Proyecto


                 timtrack
              timtrack
                  timtrack
            timtrack
              ...
About the TRASGO concept
A                               TRASGO
                   (TRAck reconStructinG mOdule)
is a dete...
About SAETAS
   A SAETA (SmAllest sEt of daTA) is the basic unit of information
 in the timtrack algorithm and in the TRAS...
About SAETAS

From the mathematical point of view will be better to use:

             Saeta: s = (X0,X’,Y0,Y’,T0,1/Vz)

 ...
L
        x




                                                                                          z




Saeta
    ...
About timtrack

TimTrack is the algorithm developed to estimate SAETAS
1. It is based on a Least Squares Method (LSM)
2. I...
About timtrack

   1st. Step
  - To define the model, giving the cuantities that are measured
as function of the parameter...
x                                                           Times
Example                                                 ...
x                                                          Times

X-type plane
                                           ...
x                                                          Times

X-type plane
                          T                ...
x                                                           Times

X-type plane
                           Ti             ...
x                                                  Coordinates

X-type plane
                                             ...
x
                                                   Ti


Y-type plane
                                                   ...
About timtrack
1st. Step

  - To define the model giving the cuantities to be measured as
function of the parameters of th...
About timtrack
2nd. Step
- To build the function S to be minimized




                     x



                         ...
About timtrack
2nd. Step
- S is a sum over n planes:




                                                                 ...
About timtrack
2nd. Step
- The expansion of the S function is:




                                                       ...
About timtrack
2nd. Step
- That can be written in a more compact way:


   where:
                                        ...
About timtrack
K (configuration Matrix): depend on the detector layout




                                               ...
About timtrack

a (vector of reduced data): depend on the data
(They are just weighted sums and differences of the measure...
About timtrack
3rd. Step
 - To apply to LSM method.

   From:



                                      leads to:

  As K i...
About timtrack
3rd. Step
 - Set of solutions (is just the Cramer rule):




                                              ...
About timtrack
Error analysis
- The error matrix is




- Incertitudes can be easily calculated from the K matrix elements...
About timtrack

  Comments
     - The method can be easily extended when there are correlations
between some of the measur...
About timtrack
Other strip-like detector layouts
(with the same K-matrix structure)




                                  ...
About timtrack
Strip-like detectors with any shape:

                                     x           x

                 ...
About timtrack
Strip-like detectors with any shape:




                                                                  ...
About timtrack
Strip-like detectors with any shape:




                                                  where:




     ...
About timtrack
Pads or pixel detectors :
                                                   ∆Yi


          X


          ...
About timtrack
Pads or pixel detectors :




                                                                             ...
About timtrack
Pads or pixel detectors :




                                                  where:




                ...
About timtrack

Other strip-like detector layouts
(with different K-matrix structure)




                                ...
About timtrack
    Other strip-like detector layouts
    (with different K-matrix structure)

                            ...
About timtrack
Other strip-like detector layouts (with different K-matrix structure)
                                     ...
About timtrack
Other strip-like detector layouts
(with different K-matrix structure)




              Remember:
         ...
About timtrack
Other strip-like detector layouts
(with different K-matrix structure)
Again:




                          ...
About timtrack
Other strip-like detector layouts
(with different K-matrix structure)




                                 ...
About timtrack
 Other strip-like detector layouts
 (with different K-matrix structure)




The solution of                ...
About timtrack

  Comments
     - The “problem” of the method is that there is an inversion of a
matrix. Sometimes it may ...
About timtrack
 A typical example
 2 parallel scintillators
                                          T’2
                ...
About timtrack
A typical example: 2 parallel scintillators: different properties




                                     ...
About timtrack
A typical example: 2 parallel scintillators: identical properties




                                     ...
About timtrack




                  Drift Chambers




                                                                  ...
About timtrack
Drift Chambers

              x


                                                           z
            ...
About timtrack
  Drift Chambers
1 Step. To build the model:
   In a typical Drift Chamber each layer provides two
 data:
-...
About timtrack
 Drift Chambers
The time measured by a DC has 3 components:

                     s d f
                   ...
x
         (Xi,0, Zi)      θi
                              →
                              h       u          (Xp,Yp)

