J A Garzon Tim Trackfor Trasgos
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Transcript of J A Garzon Tim Trackfor Trasgos
Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
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Proyecto
A Tracking Algorithm forTRASGOS
timtrack
Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
About the TRASGO conceptA TRASGO
(TRAck reconStructinG mOdule)
is a detector able to work stand-alone offering full capabilities of timing and tracking of charged particles
DAQ ElectronicsNetwork
Power supplies
Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
About SAETASA 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 trackIn 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
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
T0
Vz
y
xL
z=0Y0
X0
X’
Y’
z
V
Saeta
Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
About timtrack
TimTrack is the algorithm developed to estimate SAETAS1. 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
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
y
x
z=0
z
z=zi
TimesExample Strip-like detector
X-type plane
T T’
0
0
Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
T0
Y’
y
x
z=0Y0
X0
X’
z
V
z=zi
Times
X-type plane
T’T
Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
T0
Y’
y
x
z=0Y0
X0
X’
z
z=zi
Times
X-type plane
V
T’
T
Vz
Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
T0
Y’
y
x
z=0Y0
X0
X’
z
V
z=zi
TiT’i
Times
X-type plane
Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
T0
Y’
y
x
z=0Y0
X0
X’
z
V
z=zi
Coordinates
Xi
X-type plane
Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
T0
Y’
y
x
z=0Y0
X0
X’
z
V
z=zi
Yi
Ti
T’i
Y-type plane
Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
About timtrack1st. 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
About timtrack2nd. Step- To build the function S to be minimized
T0
Y’y
x
Y0
X0
X’V
n planes
Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
About timtrack2nd. 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
About timtrack2nd. Step- The expansion of the S function is:
Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
About timtrack2nd. 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
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
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
About timtrack3rd. 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
About timtrack3rd. 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
About timtrackError 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
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
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
About timtrackStrip-like detectors with any shape:
x
ymin YBack y
(X,Y)XBack
XFront
y
x
vs2
vs1
Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
About timtrackStrip-like detectors with any shape:
Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
About timtrackStrip-like detectors with any shape:
where:
Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
About timtrackPads or pixel detectors :
Y0
X0
zi
z
Y
X
z=0
Xi
Yi
∆Xi
∆Yi
Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
About timtrackPads or pixel detectors :
Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
About timtrackPads or pixel detectors :
where:
Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
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
About timtrackOther strip-like detector layouts (with different K-matrix structure)
y
x L
z=0
’
z
V
Ki
New transverse coordinates defined by an angle φ:
Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
Other strip-like detector layouts (with different K-matrix structure)
About timtrack
y
XBack
φYBack YFront
XFront
x
Kim
K=0
Kip
(Xp,Yp)K
+
-vs sinφ
y
XB
φ
vs
YF YB
XF
xTi’
Ti
X
Y
vs cosφ
Ki
-
K=0
K
Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
Other strip-like detector layouts (with different K-matrix structure)
About timtrack
Remember:
ii
ii
sc
ϕϕ
sincos
==
Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
About timtrackOther 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
About timtrackOther strip-like detector layouts (with different K-matrix structure)
Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
About timtrackOther 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
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
A typical example2 parallel scintillators
About timtrack
vs2
vs1
z2z1
L1
➱
➱
T’1
T1 T2
T’2
z
(Yo,Y’,V,T0)➱
➱
y
L2
svT
=τ
Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
About timtrackA typical example: 2 parallel scintillators: different properties
Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
About timtrackA typical example: 2 parallel scintillators: identical properties
Juan A. Garzón: 2nd. Workshop on the Trasgo Project. S. Compostela Feb. 5th-6th. 2010
The END
Thanks!