Signal Processing for Radiation Detectors E-Book

Mohammad Nakhostin

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 878

Veröffentlichungsjahr: 2017

Beschreibung

Presents the fundamental concepts of signal processing for all application areas of ionizing radiation This book provides a clear understanding of the principles of signal processing of radiation detectors. It puts great emphasis on the characteristics of pulses from various types of detectors and offers a full overview on the basic concepts required to understand detector signal processing systems and pulse processing techniques. Signal Processing for Radiation Detectors covers all of the important aspects of signal processing, including energy spectroscopy, timing measurements, position-sensing, pulse-shape discrimination, and radiation intensity measurement. The book encompasses a wide range of applications so that readers from different disciplines can benefit from all of the information. In addition, this resource: * Describes both analog and digital techniques of signal processing * Presents a complete compilation of digital pulse processing algorithms * Extrapolates content from more than 700 references covering classic papers as well as those of today * Demonstrates concepts with more than 340 original illustrations Signal Processing for Radiation Detectors provides researchers, engineers, and graduate students working in disciplines such as nuclear physics and engineering, environmental and biomedical engineering, and medical physics and radiological science, the knowledge to design their own systems, optimize available systems or to set up new experiments.

Leseprobe

Table of Contents

Cover

Title Page

Preface

Acknowledgement

1 Signal Generation in Radiation Detectors

1.1 Detector Types

1.2 Signal Induction Mechanism

1.3 Pulses from Ionization Detectors

1.4 Scintillation Detectors

References

2 Signals, Systems, Noise, and Interferences

2.1 Pulse Signals: Definitions

2.2 Operational Amplifiers and Feedback

2.3 Linear Signal Processing Systems

2.4 Noise and Interference

2.5 Signal Transmission

2.6 Logic Circuits

References

3 Preamplifiers

3.1 Background

3.2 Charge‐Sensitive Preamplifiers

3.3 Current‐Sensitive Preamplifiers

3.4 Voltage‐Sensitive Preamplifiers

3.5 Noise in Preamplifier Systems

3.6 ASIC Preamplifiers

3.7 Preamplifiers for Scintillation Detectors

3.8 Detector Bias Supplies

References

4 Energy Measurement

4.1 Generals

4.2 Amplitude Fluctuations

4.3 Amplifier/Shaper

4.4 Pulse Amplitude Analysis

4.5 Dead Time

4.6 ASIC Pulse Processing Systems

References

5 Pulse Counting and Current Measurements

5.1 Background

5.2 Pulse Counting Systems

5.3 Current Mode Operation

5.4 ASIC Systems for Radiation Intensity Measurement

5.5 Campbell’s Mode Operation

References

6 Timing Measurements

6.1 Introduction

6.2 Time Pick‐Off Techniques

6.3 Time Interval Measuring Devices

6.4 Timing Performance of Different Detectors

References

7 Position Sensing

7.1 Position Readout Concepts

7.2 Individual Readout

7.3 Charge Division Methods

7.4 Risetime Method

7.5 Delay‐Line Method

References

8 Pulse‐Shape Discrimination

8.1 Principles of Pulse‐Shape Discrimination

8.2 Amplitude‐Based Methods

8.3 Zero‐Crossing Method

8.4 Risetime Measurement Method

8.5 Comparison of Pulse‐Shape Discrimination Methods

References

9 Introduction to Digital Signals and Systems

9.1 Background

9.2 Digital Signals

9.3 ADCs

9.4 Digital Signal Processing

References

10 Digital Radiation Measurement Systems

10.1 Digital Systems

10.2 Energy Spectroscopy Applications

10.3 Pulse Timing Applications

10.4 Digital Pulse‐Shape Discrimination

References

Index

End User License Agreement

List of Tables

Chapter 02

Table 2.1 Some basic properties of the Laplace transform [1, 2].

Table 2.2 The Fourier and Laplace transforms of some common pulses.

Chapter 04

Table 4.1 The shape factors for some of the common filters.

Chapter 09

Table 9.1 Some properties of

z

‐transform.

List of Illustrations

Chapter 01

Figure 1.1 The induction of charge on a conductor by an external positive charge

q

(top) and the density of the induced surface charge on the conductor (bottom).

Figure 1.2 The induction of current by a moving charge between two electrodes. When charge

q

is close to the upper electrode, the electrode receives larger induced charge, but as the charge moves toward to the bottom electrode, more charge is induced on that electrode. If the two electrodes are connected to form a closed circuit, the variations in the induced charges can be measured as a current.

Figure 1.3 The induction of pulses on the segments of an electrode. In a segmented electrode, charge is initially induced on many segments, but as the charge approaches the electrode, the largest signal is received by the segment, which has the minimum distance with the charge.

Figure 1.4 The calculation of induced charge on an electrode by using Gauss’s law.

Figure 1.5 The arrangement of a detector–preamplifier and its equivalent circuit.

Figure 1.6 The classification of gaseous detectors based on the amount of charge generated in the detector for a given amount of ionization.

Figure 1.7 The cross section of a parallel‐electrode ionization chamber used in deriving the shape of pulses induced by ion pairs released at the distance

x

∘

from the anode of the detector.

Figure 1.8 (Top) Time development of an induced current pulse on the anode of a planar ionization chamber by the motion of electrons and positive ions. The figure is drawn as if the electron drift velocity is only five times faster than the ion drift velocity. (Bottom) The induced charge on the anode.

Figure 1.9 The output voltage pulse of an ionization chamber for different circuit time constants.

Figure 1.10 The structure of gridded ionization chamber and the weighting potential of the anode.

Figure 1.11 Schematic drawing of the relationship between a particle’s Bragg peak and the shape of a current pulse from a BCS detector.

Figure 1.12 The structure and distribution of electric field in a parallel‐plate avalanche counter designed for X‐ray detection.

Figure 1.13 (Top) The electron‐ and positive ion‐induced current pulses in a parallel‐plate avalanche counter. (Bottom) The time development of a charge pulse in a parallel‐plate avalanche counter.

Figure 1.14 A transmission avalanche counter and the shape of current and charge pulses induced by a charged particle.

Figure 1.15 An illustration of cylindrical proportional counter and its cross section.

