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:
line);
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
Lorentzian, L(r):
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
function:
where
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
beam)
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
whithin a
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
and 
.
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.
Acknowledgements
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.