ATLAS is a general purpose spectrometer in preparation to take data on the Large Hadron Collider at CERN. It will start its operation in autumn 2007. Charged particle tracking is realized by the Inner Detector. ID consists of two silicon subsystems: Pixel Detector and Semiconductor Tracker complemented by straw proportional gas chambers. In order to exploit the excellent intrinsic resolution of the precision tracking devices a high accuracy alignment is required. In this report the strategy to align silicon detectors of the ATLAS ID will be reviewed together with the current status of preparation

Bruckman de Renstrom, P

CERN Document Server

Alignment Strategy for the ATLAS TrackerPawel Bru¨ckman de Renstrom1University of Oxford,DWB, Keble Road, Oxford OX1 3RH, UKandInstitute of Nuclear Physics PAN, ul. Rdzikowskiego 152, Krako´w 31-342, PLEE-mail: p.bruckman1@physics.ox.ac.ukAbstractATLAS is a general purpose spectrometer in preparation to take data on the Large Hadron Collider at CERN. Itwill start its operation in autumn 2007. Charged particle tracking is realised by the Inner Detector. ID consistsof two silicon subsystems: Pixel Detector and Semiconductor Tracker complemented by straw proportional gaschambers. In order to exploit the excellent intrinsic resolution of the precision tracking devices a high accuracyalignment is required. In this report the strategy to align silicon detectors of the ATLAS ID will be reviewedtogether with the current status of preparation.1. IntroductionThe silicon tracking system of the ATLAS InnerDetector (ID) (1; 2) is composed of two subsys-tems: the Pixel Detector and the the SemiConduc-tor Tracker (SCT). Altogether it consists of 5832individual silicon modules which amounts to 34992degrees of freedom (DoF) 2 . These are arranged inthree Pixel and four SCT cylinders in the barrelpart and three Pixel and 9 SCT disks in each of theend-caps. 50× 400µm pixels provide a 2D readoutwith 14 × 115µm resolution respectively 3 . SCTmodules consist of two single-sided back-to-backstrip detectors with a relative 40 mrad stereo angle.1 On behalf of the ATLAS Inner Detector alignment com-munity2 Each module, assumed to be rigid, has three translationaland three rotational DoF’s.3 Based on single pixel binary readout. This can be furtherimproved (3)Barrel SCT modules have parallel strips with 80µmpitch while end-cap ones have a fan-out structure.In the barrel resolution in the direction perpendic-ular to strips is 23µm per side while the stereo an-gle provides 580µm resolution along strips. Moredetails about the Pixel and the SCT systems canbe found elsewhere (3; 4).Alignment corrections are defined in the localreference frames of the modules with local X alongthe sensitive direction 4 and local Y being the or-thogonal in-plane direction.2. The Alignment StrategyThe Transition Radiation Tracker (TRT) strawtubes are arranged into 96 barrel modules and 28end-cap disks. These make the basis of alignmentparameters. Being a drift device, TRT also needs4 Parallel to the short pixel side and across SCT strips.Preprint submitted to Elsevier Science 17 January 2007T0 calibration at a single straw level and RT 5calibration with some coarse granularity. Conse-quently, TRT alignment and calibration representsdifferent challenges to the ones associated with thesilicon system. The current strategy assumes an in-trinsic alignment of the silicon tracker followed byTRT alignment to the tracks extrapolated from thesilicon. An alternative approach integrating align-ment of both silicon and TRT in single algorithmis now undergoing initial validation 6 .The overall strategy for the alignment of the sil-icon tracking system relies on track-based oﬄinealignment algorithms complemented by the Fre-quency Scanning Interferometry (FSI) system inthe SCT. The two have complementary roles as ar-gued in section 4. The initial alignment is providedby the mechanical and optical surveys of the as-built geometry.3. Track Based Alignment AlgorithmsThree independent algorithms for track basedalignment of the ID silicon detectors have been de-veloped alongside. All three are based on recon-structed track-to-hit residuals which carry infor-mation about track fit quality, ergo quality of thealignment. All described methods have been im-plemented in the Athena (5) framework and makepart of the official ATLAS software.Track based alignment inherently suffers from socalled “weak modes” which correspond to detectordeformations which do not (significantly) compro-mise χ2 of track fits. Such deformations often leadto biases on reconstructed track parameters. Someof these