Nuclear Instruments and Methods in Physics Research A 436 (1999) 85}90
Soft X-ray response of a CCD with a grating spectrometer
M. Shouho , K. Katayama , H. Katayama , T. Kohmura , H. Tsunemi ,
S. Kitamoto *, K. Hayashida , E. Miyata , K. Hashimotodani , K. Yoshita ,
K. Koyama, G. Ricker, M.W. Bautz, R. Foster, S. Kissel
Department of Earth & Space Science, Graduate School of Science, Osaka University, 1-1 Machikaneyama-cho,
Toyonaka, Osaka 560-0043, Japan
CREST, Japan Science and Technology Corporation (JST), 4-1-8 Honmachi, Kawaguchi, Saitama 332, Japan
Department of Physics, Graduate School of Science, Kyoto University, Kitashirakawa-Oiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan
Center of Space Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Abstract
We calibrate the X-ray imaging spectrometers, which are CCD cameras installed on the ASTRO-E satellite, by using
dispersed continuous soft X-rays from a grating spectrometer. We obtained the signal-pulse height and energy-resolution
as a function of X-ray energies continuously. However, the wings of the line spread function of the grating distorts the
center of the signal-pulse height derived by a simple analysis. An estimation of this distortion is presented. We also
describe two methods of extracting the pure signal-pulse-height distribution from the data using the spectrometer. A brief
description of the low-energy tail is presented. 1999 Elsevier Science B.V. All rights reserved.
PACS: 07.85.F; 85.60.G; 95.55.A
Keywords: CCD; X-ray; Grating; Signal-pulse height
1. Introduction
The response function of a charge coupled device
(CCD) has been investigated by some authors
[1}3]. The CCD response for monochromatic
X-rays has some structures: e.g., a low-energy tail,
an escape peak, and a low-energy peak [4]. Both
the amount and the shape of these structures are
* Corresponding author. Department of Earth & Space
Science, Graduate School of Science, Osaka University, 1-1
Machikaneyama-cho, Toyonaka, Osaka 560-0043, Japan, Tel.:
#81-6-6850-5478; fax.: #81-6-6850-5539.
E-mail address: [email protected] (S. Kitamoto)
functions of incident X-ray energy. The grating
spectrometer is very useful for the measurement of
the pulse-height distribution of a CCD, because
a CCD can obtain the dispersed spectrum in a certain energy range in one exposure [5].
We are now calibrating the CCD camera, the
X-ray imaging spectrometer (XIS) for the ASTROE satellite, which will be launched in early 2000.
The CCD chips are of the frame transfer type. Their
imaging area has 1024 pixels ; 1026 pixels and the
physical size of about 1 in. ; 1 in. The CCD has
four readout nodes and 256 pixels of each horizontal line are read out from each node. We call this
CCD structure segment, and treat the data from
each segment separately. The details of the XIS
0168-9002/99/$ - see front matter 1999 Elsevier Science B.V. All rights reserved.
PII: S 0 1 6 8 - 9 0 0 2 ( 9 9 ) 0 0 6 0 2 - 6
SECTION I.
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M. Shouho et al. / Nuclear Instruments and Methods in Physics Research A 436 (1999) 85}90
have been previously published by Hayashida et al.
[6].
In this work, we report the study of the response
function in the soft X-ray region (0.3}2.2 keV) of
one of the XIS #ight models (XIS FM), using a grating spectrometer. The e!ect of the line spread function of the grating is discussed, and two methods
for the extraction of the signal-pulse-height distribution are described.
2. Experiment and results
2.1. Date reduction
We expose the XIS CCD to dispersed soft X-rays
from the Si-K edge spectrometer, Model FFS-II
(SES) supplied by Hettrick Scienti"c Inc. [7,8]. The
details of the spectrometer system have been described by Hashimotodani et al. [5]. The schematic
illustration is shown in Fig. 1. We install the CCD
chip at the focal plane, 775 mm from the grating
center, and set the CCD chip so that the dispersion
direction is parallel to the serial register (that is
parallel to the CCD X-direction). We move the XIS
along the X-ray dispersion direction and obtain
data at seven di!erent positions to cover an energy
range from 0.25 to 2.5 keV for all segments. We
select X-ray events with signal-pulse heights above
&180 eV and charge distributions that "t the grade
classi"cation, with a split threshold of &70 eV, as
described by Gendreau [9].
