Digital Positron Lifetime @ EPOS - Positron Annihilation in Halle

Positrons EPOS Digital Positron Lifetime The Influence of Noise Next Tasks Conclusion 

Digital Positron Lifetime @ EPOS 

Arnold Krille 1 Wolfgang Anwand 2 Marco Jungmann 1 Nicki 

Hinsche 1,2 Reinhard Krause-Reberg 1 

1 Department of Physics, Martin-Luther-University Halle-Wittenberg, 06108 Halle, Germany 

2 Institut of Ion Beam Physics, Research Center Dresden-Rossendorf, 01314 Dresden, Germany 

University Leipzig – Oktober 22th, 2008 

DPL @ EPOS A Krille, et al.


Contents 

1 Introduction: Positrons in Material Research 

2 Introduction: EPOS 

3 Digital Positron Lifetime 

4 The Influence of Noise 

5 Next Tasks 

6 Conclusion 



Positrons 

für 22-Na: 

Quant 

(1.27 MeV) 

Positroneneinfang durch Kristalldefekte 

Quant (511 keV) 

• Positronen-Wellenfunktion wird im Defekt lokalisiert 

• Annihilationsparameter ändern sich, wenn Positron im Defekt zerstrahlt 



Positrons: Decay Parameters 









Fields of Usage 



EPOS @ ELBE 



Basic Concept 

Schema des EPOS-Systems 

EPOS Systems 



Key features of EPOS 

Positrons by pair production 

Unique time structure 

High repetition rate (77ns) 

Sharp pulses (∼5ps) 

Machine pulse for start of lifetime measurements 

Good timing resolution 

Full digitial measurement and control 

Project started 2001 

First positrons planned for end 2008 

User dedicated facility 

User access should start 2009/2010 



Basic Setup 

Analog Setup: 

γ-quants detected by scintillator and 

photomultiplier 

Energy-discrimination with SCA 

Event extraction with CF 

Time measurement with TAC 

Spectrum with MCA 

Start Stop 

Detektor Detektor 

SCA 

CF 

Start Stop 

DPL @ EPOS A Krille, et al. 

TAC 

MCA 

PC 

SCA 

CF


Analog vs. Digital 

The task 

Replace all the (50+ years old) analog 

electronics with PC, digitizer and 

mathematics. 

Benefits of digital processing: 

+ Cheaper 

+ Simplier 

+ Better time base 

+ Easy to extent/change 

- Less knowledge available 

? Better timing resolution 



The Algorithms to Extract the Timing Information 

0.2 

0 

-0.2 

-0.4 

-0.6 

-0.8 

-1 

-1.2 

-1.4 

Pulse 

25 30 35 40 45 50 55 60 

How to extract the timing information? 



Algorithms: PolyCF 

0.2 

0 

-0.2 

-0.4 

-0.6 

-0.8 

-1 

-1.2 

Minimum 

-1.4 

Pulse 

25 30 35 40 45 50 55 60 

1 By simple polynom interpolation of 3rd order. 

1 Find and interpolate the 

extremum 1 

2 Determine the zeroline (and 

its deviation) before the 

extremum 

3 Interpolate the constant 

fraction point on the rising 

slope between zeroline and 

extremum 1 

4 Lifetime = 

tChannel 1 − tChannel 2 




0.2 

0 

-0.2 

-0.4 

-0.6 

-0.8 

-1 

-1.2 

Zeroline 


-1.4 

Pulse 

25 30 35 40 45 50 55 60 



extremum 1 



extremum 




extremum 1 






0.2 

0 

-0.2 

-0.4 

-0.6 

-0.8 

-1 

CF 0.2 

-1.2 



-1.4 

Pulse 

25 30 35 40 45 50 55 60 



extremum 1 



extremum 




extremum 1 






0.2 

0 

-0.2 

-0.4 

-0.6 

-0.8 

-1 

CF 0.2 

-1.2 



-1.4 

Pulse 

25 30 35 40 45 50 55 60 


extremum 1 



extremum 




extremum 1 



Similar to analog constant fraction, called true constant fraction by 

[Bečváˇr, 2007]. 



Algorithms: integral Constant Fraction (iCF) 

1 Integrate the pulse 

2 Filter on risetime of integrated signal 

rightarrow Pulse-shape of original signal 

3 Do true constant fraction like before on integrated signal 

Seems to give better timing resolution of 144ps [Bečváˇr, 2007]. 



