In the following the main results of the on-ground calibration analysis are presented, together with the overall MECS performance.
The lack of a temperature readout from the Test Equipment did not allow us to investigate the gain dependence on temperature during the MECS calibration at the PANTER facility. However, during the integrated satellite tests in ESTEC in October/November 1995, we were able to collect useful data for the ME1 and ME3 units. A preliminary analysis of these data indicates that the gain is anticorrelated with the temperature, and that variations of produce variations of 1.5% in the gain. A more accurate measurement of this dependence will be performed during the in-flight Science Calibration and Verification (SVP) Phase.
A dependence of the gain on the position is present in all three detectors (in the sense that a photon falling at the edge of the detector will be revealed in a different PHA channel than a photon falling close to the center); this dependence can be calibrated by analysing individual spectra of each spot of the multipinhole measurements. The core of the line in each spectrum has been fitted with a gaussian, and the peak position in channels has been associated to the spot position in pixels, obtaining a sparse set of values . For each data acquisition, a gain map has been derived with a bi-quadratic interpolation of the above values on each pixel within the detector window. The values have been normalized to the gain at the detector center, obtaining a relative gain map . The relative gain has been found to be extremely stable with energy, as well as unaffected by time variations of the absolute gain (this is not surprising as the spatial dependence of gain is due to geometrical disuniformities in the PMT anodes and/or in the Suprasil quartz window); therefore, the gain maps of all the multipinhole measurements at all energies can be averaged to produce a single high accuracy gain map per detector unit.
The relative gain maps are shown in Fig. 3 (click here) for the three ME1, ME2, and ME3 units, respectively. The range of the relative gain (assuming 1.00 in the detector centre) is 0.90-1.10 for ME1, 0.99-1.06 for ME2 and 0.96-1.03 for ME3, with a rms error <0.002 on almost all the field of view (excluding the calibration sources region where data were extrapolated).
Energy-to-channel conversion, energy resolution, and spectral profile of the MECS instrument have been determined from a detailed analysis of the calibration spectra. For each PANTER calibration line (see Table 3 (click here)), on-axis and off-axis MU measurements have been analysed.
Energy spectra have been accumulated by selecting data in Burst Length in order to reject both double events (long BL) and events that convert in the scintillation region (short BL), as will be explained in Sect. 4.7.4 (click here). The relative gain maps (see Fig. 3 (click here)) have been used to correct for the position gain dependence. Temporal gain dependence, mainly due to the temperature, have been taken into account by using the mean gain of the two inner calibration sources.
Figure 4 (click here) shows the Cr line spectrum as detected by the ME2 unit as an example. Apart from the main peak, the spectrum shows several characteristics. In the low energy part are clearly present some features produced by the escape of fluorescence photons from the detector gas cell; they are present only for incident energies greater than 4.78 keV (the Xe L-edge). The phenomenon strictly depends on the geometry of the cell and on the gas filling pressure. In the case of the MECS, fluorescence photons mainly escape from the Be window and the escape fraction is expected to decrease when the energy increases, due to the greater penetration depth of the incident photon.
Figure 4: Energy spectrum of the Cr line (5.42 keV) with the fitting curve superimposed
The bridge connecting escape and main peaks is due to the loss of a part of primary electrons for window attachment. In fact, in consequence of the primary interaction of the X-ray photon with the Xe atoms, an electron cloud is produced. This cloud diffuses toward the scintillation region under the effect of the drift electric field. However, if the primary interaction takes place near the Be window, part of electrons is captured by the window itself, producing a smaller energy deposit (Inoue et al. 1978).
The spectra are fitted as a whole (see as example the continuous line in Fig. 4 (click here)) by a function which is a sum of various components: a gaussian for the main peak, four gaussian for the escape peaks, and an exponential plus a constant to model the electron attachment phenomenon. For energies below 4.78 keV, the fitting model is simplified due to the absence of the escape peaks.