Figure 1.16 The shape of output voltage pulses from a proportional counter with different circuit time constants.

τ

1

and

τ

2

are the time constants of the circuit.

Figure 1.17 The difference in the shape of charge pulses initiated with a point‐like ionization and an extended ionization.

Figure 1.18 (Top) The structure of an MWPC and (bottom) variation of the electric field along the axis perpendicular to the wire plane and centered on the wire [17, 18].

Figure 1.19 Schematic view of a GEM hole and electric field distribution.

Figure 1.20 The typical shape of a current pulse induced in a typical GM counter.

Figure 1.21 The shape of output pulses from a GM tube and illustration of dead time and recovery time.

Figure 1.22 (a) Simplified band structure of an intrinsic semiconductor material. (b) Band structure of an

n

‐type semiconductor. (c) Band structure of a

p

‐type semiconductor.

Figure 1.23 A simple semiconductor detector arrangement.

Figure 1.24 The structure of a

p–n

junction.

Figure 1.25 A

p–i–n

diode structure.

Figure 1.26 Some common geometries of germanium detectors.

Figure 1.27 (a) A schematic representation of planar germanium detector and (b) the time profile of the pulses due to interaction in different locations inside the detector.

Figure 1.28 (Left) Cross section of a true coaxial germanium detector and (right) calculated waveforms for interactions in different locations.

Figure 1.29 The electric field distribution and samples of calculated pulses from a closed‐end coaxial germanium detector.

Figure 1.30 The structure of a double‐sided orthogonal strip detector.

Figure 1.31 The structure and electric field distribution in a planar silicon detector.

Figure 1.32 The shape of induced currents in a planar silicon

p–n

junction. The calculations correspond to a detector with

d

 = 500 µm,

x

∘

 = 250 µm,

E

min

 = 0.1

E

crit

, and

N

D

 = 10

12

 cm

−3

.

Figure 1.33 Schematic layout of an SSD and weighting field of one strip. The induced current waveforms are shown at the bottom of the figure. It is seen that while the direction of the drift velocity of charge carriers is constant, the direction of weighting field around the strip changes, which can lead to bipolar current pulse.

Figure 1.34 Principles of a semiconductor drift detector.

Figure 1.35 Current and charge pulses from a transmission silicon detector.

Figure 1.36 Schematic of a simple planar compound semiconductor detector and charge pulses calculated for various interaction points in a 1 mm thick CdTe detector.

Figure 1.37 A schematic illustration of charge pulses with and without charge trapping and de‐trapping effects.

Figure 1.38 (a) The structure of a coplanar detector. (b) The weighting potentials of the collecting and non‐collecting anode electrodes.

Figure 1.39 A pixel detector and a typical plot of the weighting potential along the

z

‐axis through the middle of the pixel.

Figure 1.40 Energy bands in an activated crystalline inorganic scintillator.

Figure 1.41 Schematic energy level diagram for an inorganic scintillator molecule. The upward pointing arrow refers to excitations, the downward pointing dashed arrow refers to decay without scintillation, and solid downward arrows refer to light emission.

Figure 1.42 Schematic representation of a photomultiplier tube and its operation.

Figure 1.43 Schematic diagrams of a resistor chain voltage divider circuit.

Figure 1.44 The use of stabilizing capacitors in a voltage divider with negative polarity.

Figure 1.45 A schematic representation of Cockcroft–Walton voltage divider.

Figure 1.46 The equivalent circuit for a PMT readout. A PMT is shown as a current generator.

Figure 1.47 PMT output voltage pulses for different circuit time constants.

Figure 1.48 Schematic structure of a reach‐through APD and its electric field distribution.

π

represents either lightly doped

p

‐type material or intrinsic material.

Figure 1.49 The operation of a single photodiode in Geiger mode.

Figure 1.50 A schematic representation of an SiPM and its equivalent circuit.

Chapter 02

Figure 2.1 The basic characteristics of a detector pulse.

Figure 2.2 An illustration of preshoot, undershoot, and pulse ringing.

Figure 2.3 An illustration of unipolar, bipolar, and logic pulses.

Figure 2.4 The operational amplifier.

Figure 2.5 A block diagram of an operational amplifier with feedback.

Figure 2.6 A sum circuit using an operational amplifier.

Figure 2.7 Unity gain buffer or voltage follower.

Figure 2.8 Signal processing system as an operator.

Figure 2.9 Basic relationships between terminal variables for electrical components.

Figure 2.10 The input–output relation of a simple

RC

circuit.

Figure 2.11 Representation of the unit length, shifted and scaled delta functions.

Figure 2.12 The unit step function.

Figure 2.13 The output of an

RC

integrator for a rectangular input pulse.

Figure 2.14 The output pulse of a

CR

differentiator for a rectangular input pulse.

Figure 2.15 The operational impedance of resistors, capacitors, and inductors.

Figure 2.16 Illustration of system stability from the system poles’ locations in the pole–zero plot.

Figure 2.17 Dependence of the frequency components of a rectangular pulse on its duration.

Figure 2.18 Impedance functions for resistors, capacitors, and inductors.

Figure 2.19 The input and output impedance of an amplifier.

Figure 2.20 The gain function for ideal and practical filters.

Figure 2.21 The absolute value and phase of the transfer function of an

RC

and a

CR

filters.

Figure 2.22 The unit step responses of a second‐order low‐pass filter for different values of

Q

.

Figure 2.23 (a) Series connection of two RC filters without isolation and (b) with isolation by a buffer amplifier.

Figure 2.24 The effect of noise on a detector pulse amplitude.

Figure 2.25 Illustration of Gaussian noise parameters.

Figure 2.26 (a) A noise signal in time domain. (b) The power spectral density of the noise signal.

Figure 2.27 Representation of a noise voltage and a noise current source.

Figure 2.28 Input and output noise signals of an LTI system.

Figure 2.29 Representation of thermal noise in a resistor with (a) a voltage noise source and (b) a current noise source.

Figure 2.30 Equivalent circuit of a real resistor with negligible parasitic inductance.

Figure 2.31 An amplifier noise model, where the noise is represented with a pair of noise sources at the input of a noiseless device.