Fig. 2. Two-dimensional plot of the X-ray events. The horizontal axis is the CCD position, which is the direction of the
dispersion, and hence corresponds to the incident X-ray energy.
The vertical axis is the signal-pulse height with the unit of the
ADC channel (ADU). Each dot shows one X-ray event.
The data reduction is as follows (see also Ref.
[10]). We produce a two-dimensional plot, shown
in Fig. 2, by assigning one axis as the position along
the dispersion direction and the other as the signal-pulse height of the X-ray events measured
with the CCD. Since X-ray energy is speci"ed by
the position along the dispersion direction, this
Fig. 1. The side view of the silicon edge spectrometer.
M. Shouho et al. / Nuclear Instruments and Methods in Physics Research A 436 (1999) 85}90
87
two-dimensional plot directly shows the relation
between the incident X-ray energy and the signalpulse height. However, there are higher-order
dispersed X-rays. Furthermore, we can see several
horizontal lines in Fig. 2, which means that there
are X-rays which are not dispersed by the grating.
2.2. Energy-PH and energy-FWHM relation
In this subsection, we derive the mean signalpulse height and the energy resolution as functions
of the incident X-ray energy, by simple Gaussian
"tting. We extract each order light from the twodimensional plot, shown in Fig. 2, by applying the
upper and lower boundaries on the signal-pulse
height. The boundaries are determined so as to
delineate an appropriate area which includes the
position of the dispersed light. The resultant X-ray
spectrum of the "rst-order light as a function of the
incident X-ray energy is shown in Fig. 3.
A histogram of the signal-pulse height obtained
using the CCD (signal-pulse-height distribution) in
a narrow range of incident X-ray energy exhibits
a peak whose shape can be approximately
simulated by a Gaussian function. We "t the signal-pulse-height distributions with a Gaussian
model. The center value of the Gaussian (PH) is
plotted as a function of the incident X-ray energy
(energy-PH relation) in Fig. 4. The width of
the Gaussian in terms of FWHM is plotted as
a function of the energy (energy-FWHM relation)
in Fig. 5.
Fig. 4. Energy-PH relation of the XIS #ight model (FM) (Segment B) as a function of X-ray energy. The data are for events of
Grade 0#2#3#4#6, in "rst-, second-, third-, and fourthorder light.
Fig. 5. Energy resolution (FWHM) of the XIS FM (Segment C)
as a function of X-ray energy. The data are for events of Grade
0#2#3#4#6, in "rst-, second-, third-, and fourth-order
light.
Fig. 3. Dispersed X-ray spectrum of "rst-order light.
The lower panel of Fig. 4 shows the residuals of
the data from the best-"t linear model. We obtain
the relation between the incident X-ray energy and
PH with an error of less than &7 eV (&2 ADU)
for the energy range of 0.3}1.85 keV. However there
is a jump of &12 eV (&4 ADU) around
1.9 keV. The interpretation of this jump will be
discussed in Section 3.
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M. Shouho et al. / Nuclear Instruments and Methods in Physics Research A 436 (1999) 85}90
We "t the energy-FWHM relation with a formula written as
E
FWHM"2.355;u p#f;
u
(eV)
(1)
where E is the incident X-ray energy, u is the mean
ionization energy per one electron}hole pair, f is
the Fano factor, and p corresponds to system
noise including readout noise. The best-"t values
are p"0.62$0.02 and f"0.123$0.001, where
we assume that u is constant at 3.65 eV. We found
an energy resolution of &40 eV at O-K (0.52 keV),
and &60 eV at Mg-K (1.25 keV).
