A technical guide to silicon photomultipliers (MPPC) - Section 4

Sometimes referred to by other terms such as a datapoint, a sampling, a reading, or an event, a measurement is a single experimental attempt [temporally (per a duration of time) and spatially (per a detector channel and within its physical size and field-of-view)] to quantify an optical signal.

The result of a measurement is thus a piece of quantitative data that represents essential information about the true signal. Measurement is a very fundamental and seemingly simple concept, so why is it explored here? There are 3 important points to keep in mind:

- Measurement frequency: Understanding the required bandwidth for a measurement is of paramount importance to proper identification and definition of an application’s requirements and in order to compare those requirements with characteristics of candidate photodetectors. Fundamentally, based on Nyquist’s sampling theorem, the sampling frequency must be at least twice the measurement frequency, which in turn would be equal to the frequency of the signal’s highest-frequency component that is intended to be detected. Furthermore, as discussed before, a readout amplifier circuit’s cutoff frequency at -3 dB should be designed to be at least twice that of the measurement frequency (but as a general rule of thumb, 4 times is an advisable design target).

For better illustration, the following examples portray cases in which a detrimental bandwidth mismatch is present:

• Using an amplifier with a cutoff frequency of 1 MHz to measure pulses with frequency of 900 kHz and rise/fall times of 1 μs.
• Using an imager with a spatial resolution of 10 lp/mm to contact-image a min. feature size of 20 μm. [Reason: 10 lp/mm is theoretically able to observe a min. feature size of 1 mm /(2 × 10) = 50 μm]
• Using an oscilloscope with a sampling rate of 150 MHz to look for multiple randomly-occurring events with durations of 10 ns each (Reason: 150 M < 2 × 1/10 n = 200 M).

- Measurement resolution and range: Besides measurement frequency, the resolution of the measurement instrumentation in its ability to accurately resolve the smallest expected quantity of or change in the parameter (that is to be measured) over the full range of its expected values is also of great importance. The following are examples in which there is a detrimental mismatch between signal characteristics and measurement resolution and range:

• Using an 8-bit digitizer with a conversion factor of 500 ke-/LSB to plot pulse height distribution for up to 150 p.e. pulses of a MPPC at gain = 10⁶ (Reason: 150 × 10⁶ / 5 × 10⁵ = 300 > 2⁸).
• Using a detector with a rise time of 10 ns to discriminate the pulse shapes of 2 signals with rise times of 1 ns and 8.5 ns.
• Using a spectrometer with a resolution of 30 nm to distinguish emission or excitation peaks 10 nm apart.
• Using a 16-bit/sample ADC with a bit rate of 50 Mbps to record the output waveform of an MPPC with a dark count rate of 4 Mcps for under dark conditions. (Reason: 50 M / 16 < 4 M)

- Normalizations: While some signal characteristics (like amplitude, timing or frequency) can be appropriately obtained from measuring a single parameter (whether once or a multitude of times), others (like flux or power) would by definition include normalizations to time and/or spatial information and hence require measurements of 2 or more parameters in order to be quantified.

These differences are important, since a typical instrument designer is naturally concerned with the performance of her overall instrumentation: she could be designing for an application condition that combines a series of measurements and contains one or more normalizations instead of consisting of a single parameter alone. In order to assess a photodetector’s suitability for a given application, one must bear that in mind and see how the way detector characteristics have been specified compares with the designer’s intended application conditions and target requirements.

Towards that, one would begin by finding out to what temporal or spatial parameters a stated application condition might have been normalized; when in doubt, one should make sure about the dimension or unit of the application condition in question. Furthermore, it is also important to understand the scope of those normalizations.

For example, one needs to examine whether the incident light “power” is applied to the entirety of a detector’s photosensitive area or normalized to pixel count or unit of area. As another example, it is important to verify whether peak power or average power is meant when a reference to incident light “power” is made; peak and average power have different temporal normalizations in that the former is the ratio of energy content of a single pulse to the time duration of that pulse while the latter takes the time in between consecutive pulses into account. As a further example, if various spectral band components of a broad spectrum of light are to be detected by different detector channels separately (applicable to 1D or 2D serial- or parallel-readout multichannel detectors), performance of each detector channel must be assessed independently in accordance to its particular expected input light signal conditions.

