1

Analysis of the Stereo Hits and the 2D Circle Fitter

Hans Wenzel, Hogan NguyenFeb 9th, 2011

Introduction

Hans 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.cc

We 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.

2

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

3

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

4

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

~4 mm Gaussiansigma

Correlationdepending on“Configuration of Stereo Hit”

even planes odd planes

cos(polar)=0.3

5

Stereo Hit Resolution Dependence on the 6 Configurations

cos(polar)=0.3

6

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

7

Radius of Stereo Hit - Radius of True Hit (millimeters)

Configurationnumber

sigma = 2.0 mmfor all configurations

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

cos(polar)=0.3

8

Fit Consistency

allow 1 iteration to refit excluding theworse chi2 contributor

Straw wall and wireREMOVED from G4 simulation

cos(polar)=0.3

9

allow 1 iteration to refit excluding theworse chi2 contributor

Straw wall and wireINCLUDED in the G4 simulation

Fit Consistency

More materialincreases the Number of Low ProbabilityFits

10

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

11

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

12

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.cc

access and analyze the Clusters:HitMakers/src/ReadDPIStrawCluster_plugin.cc

run it:HitMakers/test/makeDPIStrawClusters.py(makes StrawHits-> Clusters --> analyzes )

working on:

r-z fit, comparing found hits with hits associated to conversion electron (ConvElecUtilities), properclasses to output --> input to final fitter.

13

Back up

14

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

Straw Wall and Wire Removed from G4 Simulation