Investigation of digital timing resolution and further improvement by using constant fraction signal time marker slope for fast scintillator detectors

Accepted Manuscript Investigation of digital timing resolution and further improvement by using constant fraction signal time marker slope for fast scintillator detectors Kundan Singh, Davinder Siwal

PII: DOI: Reference:

S0168-9002(18)30003-2 https://doi.org/10.1016/j.nima.2018.01.003 NIMA 60428

To appear in:

Nuclear Inst. and Methods in Physics Research, A

Received date : 1 July 2017 Revised date : 29 December 2017 Accepted date : 2 January 2018 Please cite this article as: K. Singh, D. Siwal, Investigation of digital timing resolution and further improvement by using constant fraction signal time marker slope for fast scintillator detectors, Nuclear Inst. and Methods in Physics Research, A (2018), https://doi.org/10.1016/j.nima.2018.01.003 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

*Manuscript Click here to view linked References

3

Investigation of digital timing resolution and further improvement by using constant fraction signal time marker slope for fast scintillator detectors

4

Kundan Singha,b , Davinder Siwalc,∗

1

2

5 6 7 8

9

a Inter

University Accelerator Centre, Aruna Asaf Ali Marg, New Delhi-110067, India of Computer & System Sciences, Jawahar Lal Nehru University, New Delhi-110067, India c Department of Physics, Panjab University, Chandigarh-160014, India

b School

Abstract

10

A digital timing algorithm is explored for fast scintillator detectors, viz. LaBr3 ,

11

BaF2 , and BC501A. Signals were collected with CAEN 250 mega samples per

12

second (MSPS) and 500 MSPS digitizers. The zero crossing time markers (TM)

13

were obtained with a standard digital constant fraction timing (DCF) method.

14

Accurate timing information is obtained using cubic spline interpolation of a

15

DCF transient region sample points. To get the best time-of-flight (TOF)

16

resolution, an optimization of DCF parameters is performed (delay and con-

17

stant fraction) for each pair of detectors : (BaF2 -LaBr3 ), (BaF2 -BC501A), and

18

(LaBr3 -BC501A). In addition, the slope information of an interpolated DCF

19

signal is extracted at TM position. This information gives a new insight to un-

20

derstand the broadening in TOF, obtained for a given detector pair. For a pair

21

of signals having small relative slope and interpolation deviations at TM, leads

22

to minimum time broadening. However, the tailing in TOF spectra is dictated

23

by the interplay between the interpolation error and slope variations. Best TOF

24

resolution achieved at the optimum DCF parameters, can be further improved

25

by using slope parameter. Guided by the relative slope parameter, events selec-

26

tion can be imposed which leads to reduction in TOF broadening. While the

27

method sets a trade-off between timing response and coincidence efficiency, it

28

provides an improvement in TOF. With the proposed method, the improved

29

TOF resolution (FWHM) for the aforementioned detector pairs are ; 25% (0.69 ∗ [email protected]

1

30

ns), 40% (0.74 ns), 53% (0.6 ns) respectively, obtained with 250 MSPS, and

31

corresponds to 12% (0.37 ns), 33% (0.72 ns), 35% (0.69 ns) respectively with

32

500 MSPS digitizers. For the same detector pair, event survival probabilities

33

are ; 57%, 58%, 51% respectively with 250 MSPS and becomes 63%, 57%, 68%

34

using 500 MSPS digitizers.

35

Keywords: Scintillator detectors, Signal digitizers, Digital constant fraction,

36

Interpolation error, Time-of-Flight

37

1. Introduction

38

In recent years, waveform digitizers combined with digital pulse process-

39

ing (DPP) techniques found widespread use in the analysis of detector signals.

40

With the advent of faster ADCs (flash ADCs), advancement in CMOS technol-

41

ogy, and availability of high speed interfaces, larger throughput rates can be

42

achieved, compared to analog counterpart [1]. Fast signal digitizers with high

43

amplitude resolutions (≥ 12-Bit) and sampling rates (≥ 100 MHz) are now com-

44

mercially available. This permits a closer look at signal dynamics, related to

45

the characteristics of incoming particles incident on the detector surface. Since

46

detector signals are directly fed to the digitizer without going through analog

47

electronic chain, they receive minimum distortion. Also they can be processed

48

with faster algorithms, leading to minimum system dead time. For instance, in

49

a low energy neutron induced γ-ray spectroscopy measurements using NaI (Tl)

50

detector, a digital (analog) system has a dead time of 3.6% (5%) at event rate of

51

18 kHz, while it becomes 8.5% (14%) at 54 kHz [2]. In addition, DPP provides

52

an easy software approach and implementation, scalable to handle high density

53

of signals in a modular way, which otherwise becomes difficult with a standard

54

analog based NIM electronics. Such techniques have already been implemented

55

on large-scale, for instance AGATA [3], INGA [4] arrays, dealing with large

56

number of channels for the γ-ray spectroscopic studies. Similar initiatives are

57

also taken by the NEDA [5], VANDLE [6], and NSCL groups [7], for the precise

58

measurement of neutron time-of-flight (TOF).

2

59

A signal digitizer produces a stream of discrete sample points, mimics the

60

analog signal, encoded with incident particle characteristics. The informations

61

such as particle identification, arrival time, and energy deposited in the detec-

62

tor medium can be decoded from input sample streams by digital means. The

63

energy information can be obtained from a moving window and trapezoidal al-

64

gorithms [8, 9, 10, 11]. It has been found that trapezoidal algorithm produces

65

the energy resolution (FWHM) of < 2% at 1.33 MeV for LaBr3 detector, using

66

100 and 250 mega samples per second (MSPS) digitizers [7]. The particle iden-

67

tification, for instance n-γ discrimination in a BC501A detector can be achieved

68

by using digital charge integration algorithms [12, 13]. This technique can be

69

used for neutron source identification with high accuracy [12]. Informations

70

such as particle arrival timing, can be extracted by a precise time marker (TM)

71

position, obtained from a digital constant fraction (DCF) algorithm [14]. For

72

instance, LaBr3 detectors produce the timing resolution of 576 ps [14] and 350

73

ps [7], achieved with linear and cubic interpolations respectively. Further in-

74

vestigations are attempted by the NEDA group proposing a new pulse-timing

75

algorithm based on interpolation of the points continuous up to second order

76

derivative, and achieved the best resolution as 660 ps for a BC501A detector

77

[5]. VANDLE group have compared a standard DCF algorithm with fitting and

78

weighted average timing methods, and developed a robust comparison proce-

79

dure [6]. In this work we have investigated the TOF resolution using a standard

80

DCF algorithm only. Present study is an effort to understand the digital timing

81

method with fast scintillator detectors, and create a benchmark of best time

82

resolution. Further, a new analysis method is proposed to improve the TOF

83

resolution. These findings have a potential application in future experiments at

84

IUAC [15].

