UNIVERSITY OF BERGEN. PET detector. The building of a 3x3 matrix prototype PET detector. Tjalve Svendsen Steffen Mæland Rune Hauge

Transcription

1 UNIVERSITY OF BERGEN PET detector The building of a 3x3 matrix prototype PET detector Tjalve Svendsen Steffen Mæland Rune Hauge

2 P a g e 1 Table of contents 1 Introduction Theoretical background Scintillation PET-scanners Materials and equipment Photodetectors Pre-amplification Scintillating crystals UV-LED pulser The setup The printed circuit board (PCB) The aluminum casing Initial testing MPPC testing Data acquisition The experimental setup Measurements and results Qualitative analysis of output signal Quantitative analysis estimating number of detected photons Crosstalk Conclusion and outlook References Appendix The PCB schematic The PCB single schematic The PCB layout The aluminum casing 3d model MPPC datasheet... 21

3 List of Abbreviations P a g e 2 Abbreviations ADC APD CT MPPC PET PMT DAQ LED Description Amalog-to-Digital Converter Avalanche Photodiode Computed Tomography MultiPixel Photon Counter Positron Emission Tomography Photomultiplier Tube Data Acquisition System Light Emitting Diode

4 P a g e 3 1 INTRODUCTION In this paper we will look at the making of a simple scintillation detector, consisting of an array of nine crystals coupled to silicon photodetectors. The photodetectors are then connected to a PCB circuit board containing pre-amplifiers which amplifies the signals and sends it via an ADC (Analog to Digital Converter) to a computer for the signal readout in LabView. The goal of this project has been to design and build such a setup and make it proper for testing of different crystals. An important part of this has been to make a box as lightproof as possible and put the electronics and the photodetectors inside. The crystals have to be individually wrapped with aluminum tape so the crystals will not affect one another. There will, however, always be some physical crosstalk between them, which has to be measured. One of the settings where these kinds of detectors are being used is in the so-called PET-scanners at hospitals. The PET (Positron Emission Tomography) technology makes it possible to find out where more active cells, like tumor cells, are located inside a patient s body. This technology (especially used combined with CT-scanners) has in many ways revolutionized tumor imaging in that sense that it makes it possible to get an image of a tumor in 3-D. The scintillation detector is also central at the LHC project at CERN, for instance at the PHOS (PHOton Spectrometer) experiment at ALICE, consisting of crystals. Here, the purpose is to detect highenergy photons created in collisions and decay processes, and make it possible to measure their energy. 2 THEORETICAL BACKGROUND 2.1 SCINTILLATION When gammas traverse matter such as the crystals, they can be absorbed after interacting with the atoms inside. The energy transferred from the gammas excites electron-hole pairs in solid structures which recombine of localized centers. This will lead to the emission of visible light which can be detected by the photodetectors. The number of excited states will be depending of the energy of the incoming gamma. Therefore the number of scintillation light photons will be proportional to the energy of the incoming radiation. The gammas can interact with matter in different ways. One is, as described above, the photoelectric effect. Other important interactions are Compton scattering and pair production. Photoelectric effect is when a photon interacts with, and transfers all its energy to a bound electron so that the electron is ejected from the atom. The photoelectron will move away from the atom with a kinetic energy equal to the energy of the incoming photon minus the binding energy between the electron and the atom. Compton scattering is when an incoming photon interacts with an electron and transfer some of its energy to the electron. The photon then continues its movement, but with less energy and with a different direction. The electron will move away from the atom with kinetic energy equal to the energy transferred from the photon minus the binding energy between the electron and the atom. The direction of the outgoing electron will be according to the photons in such a way that resultant movement of the two correspond to the movement of the incoming photon.