can be eliminated by introducing a com-mon vertex constraint, constraints on track param-eters coming from external tracking systems or di-rect constraints on the alignment parameters. Cos-mic events, representing off-axis continuous helicesacross the whole detector volume, also provide apowerful handle against some weak modes. Trackbased algorithms include implementations of theabove mentioned functionalities.5 Relationship betveen the drift time and the distancefrom the anode wire.6 TRT is believed to help constraining track curvature,hence to eliminate notorious sagitta distortions.3.1. Real Data ChallengesTrack based algorithms were applied to two realexperimental setups. In summer 2004 the Com-bined Test Beam (CTB) collected first ever realdata from all ATLAS subsystems combined (6).The ID silicon geometry consisted of six Pixel mod-ules and eight SCT ones arranged in a tower. SCTmodules were exactly perpendicular to the beamline, while Pixel modules were arranged with a tiltangle of around 20 deg. CTB benefited from abun-dant event statistics at different beam momenta 7while a very small setup and the layout creatingill-defined modes (collimated beam through a nar-row tower of modules) were of clear disadvantage.Data were taken with and without magnetic field.In June 2006 integrated SCT and TRT barrel de-tectors recorded over 400,000 cosmic events in theATLAS surface building (SR1). SCT took datawith 468 out of 2112 barrel modules in the two op-posite wedges of the detector extending over its fulllength. Pixels were not present and there was nomagnetic field to reconstruct cosmic ray momenta.3.2. Robust AlignmentThe robust alignment approach is an iterativemethod to align any kind of silicon detector withoverlapping modules. In each iteration alignmentcorrections are calculated out of measurements ofmean residuals R¯i and mean φ and z overlap resid-uals O¯Ri,φ/z . i stands for either X or Y labellingresiduals along the local axes of the module as de-fined in section 1. The method aims at correctingtwo to three DoF’s only, i.e. two translations in theplane of the module and if possible systematic ra-dial translations. The three different residual andoverlap residual measurements are combined ac-cording to the formula:aj = −3∑j=1sj(δsj)2/3∑j=11(δsj)2s1 = R¯; s2 =∑O¯Rφ; s3 =∑O¯Rz .(1)Alignment corrections (1) relate module positionto its adjacent neighbours via φ and z overlaps.The7 2-180 GeV/c with O(105) tracks/module/energy2φData PIXEL R / ndf 2χ 127.1 / 17Prob   7.047e-19Constant  31.5±  7784 Mean      0.000053± 0.001548 Sigma     0.00008± 0.01172 Residual in mm-0.15 -0.1 -0.05 0 0.05 0.1 0.15Hits010002000300040005000600070008000φData SCT R / ndf 2χ 50.47 / 23Prob   0.0007981Constant  42± 1.873e+04 Mean      0.0000576± 0.0005408 Sigma     0.00009± 0.02223 Residual in mm-0.2 -0.15 -0.1 -0.05 -0 0.05 0.1 0.15 0.2Hits02000400060008000100001200014000160001800020000a bFig. 1. Local X residual distributions in CTB Pixel (a)and SCT (b) detectors. Dark-shaded histograms are theinitial geometry while the light-shaded ones after the Ro-bust alignment has converged.method heavily relies on iteration. More details canbe found in (7).The method was first validated on the CTB data.It provided fast and stable results. Figure 1 showsthe improvement to the local X residuals in Pixelsand SCT due to the alignment. Convergence wasalways reached within 15 iterations.Robust method has also been applied to the SR1cosmic data. The analysis is ongoing but the pre-liminary results prove validity of the algorithm.3.3. Global χ2 AlignmentThe Global χ2 algorithm is based on the min-imisation of the χ2 defined as:χ2 =∑tracksrT V −1r (2)with respect to the alignment parameters. r is thevector of hit residuals to the fitted track and Vis its covariance matrix. The residuals depend onthe track parameters (pi) as well as on the subsetof alignment parameters related to the intersectedmodule (a). The generic solution for alignment cor-rections reads:δa = −( ∑tracksdrTdaV −1drda)−1∑tracksdrTdaV −1r (3)withdrda=∂r∂a+∂r∂pidpida(4)dpida can be obtained by differentiating similar ex-pression for a single track fit to the reconstructedhits in the detector. More details about the methodcan be found elsewhere (8). The method has a bigadvantage of properly treating all correlations be-tween residuals arising from common track param-eters and Coulomb scattering. There is a price topay. The solution 3 requires inverting a symmet-ric matrix of size N where N is number of DoF’sof the problem. In case of ATLAS ID it representsan important numerical challenge. To make thingsworse, the