I would like to couple a 2x2 silicon photomultiplier array (where each of the silicon photomultipliers serves as a "pixel" analog output) with a plastic scintillator piece in order to measure the intensity of light that is emitted when incident radiation passes through the scintillator. The purpose of this project is to (hopefully) detect cosmic-ray muons that exist at a natural background flux. I am a member of a high school research team (we are extremely amateur) that would like to detect this muon background and study whether we can track the positioning and trajectory of incident muons at a lower cost than the utilization of scintillating fiber or drift chambers.
The above diagram I made shows a crude depiction of the coupling of the scintillator and the 2x2 photomultiplier array. The purpose of the array is to look for a simultaneous signal "jump" that hopefully will be distinguishable from the dark count in the device. This will enable a muon transmission incidence to be determined according to the signal strength and replication in each of the four pixels via a chi-square test. We also intend to measure a 2-D coordinate approximation of the muon incidence based on the premise that all of the light from the transmission will attenuate evenly throughout the scintillating plastic, such that the position is triangulated by measuring the differential intensities of light received by each of the four pixel readouts (this is similar to the function of a gamma camera minus the collimator component. This is a goal we will likely not reach to an adequate degree of accuracy, but muon detection in general will be sufficient for our purposes).
Above is an extremely bare-bones schematic of our device that we are constructing, showing four scintillator pieces each coupled with 2x2 silicon photomultiplier arrays. The dimensioning of the device enables a small fraction of the total muon flux to be measured at a time. The trajectory will hopefully be constructed by combining the differential signals from all of the scintillator-array couplings, which will enable 2D coordinates to be established in each layer, and therefore a 3D trajectory when all of those are determined.
I have calculated a conservative "minimum" threshold of light intensity that would distinguish a muon incidence in this set-up, based on the properties of muon attenuation in materials and that of the scintillator itself (in this case a polyvinyltoluene-based compound). Based on a formula provided by SensL whitepaper documentation and its quoted photon detection efficiency for the array in question, I have determined that this threshold corresponds to a firing of at least 25 microcells at once within each of the four photomultiplying pixels (more on the microcells below). I have also tried to determine what the signal from the photomultipliers would look like on an oscilloscope before hand, but the research I have done has yielded formulas which involve advanced simulation techniques that I am not currently equipped to perform, or mathematical expressions that include components such as Fourier transforms that I could learn if I really need to, but am not familiar with (I have only taken two semesters of calculus). However, I first wanted to see if there was an easier way to simply design a read-out circuit for the photomultipliers.
My question: Based on the specifications provided for the photomultiplier array shown at the bottom, how can I determine the specification and circuit layout for a transimpedance amplifier (to convert current fluctuation into voltage fluctuation) and analog to digital conversion module, such that a digital readout of the photomultiplier activity can be communicated via USB to a desktop computer? Do I need to know the exact shape, frequency, and amplitude of the analog signal to do this? If so, what is the best way to go about that (i.e. where can I find a good source which walks through that process?) The SensL documentation tends to show a signal output of ~10mV over a span of ~50 ns at a time.
The array in question is sold by SensL and is identified by the following:
ArrayC-60035-4P-EVB
The 2x2 photomultiplier array is shown in the following images (Note: the source for all of these images/figures is SensL documentation): 
This just shows the device in question, the ArrayC-60035-4P-EVB (a 2x2 silicon photomultiplier array with an attached evaluation board made by SensL)
The photomultipliers are supplied a break-down voltage such that an electric field of >5*10^5 V/cm is generated within the depletion region of the silicon substrate, which enables charge amplification via impact ionization. The breakdown voltage is supplied (~24.5 V for this product) with an additional over-voltage of 2.5 V as specified by the manufacturer. Each of the 4 silicon photomultiplier pixels that compose a single array consists of 18,980 microcells. Each of these microcells consists of an avalanche photodiode in Geiger-mode, and a quench resistor. When a photon is incident upon one of these avalanche photodiodes, there is a rapid discharge current that decays exponentially when the voltage spike is dissipated across the quench resistor. A scaling output forms when the currents of all of these microcells are summed to show the approximate number of microcells discharging at a given time, which is indicative of the intensity of incident light, based on the particular quoted gain for the photomultiplier.