5 P a g e 4 Illustration 2.1: Compton scattering. The incoming photon is being scattered and transfers some of its energy to the electron If an incoming photon has energy greater than the rest energy of two electrons, it can convert into an electron-positron pair. This process is called pair production. Because it requires such high energies, this process will not be relevant as an interaction in our crystals. At LHC, however, with high-energetic photons, pair production is significant. A photon can also be scattered by an electron by colliding elastically with it so the photon changes direction. No energy has been transferred to the electron so this process does not lead to an excitation or ejection of the electron. This type of scattering is called Rayleigh scattering. 2.2 PET-SCANNERS A PET-scanner is basically a ring of these scintillating crystal detectors, where the patient is laid inside this ring. A radioactive tracer, most commonly fluorodeoxyglucose (FDG), is injected to the patient. Since more active cells like tumor cells need a lot of energy, they will try to get this energy from the tracer, which is a sugar. A result of this is that the tracer will attach to these cells. As it is unstable the FDG will decay ( ), and send out a positron. The positron will soon annihilate with an electron and two photons will be sent out in opposite directions. The detectors in opposite ends of the tube will detect these photons and give the line of which the annihilation has taken place. When two photons are detected within a certain time frame, the scanner will pick this out as a coincident. This gives us three possibilities for what has happened. First, of course, is the possibility of this being a true coincident, meaning the photons are traveling from an annihilation point without any scattering or other interactions. Second, a scattered coincident, is when one or both photons from the annihilation is being scattered by the patient s tissue on the way towards the detection points, making the line between them not over the actual point of annihilation. The third possibility is that two photons from different annihilations are detected within one timeframe. This is called a random coincident.

6 P a g e 5 Illustration 2.2: Three different coincident can occur when detecting photons within a timeframe in a PET-scanner. The outer circle represents the crystals, the oval is the patient s body, and the small dots are points of annihilation. The random and the scattered coincident will make the image of the tumor more blurry, and it is therefore desirable to exclude them out from the final image. This can partly be done by making better detectors. For instance will photons that undergo Compton scattering loose some of their energy, and if the crystals then have high energy resolution, it will be possible to distinguish scattered photons from non-scattered photons [Sæterstøl 2010]. 3 MATERIALS AND EQUIPMENT 3.1 PHOTODETECTORS In order for the scintillation light from the crystals to be detected and analyzed, it has to be converted to an electrical signal and amplified to voltage levels that suit the data acquisition equipment. For detecting scintillation light there are mainly two types of detectors in use; photomultiplier tubes (PMT) and semiconductors. Photomultiplier tubes have been around for decades and are commonly used in PET and for other purposes, but have their downsides in being quite large and having poor quantum efficiency, meaning only a small fraction (typically 20-30%) of incident photons will trigger a signal [Sæterstøl 2010]. This work will focus on semiconductor detectors. Semiconductors Semiconductor detectors do not only have higher quantum efficiency than PMTs, but can also be made considerably smaller in size; they have lower power consumption, and might become cheaper. Unlike PMTs they are insensitive to magnetic fields, which is a useful property if being used in particle accelerators or in combined PET/MRI (Magnetic Resonance Imaging) scans, where strong magnetic fields are present.

7 P a g e 6 A material s ability to conduct electricity depends on the structure of its energy bands. The energy levels of the electrons in a solid are grouped into bands which are either allowed or forbidden, as illustrated in figure A. Forbidden Allowed, empty Allowed, occupied (a) Conductor (b) Conductor (c) Insulator (d) Semiconductor Illustration 3.1: The energy bands of a conductor, semiconductor and insulator. Figure taken from [Tipler, Llewellyn 2008] In a conductor, the outer (valence) electrons can easily be moved to higher, unoccupied energy levels by applying an electrical field, which allows the electrons to move in the material. For the material in Illustration 3.1(a), electrons can be excited to nearby states since the valence band is only partially filled. Ill. 3.1 (b) shows another possible configuration for a conductor, where the valence band and the next allowed band, the conduction band, overlap. If these two bands are separated by a forbidden band, and the valence band is full, electrons cannot be moved to the conducting band unless exposed to a very strong electrical field. For field strengths lower than this dielectric breakdown strength, the material acts as an insulator. Ill. 3.1 (d) shows a material where the forbidden energy gap is small enough to allow for thermal excitation of electrons from the valence band to the conduction band. Once lifted to the conduction band the electron can be accelerated by an electric field, leaving a hole in the valence band free for nearby electrons to occupy. Filling the hole creates another one, making the hole act as a positive current moving in the direction of the applied field, while the negative electron moves in the other direction. For a pure semiconductor the number of electrons and holes are the same. This is however not the case if impurity atoms are added to the semiconducting material, a process known as doping. A doped semiconductor has discrete energy levels in the forbidden band, making it susceptible to either giving off more electrons than holes or creating more holes than electrons, depending on the impurity energy levels being close to the conduction band, or to the valence band. The first has negative charge carriers and is therefore called n- type semiconductor, while the latter has positive charge carriers and is called p-type. If bringing n- and p- type materials in contact with each other in a diode, some of the electrons in the n-type material will fill the holes in the p-side of the contacting surface, leaving a slight positive charge on the n-side. An electric field is established, accelerating any free charge carriers to one of the sides, and thereby creating a depleted region in the junction between the n- and p-side. If a photon hits a bound electron in the depleted area and excites it to the conduction band, the electron and hole will drift towards each of the sides and a current flow through the diode. This weak current can be amplified by applying a reverse bias voltage; by increasing the electric field in the junction, electron-hole pairs can be accelerated enough to generate secondary electron-hole pairs, which again can generate new pairs and so on. When operated in a specific voltage interval, the signal for the diode will be proportional to the energy of the incident photon. If