In some cases, as for the Ti spectrum shown in Fig. 5 (click here), there is clear evidence of a secondary, unresolved peak, the two components being the and Ti lines; a better fit is then obtained by using two gaussian curves (the dotted curve in Fig. 5 (click here) represents the fit with a single gaussian, only).
Figure 5: Energy spectrum of the Ti line (4.52 keV) of the central peak region. The dotted line refers to a single gaussian fit; the continuous line represents the double gaussian fit
In Table 4 (click here) the total escape fractions are reported. The experimental values are in good agreement with the prediction of a numerical model of the detector; no variation has been found as a function of the incident photon position.
Table 4: Experimental total escape fraction
Figure 6 (click here) shows the results of the gain analysis for the detector unit ME2 (ME1 and ME3 units present a similar behaviour). The discontinuity at 4.78 keV (the jump in the detector gain) is caused by a decrease in the photon-electron conversion efficiency of the gas at the Xe L-edge (Santos et al. 1991; Dos Santos et al. 1993). This effect was also found in the EXOSAT, Tenma (White 1985), and Spacelab GSPC detectors. The solid straight line in Fig. 6 (click here) corresponds to the best fit of the experimental points on each side of the edge (Mg, Al, Si, P, Ag and Ti lines for the left side; Cr, Fe and Cu lines for the right side).
Figure 6: Gain vs. energy relationship for the ME2 detector unit. The discontinuity region due to the L-jump is zoomed in the insert
The fit procedure performed with the law
with Gain expressed in channel and E expressed in keV, gives the best A, and coefficients for each detector unit; the derived value of the L-jump discontinuity, averaged over the three units, is eV, in good agreement with previous measurements (Lamb et al. 1987; Dos Santos et al. 1993).
The spectral analysis allows to derive the energy resolution of the three MECS units for each PANTER calibration line.
The experimental values, in the form of Full Width Half-Maximum (FWHM),
have been fitted by:
where E is expressed in keV. The best fit values for the parameter A are , and for ME1, ME2 and ME3 respectively, in agreement with the expectation for this kind of detector. In fact, the theoretical limit for the energy resolution of a GSPC is:
where F is the Fano factor and N is the mean number of primary electrons produced by the X-ray photon. For the Xenon, typical value of the Fano factor is . The mean energy to produce an electron-ion pair in Xenon is 22 eV. Using these values, the theoretical limit for the energy resolution is % at 6 keV (Ramsey et al. 1994).
In the central region of the detector gas cell (10 mm radius) no position dependence of the energy resolution is pointed out within the experimental errors.
As an example, the ME1 spectral resolution versus energy is plotted in Fig. 7 (click here).
Figure 7: Spectral resolution vs. energy relationship for the ME1 detector unit
The position response of the detector is affected by some nonlinearities coming from three main contributions. The first most likely derives from spatial disuniformities in the PMT gain; the second one is due to a geometrical effect, i.e. different scintillation positions are seen by the PMT under different solid angles, leading to a variation in the light collection and then to an erroneous determination of the scintillation event position. These two effects are energy independent. The third contribution may be related to the distortion of the electric field near the Be window, due to a slight curvature of the window itself. This effect is more enhanced at low energy because of the shorter mean penetration depth of low energy photons (0.4 mm being the mean penetration depth of 1.5 keV photons with 1 atm of Xe) that produce a shift of the scintillation point with respect to the point in which the X-ray photo-absorption occurs.
In order to correct for these effects, the multipinhole measurements have been analysed; for each energy at least one measurement has been made and, in some cases, a scan has been performed, shifting the mask by steps usually of 1 mm or (sub)multiple, in order to have a fine coverage of the detector sensitive area with a grid of mm. As a preliminary step, the detector electronic axes were verified to be aligned with the detector geometrical axes (determined by the strongback ribs) by using FF measurements at low energies, where the shadow produced by the window strongback is clearly visible. This allowed to correct for a slight rotation () between multipinhole mask and detector axes.