With the above caveats in mind, we proceed to introducing methods of measuring MPPC characteristics. In what follows, we will focus on the characterization of Hamamatsu’s S13360-3050CS as an example, but please be assured that these measurement methods can be adapted to other MPPC models with little or no adjustments.

Before we begin, however, let’s briefly discuss the choice of a suitable power supply to bias the MPPC. At Hamamatsu Photonics, we typically utilize a source meter to bias the MPPC, since it allows us to control the applied voltage via a PC connection and also to set a max. voltage of 80 V for safe biasing of the MPPC. Furthermore, a source meter enables automated I-V curve characterization and can thus be used in QC screening of mass-produced parts. Therefore, despite its relatively high cost, a source meter is recommendable as a suitable biasing solution in performing the measurements described hereinafter.

- Measurement principle: MPPC gain is the factor by which Geiger-mode avalanche (whether initiated by the photoelectric effect or thermal carrier excitation) multiplies the initiating electron to form the MPPC’s output charge per avalanche. Following the mechanism that we explained in Section 1, that gain is proportional to overvoltage (Vover), which is the difference between the bias voltage applied to the MPPC and the MPPC’s inherent breakdown voltage (VBR).

The simplest measurement of VBR can be derived from the x-intercept of a MPPC’s gain vs. bias voltage plot. Assuming a proportionality factor of A between gain and overvoltage, we can say Gain = A x V_over = A x (V_bias - VBR), and at the gain-voltage plot’s x-intercept (at which Gain = 0), V_bias thus corresponds to the breakdown voltage.

Determining the V_BR of MPPC before beginning other measurements is practically beneficial and recommendable. Most MPPC characteristics whose measurement we are going to introduce in this section, namely photon detection efficiency, dark count rate, prompt or delayed crosstalk probability, and afterpulse probability, are dependent on V_over. Additionally, V_BR differs between each and every pair of MPPCs even if they are the same product – for example, amongst a small batch of S13360-3050CS, V_BR of each is different from the rest; operating them at the same applied bias voltage would likely result in differing characteristics. It is thus recommended to compare or calibrate the characteristics of MPPCs at the same overvoltage (or the same gain if practical).

- Measurement setup: Figure 4-1 shows the gain measurement setup. In this setup, the MPPC is placed inside a dark box and electrically connected to it (if metallic) via a common ground in order to decrease the parasitic impedance that forms between them. Output of the charge amplifier goes to a shaping amplifier, which is followed by a MCA. Finally, a dedicated FPGA circuit sends the MCA output to a PC through a USB connection. We analyze the data coming from the MCA with a LabVIEW software program in this setup.

- Measurement procedure: In our setup, the MCA output is used to produce a histogram of the shaping amplifier’s output pulses; this histogram would consist of pulse count and digitized pulse height (proportional to the MPPC’s output charge) as its y and x axes, respectively. Figure 4-2 shows an example of this histogram. As shown, the histogram has several peaks, which correspond to (from left to right) the noise pedestal (population of readout noise pulses) and populations of 1 p.e., 2 p.e., ... pulses of the MPPC. Based on the properties of these peaks, we can compute the net output charge corresponding to a 1 p.e. pulse by calculating the peak-to-peak interval between any two consecutive peaks (excluding the pedestal) along the x-axis after which we convert the interval value (in digital counts [LSB]) to equivalent charge amount based on the charge amplifier’s gain [V/C] and the MCA’s A/D conversion factor [LSB/V]. This 1 p.e. equivalent charge is, by definition, equal to the gain of the evaluated MPPC at the applied bias voltage. We repeat this measurement process for various applied voltages to obtain the gain-voltage plot. We then perform linear fitting on the resulting plot; the x-intercept of the fitted line represents V_BR of the MPPC under evaluation.

It is noteworthy to point out a potential pitfall in performing this measurement: the MPPC output pulse populations must be sufficiently large to be statistically significant in order to create a meaningful histogram. This condition could be difficult to attain for low overvoltage levels or if the MPPC’s dark count rate is too small. In such scenarios, low-intensity illumination of MPPC photosensitive area should be utilized to increase the output pulse counts.

- Measurement result: Figure 4-3 shows the gain-voltage plot and its linear fit for S13360-3050CS. From this plot, we conclude that V_BR of this MPPC is 51.29 V.

