3 Performance of PSPCs

The performance and characteristics of the flight PSPCs were measured extensively. Here we present some results on their energy and position response measured with 8 keV X-rays collimated to 150 $\mu$m radius at an applied anode voltage of 1700 V. The collimated X-rays were projected on $87\times120$ grid points at 0.94 mm intervals on PSPC aperture. It has been noticed at the previous calibration of WXM/HETE-1 (Yamauchi et al. 1997; Tokanai 1997) that the self-induced space charge effect degrades energy resolution and its linearity at high anode voltages. In the HETE-2 counters, the energy resolution becomes worse at $\ge 1600$ V while the position resolution gradually improves at higher voltages and reaches 0.6 mm (FWHM) around 1700 V. Therefore we choose to operate around 1650 V in order to achieve good position resolution of <1 mm, which is required for PSPC/WXM to localize GRBs with 10$^\prime$ accuracy in 2-second integration time. Here we present some results from a counter at 1700 V anode voltage.

The linearity of the output pulse height (sum of the charges collected at the left and right ends) to the incidence photon energy was measured for one PSPC using monochromatic X-ray beams with energies 6-24 keV with 2 keV step. While at the applied voltage of 1400 V there is a good linearity between them, at 1700 V the linearity is not conserved due to the self-induced space charge effect. The energy resolution is mostly uniform (22% at 8.04 keV with 1700 V anode voltage) except near the wire ends ($\pm 60$ mm) where the electric field is distorted by the wall of the counter.

The position of an incident X-ray is determined from X = L / (L + R), the ratio of the charge collected at the left and right ends of the anode wire. Ideally the ratio X is expected to have a linear relation with the incident position x along the anode. In reality there is nonlinearity near the ends of anode wire (Fig. 2). We use an empirical analytical formula to calculate the incident position $x_{\rm cal}$ from the measured charge ratio X. The parameters of the formula are determined for each anode wire by fitting the measured curve. The position resolution was also found to be mostly uniform at 0.6-0.7 mm except near the wire ends. In Fig. 3 the position resolution expressed by the FWHM of the distribution of $x_{\rm cal}$ is plotted against incident position x.

  

Figure 2: The relation between pulse height ratio L/(L+R) and incident position of X-rays

  

Figure 3: Position resolution (FWHM; mm) as a function of incident position along the anode wire