  ...
About timtrack
Some definitions:
                              X


                             θ
                        ...
Particle

                           d
y                                 Yi
                       s          wire

      ...
About timtrack

 Drift Chambers
1.Time of flight of the particle from z=0 to z=zplane
  (Approach without slope correction...
About timtrack

 Drift Chambers
1.Time of flight of the particle from z=0 to z=zplane
  (Approach with slope correction)

...
About timtrack
   Drift Chambers
  2nd. Step
- S is a sum over n planes:




                           s d f
            ...
About timtrack
Drift Chambers

Now, the model is not linear, and the saeta has to be
 found iteratively

• Calculate a Sae...
About timtrack
Drift Chambers




  Cut




                                                                              ...
About timtrack
Drift Chambers




                                                                                   Proye...
About timtrack
Drift Chambers




                                                                                   Proye...
About timtrack
Drift Chambers




                                                                                   Proye...
About timtrack
3rd. Step
 - Set of solutions (is just the Cramer rule):




                                              ...
timtrack: Simulation of a MDC track calculated with Mathlab

Params         Generated    1. fit        1. Sl.Cor    2.Sl.C...
Variante-Covariance Matrix (alter 1st. Slope correction)

[0.00046,        1.7e-22,            -3.8e-21,   -1.32e-06,     ...
About timtrack
         Comments and Summary
      - timtrack seems to offer a promising alternative for the tracking of c...
The END

                           Thanks!




                                                                          ...
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Jag Tim Track Gsi 20 Nov09 Short

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Juan Antonio Garzón talk about the Timtrack software.
GSI, Germany, November 2009.

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Jag Tim Track Gsi 20 Nov09 Short