Figure 2.32 The noise of an amplifier with resistor feedback.

Figure 2.33 The elements of creating an interference problem, a source of interference, a receptor, and a coupling channel.

Figure 2.34 Faraday cage with input and output for signal and detector bias.

Figure 2.35 Ground loop between two circuits.

Figure 2.36 (a) Ground loop acting as antenna and (b) minimizing the induction of signal in a ground loop by minimizing the enclosed area.

Figure 2.37 Interference due to a common ground.

Figure 2.38 Production of interference signals due to vibrations (microphonic noise) in a detector system.

Figure 2.39 The structure of a coaxial cable.

Figure 2.40 Schematic representation of a small portion of a transmission line [22].

Figure 2.41 Schematic representation of the response of a real cable to an input step pulse.

Figure 2.42 Some examples of pulse reflection scenarios.

Figure 2.43 The effect of reflection on the risetime of a pulse for different cable delays.

Figure 2.44 Step functions applied to a cable mismatched on both ends.

Figure 2.45 (a) Elimination of reflections in splitting a pulse by two cables. (b) Equivalent circuit looking from the end of the first cable.

Figure 2.46 Circuit diagram of a simple active splitter [26].

Figure 2.47 An illustration of a typical logic pulse.

Figure 2.48 Truth tables and electronic symbols of some common logic gates.

Figure 2.49 The logic symbol of a flip‐flop and an SR flip‐flop made from a pair of cross‐coupled NOR gates.

Figure 2.50 A crossed NOR flip‐flop.

Chapter 03

Figure 3.1 (a) Basic elements of a charge‐sensitive preamplifier. (b) The equivalent circuit with a detector connected to the input.

Figure 3.2 (a) An operational amplifier with an impedance connecting output to input. (b) The equivalent circuit.

Figure 3.3

n

‐Channel JFET cross section and its symbol.

Figure 3.4 The dependence of

I

d

on

V

ds

for different values of

V

gs

in a JFET.

Figure 3.5 (a) Field effect transistor equivalent circuits. (b) Modified circuit at high frequencies.

Figure 3.6 An enhancement mode MOSFET and its symbol.

Figure 3.7 A simplified model of detector–preamplifier.

Figure 3.8 First‐order model of operational amplifier behavior at high frequencies.

Figure 3.9 The effect of preamplifier risetime on the time profile of a charge pulse.

Figure 3.10 Standard charge‐sensitive preamplifier with resistive feedback. The block T.A. is a non‐inverting high‐gain transimpedance amplifier.

Figure 3.11 Preamplifier reset by continuous optical feedback.

Figure 3.12 A schematic representation of a pulsed optical feedback preamplifier.

Figure 3.13 A simplified diagram of transistor reset preamplifier system and the output waveform of the preamplifier.

Figure 3.14 An illustration of the continuous drain feedback preamplifier reset.

Figure 3.15 A schematic cross section of the Pentafet.

Figure 3.16 Preamplifier with clipping network and gain stage.

Figure 3.17 The common methods of detector and preamplifier coupling.

Figure 3.18 Two different approaches for ac coupling of detector and preamplifier.

Figure 3.19 Waveforms at the output of a charge‐sensitive preamplifier at high rates.

Figure 3.20 The arrangement for the application of test input and a simple protection circuit.

Figure 3.21 The charge‐sensitive loop of a preamplifier consisting of a JFET and a commercial op‐amp [41].

Figure 3.22 The basic structure of a current‐sensitive preamplifier.

Figure 3.23 Schematic diagram of a current‐sensitive preamplifier by using a charge‐sensitive loop.

Figure 3.24 Principles of a voltage‐sensitive preamplifier and its equivalent circuit. The detector is dc coupled.

Figure 3.25 (a) Parallel and series noises in a detector–preamplifier system. (b) The equivalent noise circuit with a single source of voltage noise.

Figure 3.26 (a) A detector and charge‐sensitive preamplifier connection and (b) its noise equivalent circuit.

Figure 3.27 The conversion of the series noise generators to their equivalent parallel noise generator.

Figure 3.28 The equivalent circuit of current‐sensitive preamplifier for noise analysis.

Figure 3.29 Noise analysis of a voltage‐sensitive preamplifier.

Figure 3.30 Preamplifier with paralleled FETs.

Figure 3.31 Relative weight of noise contributions from leakage currents and feedback resistor.

Figure 3.32 (a) Preamplifier reset by using a MOSFET in unsaturated region. (b) Preamplifier reset by pulsed reset mode.

Figure 3.33 ASIC preamplifier with adjustable gain, leakage current compensation, polarity section, and test input.

Figure 3.34 Block diagram of a preamplifier for a PMT with positive bias voltage.

C˳

is the capacitance of the anode to ground and

C

in

is the input capacitance of the preamplifier.

Figure 3.35 Block diagram of (a) an integrating and (b) transimpedance preamplifier for PMTs with negative bias (anode grounding).

C˳

is the capacitance of the anode to ground and

C

in

is the input capacitance of the preamplifier.

Figure 3.36 Photodiode–preamplifier connection and its equivalent circuit.

Figure 3.37 Classic approaches for the readout of a SiPM.

Chapter 04

Figure 4.1 Simplified block diagram of an MCA‐based energy spectroscopy system and signals waveforms in different stages.

Figure 4.2 (a) An ideal distribution of the amplitude of the pulses for the same amount of energy deposition in a detector. (b) A realistic distribution of the amplitude of the pulses described with a Gaussian function.

Figure 4.3 The effect of energy resolution on the separation of two close energy lines.

Figure 4.4 The effect of noise on the amplitude of pulses of the same original amplitude and the resulting pulse‐height distribution.

Figure 4.5 A comparison of the spectroscopic performance of LaBr

3

(Ce) and NaI(Tl) scintillation gamma‐ray detectors.

Figure 4.6 The ballistics deficit effect caused by finite risetime of pulses.

Figure 4.7 (a) Illustration of tail pulse pileup event and (b) head pulse pileup event.

Figure 4.8 Baseline shift in CR coupling networks.

Figure 4.9 Signal and noise at the input of a filter and the output signal and noise mean square.