85

This paper is organized as follows : The experimental set up along with

86

signal recording using a VME based digital data acquisition system, for various

87

fast scintillator detectors, namely, BaF2 , BC501A, and LaBr3 , are described

88

in section 2. The construction of a DCF signal from a stream of anode signal

89

sampling points, is mentioned in section 3. LaBr3 and BC501A detector anode 3

90

DCF pulse slope relationship at TM position, as a function of pulse peak height

91

is described in section 4. To get the best timing response, TOF optimization

92

curves for various detectors pairs, are addressed in section 5. Due to digital

93

sampling, sources of TOF broadening, namely : interpolation and slope errors,

94

are addressed in section 6. Improved TOF results and conclusions are discussed

95

in section 7.

96

2. Experimental arrangement and data recording

97

A schematic diagram of our experimental arrangement is shown in Fig 1.

98

It shows three detector pairs (Det1-Det2) of fast scintillators ; (BaF2 -LaBr3 ),

99

(BaF2 -BC501A), and (LaBr3 -BC501A), labeled as : “BaL”, “BaB”, and “LB”,

100

respectively for the TOF measurement. The figure also shows the electronic

101

chain used for trigger generation and waveform acquisition. In case of LaBr3

102

detector, maximum anode signal amplitude of ∼ 80 mV was observed, we there-

103

fore amplified the signal with Ortec VT120C current amplifier of fixed gain 20

104

(not shown in Fig. 1). Both the detectors in each pair were placed at an angle of

105

180 degree to capture the back-to-back γ-rays emitted by a 22 Na source (having

106

an activity of 20 kBq.). Detector specifications along with hardware settings are

107

described in Table 1. Bias voltage and threshold values were chosen according

108

to a typical nuclear physics experiment. Coincidence γ-rays waveforms were

109

recorded using

110

This recording was carried out at heavy ion accelerator laboratory, IUAC, New

111

Delhi [15].

22

Na source with a VME based digital data acquisition system.

112

A TOF spectrum was generated using “Det1” and “Det2” anode signals,

113

where respective detector front surfaces were located at 5 cm and 20 cm away

114

from

115

and LaBr3 detectors were 2.6 ns, 4.5 ns, and 5.5 ns respectively. Anode signals

116

from both detectors were fed to quad linear fan-in/fan-out (FIFO) 748 module

117

from Phillips. FIFO produces three identical output signals resulted from each

118

pair of anode signal. One of the FIFO output was fed to a leading edge discrimi-

22

Na source respectively. Typical risetime observed for BaF2 , BC501A,

4

PMT Bias

22

PMT Bias

Na F2

F1

Det1

Det2

F1 =5 cm, F2=20 cm

Anode

Anode

PHILLIPS Linear FIFO 748

Di = 139 cm, i=0, 1, 2, 3

Leading Edge Discriminator

Ortec

(LED) 711

Coincedence

D2

D3

Logic Unit CO4020 D1

TRG−IN

D0

CH0

CAEN

CH2

Digitizer CH1

Optical

Tx

Tx

link to PC

Rx

Rx

CH3 DT5730 or V1720

Det1

Det2

BaF2-LaBr3

BaF2

LaBr3

40

BaF2-BC501A

BaF2

BC501A

190

LaBr3 -BC501A

LaBr3

BC501A

211

Detector Pair

Tx : Transmitter Rx : Receiver

Coinc. Rate (Hz)

Figure 1: (Colour Online) A schematic diagram of an experimental setup, used for the digital pulse processing is displayed. All the detector pairs with corresponding coincidence rates are mentioned in the table. See text for the detailed explanation of experimental setup.

119

nator (LED) logic 711 module. LED threshold was set well above the noise level

120

for each data set, as mentioned in Table 1. The NIM signal outputs from LED

121

were sent to a coincidence module CO4020. A logical AND (coincidence) func-

122

tionality was configured in CO4020 module, delivering a trigger signal, which

123

was further used to validate the events of interest in digitizer. The other two

124

signals from FIFO corresponding to (CH0, CH1) from “Det1”, and (CH2, CH3)

125

from “Det2”, traveled equal cable length of 139 cm, before feeding the digitizer.

126

These signals are depicted in Fig. 1. Individual detector signals were used for

127

self timing measurement, while TOF was generated between each pair of CH0

128

and CH2 signals.

5

Table 1: Crystal and PMT dimensions along with scintillation properties. The table also reports the high voltage bias and LED threshold used in the data collection.

Detector Crystal size (D × H) Light Yield/MeV Decay Time (ns) PMT Diameter PMT type ′′

′′

1.5 × 1

BaF2 LaBr3

′′

6500 [17, 18] ′′

1.5 × 1.5 ′′

′′

BC501A 5 × 5

60000 [19] 1620 [20, 21]

630 ns [17, 18] < 30 ns [19] 3.2 ns [20, 21]

XP2020Q (Photonic) -1850

-25

′′

R2083 (Hamamatsu) -900

-25

′′

R4144 (Hamamatsu) -1700

-25

2

2

5

129

To perform the timing resolution investigations and comparison, coincidence

130

data were collected with two sets of CAEN signal digitizers. One set was col-

131

lected with a single width, VME based V1720 digitizer having 12-Bits ADC

132

and bandwidth of 125 MHz [16]. This module has 8 channels, can be operated

133

with a sampling rate of 250 MSPS, and provides 4 ns of digital sampling period.

134

Since all the fast scintillator anode signals exists up to 60 ns, we set post trigger

135

length as 800 samples (3.2 µs), while the signal acquiring window was kept as

136

1024 samples (≃ 4 µs), sufficient to collect an entire pulse. The other data set

137

was collected with DT5730 Desktop digitizer having 8 input channels, 14-Bits

138

ADC, and bandwidth of 250 MHz [16]. This module was operated at a sampling

139

rate of 500 MSPS, providing 2 ns of digital sampling period. Here we set the

140

post trigger length of 400 samples (800 ns) with a signal acquiring window of

141

630 samples (≈ 1.2 µs). For both digitizers, the dynamic amplitude range of

142

ADC was configured as -2V (0.488 mV and 0.122 mV precision for 250 and 500

143

MSPS digitizer respectively) to capture large signal height without saturation.