- Measurement procedure: Figure 4-5 shows a measured I-V curve of S13360-3050CS under various luminance levels coming from the light source. Under dark condition, the I-V curve comprises bulk current and surface leakage current. The latter strongly affects the I-V curve’s baseline under dark condition and the resulting V_peak. By illuminating MPPC with the light source, however, we can ignore the baseline and calculate the V_peak reliably. In practice, one should experimentally determine the suitable LED luminance by repeating the I-V curve measurement for various light levels while avoiding excessive illumination of the MPPC.

- Measurement result: Table 4-1 shows the Vpeak measurement results for three units of S13360-3050CS. For reference, measured VBR of each of those MPPCs (via the x-axis intercept method) has also been listed. As you can see, the difference Vpeak − VBR has the same value amongst all three.

Table 4-1 Vpeak (and VBR) measurement result for 3 pcs of S13360-3050CS

The following are typical examples of instruments that can be used in this measurement setup:

Pulse light source: PLP-10 (Hamamatsu)
Wavelength: 408 nm (several other wavelengths such as 655 nm, 851 nm, etc. are also available)
Pulse width: 88 ps FWHM (wavelength dependent)
Optical attenuator⁶: DA-100-3U-850-50/125-M-35 (OZ Optics)
Integrating sphere: 3P-GPS-033-SL (Labsphere)
Power meter: 2936-R (Newport)
Bias supply: GS610 (Yokogawa) or 2636B (Keithley) and the like
Amplifier: Linear amplifier (internal product and not for sale), bandwidth: 450 MHz
Oscilloscope: SDA 760Zi (LeCroy)

Measurement software program is written in LabVIEW 2010.

The pulsed light source used in this measurement should emit monochromatic light and must have a pulse width shorter than the MPPC rise time (which is on the order of a few nanoseconds).

In utilizing the integrating sphere, we mount the MPPC and the power meter’s photodiode head on two output ports of the sphere. To hold it on the output port, the MPPC is mounted using a fixture with a small aperture radius (0.5 mm or 0.3 mm depending on the MPPC’s photosensitive area in order to ensure the illumination of the MPPC photosensitive area only).

The ratio of output light levels of the sphere’s two ports should be measured in advance by mounting the same photodiode head on each port and dividing the resulting power meter outputs. It should be emphasized that light intensity in determining the output power ratio of the sphere’s ports should be high enough to allow for the power meter’s photodiode head to detect it with good accuracy through the small aperture of MPPC’s fixture. When using a pulsed light source as in our case, higher light intensities can be achieved by increasing the light pulse frequency.

To ensure high S/N for good measurement accuracy, the output amplifier used to read the MPPC must have relatively low levels of noise. Since an amplifier’s noise performance and its bandwidth are competing factors, it is acceptable to compromise on the bandwidth even if that would result in the distortion of the MPPC output pulse shape.

For digitization and analysis of the linear amplifier’s output pulses, we use the oscilloscope SDA 760Zi (LeCroy), which has the capability to perform PHA/PHD (i.e. create pulse height analysis/distribution histograms) at a high data throughput.

- Measurement procedure: Figure 4-7 shows a flowchart of our PDE measurement program’s underlying algorithm. We wrote this program to automatically measure MPPC’s PDE vs. bias voltage.

- Measurement result: Figure 4-9 shows the result of measuring S13360-3050CS’s PDE with our setup.

To exclude this degradation of measurement by pulse pileup, we can use a high-pass filter for pulse shaping after the linear amplifier’s output. As a result, output pulse widths become narrower and pileup is decreased as shown in Figure 4-11.

- Measurement setup: Figure 4-12 shows the measurement setup.

Amplifier: Linear amplifier (internal product and not for sale), bandwidth: 1 GHz
High-pass filter: internally made and caged in test box
Counter: 53131A (Agilent)

In this setup, the linear amplifier should have sufficient bandwidth to replicate the MPPC rise time (as the highest-frequency component of the MPPC output) in order to effectively reject the pulse pileup effect. For a detailed explanation on how to determine the readout amplifier’s optimal bandwidth, please refer to Section 2.

