 Nominal geometry - no misalignments: Pulls of all corrections of ~unit width and centred at zero Pulls in diagonal base Alternative options as suggested by V. Blobel under investigation!  =0.94

Vertex 2006 Perugia, September 2006 P. Brückman de Renstrom Alignment Strategy for ATLAS p17 |  |<1 with Global  2 alignment – perfect detector DoF’s. Ample ~7,500,000 muon tracks used! Corrections x100 Statistics is significant enough to detect systematic effects. There may be a hint of such: This one can be efficiently constrained using a common vertex requirement. x100

Vertex 2006 Perugia, September 2006 P. Brückman de Renstrom Alignment Strategy for ATLAS p18 |  |<1 with Global  2 alignment – perfect detector Pulls of alignment corrections Typical errors < 10μm Nominal geometry - no misalignments: Pulls of all corrections of ~unit width but systematic effects start to kick in.  They all disappear after a cut on “low modes” PIXEL DoF’s. Ample ~7,500,000 muon tracks used! pdsyevd of ScaLAPACK on a ||-cluster AMD Opteron (64-bit). Pulls in diagonal base

Vertex 2006 Perugia, September 2006 P. Brückman de Renstrom Alignment Strategy for ATLAS p19 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. 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 - approach Slides from Roland Haertel and Bjarte Mohn

Vertex 2006 Perugia, September 2006 P. Brückman de Renstrom Alignment Strategy for ATLAS p20 Slides from Roland Haertel and Bjarte Mohn Local  2 alignment - functionality Algorithm tested with combined test beam, cosmic test and full ATLAS geometry setup. Statistical 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. Some 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 a x distribution and flow for full ATLAS setup:

Vertex 2006 Perugia, September 2006 P. Brückman de Renstrom Alignment Strategy for ATLAS p21 Local  2 alignment – cosmic performance Alignment of SCT barrel cosmic test setup with 36k tracks. Flow of alignment parameter a x for all modules of barrel layer 2 through the iterations Development of the width and mean of the residuals over iterations Slides from Roland Haertel and Bjarte Mohn width mean

Vertex 2006 Perugia, September 2006 P. Brückman de Renstrom Alignment Strategy for ATLAS p22 Local  2 alignment – cosmic performance Alignment of SCT barrel cosmic test setup with 36k tracks. Slides from Roland Haertel and Bjarte Mohn BEFORE AFTER  = > μm  =99.5 -> μm  =96.1 -> μm  = > μm rnd misal:

Vertex 2006 Perugia, September 2006 P. Brückman de Renstrom Alignment Strategy for ATLAS p23 Frequency Scanning Interferometry 842 simultaneous length measurements in SCT! Barrel SCT End-cap SCT (3x[80+16])+(2x72)=512 B3B4,5,6 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 10  m in 3D. Slides from Stephen Gibson

Vertex 2006 Perugia, September 2006 P. Brückman de Renstrom Alignment Strategy for ATLAS p24 Ratio of phase change = Ratio of lengths  /c]D   /c]L  Slides from Stephen Gibson

Vertex 2006 Perugia, September 2006 P. Brückman de Renstrom Alignment Strategy for ATLAS p25 FSI grid nodes attached to inner surface of SCT carbon-fibre cylinder Barrel FSI Slides from Stephen Gibson

Vertex 2006 Perugia, September 2006 P. Brückman de Renstrom Alignment Strategy for ATLAS p26 Distance measurements between grid nodes precise to <1 micron Barrel FSI (1/4) Slides from Stephen Gibson

Vertex 2006 Perugia, September 2006 P. Brückman de Renstrom Alignment Strategy for ATLAS p27 End-cap FSI (1/18) Slides from Stephen Gibson

Vertex 2006 Perugia, September 2006 P. Brückman de Renstrom Alignment Strategy for ATLAS p28 FSI barrel-flange component (1/48) Slides from Stephen Gibson

Vertex 2006 Perugia, September 2006 P. Brückman de Renstrom Alignment Strategy for ATLAS p29 Time + spatial frequency sensitivity of FSI complements track based alignment:  Track alignment seeks average alignment over interval t 0 -t 1 = 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 t i, t 0 <t i <t 1 2.Track recorded at time t i is reconstructed using FSI module correction at time t i. 3.Offline alignment uses FSI corrected tracks to solve for high spatial frequency modes, averaged over t 0 <t i <t 1, low frequency modes frozen. 4.Subsequent reconstruction of track at time t j uses average alignment from a track-based algorithm + time dependent FSI module correction, t j, t 0 <t j <t 1 Spatial frequency eigenmode FSI Time seconds minutes hours days months Tracks FSI: integration with track alignment Slides from Stephen Gibson

P. Brückman de Renstrom Alignment Strategy for ATLAS Vertex 2006 Perugia, September 2006 p30 SCT photogrammetry in SR1 SCT Barrel photogrammetry survey in SR1 has been completed early this year. SCT-TRT relative position survey also performed. Slides from Muge Unel

P. Brückman de Renstrom Alignment Strategy for ATLAS Vertex 2006 Perugia, September 2006 p31 Interlinks: Deformations? Circles (colored) are fits, black curves are guidelines for ellipses using the scaled up differences of data points (col) to the circles B3B4 B5B6 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

P. Brückman de Renstrom Alignment Strategy for ATLAS Vertex 2006 Perugia, September 2006 p32 Mean: -2.5 µm Sigma: 2.7 µm Mean: -0.2 µm Sigma: 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 Module survey in Pixel Endcap Delta X = X measured - X nominal Delta Y = Y measured - Y nominal Slides from Tobi Golling

P. Brückman de Renstrom Alignment Strategy for ATLAS Vertex 2006 Perugia, September 2006 p33 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 predicted position from survey represents alignment correction Reference modules Test Reference modules (Current alignment) (Survey alignment) Step 1 Step 2 Slides from Tobi Golling

