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3. Instrument performance

3.1. Introduction

In Table 3 (click here) a summary of the performance characteristics is presented. Most data derive from measurements on a full scale prototype instrument. The operating conditions were: input photon rate up to 2400 c s-1, a 60Co background rate of up to 1000 c s-1 and a temperature range between 0 and 40 tex2html_wrap1594 C. The maximum microvibration level was 20 mg in the frequency range between 0 and tex2html_wrap_inline1780 Hz.


Quantum efficiency

2 keV 10%
10 keV 100%
30 keV 40%
Energy resolution (collimated) (full area)
2 keV 25%
6 keV 16% 20%
22 keV 19% 22%
Position readout
number of pixels tex2html_wrap_inline1782
nominal pixel size tex2html_wrap_inline1784 [mm2]
differential non-lin. (90%) <0.5 [pixel]
integral non-lin. (90%) <1.0 [pixel]
Position resolution x-dir [pixel] y-dir [pixel]
2 keV <1 <1.5
8 keV <1 <1
22 keV <2 <2
Table 3: Detector performance characteristics, the optimum quantum efficiency and position and energy resolution is reached at 10 keV. All parameters are as foreseen

3.2. Effective area

The factors that influence the effective area include:

The on-axis detector effective area, as derived from a numerical instrument model, is shown in Fig. 8 (click here) as a function of incident photon energy. At low energies the efficiency is limited primarily by the transmission of the thermal foil and the beryllium detector entrance window. At high energies the efficiency is limited by the absorption of the gas. The thermal foil consists of a 7.6  tex2html_wrap_inline1626m thick kapton filter, aluminium plated by two layers of 0.1  tex2html_wrap_inline1626m on each side, the beryllium foil is 150  tex2html_wrap_inline1626m thick. The figure does not include the instrument Life Time Fraction. The instrument LTF (This is the inverse of the instrument dead time) is measured once every second during the observations.

Figure 8: The total calculated on-axis detector effective area. At low energies the effective area is limited by the thermal foil and detector window. At high energies the efficiency is mainly limited by the stopping power of the detector gas. The maximum effective area is 138 cm2 at 10.5 keV

3.3. Energy response

3.3.1. Energy to channel conversion

The energy of an X-ray photon is derived from the main anode (A1) Pulse Height (PH) and digitised in 4096 ADC channels. In the normal operational mode (NM), binning takes place into 31 energy channels. Figure 9 (click here) gives the relation between the energy channel boundaries and the photon energy for the two Wide Field Cameras at their nominal detector gain. The width of the channels is chosen such that for an average astronomical spectrum, which falls exponentially off to higher energies, the counts in each channel are of the same order of magnitude.

The relation between PH and the corresponding X-ray energy as a function of energy has been calibrated. The calibration has been performed in detail for a small part of the sensitive area, called the Reference Location (RL). The full sensitive area has been calibrated by measuring the gas gain for each pixel with respect to RL, as described in Sect. 3.3.2 (click here). The measurements at RL have been performed by means of radioactive sources. Also a fluorescence source with an interchangeable target stimulated by a radioactive alpha emitter was used.

At the nominal gain level the energy - PH relation is non-linear due to space charge effects in the avalanche. A second order polynomial is least square fitted to the data points up to 8 keV as shown in Fig. 10 (click here). The statistical error in PH is less than 20 eV FWHM. A discontinuity in the energy - PH relation at the 4.8 KeV Xe L-absorption edges is included. We found an optimum fit for a discontinuity of 65 eV. This value is in good agreement with the value reported by Santos et al. (1991).

Figure 9: The relation between the logarithm of the photon energy and the energy bands for the two instruments at nominal gain. The instruments show a small difference due to slightly different gain settings

Figure 10: The detector gain is shown as a function of energy, the response is non-linear at higher energies due to space charge effects in the avalanche. The drawn line is a second order polynomial fit to the data below 8 keV

3.3.2. Positional dependence of the gain

  The gas gain of the detector is depending on the position of the photon in the sensitive area. The variation of the gain over the sensitive area was measured by irradiating the full sensitive area. For each irradiated pixel the gain relative to the gain at the Reference Location (RL) was determined. In Fig. 11 (click here) a typical plot is shown of the relative gain as a function of the position along a cross section of the sensitive area in the y-direction. This is the direction perpendicular to the anode wires. In the graph open areas indicate the obscuration by the window support structure. The statistical error in the data points is less then 1% FWHM.