The time constant of high-pass filter should be set according to the pulse shape of the MPPC that you want to evaluate. For the purpose of characterizing S13360-3050CS, we use the high-pass filter with 100 pF capacitor and 51 Ω resistor.

As explained in Section 1, the high-pass filter decreases the output pulse height and so extra amplifier gain might be required for effective pulse output measurement. In that case, one solution is implementing another linear amplifier between the first stage and the high-pass filter. We use Mini-Circuit ZX60-14012L-S+ for this purpose.

- Measurement procedure: Figure 4-13 shows the flowchart of this measurement program’s algorithm.

The counting integration time for each threshold value should be reasonably large enough to exclude statistical fluctuation of the measured count. For the case of S13360-3050CS, we set the integration time to 2 seconds. If DCR of the measured MPPC is small because of its small photosensitive area or low temperature or other factors, integration time should be set longer.

- Measurement result: Figure 4-14 shows the measurement result for S13360-3050CS with and without high-pass filter. The high-pass filter’s effect is clearly appreciable. Figure 4-15 shows the step plot for various overvoltages (with high-pass filter); we can see the increases in gain, DCR and prompt crosstalk probability. Figure 4-16 shows the DCR and prompt crosstalk probability obtained by this measurement.

- Measurement principle: In this measurement, we measure various MPPC characteristics by detecting MPPC output events with digitizer and software processing of the resulting data. This approach is commonly referred to as digital pulse processing (DPP).

For the sake of our discussion, we denote an “event” as data obtained within a time window that would contain MPPC output pulses (one or more) of any height. Specifically speaking, in the case of S13360-3050CS, the full width of a single output pulse is about 200 ns; we digitize the output waveform during a time window on the order of microseconds for DCR measurement and on the order of hundreds of nanoseconds for other measurements. You should choose the time window according to your measurement objective. A smaller time window leads to the reduction of valid events and consequently to the diminishment of afterpulse output whereas a larger time window results in a larger data size for one event and thus a decrease in measurement throughput.

In a manner similar to the hardware solution (high-pass CR filter) described earlier, we resolve the issue of pulse pileup through software processing of an MPPC event using a deconvolution filter. The basic concept of this method is well-known in the digital image processing field and described in references such as [12] while its practical application to the photosensor signal processing is described in [13] (in Japanese). There are other solutions for pulse pileup rejection such as simply differentiating the output and suppressing baseline discrepancy as described in [14].

A conceptual illustration of the deconvolution filter is shown in Figure 4-17. We assume that the MPPC output can be represented by the convolution of Dirac delta-function output events and the 1 p.e. MPPC waveform. The delta-function event is free from pileup since each such pulse would have a very sharp and distinct shape. If we define the specific shape of the delta waveform and measure the 1 p.e. waveform of the MPPC under measurement, we can mathematically compute the deconvolution filter that converts the real MPPC output events to delta-function events and thus reject the pulse pileup effect. Detailed mathematical explanation of how the deconvolution filter is computed has been provided in [13] and [14].

In addition to the deconvolution filter, we use another filter to reduce white noise, which disturbs the detection of delta-function peaks. Hamamatsu’s choice of such filters is the Wiener filter that determines the reduction in pulse height of a 1 p.e. MPPC output pulse as a function of frequency by computing the Fourier transform of the 1 p.e. waveform in frequency domain after white noise filtration. Other methods are also effective; one of the simplest is to apply a low-pass filter to the event or equivalently set the oscilloscope bandwidth to a small value compared to the highest-frequency component of a 1 p.e. MPPC so that white noise can be filtered out while the MPPC output pulse maintains its amplitude.

- Measurement setup: Figure 4-18 shows the measurement setup for this method. The MPPC is placed in a black box, and we proceed to recording the dark output events.

We use the oscilloscope as a digitizer in this measurement; board-level digitizers such as Flash ADCs are also suitable if they have sufficient node sensitivity, bandwidth, and sampling rate for precisely recording MPPC output pulse shapes. For our purpose, the 1 GHz bandwidth and 10 GS/s sampling rate of oscilloscope DPO7104 (Tektronix) is adequate.

- Measurement procedure: Before starting the data collection, we first form the deconvolution and Wiener filters and then combine them.

Figure 4-19 shows how to make the deconvolution filter.