2.3. Signal-pulse-height distributions
In the above subsection, the mean and the "rst
moment (energy resolution) of the signal-pulseheight distribution were described. However, in
order to construct the response function of the
CCD, more detail on the shape of the signal-pulseheight distribution is required. We developed the
following two methods for the extraction of the
pure signal-pulse-height distribution from the data,
using the spectrometer.
In the "rst method, some emission lines, which
can be seen in Fig. 3, are used to extract the pure
shape of the signal-pulse-height distribution. In the
following, we describe this method for the O-K line.
The events around the O-K line (0.52 keV) consist of three components, the O-K line, the dispersed continuum, and nondispersed X-rays. First, we
produced an energy spectrum from a limited region
which includes the O-K line. Next, we produced
energy spectra from the two neighboring regions
which do not include the peak of the O-K line,
where we used only the data below the O-K edge.
These consist of the dispersed continuum and nondispersed X-rays, although a small amount of the
O-K lines are included. Finally, we subtract the
average of the two spectra from the spectrum including the O-K line, after correction of the area
used. If the nondispersed X-rays are smoothly distributed around the O-K line, they are not included
in the resultant spectrum. The dispersed continuum
X-rays are also almost completely subtracted, if
their intensity is a smooth function of the X-ray
Fig. 6. The pure signal-pulse-height distribution of the grade
0#2#3#4#6 events of the O-K line and the Mg-K line.
The nondispersed component has been subtracted (see text).
energy. A slight di!erence in the center energy of
the dispersed X-rays does not a!ect the resultant
spectra, because such a di!erence is much smaller
than the energy resolution of the CCD. Therefore,
the obtained spectrum should show the pure signalpulse-height distribution for the O-K X-rays. The
obtained spectrum is shown in Fig. 6. The same
method is applied for the Mg-K line and the spectrum obtained for Mg-K line is shown in Fig. 6. The
tail component of the Mg-K line is substantially
smaller than that of the O-K line.
In the above method, we can obtain a clear pure
signal-pulse-height distribution, but we can apply
this method only for some emission lines.
Thus, we develop a second method for obtaining
the signal-pulse-height distribution at other energies, where the estimated nondispersed X-rays are
subtracted. The energy spectrum of the nondispersed X-rays is estimated from the spectrum obtained
near the zeroth-order light, where no re#ectioncondition of the grating is satis"ed for the X-rays
below the applied high voltage (5 kV) of the X-ray
generator. The intensity of the nondispersed light
as a function of the distance from the zeroth-order
position is also derived from the data of the same
region. The exponential function with a constant
component "ts the data well. Extrapolating this
function, the spectrum and the intensity of the
nondispersed X-ray are estimated.
M. Shouho et al. / Nuclear Instruments and Methods in Physics Research A 436 (1999) 85}90
Fig. 7. The signal-pulse-height distribution at "ve energy positions, O-K line (0.525 keV), 0.8, 1.0 keV, Mg-K line (1.25 keV),
1.49 keV. The grade 0#2#3#4#6 events are selected. All
were derived by subtracting the estimated nondispersed X-rays.
The derived signal-pulse-height distributions for
"ve positions (O-K line (0.525 keV), 0.8, 1.0 keV,
Mg-K line (1.25 keV), and 1.49 keV) are shown in
Fig. 7. Comparing the signal-pulse-height distributions of the O-K line and Mg-K line derived by the
two independent methods, the systematic di!erence
is found to be of the order of 0.1% of the peak
count rate.
3. Discussion
We found a jump of the center value of the
signal-pulse-height distribution at the energy
around 1.9 keV. Figs. 8(a) and (b) shows the expanded dispersed X-ray spectrum, and the residuals
of the energy-PH relation from the best-"t linear
model. Although the discontinuity is near the Si-K
edge (1.840 keV), the energy is signi"cantly di!erent
from it. Thus, the discontinuity is not due to the
characteristics of the CCD.
The obtained result can be interpreted as follows.
We derived the signal-pulse height and the energy
resolution from a simple Gaussian "t. Although the
energy resolving power of the grating is much higher than that of the CCD, the line spread function of
the grating has a "nite width. This e!ect becomes
large at the high-energy part.
