august 26, 2003p. nilsson, spd group meeting1 paul nilsson, spd group meeting, august 26, 2003 test...

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


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


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


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)


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)


“Typical” track quality

2 distributions

Residual distributions

XZ-plane YZ-plane


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


“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)


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


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)


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


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)


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


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


Intrinsic Resolution

Traditional approximation:Traditional approximation:

σ2intrinsic = σ2

residual – σ2tracking

““Hypothesis test” - methodHypothesis test” - method


“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


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


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


1 Pixel and 2 Pixel Clusters

1px . 2px .

smaller threshold

larger threshold

Short pixel dimension

1,2 px clusters in test plane


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…


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


Iterative Method

Initial tracking error over-estimated

Tracking error iterated from short dimension only


Iterative Method


2px/1px After Iteration

Using initial tracking error estimate

After iterating tracking error


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

august 26, 2003p. nilsson, spd group meeting1 paul nilsson, spd group meeting, august 26, 2003 test...

Documents

nilsson slide

intrinsic resolution

x proj tracking

tracking planes

spd group meeting3

b slide

focused beam data slide

multiple scattering