P. Brückman de Renstrom Alignment Strategy for ATLAS Vertex 2006 Perugia, September 2006 p34 Summary ID of ATLAS adopted variety of techniques in order to assure optimal alignment of its precision tracking devices. ID of ATLAS adopted variety of techniques in order to assure optimal alignment of its precision tracking devices. Three independent track-based alignment algorithms are being developed for silicon, a common approach to survey constraints and a novel Frequency Scanning Interferometry system in the SCT. Three independent track-based alignment algorithms are being developed for silicon, a common approach to survey constraints and a novel Frequency Scanning Interferometry system in the SCT. All track-based algorithms have provided convincing proof of principle. Full-scale tests using large simulation samples and various misalignment scenarios are due later this year. All track-based algorithms have provided convincing proof of principle. Full-scale tests using large simulation samples and various misalignment scenarios are due later this year. Preliminary burn-in of the algorithms provided by the 2004 CTB. Preliminary burn-in of the algorithms provided by the 2004 CTB. Alignment of the actual detector becomes reality! Alignment of the actual detector becomes reality! We have collected >400k cosmic events in the SR1 building with SCT+TRT detectors. Very high assembly precision has been confirmed. PIXEL detector will take surface cosmic data separately and will be inserted into the ID in the pit. We have collected >400k cosmic events in the SR1 building with SCT+TRT detectors. Very high assembly precision has been confirmed. PIXEL detector will take surface cosmic data separately and will be inserted into the ID in the pit. FSI is getting ready to monitor SCT distortions during the PIXEL insertion process (detect shape difference before and after insertion). FSI is getting ready to monitor SCT distortions during the PIXEL insertion process (detect shape difference before and after insertion). This will be followed by pit cosmic data-taking and ultimately accelerator events. This will be followed by pit cosmic data-taking and ultimately accelerator events.

P. Brückman de Renstrom Alignment Strategy for ATLAS Vertex 2006 Perugia, September 2006 p35 BACKUP

Vertex 2006 Perugia, September 2006 P. Brückman de Renstrom Alignment Strategy for ATLAS p36 Alignment Constants Sum over neighbours, take correlations into account Correct for change in radius Sum over all modules in a ring For a perfect detector: Slides from Florian Heinemann

Vertex 2006 Perugia, September 2006 P. Brückman de Renstrom Alignment Strategy for ATLAS p37 We follow the same principle but now we have Individual 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 where New key relations! were we have defined:

Vertex 2006 Perugia, September 2006 P. Brückman de Renstrom Alignment Strategy for ATLAS p38 In order to have more quantitative insight we do projection on rigid cylinders (chain rule): The technique may prove very useful as a day-0 solution or a genuine method to reduce number of DoF’s. E.g.: think of addressing “weak modes” separately without having to worry about large matrix inversion. Simple and powerful tool on its own! Jacobian (mode itself) Projection on rigid cylinders X (  m)Y (  m)Z (  m) -198           3 0    2 0    1 0  1 -2  5 0  0 0  0 0  0 Fixed to 0 The fit settles on a minor “telescope” mode. Re-alignment of the distorted detector. PIXel detector was collectively shifted by: (  X=200  m,  Y=100  m,  Z=400  m) The resulting corrections to the rigid cylinders are:

Vertex 2006 Perugia, September 2006 P. Brückman de Renstrom Alignment Strategy for ATLAS p39 Here we show the simplest case of a direct constraint on track parameters and without the vertex fit. We start from the redefined  2 and the respective solution for track parameters: The solution is given by the modified formula where the redefined form of the track weight matrix J is used throughout: Direct Least-Squares solution to the alignment problem (3) Adding constraints on track parameters J Similarly, one can write out solution for the most general case including VTX fit and constraints on all formal parameters.

Vertex 2006 Perugia, September 2006 P. Brückman de Renstrom Alignment Strategy for ATLAS p40 Idea of the constraints on track parameters can be extended to a constraint on the mass of a known resonance (e.g. Z  +  -, J/   +  ) Constraint on mass of a resonance As a result (in full analogy to the basic constraint on track parameters) the track parameter weight matrix gets modified and there is an extra term added to the big vector of the final system of equations:

Vertex 2006 Perugia, September 2006 P. Brückman de Renstrom Alignment Strategy for ATLAS p41 FSI – Grid Line Interferometer Slides from Stephen Gibson

Vertex 2006 Perugia, September 2006 P. Brückman de Renstrom Alignment Strategy for ATLAS p42 SCT FSI System Overview SR1 Laser room Alignment rack in USA15

Vertex 2006 Perugia, September 2006 P. Brückman de Renstrom Alignment Strategy for ATLAS p43 Length extraction software Fit sinusoid to GLI intensity vs unwrapped reference phase: Search for minima using MINUIT CPU intensive: 10 x 842GLIs x 6000pts x N calls to MINUIT

Vertex 2006 Perugia, September 2006 P. Brückman de Renstrom Alignment Strategy for ATLAS p44 Dual Laser Drift Correction Use two lasers scanning in opposite directions to cancel interferometer drift errors.

Vertex 2006 Perugia, September 2006 P. Brückman de Renstrom Alignment Strategy for ATLAS p45 Grid Reconstruction Software Function: to determine 3D grid node co-ordinates from FSI 1D length data. Have performed detailed simulations of error propagation through grids using Simulgeo package (Java).  Geometry carefully modelled from engineering drawing.  Assume Gaussian 1um errors on grid lengths.  Mechanical constraints added to model rigidity of barrels / disks. Simulations show a precision of ~5um in critical direction will be possible with the installed grids. Models will be developed to allow reconstruction from database of measured lengths + error checking. 