The curve shows two components. A small scale and a large scale gain variation. The small scale component with a modulation length of 8 pixels is caused by the anode wires. The gain maxima coincide with the position in between two anode wires. At those locations the gain is less affected by space charge than at other locations. This is because the cloud of primary electrons is split up between the two anode wires resulting in a lower avalanche space charge density. As the space charge density increases with the photon energy, the modulation amplitude is much larger at 8 kev (6%) than it is at 2 keV (2%). Small deviations in the positioning of the anode wires result in an additional small scale random modulation of the gain.

The large scale component in the gain variation is almost the same for 2 and 8 keV radiation. The curves show a rather flat distribution. In the last two subwindows the gain is stepwise increased with about 6%. All other cross sections of the sensitive area in the y-direction show the same gain step. This feature is probably due to a stepwise decrease of the anode wire diameter with about 0.2  tex2html_wrap_inline1626m. At both edges of the sensitive area the gain is increasing with about 8% over a few pixels due to wall effects.

3.3.3. Energy resolution

  Up to 8 keV the pulse height FWHM (expressed in keV) at the Reference Location RL can be described by the relation tex2html_wrap_inline1830 as shown in Fig. 12 (click here). The measured FWHM is in agreement with previous results (Bruel et al. 1988). The resolution at 22 keV however is dominated by the difference in gain between events in the drift region and events in the amplification region and does not follow the relation.

The spectral resolution for full area irradiation is limited by the positional dependence of the gain. At 6 keV the resolution for full area irradiation is 20% FWHM, while for a collimated beam at RL the resolution is 17%.

Figure 11: Positional dependance of the gas gain at 2 keV (left) and at 8 keV (right). The modulation along the y-axis is caused by the anode wires and is highest at 8 keV due to the increased space charge density. The step beyond pixel 600 is probably caused by a decrease in anode wire diameter of 0.25  tex2html_wrap_inline1626m

3.3.4. Long term stability

The long term behaviour of the energy response of the WFC detectors has been monitored with the inflight calibration sources during more then two years since the final integration before launch.

During this period the energy resolution for 6 keV photons has not changed within a few percent. For 22 keV photons the energy resolution degraded from 22.7 to 24.3%, which can be explained by minute changes in the gas composition.

Figure 13 (click here) shows the pulse height as a function of time for the two WFC detectors. The statistical error in the data points is less than 0.1% FWHM. Both detectors show the same trend. It can be seen that in the first 100 days the pulse height increased by about 1%, afterwards the pulse height increased with 0.5% per 300 days. In the first period a significant part of the gain variations is due to minute movements in the housing walls and the grid system. This is caused by vibration, thermal effects and changes in the ambient pressure during qualification tests. However, the main trend in the gas gain can be explained by minute changes in the gas composition and/or a small drift in the high voltage supply. Anyway, the performance of the instrument with typical integration times of 105 s is not influenced at all by the measured variation, if necessary the gain can be regulated back to nominal by adjusting the high voltage.

3.4. Spatial response

The spatial response has been calibrated by ``flat field" measurements and by ``pinhole" measurements. A flat field response distribution is used to determine the linearity of the spatial response. For this purpose the bars of the window support structure serve as a reference pattern. A typical image of a flat field measurement at 8 keV is given in Fig. 14 (click here). It shows the number of photons counted in the detector pixels. The number of counts is a measure of the differential non-linearity i.e. the relative sizes of the pixels with respect to their nominal size. This information will be used in the image deconvolution process, described in Sect. 4.2.1 (click here), to improve the quality.

Likewise, the pinhole measurements will be used to calibrate the numerical model of the detector Point Spread Function (PSF) that is used in the image deconvolution.

3.4.1. Image linearity

A typical plot of the integral non-linearity i.e., the difference between the measured pixel position and its nominal position, is shown in Fig. 15 (click here) for 2 and 8 keV. It is given as a function of the position along a cross section of the sensitive area in the y-direction perpendicular to the wires of the main anode grid A1. The linearity curve has two components: a small scale and a large scale component.