The barycentres (in pixels) of the spot images generated by the
multipinhole mask, placed 1690 mm away from the detector, have been
calculated through a bidimensional gaussian fit. Then, taking into account
the real pitch of the holes as projected onto the Be
window, a transformation law has been derived to convert the coordinates
from pixels to millimetres. The transformation law that best fits the data
is a third order polynomial, with a dependence on the energy only in
the linear term.
where and are the original coordinates in pixels, E is the energy in keV, X and Y are the new coordinates (expressed in mm) and are the best fit parameters.
Figure 8: Multipinhole data of the Cu line for the ME3 detector unit. The position (0,0) refers to the center of the detector. Each pin connects the actual hole (point of the pin) with the measured position (pin's head). a) analysis made with a constant plate scale factor (0.17 mm/pixels); b) analysis performed by using the third order linearization polynomial
The plate scale of the three detectors is . A small anisotropy in the linear coefficients and is present between the coordinate axes: in particular, it is % for ME1, while it is negligible (<1%) for ME2 and ME3. Figure 8 (click here) shows the result of the application of the above linearization formula on the Cu line data acquired with the multipinhole mask scan.
The transformation law reported here reconstructs the position of the holes with a rms error of 90 m in a central region of 6 mm radius, and of 120 m in the whole detector. These two values should be considered upper limits with respect to the actual values because they contain also the contribution of the mask hole position uncertainties. In the linearization procedure, the energy value E will be derived from the channel-to-energy conversion law. Due to the good MECS spectral resolution, this procedure will introduce a small additional uncertainty of m. A different approach, that is a correction of the geometrical distortions based on a XY plane correction map, is under evaluation.
The Point Spread Function (PSF) of the MECS is the convolution of the MU PSF and the detector PSF. The precision with which an X-ray event is localized in the detector is essentially determined by the number of electrons which are liberated by the interaction of the photon with the Xenon gas contained in the detector cell. Thus the detector PSF is expected to be a gaussian with .
The multipinhole data acquisitions have been used to measure the detector PSF. We find the data to be in good agreement with theoretical predictions for energies E<4 keV while, for E>4 keV, the appears to be larger than expected. The disagreement between data and model is due to the fact that, at high energies, the size of the PSF becomes comparable to the size of the holes, making the pinhole approximation as a point-like source no longer valid. In principle, the of the detector PSF, at high energies, could be recovered by convolving the emission from a hole of finite size with a gaussian, and then by fitting this convolution to the experimental data. In practice, it can be more conveniently derived from the FF data, by measuring the radial distribution of photons in proximity of the detector unit edge (a preliminary analysis confirms the dependence). The MU PSF, for which a set of measurements was already obtained during previous calibration runs (Conti et al. 1994), is characterized by broad low brightness wings.
In the following we describe the on-axis MECS (MU + detector) PSF. An analysis of the off-axis PSF is currently under way, and it will be reported elsewhere. Preliminary results indicate that, for off-axis angles <10 arcmin, the departure of PSF shape from radial symmetry is relatively small, thus allowing us to apply the radial description of the on-axis PSF hereafter outlined. For off-axis angles >10 arcmin, i.e. outside the strongback region, an azimuthal dependence of the PSF becomes apparent.
In order to obtain corrected on-axis PSF images of the MECS system we have:
The fit of the radial profiles have been performed with a PSF model
which is the sum of two components: a Gaussian, G(r), and a generalized
where r is the distance from the peak of the emission and , , , , and m are the parameters of the model. As an example, in Fig. 9 (click here) the fit to Al line data is shown. As can be seen, the very high statistics ( events in each MU on-axis data acquisition) allows us to measure the PSF up to 20 arcmin corresponding to 60 pixels.
Figure 9: Differential PSF at 1.49 keV (Al line) for the ME3 detector unit
By imposing that the integral of the PSF over the entire plane
be equal to unity,
we have reduced the number of independent parameters to four: , , m, and R, where . The dependence of these four parameters on energy has been reproduced through simple algebraic functions. As an example, the fit of the values derived at the PANTER calibration lines for the parameter R is shown in Fig. 10 (click here).
