Introduction
Rekonstruction of MSC angles
σreco calibration
DEPFET H4&H5 maps
Conclusion
Spatial resolved radiation length (X /X0 )
measurements of DEPFET pixel sensors using
EUDET tracks
Ariane Frey, Benjamin Schwenker and Ulf Stolzenberg*
University of Göttingen, II. Physikalisches Institut
May 27th 2014, 16th International DEPFET Workshop
Ariane Frey, Benjamin Schwenker and Ulf Stolzenberg*
Spatial resolved radiation length (X /X0 ) measurements of DEPFET pixel sensors using EUDET tracks
University of Göttingen
1 / 12
Introduction
Rekonstruction of MSC angles
σreco calibration
DEPFET H4&H5 maps
Conclusion
Method for measuring X /X0
Measurement Procedure
Use tracks from the EUDET pixel telescope to reconstruct
angle distributions from multiple scattering (MSC) on a
central plane
The width of these distributions depend on the radiation
length X /X0 of the crossed material
Is a spatial resolved X /X0 measurement (with errors below
10%) possible, when using a EUDET telescope and a beam
energy of a few GeV?
What problems do occur during the measurement process?
Ariane Frey, Benjamin Schwenker and Ulf Stolzenberg*
Spatial resolved radiation length (X /X0 ) measurements of DEPFET pixel sensors using EUDET tracks
University of Göttingen
2 / 12
Introduction
Rekonstruction of MSC angles
σreco calibration
DEPFET H4&H5 maps
Conclusion
Multiple scattering
A particle with momentum p
and charge q crosses matter
with the radiation length X /X0
MSC projected angular
distribution (u-z plane) ≈
Gaussian function with σp given
by Highland Formula (HL)
Analog: v-z plane
Highland Formula(only small scattering angles)
r X
0.0136 · q[e]
X
σp =
·
1 + 0.0038 ln
rad
β · p [GeV]
X0
X0
V. L. Highland, Some practical remarks on multiple scattering, Nuclear Instruments and Methods,1975
Ariane Frey, Benjamin Schwenker and Ulf Stolzenberg*
Spatial resolved radiation length (X /X0 ) measurements of DEPFET pixel sensors using EUDET tracks
University of Göttingen
3 / 12
Introduction
Rekonstruction of MSC angles
σreco calibration
DEPFET H4&H5 maps
Conclusion
MSC Models
Highland model and Single Scattering model
Highland Model
MSC Simulation
104
103
102
-3
×10
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
θp [rad]
MSC simulation based on single scatterings: See R. Frühwirth, Nuclear Instruments and Methods, 2001
Ariane Frey, Benjamin Schwenker and Ulf Stolzenberg*
Spatial resolved radiation length (X /X0 ) measurements of DEPFET pixel sensors using EUDET tracks
University of Göttingen
4 / 12
Introduction
Rekonstruction of MSC angles
σreco calibration
DEPFET H4&H5 maps
Conclusion
Reconstruction of MSC angles in a EUDET teleskop
Reconstruct angles on
the DEPFET
telescope arm I
Particle crosses sensor
→ hits
23mm
27mm
DEPFET
111mm
telescope arm II
67mm
28mm
27mm
particle
p,q
Mimosa Pixel Sensoren
Pixel Pitch 18.4 µm
X/X0
Mimosa Pixel Sensoren
Pixel Pitch 18.4 µm
Ariane Frey, Benjamin Schwenker and Ulf Stolzenberg*