First, we obtain the MPPC’s 1 p.e. waveform (the method of obtaining it is explained in the next subsection), and we then define the delta-function pulse shape based on the obtained 1 p.e. waveform. We afterwards use the Blackman window function⁷ as the delta function’s shape and determine the window’s optimal width by setting various widths and checking the deconvolution result for each of them. We then perform the Fourier transform operation on each waveform and calculate the ratio of its intensity for every frequency and obtain the deconvolution component of the filter.

We then proceed to building the Wiener component of the filter by using the Fourier form of 1 p.e. pulse. We first obtain the white noise by recording the output waveform while applying a bias voltage slightly below the MPPC’s breakdown voltage and calculating the Fourier transform of the resulting noise waveform. Using the two Fourier functions, we then calculate their power ratio as described in Figure 4-19 to obtain the Wiener component of the filter.

Finally, we form the product of deconvolution component and Wiener component and perform inverse Fourier transform on the product. The resulting waveform is the pulse processing filter we want.

In this example, we use LabVIEW’s library functions for the Fourier and inverse Fourier transform operations. You can use other math library functions prepared by other programming languages (such as MATLAB); there should be no differences in the results.

After creating the filter, we take a MPPC output event and convolute the entire event with the filter to obtain the delta pulse output. The effect of deconvolution is shown in Figure 4-20, and an example of it for S13360-3050CS is shown in Figure 4-21.

Processing the filtration’s output can be performed by two approaches, which we now proceed to explain.

DCR and prompt crosstalk measurement: In the first approach, the digitizer is triggered arbitrarily; an example of the trigger source would be 417 NIM pocket pulser (made by Phillips Scientific).

Figure 4-22 shows the concept of how to obtain DCR and prompt afterpulse probability in this measurement. To each MPPC output event recorded, we apply the aforementioned filtration in order to obtain a delta-function output event and then count the number of pulses in the event with a 0.5 p.e. discriminator threshold. The DCR can thus be obtained as the following simple ratio:

[(Number of pulses)/(Event time window)].

The prompt crosstalk can also be obtained easily by counting the number of pulses with a 1.5 p.e. threshold during the same time window and calculating the following ratio: [(number of >1.5 p.e. pulses)/(number of >0.5 p.e. pulses)].

- Measurement result: Figure 4-23 shows the prompt crosstalk probability obtained by this measurement. We also plotted these counting results with and without CR filter for comparison; the effect of pileup rejection can be observed.

Figure 4-23: Prompt crosstalk comparison as measured by A. pulse counter with & without high-pass filter and B. digitizer. Use of a digitizer can cancel the effect of pulse pileup (as deduced from the linear slope) as would the use of a counter with high-pass filter.

Recovery time, afterpulse, and delayed crosstalk measurement: Figure 4-24 shows the flowchart of this measurement. In this case, we trigger the digitizer with MPPC output pulses. We then apply the filter to the output event, check whether the first pulse (used as trigger) has 1 p.e. pulse height, and reject the > 1 p.e. pulses because such pulses have differing probabilities of correlated noise pulses and hence disturb the following analysis. For the 1 p.e. pulse event, we then check arrival time and amplitude of next pulse and store the information into a memory array as part of this repetition loop.

The peak detection threshold after filtration should be as low as possible unless the remaining white noise reaches the threshold. In our example, we take the pulse height histogram of white noise output before beginning this loop, fit the histogram with Gaussian function, then take the 6σ value of the fitted function and use that value as the peak detection threshold.

After data collection, we make a scatter plot of secondary pulses (arriving after the trigger pulse) in the manner shown in Figure 4-25 whose x-axis is the arrival time of a secondary pulse and y-axis is its amplitude. In practice, for verifying the measurement process’s progress, we have created a measurement software program to show this scatter plot whenever needed.

We now study the two event groupings circled by red and blue circles in Figure 4-25. The red group most likely consists of afterpulse events of the first (trigger) pulse considering that their pulse heights are less than 1 p.e. whereas the blue group consists of a combination of delayed crosstalk and accidental dark pulses that are not related to the first pulse considering that their heights are about 1 p.e.

We now isolate these groups from the scatter plot and analyze them separately to obtain the MPPC characteristics.

- Recovery time analysis: Figure 4-26 shows the scatter plot of afterpulse events. From this, we can obtain the recovery time of this MPPC by fitting this plot to an exponential function and calculate its time constant. By this analysis, we obtain the recovery time of S13360-3050CS to be 30 ns.