Figure 4.10 Equivalent circuit of a charge measurement system for deriving the optimum shaper. The original noise sources are at the input of a noiseless preamplifier followed by a noiseless shaper.

Figure 4.11 Finding the optimum filter by splitting the filtration into a whitening step and a matched filter.

Figure 4.12 The input and output of optimum filter. The output has a cusp shape with infinite length.

Figure 4.13 (a) Finite cusp filter and (b) a finite cusp filter with a flattop region.

Figure 4.14 (a) The optimum filter in the presence of 1/

f

noise and (b) optimum filter with finite width.

Figure 4.15 (a)

CR–RC

pulse shaper and (b) its step pulse response.

Figure 4.16 Realization of a

CR

–(

RC

)

n

pulse shaper.

Figure 4.17 Step response of

CR

–(

RC

)

n

filters of different order.

Figure 4.18 First‐order active differentiator and integrators.

Figure 4.19 Two examples of second‐order active integrators for realizing Gaussian shapers.

Figure 4.20 A comparison of a bipolar and monopolar pulse of the same peaking time.

Figure 4.21 A block diagram of delay‐line pulse shaper.

Figure 4.22 A block diagram of trapezoidal filter circuit.

Figure 4.23 Trapezoidal filter output for inputs of different risetime.

Figure 4.24 Block diagram of gated integrator.

Figure 4.25 The signal waveforms at different stages of a gated integrator with semi‐Gaussian prefilter when it is fed with a pulse from a semiconductor detector.

Figure 4.26 An equivalent circuit for the calculation of the equivalent noise charge.

Figure 4.27 (a) Variations of

ENC

and its components with shaper’s time constant. (b) The effect of increase in series noise on the location of noise corner and (c) the effect of parallel noise on the location of noise corner.

Figure 4.28 An experimental arrangement for

ENC

measurement.

Figure 4.29 Noise analysis in time domain.

Figure 4.30 Basic pole‐zero cancellation circuit.

Figure 4.31 The preamplifier pulse and waveforms before and after pole‐zero cancellation.

Figure 4.32 A common pole‐zero cancellation circuit used in shaping amplifiers.

Figure 4.33 Principle of baseline restorer.

Figure 4.34 Pulse pileup detection.

Figure 4.35 (a) Operation of an integral discriminator and (b) differential discriminator or SCA.

Figure 4.36 Basics of an SCA.

Figure 4.37 Two ways of operating linear gates. In the upper part, a linear gate transmits a signal when it is accompanied with a logic pulse. In the lower part, linear gate blocks the signal if it is accompanied with a logic pulse.

Figure 4.38 Simplified peak stretcher circuit.

Figure 4.39 The operation of a peak‐sensing ADC.

Figure 4.40 Principle of a Wilkinson‐type ADC.

Figure 4.41 The block diagram of a successive‐approximation ADC.

Figure 4.42 Block diagram of successive‐approximation ADC with standard sliding scale linearization.

Figure 4.43 Block diagram of a flash ADC.

Figure 4.44 The block diagram of a classic MCA.

Figure 4.45 A block diagram of a multichannel buffer.

Figure 4.46 Illustration of the extendable and non‐extendable dead‐time models.

Figure 4.47 The variation of output rate as a function of input rate according to the two dead‐time models.

Figure 4.48 Major sources of dead time in a spectroscopy system.

Figure 4.49 Illustration of sources of dead time in a combination of pulse shaper and ADC.

Figure 4.50 A multichannel ASIC pulse processing system.

Figure 4.51 CMOS pole‐zero cancellation.

Figure 4.52 Some of the common filter topologies in ASIC systems.

Figure 4.53 A classic CMOS peak‐hold circuit.

Figure 4.54 (Top) Principle of time‐over‐threshold method. (Bottom) The dependence of ToT at the shaper output on the pulse amplitude.

Chapter 05

Figure 5.1 An illustration of detector operation in current mode.

Figure 5.2 A basic pulse counting system.

Figure 5.3 The basics of an analog count ratemeter.

Figure 5.4 A diode pump circuit.

Figure 5.5 The diode pump ratemeter combined with feedback amplifier.

Figure 5.6 A simplified circuit of a logarithmic ratemeter.

Figure 5.7 Typical signal readout methods of a GM counter. (a) Pulse readout from the anode side. (b) Pulse readout from the cathode side.

Figure 5.8 An equivalent circuit of a GM counter [17].

Figure 5.9 A hybrid dead‐time model for GM counters [19].

Figure 5.10 The use of a buffer circuit for remote probe systems.

Figure 5.11 Block diagram of a quenching circuit using a switchable power supply.

Figure 5.12 (a) Direct measurement of the output current of a detector. (b) An indirect measurement of the current by measuring the voltage drop on a load resistor by using an electrometer. The resistor

R

c

is the external resistor,

C

d

is the detector capacitance, and

R

e

and

C

e

are intrinsic resistance and capacitances of the electrometer. (c) The indirect measurement of current by integrating the current on a load capacitor.

Figure 5.13 (a) A shunt‐type current‐measuring electrometer. (b) A feedback‐type current‐measuring electrometer.

Figure 5.14 (a) A shunt‐type current integrator. (b) A feedback‐type current integrator.

Figure 5.15 A schematic of a digital electrometer.

Figure 5.16 The Townsend balance method.

Figure 5.17 An ionization chamber with guard rings.

Figure 5.18 (Top) A block diagram of current‐to‐frequency converter. (Bottom) the outputs of integrator for two different input currents.

Figure 5.19 A circuit for logarithmic current readout.

Figure 5.20 Schematic of a multichannel integrating mode ASIC.

Figure 5.21 Schematic of a photon counting system of pixel detectors.

Figure 5.22 A block diagram of a channel on ASIC with multi thresholds.

Figure 5.23 A functional block diagram for Campbell mode signal readout.

Figure 5.24 A practical Campbell mode signal readout system.

Figure 5.25 Reactor neutron flux measurement over a wide dynamic range by detectors operating in three different modes.

Figure 5.26 Operation of fission chamber in counting–Campbell mode.

Chapter 06

Figure 6.1 Some examples of time‐difference measurements between two detectors and the corresponding distributions of time differences under ideal measurement conditions (see text for details).