Spatial resolved radiation length (X /X0 ) measurements of DEPFET pixel sensors using EUDET tracks
University of Göttingen
5 / 12
Introduction
Rekonstruction of MSC angles
σreco calibration
DEPFET H4&H5 maps
Conclusion
Reconstruction of MSC angles in a EUDET teleskop
Reconstruct angles on
the DEPFET
Particle crosses sensor
→ hits
telescope arm I
23mm
27mm
DEPFET
111mm
telescope arm II
67mm
28mm
27mm
Forward- backward
Kalman Filter (KF)
pair on hits
hit on DEPFET not
needed → maps
forward KF
Take MSC in air gaps
into account
backward KF
Mimosa Pixel Sensoren
Pixel Pitch 18.4 µm
X/X0
Mimosa Pixel Sensoren
Pixel Pitch 18.4 µm
Ariane Frey, Benjamin Schwenker and Ulf Stolzenberg*
Spatial resolved radiation length (X /X0 ) measurements of DEPFET pixel sensors using EUDET tracks
University of Göttingen
5 / 12
Introduction
Rekonstruction of MSC angles
σreco calibration
DEPFET H4&H5 maps
Conclusion
Reconstruction of MSC angles in a EUDET teleskop
Reconstruct angles on
the DEPFET
Forward KF
In-State
(ηf,Cf)
DEPFET
Particle crosses sensor
→ hits
Forward- backward
Kalman Filter (KF)
pair on hits
θp
hit on DEPFET not
needed → maps
Backward KF
Out-State
(ηb,Cb)
Take MSC in air gaps
into account
θp calculated from
(mu ,mv )
Reco error σreco from
TrackState
η = (u,v,mu,mv)
Cov. Matrix C
error propagation
Ariane Frey, Benjamin Schwenker and Ulf Stolzenberg*
Spatial resolved radiation length (X /X0 ) measurements of DEPFET pixel sensors using EUDET tracks
University of Göttingen
5 / 12
Introduction
Rekonstruction of MSC angles
σreco calibration
DEPFET H4&H5 maps
Conclusion
Example of a reconstructed angle distribution
2000
1800
Reco Distr.
Truth Distr.
1600
1400
1200
1000
800
600
400
200
0
-0.001 -0.0008 -0.0006 -0.0004 -0.0002
0
0.0002 0.0004 0.0006 0.0008
θp[rad]
Composition of the Reco Distribution
Reconstructed MSC angle distribution is a convolution between the truth MSC
distribution and a Gaussian noise distribution caused by the reconstruction errors
Ariane Frey, Benjamin Schwenker and Ulf Stolzenberg*
Spatial resolved radiation length (X /X0 ) measurements of DEPFET pixel sensors using EUDET tracks
University of Göttingen
6 / 12
Introduction
Rekonstruction of MSC angles
σreco calibration
DEPFET H4&H5 maps
Conclusion
Example of a reconstructed angle distribution
2000
1800
Reco Distr.
Truth Distr.
1600
1400
1200
1000
800
600
400
200
0
-0.001 -0.0008 -0.0006 -0.0004 -0.0002
0
0.0002 0.0004 0.0006 0.0008
θp[rad]
Problem 1: Fitting the Reco Distribution
Non-Gaussian tails and convolution with Gaussian noise function complicate the fit
→ A stable fitting method is needed
Ariane Frey, Benjamin Schwenker and Ulf Stolzenberg*
Spatial resolved radiation length (X /X0 ) measurements of DEPFET pixel sensors using EUDET tracks
University of Göttingen
6 / 12
Introduction
Rekonstruction of MSC angles
σreco calibration
DEPFET H4&H5 maps
Conclusion
Example of a reconstructed angle distribution
2000
1800
Reco Distr.
Truth Distr.