The red line shows the exponential fitting of those events.

- Afterpulse analysis: Because of its nature, definition of the afterpulse probability is rather subjective due to the wide range of pulse heights and time delays that could constitute its definition. Thus, the concrete definition of MPPC afterpulse is dependent on the end-use application conditions and requirements. If the MPPC output current is read out continuously, all afterpulses and their charge contents will be integrated and included in the MPPC output current. On the other hand, when the MPPC output is read out as individual pulses, afterpulses whose pulse heights are lower than the counting discriminator threshold are ignored and would not be taken into account for assessing afterpulse probability; this means that measurement and quantification of afterpulse probability to a large extent depend on what lower-level discriminator threshold is used in the counting setup.

In the following, two definitions and analysis methods of afterpulse are showcased. The first definition simply sums the afterpulse events and calculates the percentage ratio of that sum to the total number of events. By this definition, afterpulse probability only counts the number of afterpulses whose pulse height exceeds the threshold level of the counter’s discriminator for pulse detection.

Hence, in specifying afterpulse probability based on this definition, the discriminator threshold level should be referenced.

An alternative but more complex definition utilizes a weighted integral of afterpulse events based on their pulse heights. Towards that, we first make a histogram of afterpulse events according to their arrival times (x-axis of Figure 4-26) as shown in Figure 4-27. Assuming that afterpulse probability has an exponential distribution, we fit this histogram to an exponential function to obtain the afterpulse probability distribution curve vs. arrival time. Afterwards, we calculate the product of this curve with the exponential function whose time constant corresponds to the recovery time (explained in preceding subsection) and proceed to compute the area under the resulting curve. Finally, we obtain the afterpulse probability as the ratio of this area to the total number of triggered events.

Note that compared to Figure 4-26, the y-axis now changes to frequency. The red line represents the exponential fitting of the histogram while the green line shows the product of afterpulse fitting and recovery time curve.

- Delayed crosstalk analysis: Figure 4-28 shows the histogram of the mixed events of delayed crosstalk and accidental dark pulses consisting of the events circled in blue in Figure 4-25. Different from afterpulse analysis, the resulting histogram does not appear as an exponential curve because it has two exponential components with different time constants.

To differentiate these, we have to fit this histogram to the sum of two exponential functions with different parameters. After a proper fitting is carried out, we can obtain the total number of delayed crosstalk events by calculating the area under the fitted exponential that corresponds to the delayed crosstalk component. Then, we can calculate the delayed crosstalk probability as the ratio of that area to the total number of triggered events.

Note that compared to Figure 4-26, the y-axis now changes to frequency. The red line represents the exponential fitting of the histogram while the green line shows the product of afterpulse fitting and recovery time curve.

- Delayed crosstalk analysis: Figure 4-28 shows the histogram of the mixed events of delayed crosstalk and accidental dark pulses consisting of the events circled in blue in Figure 4-25. Different from afterpulse analysis, the resulting histogram does not appear as an exponential curve because it has two exponential components with different time constants.

To differentiate these, we have to fit this histogram to the sum of two exponential functions with different parameters. After a proper fitting is carried out, we can obtain the total number of delayed crosstalk events by calculating the area under the fitted exponential that corresponds to the delayed crosstalk component. Then, we can calculate the delayed crosstalk probability as the ratio of that area to the total number of triggered events.

- Measurement results: Figure 4-29 shows the probabilities of delayed crosstalk and afterpulsing of S13360-3050CS for various overvoltages.

- Measurement principle: Here we will explain how to take the single-photon/photoelectron (1 p.e.) waveform of the MPPC. The 1 p.e. waveform is essential to making the filter required for digital pulse processing and utilization of digitizer in MPPC characterization.

- Measurement setup: The setup for this measurement would be basically similar to that of measurements using a digitizer. One difference is that the bandwidth of each measurement setup component must be high enough to avoid degrading the high frequency component of MPPC output waveform. In this case, the maximum bandwidth of 1 GHz is sufficient for taking the 1 p.e. waveform of S13360-3050CS. Another difference is that the min. data collection time window would be set by the full width of the 1 p.e. waveform. In this case of S13360-3050CS, a time window of 200 ns would be adequate.