Figure 6.2 A simple block diagram of a typical time spectrometer.

Figure 6.3 A coincidence time spectrum.

Figure 6.4 A system for selecting timing events lying in a time window by using a SCA.

Figure 6.5 Selection of events lying in a time window with a coincidence unit.

Figure 6.6 The relation of the output logic pulse of a time discriminator and the arrival time of the input pulse. Since generation of the logic pulse at time

T

∘

is not possible, the logic pulse is generated at time

T

1

while

T

1

has a precise and constant relation to

T

∘

.

Figure 6.7 (a) Principle of operation and (b) the basic structure of a leading‐edge time discriminator.

Figure 6.8 The effect of noise‐induced jitter on the time pick‐off uncertainty.

Figure 6.9 Illustration of time‐walk in a leading‐edge discriminator due to amplitude and risetime variations of input pulses.

Figure 6.10 Schematic illustration of time‐walk due to charge sensitivity of a leading‐edge discriminator. The trigger time for pulse 1 from

T

∘

moves to

T

1

due to the required charge determined by area

S

.

Figure 6.11 Timing diagram of extrapolating leading‐edge time discriminator.

Figure 6.12 Block diagrams for a CFD pulse timing.

Figure 6.13 CFD pulse shaping.

Figure 6.14 Signal waveforms in ARC timing mode CFD for ideal linear rising input pulses.

Figure 6.15 The block diagram of some commercial CFD designs by ORTEC [7, 9].

Figure 6.16 Some CFD shaping methods for integrated time pick‐off systems [30–33].

Figure 6.17 Block diagram of a timing filter amplifier.

Figure 6.18 Methods of time pick‐off from a slow pulse. (a) Zero‐crossing of double‐differentiated pulse. (b) Double delay‐line method. (c) Trailing‐edge constant fraction discrimination.

Figure 6.19 The basic configuration of a simple TAC.

Figure 6.20 Block diagram of a differential current‐mode TAC [45].

Figure 6.21 Timing diagram of a counter‐based TDC and interpolation method.

Figure 6.22 Timing diagram of a TDC with vernier principle.

Figure 6.23 An AND gate representing an overlap coincidence unit with two inputs (left) and a simple AND gate circuit based on diodes and resistors (right). If no pulses arrive at inputs, then the diodes will be conducting and the output voltage will be maintained at zero. If a pulse of amplitude

V

∘

arrives at input channels, the diodes in the other channel will continue to conduct and the output of the system will remain at zero. But if all input logic pulses arrive simultaneously, no diode will conduct and a logic pulse of amplitude

V

∘

will now be generated at the output of the circuit, indicating that a coincidence has been detected.

Figure 6.24 An anticoincidence circuit.

Figure 6.25 A schematic diagram of a lumped delay line.

Figure 6.26 Schematic diagram of a neutron time‐of‐flight spectrometer with neutron beam chopper.

Figure 6.27 A basic setup for the measurement of the time resolution of a detector(s).

Figure 6.28 The intrinsic time resolution of a scintillator.

Figure 6.29 An illustration of variations in light collection times on the time response of a scintillator.

Figure 6.30 The time response of a PMT to a δ‐function incident light pulse.

Figure 6.31 Fast–slow measurements with scintillator detectors.

Figure 6.32 Block diagram of a timing setup with scintillators coupled to photodiodes and APDs.

Figure 6.33 A setup for time resolution measurement of a germanium detector.

Figure 6.34 Arrangement for simultaneous derive of charge and current pulses from a silicon detector.

Chapter 07

Figure 7.1 The definition of spatial resolution.

Figure 7.2 Principles of position sensing with ionization detectors.

Figure 7.3 Principles of position sensing with scintillator detectors.

Figure 7.4 The inter‐pixel capacitances.

Figure 7.5 The effect of adjacent preamplifiers on the electronic noise.

Figure 7.6 Cross talk in a segmented electrode detector.

Figure 7.7 The error in the position measurement with a pixel or strip detector.

Figure 7.8 Schematic representation of the components of a transmission line.

Figure 7.9 Equivalent circuit of a resistive electrode detector and preamplifier for noise analysis.

Figure 7.10 The signal readout for position sensing with a semiconductor detector equipped with continuous resistive electrode.

Figure 7.11 Principle of an analog pulse divider.

Figure 7.12 Signal processing scheme for position sensing with digital charge divider.

Figure 7.13 Two‐dimensional position‐sensitive detectors with continuous resistive electrode.

Figure 7.14 An

x–y

distribution of a uniformly irradiated pincushion semiconductor detector. A strong distortion of the image is resulted from the nonlinear process of charge splitting.

Figure 7.15 Discrete charge division with resistor and capacitive network.

Figure 7.16 Equivalent circuits of resistive and capacitive charge dividers.

Figure 7.17 Two‐dimensional position sensing with discrete charge division.

Figure 7.18 Two‐dimensional position sensing with a combination of continuous and discrete charge division.

Figure 7.19 (Left) Splitting PMT output by using resistors. (Right) The principle of position sensing in a scintillation camera with seven PMTs.

Figure 7.20 Position multiplexing circuit with a resistor network.

Figure 7.21 The symmetric charge division multiplexing technique for a 4 × 4 input array.

Figure 7.22 Block diagram of the electronic circuit for position sensing with risetime method.

Figure 7.23 The principles of delay‐line position sensing.

Figure 7.24 Position interpolation with lumped parameter delay line.

Figure 7.25 An equivalent circuit of preamplifier and delay‐line connection [78].

Chapter 08

Figure 8.1 Scintillation light pulses from an organic scintillator initiated by particles with different rates of energy loss.

Figure 8.2 Definition of figure of merit (FOM).

Figure 8.3 Principle of a double pulse‐shaper method for risetime discrimination of charge pulses.

Figure 8.4 A basic block diagram for charge‐comparison method by using QDCs.

Figure 8.5 The scatterplot of the slow channel output vs. the pulse‐shape discrimination parameter for a planar CdTe detector. A strong pulse deficit as a function of discrimination parameter is apparent.

