wednesday, may 9 th 2007torsten beck fast pulse shape analysis for agata-germanium- detectors...
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Wednesday, May 9th 2007Torsten Beck
Fast Pulse Shape Fast Pulse Shape Analysis for Analysis for AGATA-AGATA-Germanium-Germanium-DetectorsDetectors
Torsten Beck Wednesday, 9. Mai 2007
Student seminar Student seminar Wednesday, 9. Mai. 2007Wednesday, 9. Mai. 2007
Wednesday, May 9th 2007Torsten Beck
outlineoutline
-spectroscopy with relativistic beams (RISING ) Segmented Ge-detectors (AGATA) New concept for pulse shape analysis Wavelet transformation Fast data base search (Hamming distance) Results for single interactions Complex interactions Outlook
Wednesday, May 9th 2007Torsten Beck
Gamma spectroscopy Gamma spectroscopy withwith
relativistic relativistic beamsbeams
Doppler shift ( factor of 1.5 for 40% )
Doppler broadeningdetector size ~7cm (diameter, length)distance to target ~70cm
lab [deg]
E/E
0 [%
]
Detector opening
angle =3°
Doppler broadening
=0.11
=0.43
=0.57
1
1
Doppler shift of -raysLorentz boost of -rays
gain in geometrical efficiency at forward angles in lab. system ( factor of 2 for 40% )
Wednesday, May 9th 2007Torsten Beck
Coulomb excitation of the Coulomb excitation of the 8484Kr-beamKr-beam
E [keV]C
ou
nts
E [keV]
Cou
nts
882
84Kr 2+ 0+
FWHM ~ 1.5 %FWHM ~ 1.5 %
without Doppler correction
Particle identification before and after the targetForward scattering angle selectionFixed 39.6% value ( no energy spread)Event by event Doppler correction
84Kr (113 AMeV) + Au (0.4 g/cm2)
Wednesday, May 9th 2007Torsten Beck
The The Ge-Ge-ClusterCluster detectordetector arr array RISINGay RISING
Ring Angle [deg]
Distance
[mm]
Resolution
[%]
Efficiency [%]
1 15.9 700 1.00 1.00
2 33.0 700 1.82 0.91
3 36.0 700 1.93 0.89
Total: 1.56 2.81
15 EUROBALL Cluster detectors
105 Ge crystals
Wednesday, May 9th 2007Torsten Beck
too many detectorsare needed to avoidsumming effects
Combination of:
•segmented detectors•digital electronics•pulse processing•tracking the -rays
EUROBALL
Ge Tracking Array
~ 3º
~ 1º
Idea of Idea of -ray tracking-ray tracking
Wednesday, May 9th 2007Torsten Beck
AGATAAGATADesign and characteristicsDesign and characteristics
44 -array -array for Nuclear Physics Experiments at European accelerators providing for Nuclear Physics Experiments at European accelerators providing radioactive and high-intensity stable beamsradioactive and high-intensity stable beams
Principal design features of AGATA
Efficiency: 40% (M =1) 25% (M =30)today’s arrays ~10% (gain ~4) 5% (gain ~1000)
Peak/Total: 55% (M=1) 45%
(M=30)today ~55% 40%
Angular Resolution: ~1º FWHM (1 MeV, v/c=50%) ~ 6 keV !!!today ~40 keV
Rates: 3 MHz (M=1) 300 kHz (M
=30)today 1 MHz 20 kHz
Wednesday, May 9th 2007Torsten Beck
AGATA Detector ModuleAGATA Detector Module
1 three 36-fold segmented Ge detectors2 preamplifier3 frame support4 digital pulse processing electronics5 fiber-optics read-out6 LN2 – dewar
7 target position
Ge-crystals:10 cm long, 8 cm diametertapered, hexagonal/pentagonal shapeencapsulated
Wednesday, May 9th 2007Torsten Beck
Ingredients of Ingredients of -ray Tracking-ray Tracking
Pulse Shape Analysisto decompose
recorded waves
Highly segmented
HPGe detectors
·
·
··
Identified interaction
points(x,y,z,E,t)i
Reconstruction of tracks
e.g. by evaluation of permutations
of interaction points
Digital electronicsto record and
process segment signals
1
2 3
4
reconstructed -rays
Wednesday, May 9th 2007Torsten Beck
Radius: S3 signal rise timeAzimuthal angle: S4-S2/(S4+S2) Asymmetry
Segmented detector signals
S4
S3
S2
S1
pulse shape analysis
induced charge induced charge
Wednesday, May 9th 2007Torsten Beck
~ 100 keV ~1 MeV ~ 10 MeV -ray energy
Isolated hits Angle/Energy Pattern of Hits
Photoelectric Compton Scattering Pair Production
Probability of E1st = E– 2
mc2
interaction depth
cosθ1cm
E1
EE
20
γ
γγ'
Three main interaction mechanisms
Wednesday, May 9th 2007Torsten Beck
concept of pulse shape analysisconcept of pulse shape analysis
pulse shape
wavelet transformation
wavelet transformation
database of binary signals
from simulated and wavelet transformed
puls shapes
database of binary signals
from simulated and wavelet transformed
puls shapes
calculation of hamming distancebetween seeked
position and database
calculation of hamming distancebetween seeked
position and database
selection of positions with smallest
hamming distance
selection of positions with smallest
hamming distance
calculation center of gravity
calculation center of gravity binarisationbinarisation
=3
element from database
number of flipped bits
binary signal 01001
00111
xor
waveletcoefficients binary signal
creation of the binary array, by transforming positive coefficients to 1 and negative to 0
01001-17-5-35wavelet-coeffizienten
binäre representation
hamming cloudat seek positionx = 10; y = 10; z = 55
selectedinteraction
hamming distance
found interaction positionx = 15; y = 15; z = 55
found interaction positionx = 15; y = 15; z = 55
output of interactionposition
mother-wavelet
convolution
dttfs st )()(
2/1
By using the wavelet transform the signal will be fragmented in to a time- frequency representation
signal
Wednesday, May 9th 2007Torsten Beck
What is a wavelet transformation What is a wavelet transformation and how can we use it?and how can we use it?
