Helix Track Finding and Track Fitting Algorithm A FPGA tracking - - PowerPoint PPT Presentation

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Helix Track Finding and Track Fitting Algorithm A FPGA tracking - - PowerPoint PPT Presentation

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Helix Track Finding and Track Fitting Algorithm A FPGA tracking algorithm for helix tracking using STT and MVD David Mnchow II. Physikalisches Institut Universitt Gieen Content PANDA Specifics Conformal Mapping Hough Transformation

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Helix Track Finding and Track Fitting Algorithm

A FPGA tracking algorithm for helix tracking using STT and MVD

David Münchow

  • II. Physikalisches Institut

Universität Gießen

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14.04.2009 Page 2 David Münchow

Content

  • PANDA Specifics
  • Conformal Mapping
  • Hough Transformation
  • Secondary Vertex
  • z-Direction
  • Future
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14.04.2009 Page 3 David Münchow

Situation in PANDA experiment

  • Simulated data with PANDARoot framework
  • Uses digitized hit data for STT and MVD detector

Straw Tube Tracker (STT)

  • r

Time Projection Chamber (TPC) Micro Vertex Detector (MVD)

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14.04.2009 Page 4 David Münchow

PANDA Specifics

  • Target Spectrometer

(forward detectors not used in the moment)

  • Homogenous Bz=2 T

(Solenoid)

  • TOSCA field maps
  • incl. overlap region

solenoid-dipole

  • Charged article tracks

can be described as a helix

B-field

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PANDA Specifics

  • In x,y plane, tracks can be described as

circles

  • Problem:

many circles with different radii and different centers

  • Solution:

conformal mapping

10 muons with 1 GeV simulated on PANDA root framework

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Conformal Mapping

  • Angle preserving,

not length preserving

  • Easier tracking for lines

→ transform circles to straight lines

  • Transformation:
  • Reference point must be on the circle

( ) ( )

2 2 2 2 2

y y x x r r y y y r x x x − + − = − = ′ − = ′ ( )

, , z y x

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Conformal Mapping

  • Real space
  • Conformal space
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Hough Transformation

  • Line tracking with Hough transformation
  • Take all possible lines through a point in conformal

space

  • Describe it with parameters

r and θ

  • Add it as a count to a

r-θ-matrix (parameter space)

( )

θ θ θ sin cos y x r + =

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Hough Transformation

  • Find peaks to get track parameter

radius r’ angle θ

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Secondary Vertex

  • Problem: one reference gives only tracks

through this point

  • Solution: reiterate with each hit point as reference

point

( )

, , z y x

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z-Direction

  • Find z-component with an different Hough

transformation for each found track and get parameter αoff (offset) and λ (pitch)

arctan tan y y x x y z

  • ff

− − = − = α α λ α

αoff λ x-z projection of helical track

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Results

  • Algorithm gets back helix parameters

after back-transformation to real space: xc, yc center of helix r radius αoff

  • ffset

λ pitch

found tracks

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Future

  • Testing and optimizing algorithm in the

PANDARoot framework

  • Implementation to an FPGA Platform
  • Fix point instead of float
  • 24 bit (in division and multiplikation 48 bit)
  • Hough space of 512×512 indices
  • Lookup Table for sinus: 128 indices with 16 bit
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14.04.2009 Page 14 David Münchow

Thank you