these extraordinary values will be investigated in future studies.

The 475 MeV and 210 MeV measurements in WbLS-1 resulted in small numbers of photoelectrons with broadened distributions relative to a Poisson distribution. It is also apparent that some low amplitude events with $\approx$ 1 PE contributed to the distribution, as evidence of these events are seen in some of the other measurements. The distribution broadening can be modeled by convolving the simulated distributions with a Gaussian as outlined in [@Balagura2006]. However the broadened distribution obtained using this technique were unable to reproduce the shape of the measured photoelectron distributions for all proton energies. Due to the poor agreement of distribution shapes, $\chi^2$ optimisation was quite sensitive to the selection or exclusion of the 1 PE bin in the analysis. The sensitivity of the light yield and quenching parameter to this effect is included in the statistical uncertainties for the WbLS-1 results reported in table \[tab:OptimalVals\].

The Tub 1 results are not presented, as it was not possible to obtain agreement with the simulation model that was consistent with the measured distributions across all beam energies for all materials, for any value of the tub reflectance. While the cause of this 