- Measurement procedure: We obtain the MPPC’s output waveform. Then, after checking the number of pulses in the waveform and their heights, we decide whether the triggered pulse is a genuine 1 p.e. waveform or not (i.e. prompt/delayed crosstalk or afterpulse following a dark pulse) and store an output pulse only when it is confirmed to have a 1 p.e. waveform. Afterwards, this step must be repeated a sufficient number of times to ensure the elimination of white noise by averaging all stored 1 p.e. waveforms.

- Measurement result: Figure 4-31 shows the result of measuring the 1 p.e. waveform of S13360-3050CS.

Photodetector time resolution characteristics are critical to attaining proper performance in direct-TOF (time-of-flight) applications such as TOF-PET (positron emission tomography) in medical imaging or LiDAR (light detection and ranging) in 3D scanning to determine the arrival times of signal photons or radiation. In this subsection, we will describe measuring two particularly-relevant time resolution characteristics: coincidence time resolution (CTR) and single photon time resolution (SPTR).

- Measurement principle: In TOF-PET, CTR is measured by using two detector channels, each consisting of a pair of scintillator crystal and photodetector, to detect gamma rays, having 511 keV in energy, that are emitted simultaneously from a positron decay and the resulting electron-positron annihilation.

The measurement setup is shown in Figure 4-32. The detection times obtained from detector channels 1 and 2 should ideally show the same value if each detector has the same distance from the radiation source as the other. However, variations in underlying factors such as the scintillator’s light emission yield, the photodetector’s internal charge collection efficiency, photon detection efficiency, and output pulse shape, and the output amplifier’s characteristics cause some timing variation between the two detector channels. The probability distribution curve of the timing difference between detector channels 1 and 2 has a bell-shaped Gaussian-like profile. CTR is theoretically defined by the FWHM of this distribution profile.

The result of this measurement does not represent the time resolution of the photodetector (i.e. MPPC) itself but the overall system time resolution, including the scintillator, amplifier, trigger circuitry, and other instruments utilized besides the photodetector.

- Measurement setup:

Equipment:
Radiation source: Na-22, etc.
Scintillator: LFS, LSO, LYSO, etc.
Amplifier: linear amplifier (internal product and not for sale), bandwidth: 1 GHz
Oscilloscope: SDA 760Zi (LeCroy)

Procedure:
The radioisotope should be positioned in the middle of detectors to equalize its distance from them. Originating from the annihilation of the positron byproduct of Na-22’s radioactive decay, gamma rays (if emitted in the proper opposite directions) reach detector channels 1 and 2 at the same time. The gamma rays undergo scintillation once detected, with the emitted scintillation light in turn detected by each photodetector (i.e. MPPCs). Generally speaking, CTR measurement is limited by the system’s timing jitter. To measure CTR with a specific target time jitter, the utilized output amplifier circuitry must have sufficient bandwidth to allow the jitter’s proper detection.

The amplified output pulses are then read out by a high-speed oscilloscope. The oscilloscope can calculate the time differences between coincident pairs of pulses outputted by the two detector channels, can profile the distribution of those differences (as obtained from a sufficiently-large population of such coincident pulses), and then produce the FWHM of that distribution in order to determine the measured CTR. The utilized oscilloscope should also have adequately wide input bandwidth and high sampling rate in order to resolve picosecond timing. One can also use a combination of TAC and MCA instead of a wide-bandwidth high-speed oscilloscope.

Figure 4-33 shows the linear output amplifier’s output pulse shape coming from two Hamamatsu S13360 series MPPCs. The key to high-accuracy measurement results is to decrease baseline fluctuations as much as possible. The optimal way to do so would depend on the measurement setup and the target application, but would consist of controlling the trigger threshold level, the bias voltage applied to the MPPC, and the measurement’s optical conditions amongst other factors.

- Measurement principle: SPTR is a parameter that characterizes the MPPC’s time resolution alone; this is in contrast to CTR, which evaluates a system’s overall time resolution performance. The basic idea of this measurement is to illuminate the MPPC with a single-photon input signal light level and to then determine the detection times of single photons by recording the MPPC’s output pulses (using a 1 p.e. trigger threshold level). The measurement setup is shown in Figure 4-34.