144

It was achieved by configuring the module DAC offset to -1V . The waveforms

145

were recorded and readout through the front panel optical-link available in both

146

digitizers. For each detector pair, we recorded 35,000 event pulses stored in a

147

ASCII file format. These were analysed offline using a separate C + + program.

148

All the detector pair waveforms were validated and collected under external trig-

149

ger mode for both digitizers. This method provided conditions to explore the

150

digital timing investigations similar to real experiments, based on coincidence

6

HV (V) Th (mV)

′′

151

triggering timing information.

152

3. Digital constant fraction timing algorithm

153

A scintillation detector anode pulse consists of a characteristic rising edge,

154

reflecting the circuit time constant, followed by the exponential tailing, resem-

155

bling the prompt flash decay in a crystal [21]. As an example, the digitized

156

waveform of a detector pulse is shown in Fig. 2 (a). This pulse was captured

157

with 250 MSPS digitizer generated by BC501A scintillator detector. A wave-

158

form of discrete sequence of points with sampling period of 4 ns is produced,

159

mimicking a true detector signal. The occurrence of an event can be obtained

160

by extracting the time marker (TM) position of a scintillation pulse. A versatile

161

DCF timing algorithm is used to obtain the accurate TM position [14]. From

162

the waveform sample train : “Sig[i]”, obtained from a digitizer, a DCF signal

163

can be constructed by using the following expression : DCF [i] = F ∗ (Sig[i] − BSL) − (Sig[i + ∆] − BSL)

(1)

164

Where “i” is the sample index, “F” represent constant fraction, “∆” is the num-

165

ber of samples delay, and “BSL” is the signal baseline, calculated as an average

166

over 10 samples. A typical example of a DCF signal obtained for BC501A and

167

BaF2 detector is shown in Fig. 2. It is worthwhile to notice that the BaF2 signal

168

carries only a single point in the rising edge. It thus suffer an under-sampling

169

effect due to the fact that the signal risetime is less than the sampling period.

170

Due to asynchronous signal sampling, TM position at zero crossing may not co-

171

incide with the sample time-stamp, therefore accurate position can be obtained

172

by linearly interpolating the points in the transition region (TR) of a DCF sig-

173

nal. Such procedure is easy to develop, and can be easily implemented in a

174

FPGA pulse processing units [14]. However, it has been observed that linear

175

interpolation procedure isn’t sensitive to the phase of signal points in proximity

176

of TM position, therefore deteriorates the overall timing resolution [22]. Cubic

177

spline interpolation, on the other hand provides better phase representation of

7

Raw

100

100

% F = 40

T

Amplitude (mV)

∆=3

50

CFD

Cubic Interpolation

Tangent at TM

SL : Slope

50

CFD T = 72 mV

TM = 575.19 ns 0

0

SL = -19.26 mV/ns

−50

−100

50

(a) 560

(b)

100

570

580

590

600

570

610

Amplitude (mV)

Time (ns)

580

585

Time (ns)

300

300

200

200

T = 25 mV

100

575

TM = 774.91 ns

100

SL = -6.91 mV/ns 0

0

−100

100

−200

200

(d)

(c) −300

760

770

780

790

Time (ns)

300

770

775

Time (ns)

Figure 2: (Colour Online) Panel (a) shows a digitized waveform of a BC501A signal ( • ),

collected with 250 MSPS digitizer, at a threshold of 72 mV. A 40% attenuated (  ), 3 sample delayed ( ◦ ), and a CFD (  ) waveforms are also depicted. Panel (b) displays a cubic interpolation (obtained with GSL library [23]) curve in a transition region (TR) of a DCF signal points along with tangent line. Panel (c) depicts BaF2 and associated signals for the same digitizer at 25 mV threshold, while panel (d) displays TR curve. Quantitative values of TM and SL are also depicted.

8

780

178

the signal points, with comparatively reduced time walk, and thus can provide

179

sub nano second timing resolution for fast scintillator detector like BC501A

180

[5]. We therefore pursued the cubic spline interpolation to explore the timing

181

response. A standard GNU Scientific Library (GSL) [23] cubic interpolation

182

routine is used to obtained TR curve of a DCF signal, as shown in Fig. 2 (b)

183

and (d). TM position can be obtained at zero crossing of the interpolated curve,

184

depicted as a vertical broken line in the respective figures. We further extracted

185

the slope information of signal points at TM, shown in Fig. 2 (b) and (d) along

186

with tangent line. Due to finite risetime of the waveform, the interpolation leads

187

to time broadening at TM position, σt , given by following expression : σef f ( dS dt )T M

(2)

2 2 2 σef f = σen + σeq

(3)

σt =

188

where σef f is the effective amplitude error due to noise (σen ) and A/D quan-

189

tization (σeq ) of a signal digitizer. Here σeq occurs from the two points as a

190

slope deviation with respect to ideal line. This line is formed by joining two

191

points situated at multiple of LSB units of a digitizer. At TM, σt is the time

192

broadening, and ( dS dt )T M represents the slope of a interpolated curve. Using

193

equation (3), it can be speculated that a good timing response can be achieved

194

for a signal having least amplitude fluctuations at the same time maintaining a

195

fast transition time. We can further re-write the equation (3) as :

σt =

σef f SL

(4)

196

where SL is the slope of a interpolated signal at TM position. SL gives an im-

197

portant information related to the phase variation of signal points in the DCF

198

transition region. A DCF signal with fast curvature, connected by neighboring

199

TM points, translates to minimum time broadening, whereas the points with

200

degraded slope values worsens the timing response (see Appendix). This ad-

201

ditional SL information can be used to filter out the events which lies in the

202

tailing region of time distribution. 9

0

(a)

3

SLLaBr (mV/ns)

−20

−40

Eγ = 511 keV

−60

−80

0

100

200

300

400

500

(b)

SLBC501 (mV/ns)

−20

−40

−60

−80

0

100

200

300

400

500

Peak height (mV) 10 6

9

BC501A

7

Labr

σSL (mV/ns)

σSL (mV/ns)

5

8

6

4 3 2 1

5

0

50

100

150

200

Mean peak height (mV)

4 3 2 1 0 −40

(c) −35

−30

−25

−20

−15

−10

−5

0

Mean SL (mV/ns) Figure 3: (Colour Online) Panel (a) shows the density distribution of DCF pulse slope at TM position, plotted against the pulse peak height of a LaBr3 detector, using CAEN 250 MSPS digitizer. DCF parameters ; F = 40% and ∆ = 3 samples were used in the calculation. Data obtained with

22 Na

coincidence γ-rays at a trigger 10 rate of 211 Hz. Panel (b) shows the same

distribution, obtained for the corresponding coincidence BC501A pulses. Panel (c) displays the dispersion in slope, plotted with average slope value, determined in 10 mV pulse window for each detector. Inset graph depicts a trend of slope dispersion with mean peak height, calculated for the same pulse window.