1600
1400
1200
1000
800
600
400
200
0
-0.001 -0.0008 -0.0006 -0.0004 -0.0002
0
0.0002 0.0004 0.0006 0.0008
θp[rad]
Problem 2: Gaussian noise is dominant for thin materials
→ relative errors of σreco must be known well (< 10%). To ensure this, we need:
Accurate knowledge of telescope geometry, beam energy, good tracking model
Calibration measurements for the reconstruction errors
∗
→ σreco
= λ · σreco with calibration factor λ
Ariane Frey, Benjamin Schwenker and Ulf Stolzenberg*
Spatial resolved radiation length (X /X0 ) measurements of DEPFET pixel sensors using EUDET tracks
University of Göttingen
6 / 12
Introduction
Rekonstruction of MSC angles
σreco calibration
DEPFET H4&H5 maps
Conclusion
Solution of the 1. problem: Template fits
Templates
Template: Distribution of MSC angles from simulations
Add Gaussian noise due to σreco
Template Fit
Produce several templates based on different X /X0 or σreco
values in a certain range
Compare the templates and the distribution via
Kolmogorov-Smirnov-Test (KS)
Problems
Large track sample needed
Only feasible in small X /X0 ranges
Ariane Frey, Benjamin Schwenker and Ulf Stolzenberg*
Spatial resolved radiation length (X /X0 ) measurements of DEPFET pixel sensors using EUDET tracks
University of Göttingen
7 / 12
Introduction
Rekonstruction of MSC angles
σreco calibration
DEPFET H4&H5 maps
Conclusion
σreco calibration
Best calibration scenario
Test beam (TB) calibration runs with material plane of precisely known X /X0
σreco determined from error propagation
∗
use template fits with fixed X /X0 to determine σreco
∗
→ Calibration factor λ=σreco
/σreco
Ariane Frey, Benjamin Schwenker and Ulf Stolzenberg*
Spatial resolved radiation length (X /X0 ) measurements of DEPFET pixel sensors using EUDET tracks
University of Göttingen
8 / 12
Introduction
Rekonstruction of MSC angles
σreco calibration
DEPFET H4&H5 maps
Conclusion
σreco calibration
Here: Calibration via Monte Carlo (MC) data
Use TB Run MC Simulation → X /X0 known
MSC model of the real particle: MSC simulation based on single scatterings
Tracking MSC model: Highland model
→ Correction of the errors (on σreco ) coming from HL Model in the tracking
Ariane Frey, Benjamin Schwenker and Ulf Stolzenberg*
Spatial resolved radiation length (X /X0 ) measurements of DEPFET pixel sensors using EUDET tracks
University of Göttingen
8 / 12
Introduction
Rekonstruction of MSC angles
σreco calibration
DEPFET H4&H5 maps
Conclusion
σreco calibration
Here: Calibration via Monte Carlo (MC) data
Use TB Run MC Simulation → X /X0 known
MSC model of the real particle: MSC simulation based on single scatterings
Tracking MSC model: Highland model
→ Correction of the errors (on σreco ) coming from HL Model in the tracking
Reco Distr.
σreco=150 µ rad
2400
Simu of a TB run
3.75 GeV electrons,
σreco =173µrad
Hybrid 4 module
2200
σreco=190 µ rad
σreco=250 µ rad
2000
1800
1600
1400
1200
1000
800
600
400
200
0
-3
×10
-0.3
-0.2
-0.1
0
0.1
0.2
Ariane Frey, Benjamin Schwenker and Ulf Stolzenberg*
Spatial resolved radiation length (X /X0 ) measurements of DEPFET pixel sensors using EUDET tracks
0.3
θp [rad]
University of Göttingen
8 / 12
Introduction
Rekonstruction of MSC angles
σreco calibration
DEPFET H4&H5 maps
Conclusion
σreco calibration
Here: Calibration via Monte Carlo (MC) data
Use TB Run MC Simulation → X /X0 known
MSC model of the real particle: MSC simulation based on single scatterings
Tracking MSC model: Highland model
D
→ Correction of the errors (on σreco ) coming from HL Model in the tracking
0.03
Simu of a TB run
3.75 GeV electrons,