dtttfs s )()(),( ,
Wavelet transformation
wavelet
wavelet transformation is basically a convolution between the signal to analyse and the wavelet function .
s
t
sts
1
)(,shapepulsetf )(
data
The wavelet transformation is a relatively new concept (about 10 years old). It provides a time-frequency representation:
= time shifts = time scaling
Wednesday, May 9th 2007Torsten Beck
Haar waveletHaar wavelet
elsewise
t st
st
s
0
11
01
)( 21
21
,
what is the wavelet transformation doing?
= time shifts = time scaling
Wednesday, May 9th 2007Torsten Beck
Low- (Low- (LPLP) and high pass () and high pass (HPHP) ) analysisanalysis
but the transform needs to be faster
dtttfs s )()(),( ,
information about different time intervals
filterLPtftf ii
2
)()( 1
filterHPtftf ii )()( 1
Wednesday, May 9th 2007Torsten Beck
HP LP implementationHP LP implementation
HPfirsttftf
tftf
(2))()(
(1))()(
43
21
LPfirsttf
tftftf
tftf
)(
)(
432)()(
212)()(
43
21
HPondtftf sec)3()()( 4321
the Haar wavelet coefficients give the average slope of the recent time windows
Wednesday, May 9th 2007Torsten Beck
test of wavelet transformtest of wavelet transform
)55,15,15( mmzmmymmxpulses
222 )()()( ipipip zzyyxxr
Euclidean distance
(...)(...) ipd
Wavelet distance
vs.
limit of acceptance
Wednesday, May 9th 2007Torsten Beck
binarisation of binarisation of wavelet coefficientswavelet coefficients
example of binarisation:
wavelet coefficient 5.34
-4.35 -5.98 1.34
binary coefficient 1 0 0 1
procedure is still to slow and needs to be speeded up, to solve this it is just taken the direction of the slope.
Wednesday, May 9th 2007Torsten Beck
Hamming distanceHamming distance
In information theory, the Hamming distance between two binary strings of equal length is given by the number of positions for which the corresponding symbols are different.
1 0 1 0 1 0
1 1 0 0 1 0
0 1 1 0 0 0
hamming distance =
xor
(...)ib
(...)pb
measured interaction in binary representation (...)pbbinary interaction from database (...)ib
2(...)(...) ip bxorb
Wednesday, May 9th 2007Torsten Beck
test of Hamming distancetest of Hamming distance
222 )()()( ipipip zzyyxxr
)55,15,15( mmzmmymmxpulses
(...)(...) ip bxorb
Euclidean distance
Hamming distance
vs.
limit of acceptance
Wednesday, May 9th 2007Torsten Beck
test of the methodtest of the method
)87,19,27( mmzmmymmxpulses
)5,5,5( mmzmmymmxpulses
)25,15,15( mmzmmymmxpulses
)36,15,20( mmzmmymmxpulses
mean variance = 1 mm2 elements found
mean variance = 0 mm5 elements found mean variance = 8 mm
3 elements found
mean variance = 1 mm1 element found
speed of the algorithem ~ 100 s per eventmean accuracy ±1 mm
Wednesday, May 9th 2007Torsten Beck
Complex interactionsComplex interactions
)25,15,15( mmzmmymmxpulses
)55,15,15( mmzmmymmxpulses
ppp 21
Wednesday, May 9th 2007Torsten Beck
Complex interactionsComplex interactions
)25,15,15( mmzmmymmxpulses
)55,15,15( mmzmmymmxpulses
hamming limit at 65
now there are two problems accuring
Wednesday, May 9th 2007Torsten Beck
Complex interactionsComplex interactions
it is necessary to handle two interactions in one data set
Wednesday, May 9th 2007Torsten Beck
not all combinations of wavelet coefficients can be truly converted in to a binary representation
Complex interactionsComplex interactions
+
+
Wednesday, May 9th 2007Torsten Beck
summarysummary
AGATA yields an enormous amount of data Wavelet transformation + binarisation allows a fast
determination of the interaction position~100s per event (pentium m 1.7GHz)~ 1 mm in accuracy
online Doppler shift corrections are possible for complex-interactions the pulse shape analysis is
improvable
Wednesday, May 9th 2007Torsten Beck
alternative application alternative application of the binary searchof the binary search
a fast text search can be implemented by using the wavelet transformation combined with the binary representation.
a text can be transformed in to a wavelet- and a binary representation, like this, we can search a text as shown for the -interactions in a Ge-Detector.