250 MSPS

(a)

500 MSPS

(b)

− 20 − 40

2

SLBaF (mV/ns)

0

− 60 − 80

− 20 − 40

2

SLBaF (mV/ns)

0

− 60 − 80 0

100

200

300

400

500

Peak height (mV)

Figure 4: (Colour Online) Panel (a) shows the density distribution of a slope plotted against pulse peak height for a BaF2 detector, obtained for 250 MSPS digitizer at DCF parameters ; F = 20%, and ∆ = 3. Panel (b) shows the same detector signal, obtained for 500 MSPS digitizer at DCF parameters ; F = 20%, and ∆ = 5.

11

203

4. Slope dependence on pulse peak height

204

A coincidence data of “LB” pair is analysed on event-by-event basis. The SL

205

values for both the detectors at TM position is determined from a cubic spline

206

interpolation of a DCF signal. A trend of SL with pulse peak height is revealed,

207

as portrayed in Fig. 3 (a) and (b) for LaBr3 and BC501A detectors respectively.

208

It displays LaBr3 (BC501A) Compton scattering events distribution under the

209

peak height of < 390 mV (< 240 mV), whereas the events corresponding to

210

photo-absorption of 511 keV gamma line are described inside the black square

211

box. Compared to LaBr3 detector, a wider diverging band of slope fluctuation

212

with pulse height is revealed for a coincident BC501A pulses, as shown in Fig.

213

3 (b). Slope broadening as well as the mean value are calculated for both the

214

detectors, as depicted in Fig. 3 (c). Inset figure shows the relationship between

215

slope fluctuation and mean pulse height. It varies linearly with average slope

216

and average pulse height. Slope broadening increases at larger pulse height, de-

217

spite the steep transition region (TR). This conveys an important information

218

regarding the distribution of sample points in the proximity of TM. This dis-

219

tribution is governed by the relative phase between the digitizer sampling clock

220

and arrival time of a signal. It thus introduces an increase in interpolation error

221

which further translates into broadening in slope. The overall spread, which is

222

larger for BC501A signals than LaBr3 , conveys another important information

223

about the under-sampling effect and crystal size. The ratio of signal risetime to

224

the sampling period (RTSP) is 1.12 for BC501A signal, while it becomes 1.37

225

for LaBr3 detector, it thus suffers relatively large interpolation error. The evo-

226

lution rate of slope spread with peak height is relatively faster for BC501A than

227

LaBr3 detector signals, thereby indicating that the timing error growth is more

228

significant with pulse height for a under-sampled detector signal. Furthermore,

229

the effect of under-sampling on the slope divergence is investigated for a BaF2

230

detector signal, as shown in Fig. 4. It has a RTSP of 0.65 (1.25) for 250 (500)

231

MSPS digitizer. Slope divergence makes difficult to identify the photo-absorbed

232

events in 250 MSPS compared to 500 MSPS digitizer. Thus, the study investi-

12

233

gates the usefulness of slope parameter as an additional degree of freedom for

234

a closer look to signal dynamics in TR of a DCF pulse. It therefore, would be

235

interesting to investigate the slope distribution for a variable risetime detector

236

signal because it might be useful for particle identification.

237

5. TOF optimization of fast scintillator detectors

238

A TOF resolution optimization is performed for each pair of detectors men-

239

tioned in Fig. 1, using both 250 MSPS and 500 MSPS digitizers. An offline

240

C + + program is used for the event processing, using ROOT [24] and GSL

241

libraries [23]. Prior to TM calculation, signal baseline restoration is performed

242

by eliminating DC offset, calculated as average amplitude over first 10 samples.

243

A DCF signal is generated on event-by-event basis, for each detector pair and

244

their TM are calculated using cubic spline interpolation with GSL library. To

245

save the computation time, only the sample points in TR of a DCF signal are

246

considered for the interpolation. Events having less than 3 points in TR of a

247

DCF signal for either of the two coincidence pulses are rejected out. High pre-

248

cision TM is obtained by using Bisection method from the interpolated curve.

249

A pattern of FWHM optimization, revealed for each detector pair, is shown in

250

Fig. 5. Amplitude fractions, 20%, 40%, 60%, and 80%, are used for both the

251

digitizers. Since all the detectors have the maximum peaking time ≈ 10 ns,

252

we decided to vary ∆ from 1 to 5 and 1 to 9 samples, covering the pulse peak

253

duration, for 250 MSPS and 500 MSPS digitizers respectively.

254

To keep the signal treatment identical, equal ∆ and F values are applied

255

to DCF algorithm for each pair of signals. In the case of BaF2 detector with

256

250 MSPS digitizer, reconstruction of true signal is difficult, therefore will have

257

large systematic errors. At higher F values, error contributes more to the time

258

broadening, and found to be true for all the three scintillator detectors. The

259

effect is reflected in Fig. 5 (a) for a detector pair “BaB”. It shows that the

260

smaller F values gives better resolution compared to higher ones. Since the

261

LaBr3 risetime is more than the sampling period, thus provides more stable

13

250 MSPS

2.5

=1.249 ns

FWHM40% 3,3 =1.361 ns

FWHM80% 3,3 =1.534 ns

BC501

2

1.5

(a)

1 1

1.5

2

2.5

3

3.5

4

4.5

TOF ( TM

BC501

TOF ( TM

FWHM20% =1.091 ns 5,5

2.2

500 MSPS

2

FWHM40% 5,5 =1.117 ns

1.8

FWHM60% =1.171 ns 5,5

1.6

FWHM80% 5,5 =1.236 ns

2

FWHM60% =1.452 ns 3,3

-TMBaF ) FWHM (ns)