Figure 10: The R parameter, defined as , as a function of energy for the ME3 detector unit
The complete analytical expression for the on-axis PSF is:
where R(E), , and m(E) are algebraic functions of E.
Since both G(r) and L(r) can be analytically integrated in ,
the PSF equation can be used to derive a mathematical expression for the
Integral Point Spread Function:
This equation has been used to evaluate the 50% and 80% Power Radius (PR) at three different energies for the ME3 unit; the derived values are reported in Table 1 (click here) (ME1 and ME2 units give PR values very close to the ME3 ones).
The total MECS effective area, , results
from the MU effective area (), reduced by some transmission
coefficients related to the plasma protection grid (), the
plasma/UV filters (), the Be window (), and to the detector
efficiency (); a further reduction coefficient () due to the
Burst Length selection must be also considered:
Figure 11 (click here) shows the MECS (3 units) effective collecting area as function of energy for different off-axis angles.
All the effective area components will be described in the following sections. It is important to point out that, during the on-ground calibration, measurements of the absolute efficiency have been done only for the optics. The effects of the other components are evaluated mainly by simulations.
Figure 11: The MECS effective collecting area as function of energy for different off-axis angles
The MU effective area is given by:
where and are the number of counts detected during a Mirror Unit and a Flat Field measurements respectively, and are the exposure times corrected for the instrumental dead time, and indicate the detector efficiency for MU and FF measurements respectively, is the geometrical area of the detector, and K is a correction factor taking in account the different flux, on the detector and on the Mirror Unit, due to their different distance from the X-ray beam source.
is in general different from . In fact, during a FF measurement, the X-ray flux is spread on the entire Be window and partially absorbed by the strongback structure while, during a MU measurement, the X-ray flux is well concentrated in a small region of the window due to the optics spread function, and only for particular off-axis angles it is absorbed by the strongback structure. The difference between the two values and is significant below a few keV while it becomes negligible above 4 keV.
and were computed by accumulating events in selected energy intervals. The detector energy gain was corrected for the position distortion by using the correction maps (see Sect. 4.2 (click here)), and for the time variation by using the gain of the inner calibration sources.
The instrumental background, measured in a long detector exposure with the X-ray beam switched off, was subtracted from the accumulated events. Furthermore, two regions of 3 mm radius around the inner calibration sources were excluded from the accumulation process.
For each PANTER calibration line (see Table 3 (click here))
we obtained a set of effective area values corresponding to the
different off-axis positions. Each set at energy was fitted by the
is a vignetting factor with
where and are the baricenter coordinates (mm) of the spot image during a MU measurement at off-axis , and are the on-axis focal plane coordinates, and P is the MECS plate scale factor. , , , , and are free parameters of the fitting procedure. , the maximum of the function, is the MU on-axis effective area.
Figure 12: On-axis optics effective area vs. energy for each MECS unit. The diamond markers correspond to the values (see text). The continuous lines, A(E,0), represent the theoretical expectation multiplied by a second order polynomial
Figure 12 (click here) shows the on-axis optics effective area
for each of the three MECS mirror units.
The theoretical effective area has been computed by considering the optics
coned geometry and the Au reflection coefficient (Henke et al. 1993).
The agreement between theoretical and experimental results has been
reached by multiplying the theoretical value with a second order polynomial
of energy. The best polynomial parameters are obtained by fitting experimental
data; the result of the fitting, A(E,0), are reported in
Fig. 12 (click here) as a continuous line, while the diamond markers
represent the values. The general equation becomes:
For each energy , the vignetting factor is derived by interpolation of the experimental values and .
The results shown in Fig. 12 (click here) refer to the case of an emitting source located at 130 m from the optics (PANTER configuration). The finite distance of the source produces a loss of effective area compared to the case in which the emitting source is located at infinite distance. In fact, for finite distance, the beam is divergent, and a small but not negligible fraction of the radiation is imaged in a region around the focus. This region appears as a large radius annulus in the case of on-axis source direction (), and it assumes a more complicated shape for large values. The intensity of the loss radiation is function of energy, too; being each mirror at different slope, their contribution to the finite distance radiation loss are different: high energy photons () are reflected mainly by the inner optics, while low energy photons by the entire optics system.