Timing Resolutions 

Method Lit. / Setup Resolution (FWHM) 

Analog measurements our lab: >200ps 

Polynom-Int. [Bečváˇr et al., 2005] 150ps 

4GS/s 1GHz 8bit: 

4GS/s 1GHz 8bit ∼170ps 60 Co, 230ps Si 

Gauss-Int. [Aavikko et al., 2005] 200ps 


(Smoothing) Spline [Saito et al., 2002] 118ps - 144ps 


[Bardelli et al., 2004] 100ps - 125ps 

100MS/s 50MHz 12bit: 

∼170ps 60 Co 

Integral CF [Bečváˇr, 2007] ∼144ps 



The Influence of Noise: Generated Pulses 

Input Voltage 

0.2 

0 

-0.2 

-0.4 

-0.6 

-0.8 

-1 

-1.2 

-1.4 

-1.6 

0 20 40 60 80 100 

Side Note 

Time [samples] 

Channel 1 

Channel 2 

Four pulse pairs generated 

by EPOS Software 

The EPOS Software is gone open-source and looking for users! 

See http://positron.physik.uni-halle.de/EPOS/Software. 



The Influence of Noise: Shape 

Input Voltage 

0.2 

0 

-0.2 

-0.4 

-0.6 

-0.8 

-1 

-1.2 

-1.4 

-1.6 

0 20 40 60 80 100 


Channel 1 

Channel 2 

Shaped like LSO on 

Hamamatsu H3378-50 

Risetime like 4 GS/s 



The Influence of Noise: Energy Spectrum 

Counts 

1000 

100 

10 

1 

-2 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 

Input Voltage 

Energy spectrum closely to 22 Na but idealistic. 




Energy distribution 

like 22 Na 



The Influence of Noise: Timing Distribution 

Counts 

100000 

10000 

1000 

100 

10 

1 

-0.01 -0.005 0 0.005 0.01 


Shift between pulses is Gaussian distributed. 

Shift of pulses to sampling clock is box distributed. 





like 22 Na 

Gaussian distributed 

timing 



The Influence of Noise: Bit-depth 

Input Voltage 

0.2 

0 

-0.2 

-0.4 

-0.6 

-0.8 

-1 

-1.2 

-1.4 

-1.6 

0 20 40 60 80 100 


Channel 1 

Channel 2 

Possible bit-depths: 1-32 bits 

Native double resolution also possible 





like 22 Na 



Variable bit-depth 



The Influence of Noise: Adding Noise 

Input Voltage 

0.2 

0 

-0.2 

-0.4 

-0.6 

-0.8 

-1 

-1.2 

-1.4 

-1.6 

0 20 40 60 80 100 


Channel 1 

Channel 2 





like 22 Na 



Variable bit-depth 

White noise added as 

wanted 

White noise to simulate the uncertainties of the analog electronics. 

Level can be adjusted as wanted. 



Double Resolution without Noise 

Counts 

1000 

100 

10 

Timing distribution (double resolution, no noise) 

1 

-0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02 


Determined 

Given 

No noise, native double resolution 

Given timing distribution: FWHM = 0.0023582 samples ≡ 0.589 ps 

Given distribution (−) ≡ determined resolution (×) 

⇒ Method works 



Reducing the Bit-depth 

FWHM [samples] 

1 

0.1 

0.01 

0.001 

Reduced bit-depth, no noise 

6 8 10 12 14 16 

Bit-depth 

Timing resolution at 8-bit: 0.202 samples ≡ 50 ps 



Noise of Effective Bits 


1 

0.1 

0.01 

0.001 

0.0001 0.001 0.01 0.1 

Noise-Level 

Native double resolution, noise according to effective bits added 

Strong log-log dependency of timing resolution and noise level. 



Noise and Reduced Bit-depth 


1 

0.1 

0.01 

0.001 

6 8 10 12 14 16 

Bit-depth 

Reduced bit-depth and noise from effective bits 

Timing resolution at 8-bit: 0.612 samples ≡ 153 ps 



Finally Comparing the results 


1 

0.1 

0.01 

0.001 

given timing fwhm (0.00235 samples) 

bits + noise 

bits 

noise (bits-1.5 = effective bits) 

6 8 10 12 14 16 

Bit-depth 

Noise from effective bits has most influence 

Resulting timing resolutions: 8-bit: 153 ps, 10-bit: 41 ps 



The Influence of Noise 

Level [dB] 