89
Fig. 8. The dispersed spectrum (a) and the residuals of the
energy-PH relation from the linear model (b). The estimated
deviation of the center from the real X-ray energy is plotted in
(c), where the gaussian pro"le with a standard deviation of 72
lm is assumed for the line spread function of the grating. The
contribution onto the energy resolution from this line spread
function is plotted in (d) by the standard deviation.
If the intensity of the dispersed X-rays are
smooth, the "nite width of the line spread function
reduces the energy resolution, but the e!ect on the
center energy is small. However, if the intensity of
the dispersed X-rays changes steeply as a function
of X-ray energy, the e!ect of the line spread function distorts the center energy toward the intense
X-ray direction. In Fig. 8(b), it can be seen that the
intensity-decreasing part shows negative residuals
and intensity-increasing part shows positive residuals. It should be noted that the residuals shown in
Fig. 8(b) are those from the best-"t linear model,
but not from the real center.
A simple estimation was performed assuming the
line spread function of the grating: a Gaussian
pro"le with a standard deviation of 72 lm, which is
the length of three pixels of the CCD. This resolution corresponds to &5.5 eV at 1.25 keV. If the
real center energy of the CCD response function is
linear to the incident X-ray energy, the deviation
*E of the derived center energy from the real center
energy can be estimated as
Ef (E) exp(!(E!E )/2p) dE
*E"
!E
f (E) exp(!(E!E )/2p) dE
(2)
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M. Shouho et al. / Nuclear Instruments and Methods in Physics Research A 436 (1999) 85}90
where f (E) is the intensity of the dispersed spectrum, p is the standard deviation of the Gaussian
pro"le, and E is the X-ray energy. The estimated
deviation (*E) is plotted in Fig. 8(c). The rough
shape of the residuals can simulate not only the
jump around 1.9 keV but also the small change at
1.25 keV by the Mg-K line, and 1.55 keV by the
Al-K edge. Although the energy of the jump around
1.9 keV in the data seems to be slightly smaller than
that of the simulation, this is partly due to the large
scatter of the data around 1.9 keV. In addition, the
assumed line spread function is probably too
simple to reproduce the exact deviation.
The standard deviation due to the line spread
function of the grating is plotted in Fig. 8(d). The
e!ect on the energy resolution plotted in Fig. 5, due
to this line spread function, is roughly 1.2 eV at 1.25
keV, which is much smaller than the error of the
data.
The two methods for the extraction of the
signal-pulse-height distribution are described in
Section 2.3. The "rst method is completely new,
and can be widely applied for the dispersed spectrometer. As long as the continuum is smooth, the
resultant signal-pulse-height distribution has no
ambiguity. The e!ects of the line spread function of
the grating are less than &1 ADU on the center
energy and &1.2 eV (FWHM) on the energy
resolution for the Mg-K line. For the O-K line,
these e!ects are much smaller. In the second
method, we estimate only the e!ect from the
zeroth-order light. This is insu$cient for a detailed
analysis. However, in the analysis shown in this
work, a systematic error of the order of 0.1% of the
peak count is con"rmed, indicating that it is still
useful for the study of the shape of the signal-pulseheight distribution.
Fig. 7 shows the complex behavior of the tail
component of the signal-pulse-height distribution.
The tail component consists of at least three components. One is the deviation from the Gaussian
pro"le at the low-energy part, which always
appears. The second is the large hump at the lowenergy part, which is prominent for the O-K
line and disappears for X-rays above 1 keV. The
third is the long #at tail on the low-energy side.
This component seems to decrease according to the
energy of the incident X-rays. The quantitative
analysis will be published elsewhere.
4. Conclusion
The simple analysis and results of the calibration using the dispersed continuous soft X-rays
(0.25}2.2 keV) from our grating spectrometer
are presented. In the simple analysis, the line
spread function of the grating causes a discontinuity of the pulse height. We described two methods
of extracting a pure signal-pulse-height distribution
from the data obtained using the spectrometer. We
demonstrated that the tail of the signal-pulseheight distribution consists of at least three components.
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