To obtain the correct starting from the
) values, we simulated, by means of a ray-tracing software,
both the infinity case (parallel beam) and the PANTER case (divergent
for several values of E and .
The optics geometry was followed in all its details
by the traced rays, and only the radiation reaching the focal plane
circle corresponding to the Be window, was taken into account for the
computation of the effective area.
Two different sets of values have been produced, namely
Finally, the relation between
and can be written as:
In order to avoid that the plasma particles crossing the MU can accelerate towards the Be window set at , a plasma protection grid is mounted below the optics system. The grid in Au-coated tungsten is kept at , shielding the Be window electric field. This grid causes a loss of effective area of 8% (), independent on the energy. Furthermore, to be sure that any high velocity plasma component overcoming the grid shielding doesn't impinge on the Be window, plasma filters have been placed in front of them. The filters stop also UV light photons that could extract electrons from the Be window; these electrons, accelerated by the Be window electric field towards the MECS Carbon fiber walls, should produce a background increase due to the electron bremsstrahlung emission.
The first solution adopted for plasma/UV damage protection was the use of thin Polyimide filters, as in the LECS case (Parmar et al., this volume), and the MECS on-ground PANTER calibrations were performed with this kind of filter. Unfortunately, after vibration test, one of the Polyimide filters was found to be destroyed. Now, in the flight configuration, ME2 and ME3 units are both protected by a LEXAN filter thick, aluminium plated by two layers of , each; for precautionary reason, the third unit, ME1, is protected by a thick KAPTON filter, aluminium plated by two layers of , each. Figure 13 (click here) shows the transmission efficiency for the two filters.
Figure 13: LEXAN and KAPTON filter transmission efficiency vs. energy. Circles indicate measured values (Jager 1996)
No measurements of the Be window transmission efficiency were
performed during the MECS on-ground calibrations; anyway, this efficiency
can be computed analytically by:
where is the absorption coefficient of the material at the energy E, and x is the thickness. Figure 14 (click here) shows the transmission efficiency for a layer of (window thickness) and for a layer of (window plus strongback thickness), representing the two different regions of the detector window, as shown in Fig. 2 (click here) (verification of strongback thickness from FF measurements is in progress).
Figure 14: Beryllium transmission efficiency vs. energy for two different thickness values
The gas cell absorption probability is:
where is the Xe absorption coefficient for the energy E, and D is the size of the absorption region. Figure 15 (click here) shows the gas cell efficiency obtained with D equal to the drift region depth; events that convert in the scintillation region are rejected to improve the energy resolution.
Figure 15: Gas cell absorption efficiency for the drift region vs. energy
Figure 16: Burst Length vs. energy pseudo-image for the Cu line
In Fig. 16 (click here) the BL versus energy pseudo-image (contour plot) for the Cu line spectrum is shown. The spot ``a" refers to events which convert in the drift region with a single electron cloud giving correct PHA and BL values; this kind of events make up more than 90% of the total events. The spot ``b" refers to the residual events; these events present a single electron cloud too, but an incorrect PHA value (see Sect. 4.3 (click here) for further details). The bridge between ``a" and ``b" is mainly due to events that, interacting with the Xenon near the Be window, loose part of the electrons for attachment to that window. This phenomenon is seen as a low energy tail in the line spectra (as already explained in Sect. 4.3 (click here)). The tail ``c" is due to events which are absorbed in the scintillation region producing a reduced amount of UV light (and a shorter BL), resulting in an incorrect PHA value due to the shorter path in that region. These events, in the case of the Cu line (8.06 keV), are 4.5% of the total number of events; for lower energies, this fraction decreases due to a shorter penetration depth (see Fig. 15 (click here)). The jet ``d" is due to some of double events, i.e. to events with the fluorescence photons re-absorbed inside the gas cell but at a different position from the primary conversion. This effect produces correct PHA value but a higher BL value due to the sum of the two scintillation bursts; the position detected for these events (2.4% of the total number) should be incorrect being the weighted average of the two interactions. The rejection of ``c" and ``d" events is performed by using a suitable BL selection. Such a kind of picture is typical of energies greater than 4.78 keV (the Xe L-edge); for lower energies, the regions ``b" and ``d" disappear while the ``c" region becomes negligible. A function has been derived to introduce the effect of the selection in the MECS total effective area () computation.
