Improved Cherenkov angle resolutions

Simulation is used to determine the resolution contributions for both methods, using silicon telescope (SITEL) information or the method of geometrical reconstruction (ELLIPSE). The estimated contributions from the above sources are given in Table 7.

Table 7: Summary of expected resolution contributions for the analysis of the Cherenkov angles in C₄F₁₀ using silicon telescope and elliptical fit information.

	No Mylar	Mylar
Contribution	$\sigma$($\theta_{\rm c}^{}$) (mrad)	$\sigma$($\theta_{\rm c}^{}$) (mrad)
Pressure Variation	0.02	0.02
Emission Point	0.58	0.58
Chromatic Aberr.	1.03	0.20
Finite Pixel Size	0.56	0.56
Beam Trajectory :
Silicon telescope	0.38	0.38
Elliptical Fit	0.28	0.58
Totals :
Silicon telescope	1.36	0.91
Elliptical fit	1.34	1.01

The results observed in data are summarised in Table 8 for both methods.

Table: Gaussian widths of the measured Cherenkov resolutions in data using improved beam direction estimates. This is based upon either silicon telescope information (SITEL) or geometrical reconstruction (ELLIPSE) to estimate the input beam direction for HPDs (2,3,5,6) and (4,7).

	SITEL (mrad )		ELLIPSE (mrad )
HPD	$\sigma$( $\theta_{\rm c}^{}$ )	Mean	$\sigma$( $\theta_{\rm c}^{}$ )	Mean
2 (no mylar)	1.36		1.25
3 (no mylar)	1.53		1.51
5 (no mylar)	1.06		1.16
6 (no mylar)	1.42	1.34	1.68	1.40
4 (mylar)	0.91		1.08
7 (mylar)	1.20	1.06	1.12	1.10

The observed results using the silicon telescope (SITEL) method are generally consistent with simulations, based upon three perfectly aligned silicon detector planes with pixel dimensions of 1.3 x 1.3 mm. The average of the measured resolutions using this method for HPDs (2,3,5,6) and (4,7) are 1.34 mrad and 1.06 mrad respectively. The corresponding expectations from simulation are 1.36 mrad and 0.91 mrad respectively.

The observed Cherenkov angle distributions from geometrical reconstruction (ELLIPSE) of single photon hits are shown in Figure 13, together with Gaussian fits to the core of the distributions.

Figure: Measured Cherenkov angle distributions using geometrical reconstruction based on the elliptical fitting method. Results for each of the 6 HPDs are shown. The first four, (2,3,5,6), are without mylar input filters and the second, (4,7), are with filters. The x axes are in units of milliradians.

The corresponding results for HPDs (2,3,5,6) and (4,7) are 1.40 mrad and 1.10 mrad respectively. These are also in good agreement with simulation, which predicts corresponding values of 1.34 mrad and 1.01 mrad.