2.4

FWHM20% 3,3

2

-TMBaF ) FWHM (ns)

3

1.4 1.2

(d)

1 0.8

5

1

2

Sample delay (∆BaF = ∆BC501)

3

4

5

6

7

8

9

Sample delay (∆BaF = ∆BC501)

2

2

250 MSPS

2.5

FWHM40% 3,3 =1.006 ns

LaBr3

TOF ( TM

1.5

(b)

1 1

1.5

2

2.5

3

3.5

4

4.5

FWHM60% =515.194 ps 3,3 1000

FWHM80% 3,3 =607.056 ps

800

600

(e)

400

5

1

2

Sample delay (∆LaBr = ∆BaF ) 3

4

5

6

7

3

8

9

2

FWHM40% 3,3 =1.285 ns

250 MSPS

2.5

=1.323 ns

3

FWHM60% 3,3 =1.319 ns

-TMLaBr ) FWHM (ns)

2.4

FWHM20% 3,3

3

FWHM80% =1.372 ns 3,3

BC501

2

1.5

(c)

1 1

1.5

2

2.5

3

3.5

4

4.5

5

Sample delay (∆LaBr = ∆BC501)

TOF ( TM

-TMLaBr ) FWHM (ns)

BC501

3

Sample delay (∆LaBr = ∆BaF )

2

3

TOF ( TM

FWHM40% 3,3 =453.973 ps

500 MSPS

1200

2

FWHM80% 3,3 =1.087 ns

2

FWHM20% =423.289 ps 3,3

1400

LaBr3

2

FWHM60% =1.049 ns 3,3

-TMBaF ) FWHM (ps)

FWHM20% =0.936 ns 3,3

TOF ( TM

-TMBaF ) FWHM (ns)

3

FWHM20% =1.069 ns 5,5

2.2

500 MSPS

2

FWHM40% 5,5 =1.135 ns

1.8

FWHM60% =1.209 ns 5,5

1.6

FWHM80% 5,5 =1.283 ns

1.4 1.2 1 0.8

(f) 1

2

3

4

5

6

7

8

Sample delay (∆LaBr = ∆BC501)

3

3

14 Figure 5: (Colour Online) Timing optimization curves at various DCF parameters, obtained with 250 MSPS digitizer, are shown in panels (a), (b), (c) for the detector pair ; “BaB”, “BaL”, and “LB”, respectively. Similar optimization is performed with 500 MSPS digitizer, shown in panels (d), (e), and (f) for the same detector pair. Legends depicts the minimum TOF resolution obtained for a given DCF parameter.

9

262

TM with reduced time walk compared to BaF2 detector, which translates into

263

smaller timing error. This is shown in Fig. 5 (b) for a detector pair “BaL”,

264

having dispersion curves comparatively closer than Fig. 5 (a). Dispersion dif-

265

ference reduces even further and the curves are almost insensitive to F value as

266

shown in Fig. 5 (c). This is due to the fact that both detectors have similar

267

risetime, hence similar time walk in their TM calculation. Optimization curves

268

obtained with 500 MSPS digitizer are also shown in Fig. 5 (d), (e), and (f).

269

Due to the better sampling period of 2 ns, the overall time walk gets reduced

270

for all the three scintillator detectors. Therefore in all the three pair of signals,

271

the TOF resolution gets improved as compared to 250 MSPS digitizer. Here

272

also we found similar trend and the best resolution is obtained at 20 % fraction

273

with 5 and 3 samples delay for “BaB”’, “LB”, and “BaL” pairs respectively.

274

6. Slope and interpolation errors

275

A TOF is a measure of relative time difference of DCF time markers, ob-

276

tained from the two digitized signals. In general there is no correlation between

277

the sampling clock and arrival time of the input signal, and therefore their rel-

278

ative phase is completely random. The time difference of two TM positions

279

governs the TOF centroid, while the broadening is dictated by the systematic

280

errors involved in the TM calculation. These errors are due to : detector sig-

281

nal transit time spread (because of single/multiple particle hits in a crystal),

282

interpolation error in the vicinity points, and slope variations at TM. One can

283

formulate the broadening in TOF measurement as 2 2 σT2 OF = σ∆SL + σ∆I

(5)

284

Where σ∆SL and σ∆I are the broadening due to slope variations and interpo-

285

lation errors respectively. To understand equation (5) in a systematic way, we

286

collected a high precision pulser data with 250 MSPS digitizer. Typical signal

287

risetime was 30 ns, with a constant height of 500 mV. Relative time was mea-

288

sured using DCF algorithm, from two identical digitized signals traveled through

15

10

10

-SLCh1) (mV/ns)

5 2000

Event Entries

Event Entries

5

3000

1000

500

1000 0 −0.8 −0.6 −0.4 −0.2

0

0

0.2

∆ TM (ns)

−5

−10 −0.8

3.6 3.8 4 4.2 4.4 4.6 4.8 5

∆ TM (ns)

0

Ch2

0

∆ SL (SL

∆ SL (SL

1500

4000

Ch1

-SLCh0) (mV/ns)

5000

5

(a)

(b)

10

−0.6

−0.4

−0.2

∆ TM (TM

0

0.2

3.6

3.8

4

4.2

4.4

∆ TM (TM

-TMCh0) (ns)

Ch1

4.6

4.8

5

-TMCh1) (ns)

Ch2

(c) 5

0

∆ SL (SL

−5

Event Entries

1000

Ch2

-SLCh1) (mV/ns)

10

800 600 400 200

−10

0 3.5

4

4.5

5

∆ TM (ns)

3.6

3.8

4

4.2

∆ TM (TM

4.4

4.6

4.8

5

-TMCh1) (ns)

Ch2

Figure 6: (Colour Online) Panel (a) shows the density distribution of relative slope of a BC501A anode signal, plotted against the self time marker difference. Optimum DCF parameters ; F = 80%, and ∆ = 3 are used. Same is plotted in panel (b) for unequal cable lengths having same DCF parameters. Panel (c) shows a similar distribution, obtained for a non-optimized DCF parameters ; F = 20%, and ∆ = 5. Inset of panels (a), (b) and (c) shows X-axis projection, depicting the evolution of time marker dispersion respectively. DCF pulse shape under graphical cut shown in green (“G” cut) and purple (“P” cut) colour, as depicted in panels (a) and (c) respectively are investigated in figure 7.