matrix is inherently singular which re-quires more careful treatment 8 .Validation of the Global χ2 algorithm has beendone on real data from CTB and SR1 cosmicruns as well as on fully simulated ATLAS data.On the CTB data the method converged withinfour iterations. Initial broad residual distributionstransformed into clean Gaussians with widths of10.7 µm and 19.1 µm for the Pixel modules andSCT respectively. These were consistent with theperfectly aligned simulation.The approach was also used to align SR1 cos-mic setup. Around 250,000 events were used inthis analysis. Because initial misalignments weresmall the convergence was nearly instantaneous.Second iteration already delivered the final qual-ity alignment. Results are summarised in figure 2.Correction pulls are given in the diagonal base,i.e. the base of orthogonal modes of the detec-tor deformation 9 and are sorted from left to rightby increasing eigenvalue. Structure in the rightpart of plot a shows misalignment modes whichthe available data is actually sensitive to. Plot cdemonstrates that after second iteration alignmentfully converged. After alignment the fitted widthof the residuals agreed with the one from perfectlyaligned simulation within one micron. The MonteCarlo sample was generated with the actual cosmicmuon spectrum cut-off at 200 MeV. In real datawe had some yet lower energy particles. These con-tributed to the far tails of the residual distributionbut did not affect the width of the peak region.The algorithm has also been tested on MonteCarlo data simulated through the complete ID ge-ometry. So far tests consisted of checking prop-erties of results obtained on perfectly aligned de-8 E.g. diagonalisation. Other options include precondition-ing or sequential solving with an arbitrary cut-off. Feasibil-ity of the earlier was studied and documented elsewhere (9).9 These are obtained by means of diagonalisation.3Mode Number0 500 1000 1500 2000 2500Pull-500-400-300-200-1000100200300400500Eigenmode Pulls Constant   5944Mean      0.0001945Sigma     0.06504residual [mm]-0.5 -0.4 -0.3 -0.2 -0.1 -0 0.1 0.2 0.3 0.4 0.501000200030004000500060007000SCT local XMode Number0 500 1000 1500 2000 2500Pull-500-400-300-200-1000100200300400500Eigenmode Pulls Constant  1.008e+04Mean      0.0001475Sigma     0.03194residual [mm]-0.5 -0.4 -0.3 -0.2 -0.1 -0 0.1 0.2 0.3 0.4 0.50200040006000800010000SCT local X⇔⇔a bc dFig. 2. Performance of the Global χ2 algorithm on the SR1cosmic setup (468 SCT modules). Upper plots show cor-rection pulls for the 2808 eigenmodes (a) and correspond-ing local X residual distribution (b) as obtained from theinitial geometry. Lower plots (c and d) show analogous dis-tributions on realigned geometry (after two iterations).tector. Dedicated events containing on average 10muons with 2GeV/c < pT < 50GeV/c were used.First, the full barrel part of the Pixel and the SCTdetector (21408 DoF’s) was realigned with a lim-ited statistics of 640,000 tracks. The matrix wasdiagonalised using pdsyevd routine of the ScaLA-PACK package on a AMD Opteron parallel clus-ter (9). Reconstructed pulls of the alignment cor-rections exhibited Gaussian distribution of unitwidth, as expected. A more recent test benefitedfrom an ample 7,500,000 tracks simulated into thecone of |η| < 1.0. The corresponding subset ofPixel and SCT detectors consisted of 2172 mod-ules (13032 DoF’s). With this high statistics thetypical error on the absolute position of the mod-ule was of the order of 10µm. We seem to have ob-served an over-statistical fluctuation in one of thelow modes corresponding to φ rotation of the Pixeldetector relative to SCT. This could sign a resid-ual systematic effect at some stage of the upstreamreconstruction. Fortunately, this kind of deforma-tion can be efficiently constrained using a commonvertex requirement.3.4. Local χ2 AlignmentThe Local χ2 algorithm is based on the sameansatz (3) but the full derivative (4) is reduced tojust the partial derivative with respect to a andfull covariance matrix V is replaced by its diagonalonly. As a result the system of equations breaksdown to 6× 6 blocks which are straightforward tosolve. The solution is now given by simply:δa = −( ∑tracks∂rTi∂a1σ2i∂ri∂a)−1∑tracks1σ2i∂rTi∂ari (5)This approximation is justified as long as track-ing uncertainty is smaller than measurement un-certainty which usually is a valid assumption. Be-cause all correlations via common track parame-ters as well as Coulomb scattering are ignored thismethod is inherently iterative in order to make upfor the reduced information.Local χ2 method proved its principle providinggood performance on both