wednesday, may 9 th 2007torsten beck fast pulse shape analysis for agata-germanium- detectors...

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


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


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% )


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)


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


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


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

http://www.crwflags.com/fotw/images/t/tr.gif

http://www.crwflags.com/fotw/images/h/hu.gif


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


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


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


~ 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


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


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


Haar waveletHaar wavelet

elsewise

t st

st

s

0

11

01

)( 21

21

,

what is the wavelet transformation doing?

= time shifts = time scaling


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


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


test of wavelet transformtest of wavelet transform

)55,15,15( mmzmmymmxpulses

222 )()()( ipipip zzyyxxr

Euclidean distance

(...)(...) ipd

Wavelet distance

vs.

limit of acceptance


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.


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


test of Hamming distancetest of Hamming distance

222 )()()( ipipip zzyyxxr


(...)(...) ip bxorb

Euclidean distance

Hamming distance

vs.

limit of acceptance


test of the methodtest of the method





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


Complex interactionsComplex interactions



ppp 21





hamming limit at 65

now there are two problems accuring



it is necessary to handle two interactions in one data set


not all combinations of wavelet coefficients can be truly converted in to a binary representation


+

+


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


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.


the endthe end

thank you very much

wednesday, may 9 th 2007torsten beck fast pulse shape analysis for agata-germanium- detectors...

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