8 P a g e 7 counting the number of photons is more important than determining its energy, the bias voltage can be increased to the avalanche breakdown voltage, where the avalanche of electron-hole pairs grows exponentially. A photodiode operated this way is called a Geiger-mode Avalanche PhotoDiode (G-APD), and outputs an on/off signal when hit. After being triggered, the diode has a certain recovery time before it can detect a new hit. Hamamatsu 1x1 mm MPPC Our setup will take use of the S P multipixel photon counter (MPPC) produced by Hamamatsu. This device consists of 100 pixels spread over a 1x1 mm active area, where each pixel is a Geiger-mode avalanche photodiode. Supposing the incoming light has low intensity, so the time between two hits in a pixel is shorter than its recovery time, the output signal from the MPPC will be proportional to the number of detected photons. Some characteristics for the MPPC are: Parameter Value Explanation Photon detection efficiency 65 % Depends on wavelength, indicated value is for λ = 500 nm Operating voltage 70 V Each MPPC is calibrated at slightly different voltages, the value is specified on the individual packing Dark count 600 kcps Signals not generated by light, but by unwanted effects like thermal exitation Recovery time ns Gain The intrinsic amplification of the signal Table 3.1: Hamamatsu S P at 25 C. Data taken from producer s datasheet 3.2 PRE-AMPLIFICATION The output signal from each MPPC is relatively weak, and in order to be distinguishable from noise, it requires pre-amplification before being sent to the ADC. This is done by operational amplifiers attached to the same circuit board as the MPPCs, making a combined amplifying and readout circuit, with short signal wiring and compact size compared to having external amplifiers. When subjected to a voltage difference at the input terminals, the so-called op-amp basically multiply the difference by its gain. What is important for our use is that the gain can be set to specific values by altering resistance in the circuit, and that the gain is not affected by the frequency of the signal. We will be using model AD8000 made by Analog Devices. 3.3 SCINTILLATING CRYSTALS Scintillation can occur both in organic crystals, plastics, and gases; in PET, however, inorganic crystals are most commonly used. Among these are bismuth germanate (BGO), lutetium oxyorthosilicate (LSO), and lutetium-yttrium oxyorthosilicate (LYSO). For all detector purposes, a scintillator should have the following properties [Sæterstøl 2010]: - Short decay time. The faster the crystal emits light after absorbing a gamma ray, the sharper the signal pulse will be, making it easier to distinguish two subsequent hits. - High light output. This improves the signal pulse. - High stopping power. A high-density crystal, with high effective atomic number, is more likely to stop a gamma ray and is therefore said to have high stopping power. If being used in calorimeters, the light output from the crystal should also be strongly related to the energy deposited by the incoming radiation, known as good energy resolution. Not so relevant in our case,

