Estimates of the photon yield

The number of detected photoelectrons per event is determined for various gas and aerogel radiators, using different filters. Two aerogel samples are studied, together with air and C₄F₁₀ gas radiators. Three filter configurations are tested. Either no filter is applied, or a glass or mylar filter is placed in front of the quartz input window of the HPDs.

Two complementary analyses are employed, which allow estimation of systematic uncertainties due to different methods of background subtraction, photon counting and efficiency corrections. The relevant features of the two analyses are briefly summarised here :

• Analysis 1 - Hit pixels are defined to be those with an ADC count which is greater than three pedestal sigma above the mean pedestal value for that channel. A correction is made to the observed raw photon rate when comparing with simulation, to take into account the number of signal photons which lie below this cut. This correction depends on the signal-to-noise of each channel and is estimated to represent a 15 $\pm$5% loss of signal when averaged over all channels. The number of photons detected on an active pixel is estimated using a series of intervals for each pixel, which are determined using the positions and widths of the multiple peak positions observed in LED calibration spectra. Photon counts are only accepted if they lie inside a signal region, defined to be within a three pixel border around the arc observed on a given HPD. This allows the remainder of the detector region to be used to estimate background rates. These are estimated assuming that the background distribution is uniform over the whole HPD area. For gas radiators, the background correction is small, typically $\sim$ 5%, whereas for aerogel samples it is large, between 25 and 40% depending on the filter configuration used, since the photon density is lower in this case.
• Analysis 2 - Multiple Gaussian fits are made to the observed pulse-height spectra on each pixel channel for ADC counts above a four sigma pedestal cut. By integrating the area under the signal Gaussians, and normalising to the number of recorded triggers, the numbers of photoelectrons per pixel per event are determined according to Poisson statistics. From these the total number of photoelectrons seen in all HPD's per event is obtained. Hence this analysis has no explicit background subtraction, but rather includes Rayleigh scattered photons and counts from backscattering in the total. As a consequence of the more stringent pedestal cut, contributions from electronic noise are assumed to be negligible.

Both analyses rely on simulation to correctly model the efficiency for detecting the expected number of signal photons. Analysis 1 does this explicitly, correcting the observed rate in data using factors determined from simulation. The second method includes such corrections implicitly when comparing results with simulation and assumes that the efficiencies in data and simulation are the same. Two sets of corrections are necessary. Firstly, a correction for the optical properties of the testbeam prototype, takes into account the measured values of refractive indices, aerogel clarity, transmission and reflection curves as described in Section 5. Secondly, a geometric correction is applied which takes into account losses coming from the partial detector coverage of the aergoel, air and C₄F₁₀ rings. In configuration 1 these geometric efficiencies are 15% and 25% for 5 and 7 HPDs respectively for aerogel. This correction is 25% for the C₄F₁₀ ring with 7 HPDs in both configurations.