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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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