9 P a g e 8 as we are only interested in detecting the number of incoming photons. The properties for some commonly used crystals are shown in Table 3.2. Crystal Density (g/cm 3 ) Decay time (ns) Light output (photons/mev) BGO 7, LYSO(Ce) 7, LSO(Ce) 7, LaBr 3 (Ce) 5, Table 3.2: Properties of some scintillating crystals. Parentheses indicate material used for doping. Data taken from [Sæterstøl 2010] Before selecting crystals for the detector setup, the availability of each type also has to be taken into consideration. At the Detector lab only BGO and LYSO crystals are at hand, and of these two only BGO are available in sufficient numbers of the same size. The detector setup can potentially be used as a platform for testing nine different crystals simultaneously, but as a PET prototype, it is essential for all crystals to have the same effective area and stopping power. Proper calibration of the DAQ system also requires each readout channel to be as identical as possible. Our crystal of choice for the initial setup will be 10x10x20 mm BGO. 3.4 UV-LED PULSER For testing the setup we will take use of a light emitting diode flashing in very short pulses at a constant frequency. The pulser, made by PhD student Njål Brekke, is capable of delivering pulses of down to 20 ns duration at variable intensities. A subtlety of this device is the possibility of interchanging the LED a blue LED will be used for initial MPPC testing (the MPPC is most sensitive to wavelengths 400 nm) while a LED flashing in the ultraviolet area will cause scintillation in the crystals and is convenient for testing the final detector setup. 4 THE SETUP 4.1 THE PRINTED CIRCUIT BOARD (PCB) A circuit board was needed in order to make the PET-detector. The board holds the AD8000 op-amps, capacitors, resistors, and pin-connectors needed to make the pre-amplifier. The board used in this task was made based on the circuit board design from Stian Sagevik. His design for a single MPPC pre-amp was added nine times onto the board, with all the pre-amp circuits powered from the same power supply, also on the board. The base-design and further designing of the board was done using Eagle (Easily Applicable Graphical Layout Editor) from Cadsoft (see Illustration 8.1, Illustration 8.2 and Illustration 8.3 in the appendix for design schematics and layout). The next step were to print out the circuit board layout and then to apply it on the PCB. By using UV-light, base and acid, only the desired areas of the board would be covered in copper. When the board had finished this step, the next task was to solder all the components onto the copper area of the board, according to the layout made in Eagle. This was done using a soldering iron by hand with the help of a microscope, for better view of the small components.

10 P a g e THE ALUMINUM CASING In order to make this experiment lightproof, and to have a rigid setup for the finished PET-detector, an aluminum casing to hold the PCB and the crystals was made. It was designed using Google Sketchup, and detailed sketches with measurements were sent to the mechanical workshop at the Department of Physics and Technology where the casing was built (design 3D-model can be seen in Illustration 8.4 in the appendix) The inside of the casing holds the circuit board with the MPPCs facing the top surface. This side had 9 holes drilled so that each MPPC was aligned with the outside top surface, hence getting best possible contact with the crystals placed on top. Optical gel was applied onto MPPCs for improved light connection between MPPCs and crystals. The side surfaces of the box had 20 holes drilled for the LEMO-connectors for all the in/out voltages running the circuit board. 4.3 INITIAL TESTING In addition to the frequently short-circuit testing during the soldering process, testing using a TTi QL355TP power supply and the Agilent MSO7054A oscilloscope was initiated as soon as all the components were soldered on. This revealed a significant power consumption in the pre-amp circuits, caused by high-frequency oscillations about MHz. These oscillations had their origin in the board design, and then intensified by the amplifiers. From this point the wires from the first pre-amp connecting it with the others were cut, so that only one would run during the testes, simplifying the troubleshooting. Countermeasures to the oscillations were shortening the length of the signal between the -IN pin and Feedback pin by moving the resistors as close to the amplifier as possible. Capacitors were also applied onto the board to act as dampers on the oscillations. Three capacitors with nf, nf and nf were soldered from each and pin on the amplifiers and connected with ground. These capacitor clusters were stressed to be as close to the amplifiers as possible to prevent the oscillations from occurring by shortening the way the signal had to travel. 4.4 MPPC TESTING After dealing with the oscillation problem, the focus was turned to testing the MPPCs on the board. This testing was performed in the black box made by Per-Ivar Lønne for his master thesis (see [Lønne 2010]), which provided a lightproof environment for the stripped PCB (aluminum box for this project was delayed). The setup for the MPPC-testing is shown in Illustration 4.1.

11 P a g e 10 BIAS V MPPC-testing setup Black box PCB circuit board /w single MPPC Signal generator LED pulser V V Oscilloscope Pre-amp power supply Illustration 4.1: The setup used for MPPC testing. The BIAS voltage was set to, using a Keithley 2635A sourcemeter. The pre-amp power supply was set to and, using the TTi QL355TP power supply. The pre-amp voltages were initially set to, but they were adjusted because of high power consumption at these voltages. To simulate a crystal emitting light, a fast LED pulser was used. For measuring of the signal out from the circuit board the Agilent MSO7054A oscilloscope was used. 4.5 DATA ACQUISITION The data acquisition system (DAQ) in this project was based on a Nuclear Instrumentation Module (NIM)- rack and a VersaModular Eurocard bus (VME)-rack with readout using National Instruments Labview. The VME-rack contained a PCI-bridge which was connected to the PCI-card on the computer with NI Labview running. The rack also contained two Analogue to Digital Converter (ADC) cards, of the type CAEN V1729A Switched-Capacitor Digitizer, which each has 4 input channels. Amongst several devices in the NIM-rack, only LeCroy Model 428a signal splitter was used in this project. After testing the ADCs with no signal input, channel 0 on both cards were rejected due to a high noise ration. A total of 6 channels were then usable for this project. For Labview, a virtual instrument (VI) caen-adc-simple-8chanel.vi made by Njål Brekke was used. This VI takes 8 channels as input, displaying the voltage amplitude as a waveform graph, both all channels simultaneously in one window for comparison, and as separated graphs. This VI was modified to take only 6 channels as input, and also added several statistical calculations which will be mentioned later. 4.6 THE EXPERIMENTAL SETUP The final experimental setup resembled the setup for MPPC-testing, with the LED pulser exchanged with an UV-LED, which has higher energy, suitable for crosstalk measuring.