Figure 12: The energy resolution as a function of energy, up to 8 keV it follows the relation tex2html_wrap_inline1842

The small scale non-linearity is like the variations in gain caused by the anode wires. The modulation amplitude is the same for 2 and 8 keV. The measured small scale non-linearity is the remainder of the total non-linearity caused by the anode wires. A great deal of the latter is already corrected for in the instrument software.

The large scale sawtooth shaped non-linearity component is caused by some bulging of the window support structure and of the window foil in the subwindows. The readout position of the events will be slightly shifted towards the middle of the cushion like deformations because the electric field lines always end perpendicular at the window foil. The modulation amplitude at 8 keV is smaller than at 2 keV due to deeper penetration of the high energy photons. The non-linearity at the first and the last subwindow is larger than at the others. This is because the drift regions are largely but not fully electrostatically shielded from the detector housing walls by field correction plates.

Figure 13: Long term gain stability of the two WFC flight detectors. After an initial increase, the change in gain has stabilised to less then one percent over a period of one and a half year. The variations are significant and are due to the fact that the instruments were not always completely in thermal equilibrium during the measurements

In Fig. 16 (click here) a typical histogram of the non-linearity distribution over the pixels is presented for 2 and 8 keV. In the x- and y-direction more than 90% of the pixels have a non-linearity of less than 1 pixel which is sufficient for our purpose.

3.4.2. Point Spread Function

The spatial resolution for on-axis radiation is better than 1 pixel (FWHM) between 2 and 10 keV. In the lower part of the energy range the resolution is limited by the noise of the readout electronics. In the upper part of the range the resolution is limited by the photoelectron track length.

The shape of the spatial response Point Spread Function (PSF) is an important feature for a coded mask camera.

The position and flux of X-ray sources can only be determined by deconvolution (see Sect. 4.2.1 (click here), when the PSF is exactly known.

Figure 17 (click here) shows a typical plot of the position distribution of events is shown when irradiating the detector through a 0.1 mm pinhole with 8 keV photons. Because the laboratory background per pixel is very low, the PSF could be measured in great detail. The broad distribution profile under the narrow peak (including the two peaks at both sides of the main peak in the y-direction) is caused by events disturbed by pile-up. The level is acceptably low (tex2html_wrap_inline1854).

Figure 14: Flat field measurement performed with 8 keV radiation in the SRON X-ray long beam facility. Clearly visible are the shadow of the detector window support structure, the inflight calibration sources and the modulation by the anode wires which run horizontally

3.5. Time resolution

When the WFCs are operated in their imaging mode (Normal Mode), time information is only provided for each block of four detected events. The time resolution is 0.5 ms and the time tag is valid for the last of the four events. This solution was chosen in order to reduce the number of bits per event, i.e., the telemetry rate. The arrival times of the other three events has to be estimated between this time tag and the preceeding one. The accuracy of the time tags is better then 0.08 ms, determined by the uncertainty of certain timing signals on the satellite data bus.

The time resolution in the fast non-imaging mode (High Time Resolution Mode) is 0.25 ms. In this case the time information is provided for each event. Again the precision is better than 0.08 ms.

Figure 15: The integral non-linearity is the difference between the actual and the ideal pixel positions. The left panel displays this effect for 2 keV, the right panel for 8 keV photons. The saw-tooth like modulation is caused by the curvature of the Beryllium entrance foil over the subwindows due to the pressure of the gas

Figure 16: Histogram of the non-linearity distribution for 2 keV (lower) and 8 keV (upper) illumination and perpendicular (left) and parallel (right) to the anode wires. More than 90% of the pixels have a non-linearity of less then 1 pixel (0.375 mm)

3.6. Temperature dependence

For a number of variables the temperature dependence has been measured over a temperature range of 0tex2html_wrap1594 to
40 tex2html_wrap1594 C (i.e. the nominal operational temperatures). The gas gain varies less than 2%, by means of the inflight calibration sources the actual gain is determined with an accuracy of better than 1% within 20 minutes. The gain profile over the sensitive area changes less than 0.5%. The position response varies less than 0.2 pixel. Therefore the temperature dependence can be neglected as long as the temperature stays within this temperature range.

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