σreco =173µrad
Hybrid 4 module
∗
=190
Best fit: σreco
µrad
σ
λ= σ reco;m
reco,exp
≈ 1.1
0.025
0.02
0.015
0.01
0.005
0
Dmax
160
180
200
220
240
σreco [ µ rad]
Ariane Frey, Benjamin Schwenker and Ulf Stolzenberg*
Spatial resolved radiation length (X /X0 ) measurements of DEPFET pixel sensors using EUDET tracks
University of Göttingen
8 / 12
Introduction
Rekonstruction of MSC angles
σreco calibration
DEPFET H4&H5 maps
Conclusion
DEPFET Hybrid 4 Map
X/X0[%]
v[mm]
X/X0 Map
6
area of the map
2.5
4
sensitive area
2
2
0
-2
1.5
-4
-6
Switcher
1
-8
-10
0.5
-12
-14
-4 -2
0
2
4 6
u[mm]
0
DCDB
Ariane Frey, Benjamin Schwenker and Ulf Stolzenberg*
Spatial resolved radiation length (X /X0 ) measurements of DEPFET pixel sensors using EUDET tracks
University of Göttingen
9 / 12
Introduction
Rekonstruction of MSC angles
σreco calibration
DEPFET H4&H5 maps
Conclusion
DEPFET Hybrid 4 Map
X/X0[%]
v[mm]
X/X0 Map
v profile
6
2.5
4
2
0
u profile
-2
-4
2
fitting: Gaussian fit on
distribution without tails (6%
cuts on either side)
1.5
calibration factor λ = 1.1
1
-6
0.5
-8
-10
tracksample: 1.8 Mio Tracks,
pixel size: 200µm x 200µm
use indicated profiles to
compute X /X0 in different
regions of the map
u profile: sum over 24 pixels
-2
0
2
4
6
u[mm]
0
v profile: sum over 8 pixels
Ariane Frey, Benjamin Schwenker and Ulf Stolzenberg*
Spatial resolved radiation length (X /X0 ) measurements of DEPFET pixel sensors using EUDET tracks
University of Göttingen
9 / 12
Introduction
Rekonstruction of MSC angles
σreco calibration
DEPFET H4&H5 maps
Conclusion
DEPFET Hybrid 4 Map
2
PCB+Al
PCB+Si-Chip+Al
sensitive area+Al
2.5
PCB+Al
3
PCB+Si-Chip+Al
X/X0[%]
u Profile
Alu. window
unknown
structure
Si
PCB
1.5
Si
sens.
area
unknown
structure
PCB
1
Alu. window
0.5
0
-4
-2
0
2
4
6
u[mm]
Ariane Frey, Benjamin Schwenker and Ulf Stolzenberg*
Spatial resolved radiation length (X /X0 ) measurements of DEPFET pixel sensors using EUDET tracks
University of Göttingen
9 / 12
Introduction
Rekonstruction of MSC angles
σreco calibration
DEPFET H4&H5 maps
Conclusion
DEPFET Hybrid 4 Map
sensitive area+Al
Silicon Chip+Al
X/X0[%]
v Profile
3.5
3
2.5
Alu. window
unknown
structure
Si
2
PCB
1.5
Si
sens.
area
unknown
structure
PCB
1
0.5
0
-14
Alu. window
-12
-10
-8
-6
-4
-2
0
2
4
6
v[mm]
Ariane Frey, Benjamin Schwenker and Ulf Stolzenberg*
Spatial resolved radiation length (X /X0 ) measurements of DEPFET pixel sensors using EUDET tracks
University of Göttingen
9 / 12
Introduction
Rekonstruction of MSC angles
σreco calibration
DEPFET H4&H5 maps
Conclusion
v[mm]
H4 DEPFET Map
6
X/X0[%]
DEPFET Hybrid 4 Map
2.5
X/X0=(0.160+/-0.003)%
4
2
2
Alu. window
0
1.5
-2
Si
PCB
-4
Si
sens.
area
PCB
1
-6
0.5
-8
-10
-2
0
2
4
6
u[mm]
Alu. window
0
Ariane Frey, Benjamin Schwenker and Ulf Stolzenberg*
Spatial resolved radiation length (X /X0 ) measurements of DEPFET pixel sensors using EUDET tracks
University of Göttingen
9 / 12
Introduction
Rekonstruction of MSC angles
σreco calibration
DEPFET H4&H5 maps
Conclusion
v[mm]
H4 DEPFET Map
6
X/X0[%]
DEPFET Hybrid 4 Map
2.5
X/X0=(0.510+/-0.040)%
4
2
2
Alu. window
0
1.5
-2
Si
PCB
-4
Si
sens.
area
PCB
1
-6
0.5
-8
-10
-2
0
2
4
6
u[mm]
Alu. window
0
Ariane Frey, Benjamin Schwenker and Ulf Stolzenberg*
Spatial resolved radiation length (X /X0 ) measurements of DEPFET pixel sensors using EUDET tracks
University of Göttingen
9 / 12
Introduction
Rekonstruction of MSC angles
σreco calibration
DEPFET H4&H5 maps
Conclusion
v[mm]
H4 DEPFET Map
6
X/X0[%]
DEPFET Hybrid 4 Map
2.5
X/X0=(1.960+/-0.020)%
4
2
2
Alu. window
0
1.5
-2
Si
PCB
-4
Si
sens.