289

equal cable length. The main advantage of this measurement is the same slope

290

variation involved in both the DCF signals, leading to a minimum σ∆SL . There-

291

fore, broadening in TOF is primarily governed by the interpolation error only.

292

A tiny spot of relative slope (∆SL) vs. time marker difference (∆T M ), with

293

a timing resolution of 65 ps (FWHM) is obtained [25], that matches with the 16

294

earlier investigation [14]. To investigate the effect of slope variations on self

295

time broadening, signals were collected for equal and unequal cable lengths for

296

a BC501A detector using

297

made at three digitizer channels ; Ch0, Ch1, Ch2, received by the cable lengths

298

of 137.5 cm, 137.5 cm, and 238 cm respectively. Unlike the pulser data, now

299

the equal cable length signals have the amplitude variations while retaining the

300

similar slope information. To further understand the effect of slope variation on

301

TM dispersion, three different cases are considered for self timing (ST) events,

302

Op Op that can be labeled as ; ST1,0 , ST2,1 for the optimum DCF parameters of

303

N op channel pair (Ch1, Ch0), and (Ch2, Ch1) respectively, while ST2,1 for non-

304

N op Op Op are shown in and ST2,1 , ST2,1 optimum case. Density distribution of ST1,0

305

Fig. 6 (a), (b) and (c) respectively. By the DCF algorithm optimization, it is

306

Op found that self timing dispersion for ST1,0 improves, as we go for the higher F

307

values at a given ∆. Owing to a similar sample points distribution in case of

308

Op ST1,0 DCF signals, it produces fast transition region slope at higher fraction

309

and leads to reduction in time broadening (conveyed by equation 3). Only over-

310

riding signal fluctuations, translated by the interpolation error, will contributes

311

to the resolution. A tiny ellipse oriented in Y-direction, shows a sharp distri-

312

bution obtained between ∆SL vs. ∆T M , displayed in Fig 6 (a), obtained for a

313

optimum DCF parameters ; F = 80%, and ∆ =3. A sharp timing distribution

314

is obtained with resolution (FWHM) of 74 ps [25], depicted in the inset of Fig.

315

Op 6 (a). To understand ∆SL and ∆I errors at the same DCF parameters, ST2,1

316

is investigated as shown in Fig. 6 (b). It shows an exaggerated ellipse with

317

timing dispersion increased by ∼ 2.5 times while the relative slope dispersion

318

increased by ∼ 3.5 times. This could be attributed to the fact that the signal

319

being received by Ch2 of 1 m extra cable length have delay as well as disper-

320

sion. This leads to more disperse distribution of sample points in Ch2 signal

321

than Ch1, thereby increasing the interpolation error and worsening the self time

322

broadening. Timing resolution (FWHM) of 209 ps [25] is obtained, ≈ 3 times

22

N a source. Event-by-Event signal collection was

323

Op worse than ST1,0 . To further investigate the effect of non-optimum DCF pa-

324

N op rameter on timing measurement, ST2,1 is generated for F = 20%, and ∆ =

17

325

5. This further worsens the slope as well as the interpolation error, and results

326

into a right skewed timing distribution as shown in Fig. 6 (c).

327

To get the intuitive understanding of interpolation curve shape, slope and

328

timing errors, DCF shapes are collected under graphical cut in green (“G” cut)

329

and purple (“P” cut) colour as depicted in Fig. 6 (a) and (c) respectively.

330

Corresponding sample points in the vicinity of zero crossing line for a pair of

331

mentioned channels are displayed in Fig. 7. For a “G” cut, interpolation curves

332

along with tangent direction for Ch0 and Ch1 are shown in Fig. 7 (a) while their

333

difference is plotted in panel (b). The vicinity points of two channels are almost

334

in same phase with a similar curve shape, thus tailing in ∆T M is contributed

335

by interpolation error only. However, in “P” cut the time broadening is jointly

336

governed by slope and interpolation errors. As depicted in Fig. 7 (c) and

337

(d), the interpolation curves makes a comparatively large curvature path while

338

connecting the two points. Their difference makes a curvature shape, thus

339

translates to large dispersion in timing measurement, therefore can be attributed

340

as purely a computational effect.

341

7. Results and discussions

342

In the light of section 6 discussion, tailing in timing distribution is jointly

343

governed by slope variations and interpolation errors. One can minimize these

344

errors by performing DCF parameter optimization, leading to minimum slope

345

and timing dispersion. In TOF assessment of two detector signals at a given dig-

346

itization speed, the slope variations and interpolation errors are further dictated

347

by individual detector signal risetime and respective PMT gain. Measurement

348

of a typical event distribution for “BaB” detector pair with optimum DCF pa-

349

rameter ; F = 20%, and ∆ = 3, is shown in Fig. 8. It provides best TOF

350

resolution (FWHM) as 1.24 ns with 250 MSPS digitizer. One can further im-

351

prove the timing resolution by making use of joint ∆SL and TOF information.

352

An event selection criteria can be imposed on the distribution demanding the

353

events for minimum slope straggling and good timing relationship. A typi-

18

60

(a)

60

Amplitude (mV)

40

"G" cut

40

∆ SL = -0.444 (mV/ns) 20

Ch0

∆ TM = 0.209 (ns)

20

Ch1 0

0

−20 167

20

168

169

170

171

172

173

0.5

1

∆ TM (TM

Time (ns)

Amplitude (mV)

(b)

1.5

2

-TMCh0) (ns)

Ch1

10

10

0

0

−10

10

−20

20

"P" cut ∆ SL = -3.110 (mV/ns) ∆ TM = 4.691 (ns)

Ch1 −30

Ch2

30

(c) −40

188

190

192

194

196

(d)

198

40

3.5

4

∆ TM (TM

Time (ns)

4.5

5

-TMCh1) (ns)

Ch2

Figure 7: Panel (a) shows the neighboring points to zero crossing line of a DCF signal, obtained for “G” cut, shown in figure 6 (a). Corresponding deviation in the cubic spline interpolation curves is shown in panel (b), legend depicts the values obtained at TM position of the two signals. Same argument holds for panels (c) and (d), obtained for “P” cut shown in figure 6 (c).