-20 

-30 

-40 

-50 

-60 

-70 

-80 

-90 

Filtering Noise with the Butterworth-Filter 

-100 

0 0.1 0.2 0.3 0.4 0.5 

Frequency relative of the sampling rate 

N = 1 

N = 2 

N = 3 

N = 5 

N = 10 

f = 0.1 

f = 0.2 

f = 0.3 

f = 0.4 

Butterworth lowpass (implementation taken from literature 

[Stearns, 1975]) 

Order and cutoff frequency can be set 



The Influence of Noise 

0 

-0.25 

-0.5 

-0.75 

-1 

-1.25 

0 

-0.25 

-0.5 

-0.75 

-1 

-1.25 

Unfiltered 

0 20 40 60 80 100 

f=0.1 N=1 

0 20 40 60 80 100 

0 

-0.25 

-0.5 

-0.75 

-1 

-1.25 

0 

-0.25 

-0.5 

-0.75 

-1 

-1.25 

Upper row Original signals as generated 

Lower row Filtered by lowpass 

Unfiltered 

0 20 40 60 80 100 

f=0.1 N=2 

0 20 40 60 80 100 

0 

-0.25 

-0.5 

-0.75 

-1 

-1.25 

0 

-0.25 

-0.5 

-0.75 

-1 

-1.25 

Unfilter 

0 20 40 6 

f=0.2 N 

0 20 40 6 



The Influence of Noise: Results 

Determined timing FWHM [samples] 

(Should be 0.00235) 

0.44 

0.42 

0.4 

0.38 

0.36 

0.34 

0.32 

0.3 

Best Timing Resolution 

0.05 0.1 0.15 0.2 

Cutoff Frequency [samplingrate] 

N=1 

N=2 

N=3 

N=4 

N = 1 and f = 0.05 has FWHM of 0.31 samples ≡ 75 ps. 



Comparison of the Results 

Method Relative Timing 4-GS/s “real” 

FWHM [samples] FWHM [ps] 

Vertical quantization (8-bit) 0.202 samples 50 ps 

Noise of effective 6.5 bit 0.612 samples 153 ps 

Butterworth-Lowpass 0.314 samples 75 ps 

f=0.05 N=1 

Comparing the results. 

Lowpass filtering can almost remove the effect of the noise added from 

the analog electronics. 

⇒ All with simple polynom interpolation for energy and constant fraction. 



Next Task: Comparing Photomultipliers 

Comparing Photomultipliers 


Photonis XP20Z8 

Measurement Program: 

Energy resolution (same scintillators!) 

Timing resolution (same scintillators and source/sample) 

– currently running 

Risetime, Pile-up, Pulse-Shape (DFT, etc...) 



Next Task: Comparing Scintillators 

Compare Scintillators 

BaF2 

LSO 

ZnO 

LaBr3(Ce) 

Measurement Program: 

Energy Spectrum/Resolution 

Risetime / Pulse-shape 

Relative Effectivity (through 1 

r 2 ) 

Optical Spectrum 



Thanks for your attention! 

Get the slides from http://positron.physik.uni-halle.de. 

[Aavikko et al., 2005] Aavikko, R., Rytsölä, K., Nissilä, J., and Saarinen, K. (2005). 

Stability and performance characteristics of a digital positron lifetime spectrometer. 

ACTA PHYSICA POLONICA A, 107. 

[Bardelli et al., 2004] Bardelli, L., Poggi, G., Bini, M., Pasquali, G., and Taccetti, N. (2004). 

Time measurements by means of digital sampling techniques: a study case of 100 ps fwhm time resolution with a 100msample/s, 12 

bit digitizer. 

Nuclear Instruments and Methods in Physics Research A, 521:480–492. 

[Bečváˇr, 2007] Bečváˇr, F. (2007). 

Methodology of positron lifetime spectroscopy: Present status and perspectives. 

Nuclear Instruments and Methods in Physics Research B, 261:871–874. 

[Bečváˇr et al., 2005] Bečváˇr, F., Ĉíˇzek, J., Procházka, I., and Janotová, J. (2005). 

The asset of ultra-fast digitizers for positron-lifetime spectroscopy. 


[Saito et al., 2002] Saito, H., Nagashima, Y., Kurihara, T., and Hyodo, T. (2002). 

A new positron lifetime spectrometer using a fast digital oscilloscope and baf 2 scintillators. 


[Stearns, 1975] Stearns, S. D. (1975). 

Digital Signal Analysis. 

Hayden Book Company Inc.

Digital Positron Lifetime @ EPOS - Positron Annihilation in Halle

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