Figure 8.6 Pulse‐shape discrimination of charge pulses based on a comparison of the amplitude of charge and current pulses. The slow pulse shown in the upper part of the figure produces a current pulse smaller than the amplitude of the attenuated charge pulse, while for the fast pulse shown in the lower part, the amplitude of the current pulse exceeds the attenuated pulse amplitude [24].

Figure 8.7 Schematic diagram of the electronic circuit to derive the energy and Bragg peak information of incident particles from the anode of a BCC.

Figure 8.8 The conversion of scintillation pulses to bipolar pulses through

CR

differentiation.

Figure 8.9 The dependence of zero‐crossing time to the pulse risetime and amplitude in double delay‐line shaping.

Figure 8.10 PMT current pulses of different decay time constant and the corresponding pulses after an integrating preamplifier.

Figure 8.11 An example block diagram of pulse‐shape discrimination with scintillation detectors based on zero‐crossing of double delay‐line shaped pulses.

Figure 8.12 A zero‐crossing pulse‐shape discrimination circuit for particle identification with silicon detectors [37, 38].

Figure 8.13 Block diagram for a direct estimate of pulse risetime.

Figure 8.14 The reflection of risetime in single delay‐line pulse shaping.

Chapter 09

Figure 9.1 Structure of a DSP radiation measurement system.

Figure 9.2 The waveforms illustrating the sampling and quantization.

Figure 9.3 Quantized versions of an analog detector pulse with different number of quantization levels.

Figure 9.4 An illustration of aliasing error.

Figure 9.5 Transfer function of an ideal and a perfect ADC.

Figure 9.6 ADC diagram.

Figure 9.7 The gain and offset errors in ADCs.

Figure 9.8 Illustration of nonlinearities in an ADC.

Figure 9.9 The effect of clock jitter on low‐frequency and high frequency signals.

Figure 9.10 Block diagram representation of a discrete‐time system.

Figure 9.11 Schematic representation of basic operations on sequences (a) modular, (b) adder, (c) multiplier, (d) unit delay, (e) unit advance, and (f) pick‐off node.

Figure 9.12 (a) The unit step function and (b) the unit impulse function.

Figure 9.13 Representing a digital signal as a set of weighted, shifted unit impulses.

Figure 9.14 An example describing digital convolution.

Figure 9.15 Time domain behavior of a single real‐pole casual system as a function of the pole location with respect to the unit circle.

Figure 9.16 (a) The outputs of a digital

CR

differentiator and (b) an

RC

integrator filters implemented by using Eqs. 9.49 and 9.50.

Figure 9.17 Realization diagram of a low‐pass filter with difference equation of Eq. 9.57.

Figure 9.18 The effect of moving average filters with different number of points on a detector pulse.

Chapter 10

Figure 10.1 A basic block diagram of a digital radiation measurement system.

Figure 10.2 A block diagram of an analog signal conditioning unit.

Figure 10.3 A system diagram for offline digital signal processing of a detector signals.

Figure 10.4 A basic structure of a digital system by using an FIFO to increase the rate capability.

Figure 10.5 A diagram of digital processing system with internal trigger and parallel processing for extracting various parameters from sampled pulses on FPGA.

Figure 10.6 A mixed analog–digital spectroscopy system.

Figure 10.7 Common functions in a fully digital spectroscopy system.

Figure 10.8 The correction of preamplifier decay time.

Figure 10.9 The trapezoidal shaping with MWD technique.

Figure 10.10 The trapezoidal shaping of an input exponential pulse. The output is the convolution of input pulse and the impulse response.

Figure 10.11 Trapezoidal shaping of an input exponential pulse with finite risetime. The parameters governing the filter’s risetime and flattop length are also shown.

Figure 10.12 The input and output of a cusp‐like filter.

Figure 10.13 The output of a digital finite cusp filter with a flattop region.

T

is the sampling interval.

Figure 10.14 The outputs of

CR

–(

RC

)

n

filters for

n

 = 1–4.

Figure 10.15 The separation of close PMT pulses with digital delay‐line shaping.

Figure 10.16 Baseline estimation by using the samples in a time window prior to pulse.

Figure 10.17 A simple digital trigger based on amplitude threshold.

Figure 10.18 The output of a fast trapezoidal filter for event identification.

Figure 10.19 A common method of digital pileup detection. According to the pileup inspection window, events 1, 2, 5, and 6 are pileup events.

Figure 10.20 Reconstruction of pileup events by fitting the recorded waveform with a scintillation pulse model.

Figure 10.21 The principles of digital pulse timing.

Figure 10.22 Arrangements for offline pulse timing.

Figure 10.23 A conceptual diagram illustrating the sampling and signal reconstruction. (a) Spectrum of the original signal. (b) Fourier transform of the discrete signal with

f

s

 > 2

f

max

. (c) Fourier transform of the discrete signal with

f

s

 < 2

f

max

. (d) An ideal low‐pass filter in time domain (sinc function).

Figure 10.24 Illustration of signal up‐sampling by a factor of three using a two stage process of zero add and digital low‐pass filtration.

Figure 10.25 A digital leading‐edge discriminator with linear interpolation.

Figure 10.26 The time pick‐off from a digital constant‐fraction zero‐crossing pulse.

Figure 10.27 The error resulted from the variations in the arrival times of pulses of nonlinear shape with respect to the ADC sampling phase.

Figure 10.28 (a) The maximum rise interpolation method and (b) the initial rise interpolation timing method.

Figure 10.29 The loss of timing information due to low sampling rate. The top figure shows two fast photomultiplier pulses with close time distance. The bottom figure shows the same pulses at reduced sampling rate. As a result of insufficient sampling rate, the start time of two pulses appears exactly at the same time.

Figure 10.30 The effect of ADC bit resolution on the timing accuracy.

Figure 10.31 Two common methods of the implementation of standard charge‐comparison method in digital domain. (a) The total charge contained in the entire pulse and the charge in the tail are compared. (b) The charge contained in the entire pulse and the charge contained in the fast component of the pulse are compared.

Figure 10.32 The magnitude of the Fourier transform of gamma‐ray and neutron pulses from a liquid scintillator. A difference in the frequency spectra is clear at low frequencies.

