Reconstruction method and its performance
3.1 ADC distribution
A combination of the high-gain (HG) and low-gain (LG) ADC values enables us to extend its dynamic range. The left part of Fig. 3.1 depicts a correlation between the two aforementioned values. They are fitted using a linear function as follows:
xHG =p0+p1·xLG, (3.1)
where xHG, xLG, and pi (i = 0,1) denote the HG value, LG value, and fitting parameters, respectively. Here, we define a combined ADC value using both the values. Because the HG value saturates at approximately 3000 ch, we use it as the combined ADC when it is less than the threshold of 2500 ch. Otherwise, the LG value is converted to the combined ADC to be equivalent to the HG value. Therefore, the combined ADC is given as
xcomb.= {
xHG (xHG <2500),
p0+p1·xLG (xHG ≥2500). (3.2)
where xcomb. denotes the combined ADC value.
Figure 3.2 depicts a distribution of the combined ADC value. In the figure, two peaks are observed. The left peak at approximately 800 ch, corresponds to the pedestal. It spreads due to the noise on the channel, and its mean value depends on the channel. The other peak, which is the broader one, is the MIP peak. It obeys the Landau distribution convoluted with the resolution of the channel. Hereinafter, we refer to the pedestal subtracted ADC as the ADC value.
3.1.1 Photon yield
We must confirm whether the scintillators have sufficient photon yields. To evaluate the yield, we calibrated the ADC. Because SiPMs can count the number of photons, we can estimate the photon yield of each SiPM by using the ADC values. Figure 3.3 depicts an ADC distribution.
LG-ADC LG-ADC
HG-ADC Combined ADC
(a) (b)
Figure 3.1: (a) Correlations between HG ADC and LG ADC (left) and (b) between LG ADC and combined ADC (right). HG ADC less than 2500 ch is plotted here because it saturates at approximately 3000 ch.
adc_combined Entries 1443922
Mean 896.7
Std Dev 391
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6adc_combined Entries 1443922
Mean 896.7
Std Dev 391
hadc[0][12]
ADC
Entries
MIP peak
Saturation of HG
Saturation of LG Pedestal peak
Figure 3.2: Histogram of the combined ADC. The red histogram shows the HG component, and the blue one the combined ADC value.
There exist many peaks with a narrow interval, which correspond to single photons. We estimated the number of photons at the MIP peak,Npe,M IP, using the following equation:
Npe,M IP =ADCM IP/∆ADCpe, (3.3)
whereADCM IP denotes the value at the MIP peak, and ∆ADCpe is the interval of the narrow peaks. The histogram of the photon yields is depicted in Fig. 3.4. Consequently, the SiPM detects 29±6 photons/MIP. This value is sufficiently high to distinguish a hit on the scintillator from noise events.
0 500 1000 1500 2000
10 10
210
310
410
5h_2_15
h_2_15 Entries 934011 Mean 75.11 RMS 315.4
h_2_15
ADC Value
En tr ie s
Figure 3.3: Pedestal subtracted ADC distribution. The peaks with the narrow interval shown with the triangles correspond to the photons. The right broad peak originates from MIP events.
3.1.2 Reconstruction of energy deposits on the scintillators
Because an ADC value represents the energy loss of a particle on a scintillator, each scintillation counter must be calibrated to convert the ADC value to the energy loss. The ADC value includes two dependences shown in the following. In this section, we describe the correction of the dependence and reconstruction of the energy deposit.
Hit-position dependence
Scintillators wrapped with reflector film propagate produced photons. They lose the photons despite their high transparency and the high-reflectivity of the reflectors. To measure the energy deposit, we must correct this attenuation effect. Figure 3.5 (a) depicts the scattered plot of the ADC values and hit position. It is evident that the value has hit-position dependence.
We corrected the dependence using an exponential function of the hit position, xhit, which is written as
Apos.(xhit) =ADCoffset+ exp (
−xhit−xoffset Latt.