The above schematic shows how the four photomultiplying "pixels" appear in an equivalent circuit. The outputs labeled with "F" can be ignored because we will not be using fast output in this project. the outputs labeled with "S" are the standard analog channels which we want to process the current fluctuation from.
The above schematic shows the array of microcells (avalanche photodiodes) that are embedded within each of the four photomultipliers.
The above two figures show the ports located on the evaluation board provided by SensL. This includes a common cathode and four anodes for analog signal output in the form of current fluctuation.
The above figure shows the quenching cycle on each of the avalanche photodiodes. In this project, we would like to quantify the number of discharges that occur over a small interval of time, about 500 ns.
This shows the output of individual microcells in the array.
This is the type of output we would like to achieve in the end, showing how many photoelectron amplification events are occurring at a given time, in digital form (the figure above shows an analog signal that exhibits discrete thresholding from multiple microcell discharge).
Array specifications: Number of microcells fired during desired signal: 25
Number of total microcells in photomultiplier: 18,980
Capacitance of entire device: 3400 pF
Overvoltage: 2.5 V (Breakdown voltage is 24.5V)
Microcell recharge time constant: 95ns (RC time constant, so this includes quench resistor)
Answer
I have been working with this stuff for a high energy physics detector with about 8 million of this detectors. While I've been playing around with these sensors and an oscilloscope, I wasn't involved in designing the readout electronics. We also used custom made chips, which I guess are a little out of buget for you ;-)
So sorry, this isn't an answer to your question, just my thoughts and some hints. Have fun!
- In general, a setup like yours is able to detect muons.
- The number of 25 firing pixels (we called them so) sounds reasonable, since muons don't produce many photons.
- Your sensors are not ideal. A large number of pixels usually comes with a low capacity per pixel, i.e. low signal per firing pixel. Plus, the dark rate, i.e. the number of pixels firing spontaneously (That's what you see in figure 3b!) increases a lot, and the probability of two or more pixels firing at the same time increases, too. I would have used a devices with in the order of 1000 pixels, or even less.
- By placing four arrays onto a small PCB, the manufacturer easily made a device with lots of pixels, but you shouldn't expect to get much spatial information of the trajectories from them. They are located too near to each other and will collect roughly the same amount light. This is especially true since the scintillator is quite diffuse for the produced light, and the light is reflected at the borders of the material. In addition, this makes the trigger system more complex.
- Why are you using a stack of four scintillators? Typically, two are sufficient. If the green part is a thick iron plate, this yet could be used to detect pions, which generate large signals in the upper scintillators, convert to muons in the iron, and then generate low signals in the lower scintillators.
- What's very important for your system is to detect coincidences between all sensors. Each sensor will produce signals for muons from all directions, but you only want the signals of muons passing all scintillators from top to bottom.
Each sensor should give a trigger signal, which is then fed into a fast AND gate. This way, you get a trigger signal when all sensors saw something at the same time. The signals from the sensors should be short, otherwise you'll see coincidences where there are none. And don't forget cable lengths. You can even use different lengths to compensate for the time offset due to the time of flight of the muons. - To measure the amplitude, we used a charge-to-voltage transducer with variable gain and variable integration time, which also stretched the signal over time, making everything else less time critical. The signal was then fed through a sample-and-hold mechanism to "freeze" the voltage level a certain time after the trigger signal. It could then be measured with any cheap ADC.
- If you want to measure precise amplitudes, keep in mind that your sensors are very sensitive to supply voltage (more gives higher signal, but also higher dark rate) and temperature (lower means higher signal and lower dark rate, one can increase voltage to increase signal further). Typically, you can use short light pulses (a few ns long) to measure discrete values like in figure 5 to calibrate your system.
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