# Analysis of the Stereo Hits and the 2D Circle Fitter

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## Analysis of the Stereo Hits and the 2D Circle Fitter

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Analysis of the Stereo Hits and the 2D Circle Fitter Hans Wenzel, Hogan NguyenFeb 9th, 2011

IntroductionHans implemented stereo hits, formed by the intersection of 2 clusters withina plane (0-35)A 2D Circle Fitter, using these stereo hits have been implemented inReadStrawCluster_plugin.ccWe analyze here how well this works.For simplicity, we initially remove the straw wall and wire material, to study the fitbehavior with less material.Note: We view this 2D fitter as part of the Pattern Recognition Algorithm, whose goalis to handing off good straw hits to the Kalman Fitter.

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6 Configurations for Stereo Hits

Panels Used Plane----------------------------------------------- 0 & 1 or 3 & 4 even plane 1 & 2 or 4 & 5 even plane 2 & 3 or 5 & 0 even plane 0 & 1 or 3 & 4 odd plane 1 & 2 or 4 & 5 odd plane 2 & 3 or 5 & 0 odd plane

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Example: Configuration = 1

Even plane, panels 0 and sector 1

Banana Shape Described by polar angle.

Location in Banana given by “Phi” angle.

Note the offset from Origin. For now, use adhoc correction to shift banana togo through origin. Can do rigorously later. Offset from Origin of Order 5 mm.

Difference between reconstructed position and Actual Position

Sanity

Check: polar angle = 72 degrees

Maximum shift = (19/2 mm)/tan(90-polar)*tan(30

) = 17 mm

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Comparing Reconstructed Stereo Hit Position with True Hit Position (in millimeters)

~4 mm Gaussian

sigma

Correlationdepending on“Configuration of Stereo Hit”

even planes

odd planes

cos(polar)=0.3

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Stereo Hit Resolution Dependence on the 6 Configurations

cos(polar

)=0.3

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Fit Minimizes Perpendicular Distance To Circle.

3 free parameters for a 2D circle:

X0, Y0 is the fitted center, and R is the fitted Radius

Notes

Errors Calibrated From MC

(see Next Slide)Adhoc Correction done toaccount for polar angle dependence of the StereoHit.Can do it rigorously later

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Configuration

number

sigma = 2.0 mmfor all configurations

Errors Used in the 2D Fit. Calibrate using Monte Carlo

cos(polar)=0.3

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Fit Consistency

allow 1 iteration to

refit excluding theworse chi2 contributorStraw wall and wireREMOVED from G4 simulation

cos(polar)=0.3

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allow 1 iteration to

refit excluding theworse chi2 contributorStraw wall and wireINCLUDED in the G4 simulation

Fit Consistency

More materialincreases the Number of Low ProbabilityFits

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Requirement Efficiency

0 No Cuts1 >= 15 straw hits2 >= 20 straw hits3 >= 25 straw hits4 >= 6 clusters5 >= 4 stereo hits6 fit probability > 1% 69%

Cos(polar) = 0.3

Cut Number

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cos(polar

)=0.5

32% eff

cos(polar

)=0.7

1% eff

(big drop in requiring 4 stereo hits)

(big drop in requiring 15 hits)

Cut Number

Cut Number

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Ongoing Code Development

persistent StrawCluster/StrawClusterCollection before:was Vector of StrawID's:typedef std::vector<mu2e::StrawId> StrawCluster;typedef std::vector<mu2e::StrawCluster> StrawClusterCollection;now persistent pointer to StrawHitsauto_ptr<DPIndexVectorCollection> listofptrtoHits(new DPIndexVectorCollection);DPIndexVector ptrtoHits;All code (new/old) resides in CVS:make the Clusters:HitMakers/src/MakeDPIStrawCluster_plugin.ccaccess and analyze the Clusters:HitMakers/src/ReadDPIStrawCluster_plugin.ccrun it:HitMakers/test/makeDPIStrawClusters.py(makes StrawHits-> Clusters --> analyzes )

working on

:

r-z

fit, comparing found hits with hits associated

to

conversion

electron (

ConvElecUtilities

), proper

classes to output --> input to final fitter.

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Back up

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Fit Consistency, when using ACTUAL Track position in the Fit.

Straw Wall and

Wire Removed from G4 Simulation

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