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The distribution of events for each peak finder is shown below. In the lower plot next to it, the square peak finder distribution is manually shifted by -4.8 to compare the shapes of the distribution which appear to be very similar.
One can see that the peaks roughly follow a Gaussian distribution but on the higher end, there is a very noticeable shoulder. At first, it appears to be a result of dense photons, a situation that was avoided. With the use of sparse events. A Gaussian curve was fitted to both distributions but to ignore the effects of the shoulder, only the data within 15 ADU of the bin with the maximum number of peaks was used so as to center the data used in the fit around the peak of the Gaussian. The result from this was the V1 peak finder having a mean of 141.93 ± 0.06 and a standard deviation of 8.37 and the square peak finder having a mean of 146.68 ± 0.060 and a standard deviation of 8.20 where the errors were obtained by σ/√N.
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It is possible that this shoulder is partly due to the K-beta emission of the material used in this particular experiment which happens to be copper (while the main peak is the K-alpha emission). After a quick loop-up, these values for copper are approximately 8040 keV for K-alpha and 8900 keV for K-beta which gives a 1.107 ratio of K-beta to K-alpha. If we look at the distribution of just the maximum energy pixel of each peak, as shown below, there is very visibly some type of peak on the higher energy side of the 1 pixel distribution. The main peak has a mean of 140.
k alpha = 8041, k beta = 8905 (Cu)
3 while the mean of the smaller peak is about 155. This gives a ratio of 1.104. The numbers used are approximations and the second peak is artificially shifted by the Gaussian from the first peak underlying it. So it is very likely that these two peaks are the K-alpha and K-beta lines of copper.
Closer Look at the Effect of Pixel Size
Since the square peak finder only find 4 pixel peaks, only the data for the V1 peak finder is shown below. This data consists of 29,342 peaks found from the 13 different events.
| Pixels | Peaks | Mean | Error | RMS | |
|---|---|---|---|---|---|
| 1 | 7164 | 140.24 | 0.09 | 7.45 | |
| 2 | 14926 | 142.54 | 0.07 | 8.24 | |
| 3 | 4354 | 141.53 | 0.17 | 11.44 | |
| 4 | 2898 | 146.58 | 0.18 | 9.70 |
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Lining up and Recombining Pixel Distributions
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When fit with a Gaussian in the same manner as before, the results confirm this observation. Although there is a decrease in the width, it is very small. The noticeable change in the mean is most likely due to the choice of energy used to which the peaks were shifted.
| Mean | Error | RMS | |
|---|---|---|---|
| Shifted | 141.55 | 0.06 | 8.59 |
| Unshifted | 142.06 | 0.06 | 8.72 |
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