CTB and SR1 cosmicdata. Speed of convergence lies in between theRobust and the Global χ2 algorithms. For theCTB alignment all DoF’s per module except forthe translation along the beam line were used.Alignment quality after reaching convergencewas consistent with prediction from the perfectsimulation. On SR1 cosmic data the algorithmperformed the complete alignment procedure in-volving all six DoF’s per module. Figure 3 showsthe convergence of the algorithm on real SR1 cos-mic data. Full convergence was reached after ∼10iterations. A similar exercise was performed onsimulation misaligned by as much as the specifiedassembly tolerances (4). Two main observationswere made: The convergence pattern was similarand resulted in comparable track fit quality. Themisalignments assumed for the simulation weresubstantially larger than the ones found in the realsystem. The latter indicates excellent precision ofthe entire SCT assembly.The Local χ2 algorithm was also tried on thefull ATLAS geometry using simulated events. Thetests using simulation of perfectly aligned geome-try confirmed good behaviour of the correction pulldistributions and expected convergence pattern.4a b[mm] [mm]Fig. 3. Performance of the Local χ2 algorithm on the SR1cosmic setup (468 SCT modules). Plots show the widths(a) and the means (b) of the Gaussian fit to the local Xresidual distributions in the four SCT layers as a functionof iteration number.4. Frequency Scanning InterferometryFSI is a novel stability monitoring system basedon simultaneous measurement of multiple grid lineinterferometer lengths (10). The system consists of842 grid lines arranged into a geodetic grid insidethe SCT volume. It also contains a tunable laserand the reference interferometer of precisely knownlength. Length measurement is based on observingfringes in both the measured and the reference in-terferometers while the the tunable laser scans thefrequency. Ratio of the observed phase change isequal to the ratio of interferometer lengths. Nodepositions can subsequently be reconstructed withaccuracy better than 10µm in 3D (11).FSI cannot provide absolute measurements ofSCT module positions but delivers quasi real-time(timescale ∼10 min) movement field for low spa-cial frequency eigenmodes which are very difficultto detect with the track based algorithms. Trackalignment, in turn, provides complementary infor-mation about high spacial frequency eigenmodeson much longer timescales (24h+). The FSI sys-tem will allow for corrections to be made to shortterm motions of the support structures prior to theoﬄine track alignment.5. Summary and OutlookID of ATLAS adopted a variety of techniques inorder to assure optimal alignment of its precisiontracking devices. Three independent track basedalignment algorithms are being developed to alignPixel+SCT tracker and a novel Frequency Scan-ning Interferometry system is integrated into theSCT part. All track based algorithms have pro-vided convincing proof of principle. Preliminaryburn-in of the algorithms was provided by the 2004CTB. Currently we have started aligning the ac-tual detector. Over 400k cosmic events were col-lected by integrated SCT and TRT detectors inJune 2006.Alignment analyses confirmed assemblyprecision outclassed the specified mechanical toler-ances. Large simulation datasets with misalignedgeometries of the entire ID are being prepared now.First alignment results using these data are dueearly 2007. TRT and SCT barrel parts are alreadyinstalled inside the ATLAS spectrometer. Pixel de-tector will be installed in spring 2007. FSI is get-ting ready to monitor SCT distortions due to thisprocess. This will be followed by collecting cosmicevents in the pit and ultimately by LHC accelera-tor events due late 2007.References[1] ATLAS Detector and Physics PerformanceTDR Vol. 1, CERN/LHCC/99-14.[2] ATLAS ID TDR, CERN/LHCC/97-16&17.[3] M. Cristinziani, these proceedings.[4] J. Carter, these proceedings.[5] ATLAS Computing TDR–017, CERN-LHCC-2005-022.[6] B. Di Girolamo, M. Gallas, T. Koffas, ATC-TT-IN-0001.[7] D. Hindson, DPhil Thesis, Oxford university,2004; F.Heinemann, ID Alignment Work-shop, Ringberg, 2006.[8] P. Bru¨ckman de Renstrom & S. Haywood,PhyStat05 Proceedings, IC Press, L. Lyons& M. K. U¨nel (eds), 2006.[9] M. Karago¨z U¨nel, P. Bru¨ckman de Ren-strom, K. Bernadet, A.Hicheur, CHEP06proceedings, India, 2005.[10] P. Coe et al., MST 15 11 2175-87, 2004;S. Gibson et al., OLE 43 7 815-31, 2005.[11] S. Gibson, DPhil Thesis, Oxford University,2004.5

Alignment Strategy for the ATLAS Tracker

Abstract

Similar works

Full text

Available Versions

CERN Document Server