4 Data analysis

The analysis of the point run data undergoes various phases for determining the final experimental values of the anode currents.

1.

Detection of the star's image in the camera plane. Considering the geometry of the camera and the size of the star's image at most three PMTs could be hit;

2.

Detection of background currents in the PMTs surrounding the image area to be appropriately subtracted from the star's current;

3.

Rejection of events where the star's picture could not be reconstructed. A typical of such event is a signal in a string of three PMTs whereas doublet and triplet clusters are allowed;

4.

Determination of the mean currents from the grid points.

The energy flux and the photon current, respectively, at the telescope mirrors before being reflected have been calculated as described above. For these calculations an error of 10% has been deduced for the energy flux above the atmosphere (Torres [1987]), of 2% for the extinction (Carter & Clegg [1994]; Hayes et al. [1975]) and of 1% for the z-angle dependency during the measurement yielding in an error of 10.2%. The theoretical anode currents are then calculated in a straight forward way considering the known characteristics of the different parts of the telescope, i.e. spectral reflectivity of the mirrors and the aluminum cones, spectral quantum efficiency and mean gain of the PMTs. This step of the calculation incorporates an error of 8.4% which is typical for the apparatus used. Considering all uncertainties in the calculation of the theoretical anode current a total error of approximately 13% is determined.

   
4.1 Direct current analysis

In Fig. 2 (top graph) the measured mean direct anode currents of each star I_m is plotted versus the theoretically expected currents I_th.

Figure 2: Calculated anode currents Ith (top graph) and incident photon current IPh (bottom graph) of the stars given in Table 1 versus the measured dc currents Im. A linear least square fit is plotted for both distributions

The errors assigned to the measured currents arise from statistics in the grid points and from the systematic uncertainties due to the background brightness in the surrounding pixels (see above). In spite of the various assumptions and uncertainties the data points represent very nicely a linear relationship. Using a linear least squares fit one obtains

$$I_{\mathrm{th}}=0.775(\pm0.088)I_{\mathrm{m}}+0.301(\pm0.444)~\mu\mathrm{A}.$$ (1)

It can be concluded that within the limited accuracy of the method the direct anode current is a linear measure for the photon flux of stars detected by the IACT.

4.2 Transient response for pulse operation

For the final goal of energy calibration of IACTs, the response function has to be transferred to pulse operation. The necessary general capability of the electronic circuits is given as pointed out before. For purposes of convenience and tracing the procedure the measured anode current is first related with the calculated energy flux. This is very helpful when selecting stars for angular calibration point runs. A compilation of predicted anode currents for various stellar parameters is given in Karschnick ([1996]).

In the second step the mirror area and the spectral energy flux have to be considered to calculate the spectral photon current I_Ph . This quantity is plotted in the bottom graph of Fig. 2. The parameters of the linear correlation are given by

$$I_{\mathrm{Ph}}=\frac{5.82(\pm0.49)\ 10^{14}}{{C}} \cdot ... ... + 2.82(\pm 2.33)\ 10^{8}\frac{\mathrm{Photons}}{\mathrm{s}}~.$$ (2)

When detecting pulses of Cherenkov light, the readout electronics sample the charge at the anode Q_Anode with an integration time of 30 ns leading to the number of the incident photons N_Ph given by

$$N_{\mathrm{Ph}}=\frac{5.82\ 10^{14}}{{C}}\cdot Q_{\mathrm{Anode}}~,$$ (3)

where the offset is neglected (see below). The error of N_Ph deduced from Eq. (2) is approximately 8%. The additional error introduced to the pulse branch by considering the offset is negligible. For the Q-ADC the gain of this branch has finally to be considered, resulting in a calibration function for pulse operation:

$$N_{\mathrm{Ph}}=\frac{5.82\ 10^{14}}{{C}}\cdot \frac{Q_{\mathrm{Q}}}{16}~.$$ (4)

If, for example, 1 pC is read out at the PMT, corresponding to 4 channels, approximately 36 photons have reached the telescope. The maximum value of 256 pC corresponds to about 9300 incident photons.