Two components will be present in flight:
Environmental charged particles, interacting with the gas in the detector, loose their energy producing electron clouds. The dimension of the clouds is generally bigger than the one due to X-ray photons of equivalent energy, because of the longer path the particle covers before being stopped. The Burst Length, proportional to the cloud dimension, can then be used to discriminate genuine photons from charge induced events.
Measurements of the environmental background have been performed during the PANTER and ESTEC calibration campaigns. The longest background accumulation, relative to the ME1 unit, has a duration of hours. Data used for the evaluation of the residual background have been opportunely selected in BL and in position. Figure 17 (click here) shows the image of the residual background after the BL selection applied during the data analysis. The circle indicates the region used for the analysis: the outer region is not considered in order to exclude both the two spots produced from the inner Fe calibration sources and the high density outer ring; this ring is due to events converting in the outer part of the detector (outside Be window diameter) and compressed towards the internal region by the readout system.
Figure 16: Environmental background image. The circle delimits the region for which are valid the data reported in Table 5 (click here)
Figure 17: Residual background spectrum within the circle as in Fig. 17 (click here)
The spectrum of the selected events is shown in Fig. 18 (click here). The spectrum was fitted with a constant plus a gaussian; the results of the fit are shown in Table 5 (click here). A line-type feature is evident in the central part of the spectrum. Possible explanations of this feature are: a) fluorescence by detector material (as the NiCo ring in Fig. 1 (click here)); b) re-absorption, far from the primary interaction point, of fluorescence emitted from the calibration sources; c) combination of the two above effects. The background is in any case very low and the statistics collected during the on-ground calibration does not allow a conclusive analysis of the nature of the line. A deeper analysis of the detector background will be performed with the in-flight data.
Table 5: Background counting rate: results of the fit
Estimation of the in-flight residual flux of charged particle background from previously flown (EXOSAT) and currently operating (ASCA) Gas Scintillation Proportional Counters brings to a conservative value of in the band.
Evaluation of the expected count rate from the extragalactic component of the diffuse background has been made by simulating photons coming from off-axis up to with uniform angular distribution. The spectrum used in the simulation is a power law of spectral index 1.5 corrected, at low energy, for the galactic absorption from a column of . The obtained count rate is , where is referred to the considered detector area.
We wish thank L. Scarsi for the effort he spent in supporting BeppoSAX mission, R.C. Butler for his tenacious interest in the scientific instruments, O. Citterio for the work in developing the technology and the testing methods of the Mirror Units, G. Manzo for the original contribution to the design and development of the ME detector. G. Ferrandi, E. Mattaini, and E. Santambrogio, from IFCTR Institute, provided the mechanical calibration support equipment. We thank H. Brauninger and W. Burkert for the support to the calibration activity at the PANTER facility. L. Casoli, M. Confalonieri, P. Dalla Ricca, T. Motta, A. Prestigiacomo, G. Rimoldi, A. Sada, P. Sarra, and L. Vierbi, from Laben industry, sub-contractors for the MECS instrument, assured the management of the detectors and of the data acquisition system during the calibration campaigns. S.Molendi acknowledges useful discussions with H. Ebeling on PSF models. We wish thank K. Ebisawa for the useful suggestions to improve this paper. All the activities of the Scientific Institutes have been financially supported by the Italian Space Agency (ASI) in the framework of the BeppoSAX mission.