12 P a g e 11 Illustration 4.2: Final setup overview. The BIAS voltage was set to, and split into nine parallel wires connected to each MPPC. The amplifier voltage was set to and -. The UV-LED pulser voltage were set to, and a frequency of. The UV-LED pulser was placed on top of the BGOcrystals, light-proofed from the room. A schematic overview of the setup is shown in Illustration channels from the MPPCs were connected to the DAQ-system, using NI LabView as readout. BIAS The experimental setup Aluminum casing PCB circuit board /w nine MPPCs Signal generator Crystals UV-LED pulser DAQ-system Pre-amp power supply Illustration 4.3: The setup as it was in the final experiments. To keep the crystals firmly in place on top of the casing a system of 4 bolts and nuts combined with PCB material was used to keep pressure inward on the crystals, see Illustration 4.4. Then a PCB-plate was used to apply downward pressure on the crystals, to keep them in place on the casing. Nine holes were drilled in this plate to allow a clear line of sight from the crystals and down on the MPPCs. A plastic socket was

13 P a g e 12 taped on top of one of these holes, while the others were kept lightproof. Then the UV-LED pulser was bolted in place on this socket to ensure a straight line from the UV-light to the MPPC. Illustration 4.4: Image showing the top part of the box, where the crystals and UV- LED-pulser are seated. 5 MEASUREMENTS AND RESULTS The following tests were done with the UV-LED pulser operating at 2 khz with 20 ns pulse length. Data acquisition was triggered directly by the signal generator, rather than by the MPPC output signal, in order to obtain the best test results. UV light has only been applied to one single crystal each time. 5.1 QUALITATIVE ANALYSIS OF OUTPUT SIGNAL Figure A displays a typical output signal: Illustration 5.1: Screenshot of LabView showing input graphs from the crystals

14 P a g e 13 This test was run with a relatively high light intensity, to achieve a distinct signal shape more or less unaffected by post-amplification noise. We see a main peak with duration of ns, and rise time of ns. Following the main peak is a secondary one with approximately 5% the amplitude of the first, most likely to be a so-called afterpulse from the MPPC, or some feedback error in the read-out circuit. 5.2 QUANTITATIVE ANALYSIS ESTIMATING NUMBER OF DETECTED PHOTONS To convert the output signal to an estimate of the number of detected photons per light pulse, the area under the graph is calculated and multiplied by the appropriate conversion factor: ( ) ( ) ( ) ( ) The following measurements are average values computed from approximately 6700 triggered events (the program was set to run measurements, but due to limited speed of the ADC some events will be lost). Noise in DAQ setup Noise in the DAQ setup was measured with none of the signal wires connected to the ADCs, except the trigger signal. Noise in each of the six operational ADC channels are listed in Table 5.1. Channel Average noise (V ns/2) Average noise (photon equivalents) Table 5.1: Measured noise in DAQ setup Further statistical analysis of the noise has not been carried out, but should be taken into closer consideration if the detector setup id used for detecting very low-intensity light. Although the readout during normal operation will be triggered only by pulses exceeding a threshold amplitude, integrating over the signal will still include contributions from noise. Noise in complete setup The total noise in the setup is measured with MPPC bias voltage on and all electronics running, but without any light applied to the crystals. These values include all unwanted effects influencing the output signal MPPC dark counts, background radiation, insufficient light sealing of the system, and signal noise.