19

90 80 70 60 50 40 30 20 10 0

40

2

∆ SL (SLBC501-SLBaF ) (mV/ns)

60

20 0 −20 −40

(a)

−60 4

5

6

7

8

9

10

11

12

13

14

1400

Event Entries

1200 1000 800 600 400

(b)

200 0 4

5

6

7

8

9

10

11

12

13

14

TOF (TMBC501-TMBaF ) (ns) 2

Figure 8: (Colour Online) Panel (a) displays the density distribution of slope error plotted against the γ-ray TOF, obtained for a “BaB” detector pair with 250 MSPS digitizer. An optimized elliptical shape in the vertical direction is obtained for DCF parameters ; F = 20 %, ∆ = 3, provides best TOF resolution. Events projection along X-axis (black histogram) is shown in panel (b), along with the TOF distribution obtained under graphical cut (Gaussian fitted hatched histogram), as depicted in panel (a).

20

354

cal event selection is shown under the graphical cut in Fig. 8 (a). Raw and

355

graphical cut projected events along the timing axis, are depicted as black and

356

hatched histogram respectively in Fig. 8 (b). With the proposed method the

357

TOF resolution becomes 0.748 ns at the cost of 42 % event rejection. It brings

358

a natural trade-off between the quality of timing response with coincident event

359

efficiency. Thus, the method provides an extra degree of freedom to improve

360

the broadening in TOF measurement.

361

Results obtained with 250 MSPS and 500 MSPS digitizers are shown in Fig.

362

9 (a) and (b) respectively. Grey and brown bar shows the resolution obtained

363

with raw and proposed event selection method respectively. Using 500 MSPS,

364

the raw TOF resolution (FWHM) for “BaB”, and “LB” pairs are improved by

365

12%, 17% respectively, whereas “BaL” improves significantly to 54%. With

366

the proposed method, the coincidence efficiency (event survival) for the pair

367

of detectors : “BaL”, “BaB”, and “LB”, are 57%, 58%, 51% with 250 MSPS,

368

while for identical cut it becomes 63%, 57%, 68% with 500 MSPS digitizer

369

respectively. With the proposed event selection approach, the reduction in TOF

370

broadening for the same detector pairs is 25%, 40%, and 53% obtained with 250

371

MSPS digitizer, and corresponds to 12%, 33%, and 35% for 500 MSPS digitizer

372

respectively.

373

In summary, a timing investigation is performed using standard DCF algo-

374

rithm for the pair of fast scintillator detectors. A new concept of slope differ-

375

ence at TM position, for a pair of signals is introduced. Optimization curves

376

for “BaL”, “BaB”, and “LB” are extracted for both 250 MSPS and 500 MSPS

377

digitizers. These curve reveals the best raw TOF resolution (FWHM) for pairs

378

: “BaL”, “BaB”, and “LB”, as ; 0.93 ns, 1.24 ns, and 1.28 ns respectively

379

for 250 MSPS, and becomes 0.42 ns, 1.09 ns, and 1.06 ns for 500 MSPS digi-

380

tizer. Detailed investigations are performed to understand the various sources

381

of broadening in a TOF measurement. This dispersion is investigated under

382

the light of the new variable “∆SL”. Event selection with joint use of ∆SL

383

and TOF information leads to reduction in TOF broadening. Using 250 MSPS

384

digitizer, findings are comparable to the commercial [26] and custom designed 21

2

TOF resolution (FWHM) (ns)

1.8

(a)

250 MSPS digitizer Raw TOF

1.6

With ∆SL vs. TOF selection

1.4 1.2 1 0.8 0.6 0.4 0.2 0

(BaF2 - BC501)

(LaBr3 - BC501)

(BaF2 - LaBr3)

2

TOF resolution (FWHM) (ns)

1.8

(b)

500 MSPS digitizer

1.6

Raw TOF 1.4

With ∆SL vs. TOF selection

1.2 1 0.8 0.6 0.4 0.2 0

(BaF2 - BC501)

(LaBr3 - BC501)

(BaF2 - LaBr3)

Figure 9: (Colour Online) A comparison between raw and gated TOF resolution (FWHM), obtained from 250 MSPS and 500 MSPS digitizers are shown in panels (a) and (b), for “BaB”, “LB”, and “BaL” detector pairs respectively. See text for detailed explanation.

22

385

analog electronics [27] which can be further improved with 500 MSPS digitizer,

386

therefore sets a benchmark values. The results are encouraging, and motivate

387

us to pursue the DPP implementation in nuclear physics experiments related to

388

TOF measurement.

389

8. Acknowledgment

390

One of the author (KS) acknowledges Dr. A. Srivastva, and his student L.

391

Beloni from SC & SS, JNU, for useful discussions. KS also acknowledges the

392

illuminating and technical discussions with A. Jhingan and N. Saneesh from

393

IUAC. He is thankful to Dr. P. Sugathan from IUAC, for accessing the neutron

394

detector and the radioactive source. Author (DS) acknowledges the financial

395

support recieved from UGC New Delhi, in the form of D. S. Kothari postdoctoral

396

fellowship. He is also thankful to Prof. B. R. Behera and Prof. D. Mehta at

397

PU, for their local support in the department.

398

9. Appendix

399

To understand more about the role of signal slope degradation on TOF

400

broadening, we performed a toy simulation, mimicking the neighboring points

401

of two DCF signals in the transition region. Signal points and their curvature

402

slope are depicted in Fig. 10 (a) and (b), whereas the simulation results are

403

displayed in Fig. 10 (c) and (d) respectively. First signal (S1) points are men-

404

tioned as : P1S1 , P2S1 , P3S1 , while P1S2 , P2S2 , P3S2 belongs to second signal

405

(S2), delayed by three sample units with respect to S1. Interpolation curve

406

(obtained from GSL library) is also shown as a broken black line connecting the

407

points from P1S1 to P3S1 for S1 and P1S2 to P3S2 for S2 respectively. Here, we

408

assumed the sampling time period of 4 ns while the amplitude is taken in mV

409

units. Identical slope signals are shown in Fig. 10 (a), whereas the signal with

410

degraded slope, S2, is shown in Fig. 10 (b). To make the problem simple, we

411

first investigate two identical signal points having equal slope at TM position. If

412

we make an artificial Gaussian fluctuations in the points P1S1 , P2S1 and P1S2 , 23