  1. 1. Proyecto timtrack timtrack timtrack timtrack timtrack timtrack timtrack A Tracking Algorithm for timtrack TRASGOS timtrack timtrack timtrack timtrack Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  2. 2. About the TRASGO concept A TRASGO (TRAck reconStructinG mOdule) is a detector able to work stand-alone offering full capabilities of timing and tracking of charged particles DAQ Electronics Network Power supplies Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  3. 3. About SAETAS A SAETA (SmAllest sEt of daTA) is the basic unit of information in the timtrack algorithm and in the TRASGOs concept A SAETA contains 6 parameters defining a charged particle track In a cartesian coordinate system: - X0 and Y0: 2 coordinates at a reference plane - X’ and Y’ : 2 projected slopes in planes x-z and y-z - T0 : The time at the reference plane respect a reference time - V : The velocity Saeta: s = (X0,X’,Y0,Y’,T0,V) Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  4. 4. About SAETAS From the mathematical point of view will be better to use: Saeta: s = (X0,X’,Y0,Y’,T0,1/Vz) where: V = Vz · Sqrt(1+X’2+Y’2) Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  5. 5. L x z Saeta X’ V X0 T0 Vz z=0 Y’ Y0 y Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  6. 6. About timtrack TimTrack is the algorithm developed to estimate SAETAS 1. It is based on a Least Squares Method (LSM) 2. It works directly with the primary data provided by detectors: - Coordinates: - Times: it is assumed that: all times are refered to a common t=0 (all detector are WELL synchronized) 3. It lets free the six elements of a saeta: (X0, X’, Y0, Y’, T0 and 1/Vz) Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  7. 7. About timtrack 1st. Step - To define the model, giving the cuantities that are measured as function of the parameters of the saeta Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  8. 8. x Times Example Strip-like detector X-type plane z T T’ z=zi z=0 y 0 0 Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  9. 9. x Times X-type plane z T V T’ X’ X0 T0 z=zi Y’ z=0 Y0 y Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  10. 10. x Times X-type plane T z T’ X’ V X0 T0 z=zi Vz Y’ z=0 Y0 y Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  11. 11. x Times X-type plane Ti z T’i V X’ X0 T0 z=zi Y’ z=0 Y0 y Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  12. 12. x Coordinates X-type plane z Xi V X’ X0 T0 z=zi Y’ z=0 Y0 y Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  13. 13. x Ti Y-type plane z V X’ X0 T0 z=zi z=0 Y’ T’i Y0 Yi y Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  14. 14. About timtrack 1st. Step - To define the model giving the cuantities to be measured as function of the parameters of the saeta Either or 3 equations (conditions) per plane! Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  15. 15. About timtrack 2nd. Step - To build the function S to be minimized x V X’ n planes X0 T0 Y’ Y0 y Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  16. 16. About timtrack 2nd. Step - S is a sum over n planes: K = X or Y K = Y or X Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  17. 17. About timtrack 2nd. Step - The expansion of the S function is: Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  18. 18. About timtrack 2nd. Step - That can be written in a more compact way: where: Saeta Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  19. 19. About timtrack K (configuration Matrix): depend on the detector layout Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  20. 20. About timtrack a (vector of reduced data): depend on the data (They are just weighted sums and differences of the measurements) Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  21. 21. About timtrack 3rd. Step - To apply to LSM method. From: leads to: As K is definite positive, K has an inverse and: This equation provides the saeta directly from the data Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  22. 22. About timtrack 3rd. Step - Set of solutions (is just the Cramer rule): where: Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  23. 23. About timtrack Error analysis - The error matrix is - Incertitudes can be easily calculated from the K matrix elements Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  24. 24. About timtrack Comments - The method can be easily extended when there are correlations between some of the measurements (e.G.: time readouts) - Only two planes of strip-like detectors are enough to provide unambiguously the 6 parameters of a saeta - The solution has a matrix form: It’s very easy and fast of implementing on computers -There are many detector layouts with a K matrix having the same structure (see next examples) Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  25. 25. About timtrack Other strip-like detector layouts (with the same K-matrix structure) Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  26. 26. About timtrack Strip-like detectors with any shape: x x XBack (X,Y) vs2 vs1 ymin YBack y y XFront Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  27. 27. About timtrack Strip-like detectors with any shape: Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  28. 28. About timtrack Strip-like detectors with any shape: where: Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  29. 29. About timtrack Pads or pixel detectors : ∆Yi X ∆Xi Xi X0 z zi z=0 Y0 Yi Y Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  30. 30. About timtrack Pads or pixel detectors : Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  31. 31. About timtrack Pads or pixel detectors : where: Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  32. 32. About timtrack Other strip-like detector layouts (with different K-matrix structure) Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  33. 33. About timtrack Other strip-like detector layouts (with different K-matrix structure) L x Ki z ’ V z=0 y New transverse coordinates defined by an angle φ: Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  34. 