PMT is very sensitive to light source, even few photons can be detected. So a good black box for light source is needed. The box size is about 60 cm×30 cm×25 cm. It was made of wood and painted with opaque paint several times to reduce the possibility of reflection and penetration. The light source I
used is LED. The LED was connected with function generator. The function generator can control light source by sending square pulses to LED. The light intensity, frequency and width could be adjusted through function generator. The distance between PMT and LED is about 50 cm. Because the PMT has the most sensitivity in the range from 400 nm to 500 nm, I used the blue light LED. Fig. 3.9 shows the PMT and LED in the black box.
To begin, it is necessary to test the effect of black box. A black box without any light source in it was covered by a cloth, one side of the cloth is black and the other side is reflective. I then turned on the PMT for a while. One expects that the pulse height spectrum is a pure narrow Gaussian shape. Fig. 3.10 shows the actual pulse height spectrum of pedestal in my case.
After the test round and the warming up of apparatus, I set the frequency and width of the LED to be 20 kHz and 50ns, respectively. The pulse generator sends the signal to LED and a square-wave function to DAQ as trigger simultaneously. The pulse height is from 2.45V to 2.50V. When DAQ receives the square-wave function, it opens a posterior 200ns width. The duration of the whole process which be-gins from photon emission from the LED and ends at the recording of output voltage by DAQ is about 100ns.
The fitting method is the same as the darknoise part. Fig. 3.11 shows some fitted results. Fig. 3.12 and Fig. 3.13 shows the error range and trend of Q1.
The LED data taking period includes a transition from the old building to the new one. Hence I took the data at two different locations. I separated them into LED-old and LED-new. Fig. 3.15 and Fig.
3.16 shows the error range and the trend of Q1.
Fig. 3.9: The PMT was placed on the right side, LED was attached to the black stick on the left side.
Fig. 3.10: The pulse height spectrum of pedestal.
(a)
(b)
(c)
(d)
Fig. 3.11: Some fitted data obtained by the LED method.
Fig. 3.12: The error range of Q1. The data was taken from Aug. 17 to Aug. 30..
Fig. 3.13: The Q1 value of LED-old. The horizontal axis starts from 21, which means the LED run is a continuation of 20-day darknoise run..
Fig. 3.14: The error range of Q1 of LED-new.
Fig. 3.15: The Q1 value of LED-new.
Result
Now we compare Q1 obtained by two methods and calculate the difference between them. Table 3.2 shows the maximum, minimum, average and error range of Q1. First we only discuss the darknoise and LED-old which were taken at the same place. We find that the minimum and average of Q1 are very close. The maximum Q1 of darknoise is larger than the one of LED-old by 0.00105. It is much larger than Q1 obtained the other days. If the value 0.04944 is treated as unusual, the re-calculated result of darknoise is much more consistent with LED-old. No matter we disregard the value 0.0494 or not, the result shows that using the two methods to do calibration is feasible. The difference between the two methods is less than 0.7%. Fig. 3.17 puts the Q1 of the two methods abreast.
Table 3.2: Q1 values obtained by two methods. The first row of darknoise is the whole twenty-day data and the second one is the nineteen-day data which subtracts the odd one-0.04944.
The Q1 spread is wide for one PMT. However, if there are multi-PMTs which are calibrated at the same time, this produces a distribution of Q1. Then the weighted average of Q1 can give a better accuracy[8].
Suppose we have a set of n independent measurements, xi. If the xi have different, known variances
For example, in Daya Bay experiment, there are 192 PMTs in AD. If all these PMTs are good and the variance of PMT is close to each other. Hence the Q1 values of these 192 PMTs form a Gaussian
dis-tribution. The weighted mean of Q1 is more accurate than each individual Q1 by
192
times.Fig. 3.16: Q1 obtained by two methods on each day are shown.
We can see that the Q1 of LED-new is more stable and higher than that of LED-old, though the former was just taken for a few days. The reason is probably that the old building is not built for doing expe-riment, hence its power supply and electrical system are not well grounded. This means the experiment is easily fluctuated due to external interference.
Unfortunately, the high voltage supply was set to be 1400V, and I could not measure and record the actual voltage. Hence I cannot confirm the conjecture.
Fig. 3.17 : the total trend of Q1. The darknoise and LED-old were taken in old building, the LED-new was taken in the new building.