area
PCB
1
-6
0.5
-8
-10
-2
0
2
4
6
u[mm]
Alu. window
0
Ariane Frey, Benjamin Schwenker and Ulf Stolzenberg*
Spatial resolved radiation length (X /X0 ) measurements of DEPFET pixel sensors using EUDET tracks
University of Göttingen
9 / 12
Introduction
Rekonstruction of MSC angles
σreco calibration
DEPFET H4&H5 maps
Conclusion
v[mm]
H4 DEPFET Map
6
X/X0[%]
DEPFET Hybrid 4 Map
2.5
X/X0=(1.540+/-0.020)%
4
2
2
Alu. window
0
1.5
-2
Si
PCB
-4
Si
sens.
area
PCB
1
-6
0.5
-8
-10
-2
0
2
4
6
u[mm]
Alu. window
0
Ariane Frey, Benjamin Schwenker and Ulf Stolzenberg*
Spatial resolved radiation length (X /X0 ) measurements of DEPFET pixel sensors using EUDET tracks
University of Göttingen
9 / 12
Introduction
Rekonstruction of MSC angles
σreco calibration
DEPFET H4&H5 maps
Conclusion
Results
Measurement results
(X /X0 )PCB+Si+Al = (1.96 ± 0.02) %
(X /X0 )PCB+Al = (1.54 ± 0.02) %
(X /X0 )Si+Al = (0.510 ± 0.04) %
(X /X0 )ThinSi+Al = (0.16 ± 0.003) %
Radiation length and thickness of the silicon chip
(X /X0 )SiChip = (X /X0 )PCB+Si+Al − (X /X0 )PCB+Al
= (0.42 ± 0.03) %
→ dSiChip = (390 ± 30) µm
(expected : 420 µm)
Ariane Frey, Benjamin Schwenker and Ulf Stolzenberg*
Spatial resolved radiation length (X /X0 ) measurements of DEPFET pixel sensors using EUDET tracks
University of Göttingen
10 / 12
Introduction
Rekonstruction of MSC angles
σreco calibration
DEPFET H4&H5 maps
Conclusion
Results
Measurement results
(X /X0 )PCB+Si+Al = (1.96 ± 0.02) %
(X /X0 )PCB+Al = (1.54 ± 0.02) %
(X /X0 )Si+Al = (0.510 ± 0.04) %
(X /X0 )ThinSi+Al = (0.16 ± 0.003) %
Thickness difference between silicon chip and thin silicon layer
(X /X0 )SiGap = (X /X0 )Si+Al − (X /X0 )ThinSi+Al
= (0.35 ± 0.04) %
→ dSiGap = (330 ± 40) µm
(expected : 370 µm)
Ariane Frey, Benjamin Schwenker and Ulf Stolzenberg*
Spatial resolved radiation length (X /X0 ) measurements of DEPFET pixel sensors using EUDET tracks
University of Göttingen
10 / 12
Introduction
Rekonstruction of MSC angles
σreco calibration
DEPFET H4&H5 maps
Conclusion
Results
Measurement results
(X /X0 )PCB+Si+Al = (1.96 ± 0.02) %
(X /X0 )PCB+Al = (1.54 ± 0.02) %
(X /X0 )Si+Al = (0.510 ± 0.04) %
(X /X0 )ThinSi+Al = (0.16 ± 0.003) %
Radiation length and thickness of the sensitive area
(X /X0 )ThinSi = (X /X0 )SiChip − (X /X0 )SiGap
= (0.07 ± 0.05) %
→ dThinSi = (70 ± 50) µm
(expected : 50 µm)
Ariane Frey, Benjamin Schwenker and Ulf Stolzenberg*
Spatial resolved radiation length (X /X0 ) measurements of DEPFET pixel sensors using EUDET tracks
University of Göttingen
10 / 12
Introduction
Rekonstruction of MSC angles
σreco calibration
DEPFET H4&H5 maps
Conclusion
Results
Measurement results
(X /X0 )PCB+Si+Al = (1.96 ± 0.02) %
(X /X0 )PCB+Al = (1.54 ± 0.02) %
(X /X0 )Si+Al = (0.510 ± 0.04) %
(X /X0 )ThinSi+Al = (0.16 ± 0.003) %
Radiation length of the PCB
(X /X0 )PCB = (X /X0 )PCB+Si+Al − (X /X0 )ThinSi+Al
− (X /X0 )SiGap = (1.48 ± 0.06) %
(expected : X /X0 = 1.50 %)
Ariane Frey, Benjamin Schwenker and Ulf Stolzenberg*
Spatial resolved radiation length (X /X0 ) measurements of DEPFET pixel sensors using EUDET tracks
