Figure 2
Below in Figure 2 are the histogrammed results of the "true" inelastic proton dilution factor (with a 2 ns window cut (since the sigma of the elastic distribution is about .4 ns)) from simulated data being rebinned in the fashion of the NA TOF spectra with DNL for detector 1. This is done for 212 different sets of DNL values.
Figure 2
Figure 3 is the histogrammed results of the inelastic proton dilution from finding the inelastic and elastic contributions from a two gaussian fit over a 2 ns window for detector 1. Instead of finding a single distribution, one finds two distributions do to the binning caused by the DNL. Examples of TOF spectra that give rise to these different distributions can be found in figure 5(inelastic dilution = 0.137652) and figure 6(inelastic dilution = 0.0451361).
Figure 3
Figure 4 is the ratio of the "real" inelastic proton dilution to the fit inelastic dilution can be seen for detector 1. The ratio of the true to fitted dilution factor does not distribute itself around 1 as one might expect, but in fact takes values over a range from 0 to 3.5. Thus the conclusion that can be drawn from this is that finding the dilution factor without correcting for the DNL is unacceptable.
Figure 4
Below in Figure 5 is an example of one particular set of DNL values for detector 1. By the fit methods, the inelastic dilution factor is 0.137652.
Below in Figure 6 is an another example of one particular set of DNL values for detector 1. By the fit methods, the inelastic dilution factor is 0.0451361. In this example, the fit does not represent reality due to the DNL, the height of the elastic proton distribution is 4 times higher than what it should be and the width is half the magnitude of what it should be.
