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Line 85: − + − + − + − + − # calculate the mean of this shifted and rescaled set. Since each peak is now pegged to photon count, the mean is in the units of average photons received. Based on this value, corrected by the dark count (described below), the efficiency of the SiPM can be calculated by comparing this average flux to that felt by the HPD. − This procedure is repeated with the LED and/or SiPM covered to measure the dark rate. Depending on which distribution showed the photon peaks more distinctly, either the illuminated or dark datasets were used for the gain calculation and pedestal calculation. Either way, a mean was extracted from the dark distribution to calculate the dark rate and to subtract the average dark pixel count measured from the average pixel count measured while illuminated.+ − + + +
→Analysis Approach
[[Image:PhotonPeaks_SSPM05.png|frame|Illustration of discrete peaks seen in the collected SiPM charge frequency histogram. The first peak shows the number of events in which no photons were detected, the next shows one and so forth. Note the even spacing of the peaks, showing the linearity of the device.]]
[[Image:PhotonPeaks_SSPM05.png|frame|Illustration of discrete peaks seen in the collected SiPM charge frequency histogram. The first peak shows the number of events in which no photons were detected, the next shows one and so forth. Note the even spacing of the peaks, showing the linearity of the device.]]
The first remarkable feature of the the SiPM statistics is the presence of discrete peaks in the histogram of charge collected in the SiPM (proportional to the SiPM signal (V) integral (Vs) by 1/Gain<sub>trans-impedance</sub> (A/V). This allows us to determine the charge collected per activated pixel (per photon) and therefore gives the gain of the device. This is the "self-calibration" referred to above.
The first remarkable feature of the the SiPM statistics is the presence of discrete peaks in the histogram of charge collected in the SiPM. The SiPM pulse charge is computed as the SiPM signal integral (Vs) divided by the Gain<sub>trans-impedance</sub> (V/A) of the preamplifier. This allows us to determine the charge collected per activated pixel (per detected photon) and therefore gives the gain of the device. This is the "self-calibration" referred to above.
The general analysis procedure was to
The general analysis procedure was to
# histogram the collected set of function integrals
# histogram the collected set of function integrals;
# get the pedestal: the first peak corresponds to events with no photon hits, so it properly belongs at zero [charge collected]
# get the pedestal: the first peak corresponds to events with no photon hits, so it defines zero charge collected;
# calculate the gain and rescale the histogram: the width between adjacent peaks corresponds to the the gain in units of Vs/pixel. (Using the amplifier trans-impedance gain value, this can later be converted to charge/pixel)
# calculate the gain and rescale the histogram to units of detected photons
Since each peak in the histogram shown in the figure at the right is expressed in units of photon count, the mean is the average number of detected photons per pulse. After subtracting away the contribution from the dark counts (described below), the efficiency of the SiPM can be calculated by comparing this average yield to that found by the HPD.
Efficiency calculated in the manner described is compared to the expected efficiency. Integrating the HPD response function in the frequency space weighted by the LED emission spectrum yields the mean detection efficiency of the HPD for that light source. Doing the same with the manufacturer-supplied response function of the SiPM and comparing to the figure for the HPD yields the expected SiPM efficiency relative to the HPD.
This procedure was repeated with the LED and/or SiPM covered to measure the dark rate. Depending on which distribution showed the photon peaks more distinctly, either the illuminated or dark datasets were used for the gain calculation and pedestal calculation. Either way, a mean was extracted from the dark distribution to calculate the dark rate and to subtract the average dark pixel count measured from the average pixel count measured while illuminated.
Efficiency calculated in the manner described is compared to the expected efficiency. Integrating the HPD response function in frequency space weighted by the LED emission spectrum yields the mean detection efficiency of the HPD for that light source. The same exercise was carried out using the photon detection efficiency function supplied by the SiPM manufacturer, and compared with the measured efficiency as a check that we had obtained the expected SiPM performance.
== Summary of Basic Characteristics and Comparison of SiPMs ==
== Summary of Basic Characteristics and Comparison of SiPMs ==