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Signal Processing for Radiation Detectors

Mohammad Nakhostin

This edition first published 2018© 2018 John Wiley & Sons, Inc.

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Library of Congress Cataloguing‐in‐Publication Data

Names: Nakhostin, Mohammad, 1973– author.Title: Signal processing for radiation detectors / by Mohammad Nakhostin.Description: Hoboken, NJ, USA : Wiley, 2018. | Includes bibliographical references and index. |Identifiers: LCCN 2017023307 (print) | LCCN 2017024048 (ebook) | ISBN 9781119410157 (pdf) | ISBN 9781119410164 (epub) | ISBN 9781119410140 (hardback)Subjects: LCSH: Nuclear counters. | Radioactivity–Measurement. | Signal processing.Classification: LCC QC787.C6 (ebook) | LCC QC787.C6 N35 2017 (print) | DDC 539.7/7–dc23LC record available at https://lccn.loc.gov/2017023307

Cover image: ©PASIEKA/Getty Images, Inc.Cover design by Wiley

To my daughter, Niki

Have patience. All things are difficult before they become easy. Saadi, Persian poet

Preface

Ionizing radiation is widely used in various applications in our modern life, including but not limited to medical and biomedical imaging, nuclear power industry, environmental monitoring, industrial process control, nuclear safeguard, homeland security, oil and gas exploration, space research, materials science research, and nuclear and particle physics research. Radiation detectors are essential in such systems by producing output electric signals whenever radiation interacts with the detectors. The output signals carry information on the incident radiation and, thus, must be properly processed to extract the information of interest. This requires a good knowledge of the characteristics of radiation detectors’ output signals and their processing techniques. This book aims to address this need by (i) providing a comprehensive description of output signals from various types of radiation detectors, (ii) giving an overview of the basic electronics concepts required to understand pulse processing techniques (iii), focusing on the fundamental concepts without getting too much in technical details, and (iv) covering a wide range of applications so that readers from different disciplines can benefit from it. The book is useful for researchers, engineers, and graduate students working in disciplines such as nuclear engineering and physics, environmental and biomedical engineering, medical physics, and radiological science, and it can be also used in a course to educate students on signal processing aspects of radiation detection systems.

Guildford, Surrey, UKJuly 2017Mohammad Nakhostin

Acknowledgement

I owe a special debt of gratitude to some individuals who have had a strong personal influence on my understanding of the topics covered in this book. They include Profs. M. Baba and K. Ishii and Drs. K. Hitomi, M. Hagiwara, T. Oishi, Y. Kikuchi, M. Matsuyama, and T. Sanami from the Tohoku University in Japan. I would like to extend my appreciation to the people at the University of Surrey, United Kingdom, for hosting me during the last couple of years. I should also thank Dr. A. Merati for his help with the preparation of the text. I am thankful to Brett Kurzman, Victoria Bradshaw, Kshitija Iyer, and Viniprammia Premkumar at John Wiley & Sons, in the United States and India for handling this project and for their advice on shaping the book. Finally, I gratefully acknowledge that the completion of this book could not have been accomplished without the support and patience of my spouse, Maryam.

1Signal Generation in Radiation Detectors

Understanding pulse formation mechanisms in radiation detectors is necessary for the design and optimization of pulse processing systems that aim to extract different information such as energy, timing, position, or the type of incident particles from detector pulses. In this chapter, after a brief introduction on the different types of radiation detectors, the pulse formation mechanisms in the most common types of radiation detectors are reviewed, and the characteristics of detectors’ pulses are discussed.

1.1 Detector Types

A radiation detector is a device used to detect radiation such as those produced by nuclear decay, cosmic radiation, or reactions in a particle accelerator. In addition to detecting the presence of radiation, modern detectors are also used to measure other attributes such as the energy spectrum, the relative timing between events, and the position of radiation interaction with the detector. In general, there are two types of radiation detectors: passive and active detectors. Passive detectors do not require an external source of energy and accumulate information on incident particles over the entire course of their exposure. Examples of passive radiation detectors are thermoluminescent and nuclear track detectors. Active detectors require an external energy source and produce output signals that can be used to extract information about radiation in real time. Among active detectors, gaseous, semiconductor, and scintillation detectors are the most widely used detectors in applications ranging from industrial and medical imaging to nuclear physics research. These detectors deliver at their output an electric signal as a short current pulse whenever ionizing radiation interacts with their sensitive region. There are generally two different modes of measuring the output signals of active detectors: current mode and pulse mode. In the current mode operation, one only simply measures the total output electrical current from the detector and ignores the pulse nature of the signal. This is simple but does not allow advantage to be taken of the timing and amplitude information that is present in the signal. In the pulse mode operation, one observes and counts the individual pulses generated by the particles. The pulse mode operation always gives superior performance in terms of the amount of information that can be extracted from the pulses but cannot be used if the rate of events is too large. Most of this book deals with the operation of detectors in pulse mode though the operation of detectors in current mode is also discussed in Chapter 5. The principle of pulse generation in gaseous and semiconductor detectors, sometimes known as ionization detectors, is quite similar and is based on the induction of electric current pulses on the detectors’ electrodes. The pulse formation mechanism in scintillation detectors involves the entirely different physical process of producing light in the detector. The light is then converted to an electric current pulse by using a photodetector. In the next sections, we discuss the operation of ionization detectors followed by a review of pulse generation in scintillation detectors and different types of photodetectors.