15 P a g e 14 Channel Average noise (V ns/2) Average noise (photon equivalents) Table 5.2: Measured noise in complete setup 5.3 CROSSTALK The crosstalk of the system is measured using UV-light on only one of the nine crystals, and then look at the adjacent crystals for escaped photons from the exposed one. This is a negative effect in any photon detection system, as it reduces position accuracy. Crosstalk was measured in five different configurations, in order to obtain values for all nine crystals (DAQ setup only allows six channels to be measured simultaneously, as mentioned earlier). Light output from the LED was set to a fixed level, as high as possible without causing the signal from the exposed MPPC to exceeding maximum ADC input voltage. The first column of the following tables show which crystals are tested, while the last column indicates the ratio of how much light is detected in the unexposed crystals compared to the exposed one. Crystal Avg. integ.signal Avg. integr.signal (photon (V ns/2) eqv.) 1 2 (exposed) Table 5.3: Crosstalk measurement #1 lower six crystals, no. 2 exposed Crystal Avg. integ.signal Avg. integr.signal (photon (V ns/2) eqv.) (exposed) 6 Table 5.4: Crosstalk measurement #2 lower six crystals, no. 5 exposed Crystal Avg. integ.signal Avg. integr.signal (photon (V ns/2) eqv.) 4 5 (exposed) Table 5.5: Crosstalk measurement #3 upper six crystals, no. 5 exposed % of exposed crystal % of exposed crystal % of exposed crystal

16 P a g e 15 Crystal Avg. integ.signal Avg. integr.signal (photon (V ns/2) eqv.) (exposed) 8 Table 5.6: Crosstalk measurement #4 centre-facing crystals, no. 5 exposed Crystal Avg. integ.signal Avg. integr.signal (photon (V ns/2) eqv.) (exposed) 9 Table 5.7: Crosstalk measurement #5 upper six crystals, no. 8 exposed % of exposed crystal % of exposed crystal The experiments do not show any obvious defects in light sealing between the crystals, as the measured values for unexposed crystals are of the same order of magnitude as the measured noise. We can see that the signal from measurements exposing crystal number 5 does not have as high amplitude as when exposing crystal 2 and 8. We assume this is due to some error with MPPC number 5. Because of this, the ratio between the exposed channel and the other channels (and compared to noise) is greater when exposing crystal number five then when exposing crystal 2 and 8. 6 CONCLUSION AND OUTLOOK The goal of this project was to design and build a prototype scintillation-based detector for detecting photons, using a 3x3 array of crystals. Our main focus has been the making of the detector most of the time spent working on this project has been related to testing and continuously improving performance of the read-out circuit. A major concern during the design process was ensuring optical sealing between the crystals, a task proven by experiments to be successful. Much time has also gone into studying how to use the software needed both for designing and running experiments on the setup. Intended to be a testing platform for different crystals, the detector can provide simultaneous readout of nine crystals of different size and type, limited to a maximum base area of 10x10 mm per crystal. Interchanging the crystals requires re-wrapping of the aluminum shielding covering each crystal, but this is rather quickly done. Replacing the MPPCs is also possible, by removing the bottom lid and unscrewing the fasteners. During testing of the complete setup we have mostly concerned ourselves with examining crosstalk and functionality of the pre-amp, and not the properties of the BGO crystals used. Potential improvements would be reducing noise and slightly increase pre-amp gain, in order to enhance sensitivity and resolution.

17 P a g e 16 7 REFERENCES - Sæterstøl, Jostein: Characterization of Scintillation Crystals for Positron Emission Tomography, UiB Lønne, Per-Ivar: Characterization of the MAPD3-N Multipixel Avalanche Photodiode, UiB Erdal, Hege Austrheim: Characterization of Multipixel Avalanche Photodiodes, UiB Tipler, Paul A. and Llewellyn, Ralph A.: Modern Physics, Fifth Edition, W.H. Freeman 2008

18 P a g e 17 8 APPENDIX 8.1 THE PCB SCHEMATIC Illustration 8.1: A schematic overview of the pre-amplifier circuits. On the top is the power supply, feeding all the nine circuits.

19 P a g e THE PCB SINGLE SCHEMATIC Illustration 8.2: The schematic for a single pre-amplifier circuit

20 P a g e THE PCB LAYOUT Illustration 8.3: The PCB circuit board layout

21 P a g e THE ALUMINUM CASING 3D MODEL Illustration 8.4: An exploded 3D view of the aluminum casing, with the 3x3 crystal matrix on top, and the PCB circuit board on the inside.

22 8.5 MPPC DATASHEET P a g e 21