34. About timtrack Other strip-like detector layouts (with different K-matrix structure) K x XBack x XB Ti’ K (Xp,Yp) -vs sinφ vs Kim X vs cosφ Kip φ φ YBack + YFront YF - YB y Y y Ki XF XFront Ti K=0 K=0 Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  35. 35. About timtrack Other strip-like detector layouts (with different K-matrix structure) Remember: ci = cos ϕi si = sin ϕi Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  36. 36. About timtrack Other strip-like detector layouts (with different K-matrix structure) Again: Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  37. 37. About timtrack Other strip-like detector layouts (with different K-matrix structure) Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  38. 38. About timtrack Other strip-like detector layouts (with different K-matrix structure) The solution of is (Cramer rules): Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  39. 39. About timtrack Comments - The “problem” of the method is that there is an inversion of a matrix. Sometimes it may give problems (when the matrix is not well conditioned) but there are a lot of numerical methods to do it (And it has to be done only once) Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  40. 40. About timtrack A typical example 2 parallel scintillators T’2 T’1 y ➱ vs1 ➱ ➱ vs2 (Yo,Y’,V,T0) ➱ z1 z2 z L1 T T1 L2 τ= T2 vs Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  41. 41. About timtrack A typical example: 2 parallel scintillators: different properties Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  42. 42. About timtrack A typical example: 2 parallel scintillators: identical properties Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  43. 43. About timtrack Drift Chambers Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  44. 44. About timtrack Drift Chambers x z d h s X’ V X0 T0 Y’ z=0 Y0 y Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  45. 45. About timtrack Drift Chambers 1 Step. To build the model: In a typical Drift Chamber each layer provides two data: - A coordinate: given by the cell width and orientation: cellwidth σK = 12 - A time measured by a TDC: σ = TDC resolution T Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  46. 46. About timtrack Drift Chambers The time measured by a DC has 3 components: s d f T= + + V vd vs 1.Time of flight of the particle from z=0 to z=zplane 2.Time of drift of the electrons 3.Time of the signal to the wire end Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  47. 47. x (Xi,0, Zi) θi → h u (Xp,Yp) (Xq,Yq) s0 d d0 → vd Xi s f f0 vs V (Xo,Yo) Ti To Zi y
  48. 48. About timtrack Some definitions: X θ α β Z Y Rotation θ, around z Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  49. 49. Particle d y Yi s wire ∆Y V Y’ Y’i Y0 z=0 z=Zi
  50. 50. About timtrack Drift Chambers 1.Time of flight of the particle from z=0 to z=zplane (Approach without slope correction) Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  51. 51. About timtrack Drift Chambers 1.Time of flight of the particle from z=0 to z=zplane (Approach with slope correction) Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  52. 52. About timtrack Drift Chambers 2nd. Step - S is a sum over n planes: s d f ( + + ) V vd vs Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  53. 53. About timtrack Drift Chambers Now, the model is not linear, and the saeta has to be found iteratively • Calculate a Saeta • Substitute X’ and Y’ in the formulae • Calculate the Saeta with corrected coefficients Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  54. 54. About timtrack Drift Chambers Cut Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  55. 55. About timtrack Drift Chambers Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  56. 56. About timtrack Drift Chambers Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  57. 57. About timtrack Drift Chambers Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  58. 58. About timtrack 3rd. Step - Set of solutions (is just the Cramer rule): Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  59. 59. timtrack: Simulation of a MDC track calculated with Mathlab Params Generated 1. fit 1. Sl.Cor 2.Sl.Cor 3.Sl.Cor 4.Sl.Cor X0 0.(mm) -0.07 0.06 0.06 0.06 0.06 X’ 0.1 0.098 0.1000 0.101 0.101 0.101 Y0 1.(mm) 0.998 1.000 1.005 1.005 1.005 Y’ 0.1 0.100 0.0998 0.0995 0.0995 0.0995 T0 0.(ps) 3592 1555 1307 1280 1287 1/Vz 3.3 (=c). 3.74 -3.69 1.12 1.19 1.18 Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  60. 60. Variante-Covariance Matrix (alter 1st. Slope correction) [0.00046, 1.7e-22, -3.8e-21, -1.32e-06, 0.399, 6.9e-19;] [-1.2e-22, 5.05e-08, 4.8e-07, 2.5e-24, -2.3e-18, -0.0005;] [3.16e-21, 4.86e-07, 0.00013, -1.07e-22, 1.95e-16, -0.025;] [-1.32e-06, 2.3e-24, 1.03e-22, 2.8e-08, -0.03, -7.5e-20;] [0.399 ,-2.95e-18, -3.47e-17, -0.03, 76162,7. 2e-14;] [2.3e-18, -0.0005, -0.0259, -4.31e-20, 2.97e-14, 14.99;]
  61. 61. About timtrack Comments and Summary - timtrack seems to offer a promising alternative for the tracking of charge particles in Drift Chambers - It needs only 3 layers to define a saeta (6 parameters) candidate - It works in the coordinate-times space making hit finding quite easy: once several layers define a candidate it is easy to extrapolate the candidate to another layer and to look for a signal in a given time window - Putting constraints in the model is very easy; for instance: vertex condition (it reduces the minimum number of planes to 2) - Time and velocity have big incertitudes but they are highly correlated with other parameters - With fixed time and velocity, a reduced saeta (4 params.) can be built every two planes allowing to analyze magnetic fields effect - With timtrack joined fit with several detectors families is possible. E.g. MDCs and RPCsWall, MDCs and RICH…. Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
  62. 62. The END Thanks! Proyecto Juan A. Garzón. timtrack: A tracking algorithm for trasgos. GSI 20.11 2009
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