)
, (3.4)
h
Entries 282 Mean 28.72 RMS 5.737
# of Photons
15 20 25 30 35 40 45
Entries
0 5 10 15 20 25 30
h
Entries 282 Mean 28.72 RMS 5.737
Figure 3.4: Histogram of the photon yields.
where ADCof f set, Latt., and xof f set denote an offset of the ADC value, attenuation length, and offset of the hit position, respectively. Figure 3.5 (b) depicts the result of the fitting. We can see that the function satisfactorily reproduces the dependence. Similarly, the hit position dependence in all the scintillators was corrected individually.
Temperature dependence
The gain of an SiPM decreases in proportion to its temperature. The temperature measured by the monitor system is used to correct the dependence. Figure 3.6 depicts a correlation between the measured temperature and the ADC values at the MIP peak of an SiPM. We corrected the temperature dependence by using the following linear function:
Atemp.(T) =p0+p1T, (3.5)
whereT denotes the measured temperature, and pi (i= 0,1) the free parameters. The red line shows the function, which satisfactorily reproduces the dependence. All the SiPM signals were individually corrected in the same manner.
Reconstruction of energy deposit on a scintillator The ADC values are corrected using the following formula:
ADCcor. = ADC
Apos.(xhit)·Atemp.(T). (3.6)
The corrected ADC values are converted to the energy deposit in MeV. To perform the conversion, we consider not only the conversion factor but also detector resolutions. In the following, we show the procedure to determine the aforementioned two parameters, i.e., conversion factor and detector resolutions.
ADC [ch]
Hit Position [cm]
ADC [ch]
Hit Position [cm]
1400 1200 1000 80 60 40 20 0
(a) (b)
Figure 3.5: (a) Example of the hit-position dependence. The horizontal axis represents the hit position on the scintillator and the vertical axis the pedestal subtracted ADC value. (b) The right part shows the slices along the Y-axis and the fitting result.
ADC/Apos.(xhit) [a.u.]
Temperature [℃]
Figure 3.6: Temperature dependence of an SiPM. The horizontal axis represents the temperature measured using the temperature sensor, and the vertical axis represents the ADC value at the MIP peak after the hit-position correction.
First, we measure the ADC values of each SiPM with cosmic ray muons and prepare for a histogram of the corrected ones. Next, we prepare for another histogram of the energy deposit on the scintillator using a Monte Carlo (MC) simulation, which will be detailed in the next chapter. Then, we determine the conversion factors and the detector resolutions to match the corrected ADC values and the estimated energy deposit. Figure 3.7 depicts the histograms of the corrected values and the energy deposit estimated using the MC. The blue line in the right figure represents the fitting result. Although there exists a small discrepancy between them around the corrected ADC of 4 a.u., the line agrees with the data. Consequently, their detector resolution is 0.63±0.04 MeV, as depicted in Fig. 3.8 This resolution is consistent with the statistic estimation of the number of photons detected.
mc_0_6
Entries 51014 Mean 4.474 Std Dev 1.414
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10 mc_0_6
Entries 51014 Mean 4.474 Std Dev 1.414
mc_0_6
0 2 4 6 8 10 12 14
edep_data_var 10
102
103
Projection of conv_gaus
Data_0_6
Energy Deposit [MeV] ADCcor[a.u.]
Figure 3.7: Histograms of the ADC and the energy deposit on the scintillator. The left shows the energy deposit. The right shows the ADC measured with cosmic ray muons, and the blue line represents the fitting result.
Reconstruction of energy deposit on a layer
The hit scintillators provide the total energy deposit on a layer. To discriminate a hit on a scintillator from noise, we use an energy threshold of 0.4 MeV. Figure 3.9 depicts the reconstructed energy deposit. Here, we applied a condition that a particle hits one or adjoining two scintillators on all layers, to remove multi-hit events. We can see the MIP peaks at approximately 4 MeV, which is 10 times higher than the threshold. Therefore, the threshold is sufficiently low to discriminate hit events.