Ja Garzon Tim Trackfor Trasgos

440 views

Published on

0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
440
On SlideShare
0
From Embeds
0
Number of Embeds
2
Actions
Shares
0
Downloads
2
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Ja Garzon Tim Trackfor Trasgos

  1. 1. Proyecto timtrack timtrack timtrack timtrack timtrack timtrack timtrack A Tracking Algorithm for timtrack TRASGOS timtrack timtrack timtrack timtrack Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
  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 Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
  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) Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
  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) Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
  5. 5. L x z Saeta X’ V X0 T0 Vz z=0 Y’ Y0 y Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
  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) Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
  7. 7. About timtrack 1st. Step - To define the model, giving the cuantities that are measured as function of the parameters of the saeta Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
  8. 8. x Times Example Strip-like detector X-type plane z T T’ z=zi z=0 y 0 0 Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
  9. 9. x Times X-type plane z T V T’ X’ X0 T0 z=zi Y’ z=0 Y0 y Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
  10. 10. x Times X-type plane T z T’ X’ V X0 T0 z=zi Vz Y’ z=0 Y0 y Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
  11. 11. x Times X-type plane Ti z T’i V X’ X0 T0 z=zi Y’ z=0 Y0 y Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
  12. 12. x Coordinates X-type plane z Xi V X’ X0 T0 z=zi Y’ z=0 Y0 y Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
  13. 13. x Ti Y-type plane z V X’ X0 T0 z=zi z=0 Y’ T’i Y0 Yi y Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
  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! Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
  15. 15. About timtrack 2nd. Step - To build the function S to be minimized x V X’ n planes X0 T0 Y’ Y0 y Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
  16. 16. About timtrack 2nd. Step - S is a sum over n planes: K = X or Y K = Y or X Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
  17. 17. About timtrack 2nd. Step - The expansion of the S function is: Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
  18. 18. About timtrack 2nd. Step - That can be written in a more compact way: where: Saeta Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
  19. 19. About timtrack K (configuration Matrix): depend on the detector layout Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
  20. 20. About timtrack a (vector of reduced data): depend on the data (They are just weighted sums and differences of the measurements) Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
  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 Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
  22. 22. About timtrack 3rd. Step - Set of solutions (is just the Cramer rule): where: Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
  23. 23. About timtrack Error analysis - The error matrix is - Incertitudes can be easily calculated from the K matrix elements Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
  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) Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
  25. 25. About timtrack Other strip-like detector layouts (with the same K-matrix structure) Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
  26. 26. About timtrack Strip-like detectors with any shape: x x XBack (X,Y) vs2 vs1 ymin YBack y y XFront Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
  27. 27. About timtrack Strip-like detectors with any shape: Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
  28. 28. About timtrack Strip-like detectors with any shape: where: Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
  29. 29. About timtrack Pads or pixel detectors : ∆Yi X ∆Xi Xi X0 z zi z=0 Y0 Yi Y Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
  30. 30. About timtrack Pads or pixel detectors : Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
  31. 31. About timtrack Pads or pixel detectors : where: Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
  32. 32. About timtrack Other strip-like detector layouts (with different K-matrix structure) Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
  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: Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
  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 Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
  35. 35. About timtrack Other strip-like detector layouts (with different K-matrix structure) Remember: ci = cos ϕi si = sin ϕi Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
  36. 36. About timtrack Other strip-like detector layouts (with different K-matrix structure) Again: Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
  37. 37. About timtrack Other strip-like detector layouts (with different K-matrix structure) Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
  38. 38. About timtrack Other strip-like detector layouts (with different K-matrix structure) The solution of is (Cramer rules): Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
  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) Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
  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 Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
  41. 41. About timtrack A typical example: 2 parallel scintillators: different properties Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
  42. 42. About timtrack A typical example: 2 parallel scintillators: identical properties Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
  43. 43. The END Thanks! Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010

×