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August 26, 2003 P. Nilsson, SPD Group Meeting 1
Paul Nilsson, SPD Group Meeting , August 26, 2003
Test Beam 2002 Analysis
Techniques for Estimating Intrinsic Resolution
An estimate of the intrinsic resolution of the An estimate of the intrinsic resolution of the SPD from 2003 Beam TestsSPD from 2003 Beam Tests
J. Conrad & P. NilssonJ. Conrad & P. Nilsson
August 26, 2003 P. Nilsson, SPD Group Meeting 2
Contents: Intrinsic Resolution
The 2003 test beamThe 2003 test beam Preprocessing and trackingPreprocessing and tracking Assessment of intrinsic resolutionAssessment of intrinsic resolution
Calculation of the “tracking error”Calculation of the “tracking error” Measurement error and Multiple Scattering Measurement error and Multiple Scattering
(2 different methods) (2 different methods) Residuals Residuals intrinsic resolution (3 different intrinsic resolution (3 different
methods)methods) Iterative MethodIterative Method
August 26, 2003 P. Nilsson, SPD Group Meeting 3
The 2003 Test Beam Proton/pion beam at 120 GeV/cProton/pion beam at 120 GeV/c Heavy ion beam (In) at 158 GeV/cHeavy ion beam (In) at 158 GeV/c
The study presented here is based on proton beam dataThe study presented here is based on proton beam dataSetup: Two minibuses, each with two single chip assemblies, constituting Setup: Two minibuses, each with two single chip assemblies, constituting
four reference planes (0, 1, 3 and 4). Plane 2 is the plane under studyfour reference planes (0, 1, 3 and 4). Plane 2 is the plane under study
August 26, 2003 P. Nilsson, SPD Group Meeting 4
Preproc data decoding (Noisy pixel removal) Alignment Tracking Proc. data encoding
Preprocessing and ReconstructionRaw data ConverterRaw data Converter
settings.par FILE Raw_data_file[n].dat PARAMETER n ...
raw2root
Preprocessed.root
settings.par FILE Preprocessed.root ...
analyze
Processed.root
AnalyserAnalyser
Executable
Output
Input control file
analysis.C
Executable
Output
Input control file
ROOT macro(s)
Raw data decoding Clustering of pixels Event sorting Noisy pixel removal Preproc. data encoding
CASTOR
(Step 1) (Step 3)
(Step 2) (Step 4)
ANALYSISDB
(Step 5)
www
(Step 6)
pre-analysis.CROOT macro(s)
August 26, 2003 P. Nilsson, SPD Group Meeting 5
Data Cleaning
Used dataset: c0r0_tilt0_thXXX Several noisy pixels were removed
Only events with 1 hit per reference plane were accepted (i.e. 4 reference points for the track candidate)
(Trivial alignment due to focused beam data)
August 26, 2003 P. Nilsson, SPD Group Meeting 6
“Typical” track quality
2 distributions
Residual distributions
XZ-plane YZ-plane
August 26, 2003 P. Nilsson, SPD Group Meeting 7
Assessment of Intrinsic Resolution
General strategy:General strategy: Start from measured residual distributionStart from measured residual distribution Convolution of intrinsic detector resolution (flat pdf) Convolution of intrinsic detector resolution (flat pdf)
and “tracking error” (Gauss pdf)and “tracking error” (Gauss pdf) Calculate “tracking error”Calculate “tracking error” Knowing tracking error Knowing tracking error get intrinsic get intrinsic
resolutionresolution
August 26, 2003 P. Nilsson, SPD Group Meeting 8
“Tracking Error”
Tracking Error :Tracking Error :
Contribution of the measurement error to Contribution of the measurement error to the difference the difference (x(xproj proj – x– xhithit))
In our case: In our case: x = az +b, z = 0x = az +b, z = 0 in test plane, in test plane,
b = xb = xprojproj
σtracking = σ(b)
August 26, 2003 P. Nilsson, SPD Group Meeting 9
Tracking Error (2)
Tracking error will depend on Tracking error will depend on σσii
σσ22ii = = σσ22
intrinsicintrinsic + + σσ22multiple scatteringmultiple scattering
Error on the cluster coordinates in the tracking planes
Initially assume to be width /
Select events with 1 pixel clusters in tracking planes
Has to be calculated
12
August 26, 2003 P. Nilsson, SPD Group Meeting 10
Multiple Scattering (1)Material budget (p-run)Material budget (p-run)
SENSOR (Si)
BUMP BONDS (Sn-Pb)
CHIP (Si)
Au+Cu
GLUE (Epoxy)
PCB (G10)
Thickness (m) X0(cm) x/X0(%)
1000 19.4 0.5155
75 44.37 0.0169
1 + 35 0.33 & 1.43 0.2751
725plane 1,2,4,150plane 0,3 9.36 0.7746
0.385eff 0.95 8.8x10-4
300plane 2 , 200plane 0,1,3,4 9.36 0.3205
%92.10 X
xBeamdirection
TOTALRADIATIONLENGTH
Al 10 8.9 0.0112
(Plane 2)
August 26, 2003 P. Nilsson, SPD Group Meeting 11
Assume scattering in each plane by an angleAssume scattering in each plane by an angle
where where cpcp = 120GeV, = 120GeV, zz = 1, and = 1, and x/Xx/X00 = 0.0192 etc. Air is not included = 0.0192 etc. Air is not included
(negligible).(negligible).