The suitable light source for this measurement would be able to produce light pulses of picosecond width; Hamamatsu’s PLP-10 would be one such light source.

As discussed in Section 2, MPPC’s linearity is limited by its PDE, pixel count per unit of area, and recovery time. In this subsection, we will describe a generalized measurement method to estimate the MPPC’s pulse-rate linearity.

- Measurement principle: Before we discuss the measurement procedure, let’s recall two key aspects of MPPC linearity and dynamic range from Section 1: First, a MPPC pixel cannot distinguish the number of simultaneously-incident photons upon it; the pixel response is limited to outputting a 1 p.e. pulse whose height does not depend on the number of incident photons. Second, each pixel requires a certain duration of recovery time. A photon’s incidence onto a pixel after a preceding photon’s detection cannot cause a full-height secondary output signal within the recovery time.

The first aspect (assuming we’re restricted to a fixed pixel size to maintain PDE) can be alleviated by dispersing the input light signal (using a diverging lens or by other means) to decrease the number of incident photons per unit area onto the MPPC. However, both aspects can be addressed by using a MPPC of smaller pixel size; such a MPPC would have an increased count of pixels per unit of area (i.e. more pixels within the same optical field-of-view) available to detect incident photons and a decreased pixel recovery time due to lower pixel capacitance. However, these advantages have a tradeoff of loss in PDE due to the lower fill-factor of a smaller pixel; thus, the lower limit of the linearity of such a MPPC is shifted upwards.

In order to measure MPPC linearity, we use the photon counting technique for the lower levels of the MPPC’s linearity where the signal level intensities are low and the current measurement technique (similar to measuring I/V curve) for the upper levels of MPPC’s linearity. In this measurement, we use a DC light source for implementing both techniques; we control the light level using an optical attenuator and ND filters. A key issue is accurate determination of the light intensity that the MPPC has detected at each obtained data point. This is accomplished by precise monitoring of the incident light intensity using a calibrated monitor photodiode. A peculiar aspect of doing so is in the photon-counting regime: the light intensity incident on the MPPC is adjusted to reach that regime using a precise ND filter while the calibrated photodiode can monitor the total (pre-attenuation) light intensity present with high accuracy.

- Measurement setup:

Equipment:
Light source: CW laser
Optical attenuator
ND filter
Amplifier: linear amplifier (internal product and not for sale), Bandwidth: 1 GHz
Counter: 53131A (Agilent)

Procedure:
We first measure and calibrate the ND filter’s attenuation rate using the calibrated photodiode. We recommend an ND filter that has 2-3 orders of magnitude attenuation capability. In the following measurement, the attenuation rate obtained here is used to estimate the light intensity incident onto the MPPC. One can adjust that light intensity over the MPPC’s full dynamic range (from photon counting to saturation) by controlling the optical attenuator.

Low intensity light level
While the light intensity on the MPPC is at the photon-counting level, one can measure the MPPC’s output response linearity by gradually increasing the light level. This task is similar to measuring dark counts but with the lower-level discriminator’s threshold set to be 0.5 p.e. Here, we define “photon counting level” to be a light intensity that results in MPPC output pulse heights of only 1 p.e. with enough inter-pulse time interval for continual detection of individual incident photons. Figure 4-35 shows the corresponding setup.

High intensity light level
We switch to the current measurement technique once the light intensity becomes high enough to result in the occurrence of ≥ 2 p.e. output pulse heights in order to avoid counting errors due to pulse pileup. Figure 4-36 shows the corresponding setup. In this measurement, the MPPC’s output current is measured using an ammeter, which is then followed by subtraction of dark current in order to obtain the net photon-correlated current. As increases in incident light intensity continue, one will eventually see the output’s saturation.

The combined linearity plot (of low and high input light intensities) is obtained by using the pulse count rate of the low-intensity measurement (by dividing the integrated count of detected 1 p.e. pulses at each data point by the integration time used for measuring each data point) and of the high-intensity measurement (by dividing the measured net (dark-subtracted) current by the charge output corresponding to a 1 p.e. pulse).

Figure 4-37 is the measured linearity plot of a Hamamatsu MPPC with a 15 μm pixel pitch. In this plot, the light level is indicated as number of incident photons per unit of time (in counts per second or cps).