1.2 Signal Induction Mechanism

1.2.1 Principles

In gaseous and semiconductor detectors, an interaction of radiation with the detector’s sensitive volume produces free charge carriers. In a gaseous detector, the charge carriers are electrons and positive ions, while in the semiconductor detectors electrons and holes are produced as result of radiation interaction with the detection medium. In such detectors, an electric field is maintained in the detection medium by means of an external power supply. Under the influence of the external electric field, the charge carriers move toward the electrodes, electrons toward the anode(s), and holes or positive ions toward the cathode(s). The drift of charge carriers leads to the induction of an electric pulse on the electrodes, which can be then read out by a proper electronics system for further processing. To understand the physics of pulse induction, first consider a charge q near a single conductor as shown in Figure 1.1. The electric force of the charge causes a separation of the free internal charges in the conductor, which results in a charge distribution of opposite sign on the surface of the conductor. The geometrical distribution of the induced surface charge depends on the position of the external charge q with respect to the conductor. When the charge moves, the geometry of charge conductor changes, and therefore, the distribution of the induced charge varies, but the total induced charge remains equal to the external charge q. We now consider a gaseous or semiconductor detector with a simple electrode geometry including two conductors as shown in Figure 1.2. If an external charge q is placed at distance x∘ from one electrode, charges of opposite sign with the external charge are induced on each electrode whose amount and distribution depends on the distance of the external charge from the electrode [1]:

(1.1)

and

(1.2)

where d is the distance between the two electrodes. When the external charge moves between the electrodes, the induced charge on each electrode varies, but the sum of induced charges remains always equal to the external charge q = q1 + q2. If two electrodes are connected to form a closed circuit, the changes in the amount of induced charges on the electrodes lead to a measurable current between the electrodes. As it is illustrated in Figure 1.2, when the external charge is initially close to the upper electrode, most of the field strength will terminate there and the induced charge will be correspondingly higher, but as the charge moves toward the lower electrode, the charge induced on the lower electrode increases. This means that the polarity of outgoing charges from electrodes or the observed pulses are opposite. In general, the polarity of the induced current depends on the polarity of the moving charge and also the direction of its movement in respect to the electrode. As a rule, one can remember that a positive charge moving toward an electrode generates an induced positive signal; if it moves away, the signal is negative and similarly for negative charge with opposite signs. In a radiation detector, a radiation interaction produces free charge carriers of both negative and positive signs. The motion of positive and negative charge carriers toward their respective electrodes increases their surface charges, the cathode toward more negative and the anode toward more positive, but by moving the charge away from the other electrode, the charge of opposite polarity is induced on that electrode. The total induced charge on each electrode is due to the contributions from both types of charge carriers, which are added together due to the opposite direction and opposite sign of the charges.

Figure 1.1 The induction of charge on a conductor by an external positive charge q (top) and the density of the induced surface charge on the conductor (bottom).

Figure 1.2 The induction of current by a moving charge between two electrodes. When charge q is close to the upper electrode, the electrode receives larger induced charge, but as the charge moves toward to the bottom electrode, more charge is induced on that electrode. If the two electrodes are connected to form a closed circuit, the variations in the induced charges can be measured as a current.

The start of a detector output pulse, in most of the situations, is the moment that radiation interacts with the detector because the charge carriers immediately start moving due to the presence of an external electric field. The pulse induction continues until all the charges reach the electrodes and get neutralized. Therefore, the duration of the current pulse is given by the time required for all the charge carriers to reach the electrodes. This time is called the charge collection time and is a function of charge carriers’ drift velocity, the initial location of charge carriers, and also the detector’s size. The charge collection time can vary from a few nanoseconds to some tens of microseconds depending on the type of the detector. By integrating the current pulse generated in the detector, a net amount of charge is produced, which would be equal to the total released charge inside the detector if all the charge carriers are collected by the electrodes. In most of the detectors, there is a unique relationship between the energy deposited by the radiation and the amount of charge released in the detector, and therefore, the deposited energy can be obtained from the integration of the output current pulse. Figure 1.3 shows the induced pulses when a detector’s electrode is segmented. The amplitude of the pulse induced on each segment will depend upon the position of the charge with respect to the segment. As the charge gets closer to the electrode, the charge distribution becomes more peaked, concentrating on fewer segments. Therefore, with a proper segmentation of the electrode, one can obtain information on the location of radiation interaction in the detector by analyzing the induced signals on the electrode’s segments. This is called position sensing and such detectors are called position sensitive. Detectors with electrodes divided to pixels or strips are the most common types of designs for position sensing in radiation imaging applications. It should be also mentioned that the induction of signal on a conductor is not limited to the electrodes that maintain the electric field in the detector. In fact, any conductor, even without connection to the power supply, can receive an induced signal. This property is sometimes used to acquire extra information on the position of incident particles on the detectors.

Figure 1.3 The induction of pulses on the segments of an electrode. In a segmented electrode, charge is initially induced on many segments, but as the charge approaches the electrode, the largest signal is received by the segment, which has the minimum distance with the charge.

The induced charge on an electrode by a moving charge q can be computed by using the electrostatic laws. This approach is illustrated in Figure 1.4 where the charge q is shown in front of an electrode. The induced charge Q on the electrode can be calculated by using Gauss’s law. Gauss’s law says that the induced charge on an electrode is given by integrating the normal component of the electric field E over the Gaussian surface S that surrounds the surface of the electrode:

(1.3)

where ε is the dielectric constant of the medium. The time‐dependent output signal of the detector can be obtained by calculating the induced charge Q on the electrode as a function of the instantaneous position of the moving charges between the electrodes of the detector. However, this calculation process is very tedious because one needs to calculate a large number of electric fields corresponding to different locations of charges along their trajectory to obtain good precision. A more convenient method for the calculation and description of the induced pulses is to use the Shockley–Ramo theorem. The method is described in the next section, and its application to some of the common types of gaseous and semiconductor detectors are shown in Sections 1.3.1 and 1.3.2.

Figure 1.4 The calculation of induced charge on an electrode by using Gauss’s law.

1.2.2 The Shockley–Ramo Theorem

Shockley and Ramo separately developed a method for calculating the charge induced on an electrode in vacuum tubes [2, 3], which was then used for the explanation of pulse formation in radiation detectors. Since then, several extensions of the theorem have been also developed, and it was proved that the theorem is valid under the presence of space charge in detectors. The proof and some recent reviews of the Shockley–Ramo theorem can be found in Refs. [4–6]. In brief, the Shockley–Ramo theorem states that the instantaneous current induced on a given electrode by a moving charge q is given by

(1.4)

and the total charge induced on the electrode when the charge q drifts from location xi to location xf is given by

(1.5)

In the previous relations, v is the instantaneous velocity of charge q and φ∘ and E∘ are, respectively, called the weighting potential and the weighting field. The weighting field and the weighting potential are a measure of electrostatic coupling between the moving charge and the sensing electrode and are the electric field and potential that would exist at q’s instantaneous position x