Remember the position in the previous plane, project into the nextRemember the position in the previous plane, project into the next
Multiple Scattering (2)
)ln(038.0100
6.130 X
xXx
cpMeV z
August 26, 2003 P. Nilsson, SPD Group Meeting 12
Results:Results:
The MS contributions, i.e. theThe MS contributions, i.e. thesquare of widths of the MS square of widths of the MS gaussians (the position gaussians (the position distributions) are then distributions) are then added to added to the position errors of the cluster the position errors of the cluster positionspositions
Multiple Scattering (3)
August 26, 2003 P. Nilsson, SPD Group Meeting 13
The χ2 Method (Tracking error cont.)
In the XZ-projection plane:
2
track
2
track
• Idea: use 2 information to calculate the track resolution by varying the track fit constant (x,y = f(z) = az + b, vary b and redo the 2 calculation)• The track resolution can be read out from the resulting parabolas
2 = 1 XZ, track
For a 68% confidence interval:
In the YZ-projection plane:
2 = 1 YZ, track
For a 68% confidence interval:
XZ-plane
YZ-plane
August 26, 2003 P. Nilsson, SPD Group Meeting 14
Analytic Calculation (Tracking error cont.)
2
1
1
2
22
2
2
2
)(
i
z
i
z
i
i
i
i
i
i
i
i
a
2
1
2
22
2
2
2
2
)(
i
z
i
z
i
i
z
i
i
i
i
i
i
i
b
For a linear fit
the errors in the fit parameters can be calculated using standard error propagation. They are found to be
where i is the error in the variable zi.
XZ, Analytical = YZ, Analytical
bazzfx )(
Because of rotated tracking planes
August 26, 2003 P. Nilsson, SPD Group Meeting 15
Intrinsic Resolution
Traditional approximation:Traditional approximation:
σ2intrinsic = σ2
residual – σ2tracking
““Hypothesis test” - methodHypothesis test” - method
August 26, 2003 P. Nilsson, SPD Group Meeting 16
“Hypothesis Test” Method
Toy MC to convolute: Toy MC to convolute: Gauss (estimated tracking error)Gauss (estimated tracking error) Flat (intrinsic resolution = )Flat (intrinsic resolution = )
Loop over parameter w and test hypothesis:Loop over parameter w and test hypothesis: “ “Data compatible with simulated Data compatible with simulated
distribution”distribution” Reject hypothesis if test statistics < critical Reject hypothesis if test statistics < critical
value (Kolmogorov-Smirnov / value (Kolmogorov-Smirnov / χχ22 test) test)
12/w
August 26, 2003 P. Nilsson, SPD Group Meeting 17
Result: sample output of routine
This file contains 6891 tracks<< Processing tracks... >>6857Using offset: -9.036e-05Hypothesis accepted by KS 20 0.015 Hypothesis accepted by KS 21 0.0155 Hypothesis accepted by KS 22 0.016 Hypothesis accepted by KS 23 0.0165 Hypothesis accepted by KS 24 0.017 Loop completedTracking resolution 0.01117Start value 0.005End value 0.0175Step size 0.0005Number of pseudo-events 100000
Short pixel dimension
Residuals from data + toy MC
August 26, 2003 P. Nilsson, SPD Group Meeting 18
Results: Intrinsic resolution for different thresholds
Threshold
Short pixel dimension,
1 pixel cluster in test plane
Error bars correspond to hypotheses that were not rejected by the tests
August 26, 2003 P. Nilsson, SPD Group Meeting 19
1 Pixel and 2 Pixel Clusters
1px . 2px .
smaller threshold
larger threshold
Short pixel dimension
1,2 px clusters in test plane
August 26, 2003 P. Nilsson, SPD Group Meeting 20
Iterative Method
Tracking error estimate relies on knowledge Tracking error estimate relies on knowledge of 1 pixel intrinsic resolution at a given of 1 pixel intrinsic resolution at a given thresholdthreshold
use the newly found intrinsic resolution use the newly found intrinsic resolution to re-estimate the tracking resolutionto re-estimate the tracking resolution
Iterate to get the final tracking errorIterate to get the final tracking error
However…
August 26, 2003 P. Nilsson, SPD Group Meeting 21
Iterative Method
Tracking planes were run at PRE_VTH 200 and were not identical to test plane (300 m sensor vs 200 m)
Try to find conditions when intrinsic resolution of test plane is comparable to tracking planes
Probability to obtain 1 or 2 px clusters is proportional to size of sensitive region
Use ratio between 1 and 2 px clusters to find threshold where test plane has similar resolution as tracking planes
Deviation from 1 of number of 1 to 2 px clusters in test plane to the tracking planes as a function of PRE_VTH
Use intrinsic resolution at PRE_VTH 170 to get new tracking error
August 26, 2003 P. Nilsson, SPD Group Meeting 22
Iterative Method
Initial tracking error over-estimated
Tracking error iterated from short dimension only
August 26, 2003 P. Nilsson, SPD Group Meeting 24
2px/1px After Iteration
Using initial tracking error estimate
After iterating tracking error
August 26, 2003 P. Nilsson, SPD Group Meeting 25
Conclusions
Results for 1 pixel and 2 pixel clusters (no Results for 1 pixel and 2 pixel clusters (no tilt) at ~30 mV (tilt) at ~30 mV (PRE_VTH 210PRE_VTH 210):):
σσ1px1pxshortshort= ( 8.9 ± 1.0 ) µm= ( 8.9 ± 1.0 ) µm
σσ1px1pxlong long = (120.4 ± 1.7 ) µm= (120.4 ± 1.7 ) µm
σσ2px2pxshortshort= ( 8.2 ± 0.9 ) µm= ( 8.2 ± 0.9 ) µm
σσ2px2pxlong long = (116.0 ± 1.7 ) µm= (116.0 ± 1.7 ) µm
Final tracking error: σσTrackTrack== 10.6 m
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