University of Göttingen
10 / 12
Introduction
Rekonstruction of MSC angles
σreco calibration
DEPFET H4&H5 maps
Conclusion
DEPFET Hybrid 5 Map
14
Capacities
12
14
10
12
8
10
6
X/X0[%]
v[mm]
X/X0 Map
8
4
6
2
4
0
2
-2
-10
-8
-6
-4
-2
0
u[mm]
0
Ariane Frey, Benjamin Schwenker and Ulf Stolzenberg*
Spatial resolved radiation length (X /X0 ) measurements of DEPFET pixel sensors using EUDET tracks
University of Göttingen
11 / 12
Introduction
Rekonstruction of MSC angles
σreco calibration
DEPFET H4&H5 maps
Conclusion
Conclusion and future plans
Conclusion
A method to estimate the spatial resolved radiation length has been developed
and tested on TB data
Relative and absolute values of X /X0 can be determined
A calibration of the reconstruction errors is needed for a precise measurement of
the radiation length of thin materials ( 100 µm Si)
Future plans
What are the effects of other systematicals like energy loss of the particle beam
in the telescope?
Larger track samples/merging track samples: Improve spatial resolution in the
map and reduce statistical errors of the pixels
Ariane Frey, Benjamin Schwenker and Ulf Stolzenberg*
Spatial resolved radiation length (X /X0 ) measurements of DEPFET pixel sensors using EUDET tracks
University of Göttingen
12 / 12
Introduction
Rekonstruction of MSC angles
σreco calibration
DEPFET H4&H5 maps
Conclusion
Many Thanks for your
attention!
Ariane Frey, Benjamin Schwenker and Ulf Stolzenberg*
Spatial resolved radiation length (X /X0 ) measurements of DEPFET pixel sensors using EUDET tracks
University of Göttingen
12 / 12
Introduction
Rekonstruction of MSC angles
σreco calibration
DEPFET H4&H5 maps
Conclusion
Back Up Slides
Ariane Frey, Benjamin Schwenker and Ulf Stolzenberg*
Spatial resolved radiation length (X /X0 ) measurements of DEPFET pixel sensors using EUDET tracks
University of Göttingen
12 / 12
Introduction
Rekonstruction of MSC angles
σreco calibration
DEPFET H4&H5 maps
Conclusion
Kolmogorov Smirnov Test
Used for testing, if two data sets are based on the same PDF
Test parameter: maximum distance between the two
cumulative distributions
Used here: 5 % significance level
Critical value for the test parameter: Dmax =
N: Number of data points
1.36
√ ,
N
Ariane Frey, Benjamin Schwenker and Ulf Stolzenberg*
Spatial resolved radiation length (X /X0 ) measurements of DEPFET pixel sensors using EUDET tracks
University of Göttingen
12 / 12
Introduction
Rekonstruction of MSC angles
σreco calibration
DEPFET H4&H5 maps
Conclusion
Forward and Backward KF
Forward KF
gives In-State
prediction of track state on
sensor i+1 based on tracks
state i
ηi+1 = Fi→i+1 ηi
Vi+1 =
T
Fi→i+1 Vi Fi→i+1
+ QF;i
Backward KF
gives Out-State
prediction of track state on
sensor i based on tracks
state i+1
ηi
= Fi+1→i ηi+1
Vi
= Fi+1→i Vi+1 F T i+1→i
+
QB;i+1
F : Extrapolation matrix
Q: MSC effects
Ariane Frey, Benjamin Schwenker and Ulf Stolzenberg*
Spatial resolved radiation length (X /X0 ) measurements of DEPFET pixel sensors using EUDET tracks
University of Göttingen
12 / 12