100

P1S1

P1S2

∆ SL ( SL -SLS1 ) (mV/ns)

100

(a)

0

P2S1

P2S2

S2

−100 TMS1 = 6.57 ns SLS1 = -27.54 mV/ns TMS2 = 18.57 ns

−300 1000

P3S1

SLS2 = -27.54 mV/ns

1

2

3

4

P1S1

5

6

7

P2S2

P2S1

P3S2

−100 TMS1 = 6.57 ns SLS1 = -27.54 mV/ns

−300

TMS2 = 18.06 ns

0

60

dSL

30

dSL

0

dSL

-40

−50

4

100

(b)

P1S2

0

−200

50

dSL

P3S2

Event Entries / 50 ps

Amplitude (mV)

−200

(c)

80

60

8

10

12

14

10

12

14

FWHMdSL60 = 1.26 ns FWHMdSL30 = 0.712 ns FWHMdSL0 = 0.495 ns FWHMdSL-40 = 0.824 ns

40

20

P3S1

6

(d)

SLS2 = -14.86 mV/ns

0

1

2

3

4

5

6

Sample Number

7

0

4

6

8

TOF (ns) ( TM -TMS1 ) S2

Figure 10: (Colour Online) Panel (a) : Displays neighboring points around time marker position for signal S1 and 3 sample delayed signal S2 with identical slope values. Panel (b) : Same as panel (a) with degraded slope value in signal S2, introduced by moving the point P1S2 (P2S2 ) to 30 mV (-30 mV). Density distribution between slope difference and TOF, resulted from the fluctuating points P1S1 (P1S2 ) and P2S1 (P2S2 ) is shown in panel (c), while panel (d) depicts the TOF distribution.

24

413

P2S2 (run for 1000 events) each with a width of 5 mV (standard deviation) while

414

keeping P3S1 and P3S2 at fixed location (labeled as dSLSym ), it translates to

415

a sharp distribution in ∆SL vs. TOF space, density plot labeled as dSL0 is

416

depicted in Fig. 10 (c). Corresponding TOF distribution is shown in Fig. 10

417

(d), provides a sharp TOF distribution with resolution (FWHM) of 0.495 ns.

418

However, if we make an asymmetric fluctuations (labeled as dSLAsym ), for in-

419

stance 5 mV in P1S1 , P2S1 , and 10 mV in P1S2 , P2S2 , it disturbs the ∆SL vs.

420

TOF relationship. Outcome result labeled as dSL−40 is displayed in Fig. 10

421

(c), events are shifted downside to -40 units for the comparison purpose only.

422

Projected TOF spectrum shows that the events gets translated to the tailing

423

part of the distribution, thereby making a width of 0.824 ns which is 66% more

424

than dSLSym case. Further, we considered the case where the slope of S2 gets

425

degraded by a factor of two compared to S1 by moving the points P1S2 , P2S2 ,

426

P3S2 to 30 mV, -30 mV, and -100 mV respectively, as shown in Fig. 10 (b).

427

If we again introduce the amplitude broadening similar to dSLSym , we found

428

comparatively broader distribution of events, dSL30 , as shown in Fig. 10 (c). It

429

is evident from the Fig. 10 (d) that the temporal resolution worsens by 44%,

430

as a manifestation of degraded slope value for signal S2. Further investigation

431

of asymmetric broadening, similar to dSLAsym , an exaggerated distribution of

432

the events is revealed, depicted as dSL60 in Fig. 10 (c). It therefore, renders to

433

increase in TOF width as 1.26 ns, displayed in Fig. 10 (d). Thus, a simple toy

434

simulation demonstrates a deep connection between the ∆SL and TOF width

435

which decides the fate of timing response in a digital system.

436

437

References

438

[1] M. J. Koskelo et al., Nucl. Instr. and Meth. A 422 (1999) 373.

439

[2] S. Mitra et al., Appl. Radiat Isot. 61 (2004) 1463.

440

[3] S. Akkoyun et al., Nucl. Instr. and Meth. A 668 (2014) 26.

25

441

[4] R. Palit et al., Nucl. Intsr. and Meth. A 680 (2014) 90.

442

[5] V. Modamio et al., Nucl. Instr. and Meth. A 775 (2015) 71.

443

[6] S. V. Paulauskas et al., Nucl. Instr. and Meth. A 737 (2014) 22.

444

[7] C. J. Prokop et al., Nucl. Instr. and Meth. A 792 (2015) 81.

445

[8] A. Georgiev et al., IEEE Trans. Nucl. Sci. 41 (1994) 1116.

446

[9] A. Georgiev and W. Gast, IEEE Trans. Nucl. Sci. 40 (1993) 770.

447

[10] J. Stein et al., Nucl. Instr. and Meth. B 113 (1996) 141.

448

[11] V. T. Jordanov and G. Knoll, Nucl. Instr. and Meth. A 345 (1994) 337.

449

[12] M. Flaska, S. A. Pozzi, Nucl. Instr. and Meth. A 577 (2007) 654.

450

[13] M. Flaska et al., Nucl. Instr. and Meth. A 729 (2013) 456.

451

[14] A Fallu-Labruyere et al., Nucl. Instr. and Meth. A 579 (2007) 247.

452

[15] http://www.iuac.res.in/

453

[16] http://www.caen.it/

454

[17] P. Schotanus et al., Nucl. Instr. and Meth. A 238 (1985) 564.

455

[18] M. Mosyznski et al., Nucl. Instr. and Meth. A 226 (1984) 534.

456

[19] A. Iltis et al., Nucl. Instr. and Meth. A 563 (2006) 359.

457

[20] T. Szczesniak et al., IEEE Trans. Nucl. Sci. 57 (2010) 3846.

458

[21] G.F. Knoll, Radiation Detection and Measurement, Third ed., John Wiley,

459

New York (2000).

460

[22] L. Bardelli et al., Nucl. Instr. and Meth. A 521 (2004) 480.

461

[23] https://www.gnu.org/software/gsl/

462

[24] R. Brun, F. Redemakers, Nucl. Instr. and Meth. A 399 (1997) 81. 26

463

[25] Kundan Singh and Davinder Siwal, Private Communication (2016).

464

[26] A. Jhingan et al., Nucl. Instr. and Meth. A 585 (2008) 165.

465

[27] S. Venkataramanan et al., Nucl. Instr. and Meth. A 596 (2008) 248.

27