Nuclear Instruments and Methods in Physics Research A 477 (2002) 155–160
Application of a finite size of the charge cloud shape generated
by an X-ray photon inside the CCD
H. Tsunemia,b,*, J. Hiragaa,b,1, E. Miyataa,b
a
Department of Earth and Space Science, Graduate School of Science, Osaka University, 1-1 Machikaneyama-cho,
Toyonaka, Osaka 5600043, Japan
b
CREST, Japan Science and Technology Corporation (JST), Japan
Abstract
A mesh experiment enables us to specify the X-ray landing position on a charge-coupled device (CCD) with subpixel
resolution. By this experiment, we find that the final charge cloud shape generated by Ti–K X-ray photons (4:5 keV) in
the CCD is about 1:5 1:1 mm2 (standard deviation). An X-ray photon photoabsorbed in the CCD generates a number
of electrons, forming an X-ray event. It becomes up to a 4-pixel-split event since the pixel size of the CCD used (12 mm
square pixel) is bigger than the charge cloud size. Using the mesh experiment, we can determine the X-ray landing
position on the CCD. In this way, we can compare the estimated X-ray landing position with the actual landing position
on the CCD. Employing the charge cloud shape, we can improve the position resolution of the X-ray CCD by referring
to the X-ray event pattern. We find that the position accuracy of our method is about 1:0 mm: We discuss our method,
comparing it with the charge centroid method. r 2002 Elsevier Science B.V. All rights reserved.
PACS: 07.85.m; 29.40.Wk; 95.55.Aq
Keywords: Mesh experiment; Charge-coupled device; Charge centroid method; Cloud shape method
1. Introduction
A charge-coupled device (CCD) has relatively
good spatial resolution and high quantum
efficiency for both X-ray and optical regions. It
consists of many small pixels about 10 mm in
size. Each pixel consists of 2–4 electrodes which
*Corresponding author. Department of Earth and Space
Science, Graduate School of Science, Osaka University,
1-1 Machikaneyama-cho, Toyonaka, Osaka 5600043, Japan.
Tel.: +81-6-850-5477; fax: +81-6-850-5539.
E-mail address: [email protected]
(H. Tsunemi).
1
Partially supported by JSPS Research Fellowship for Young
Scientists, Japan.
are responsible for the nonuniformity of
the detection efficiency over the pixel. The output
of the CCD comes from each pixel, resulting in
a spatial resolution of pixel size. X-ray
photons photoabsorbed in the CCD generate
a number of electrons of about E=3:65 eV; where
E is the incident X-ray energy. These electrons,
generated in a very small region [1], become
a finite-size charge cloud through diffusion
when they are collected into the potential
well under the electrodes [2]. They are called ‘an
X-ray event’, forming an island, i.e., a series of
connecting pixels having signals. The pixel with
the largest signal in the X-ray event is called the
‘event pixel’.
0168-9002/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved.
PII: S 0 1 6 8 - 9 0 0 2 ( 0 1 ) 0 1 8 7 7 - 0
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H. Tsunemi et al. / Nuclear Instruments and Methods in Physics Research A 477 (2002) 155–160
When an X-ray photon is photoabsorbed in the
field-free region, under the depletion layer, the
charge cloud expands and forms a multipixel event
consisting of more than four pixels. In contrast,
when it is photoabsorbed in the depletion layer,
the entire charge is collected into the potential well
with relatively small spread. When the X-ray
landing position is far from the CCD pixel
boundary, the entire charge is collected into one
pixel. When it is close to the CCD pixel boundary,
the charge splits into 2–4 pixels depending on the
landing position. Thus, X-rays photoabsorbed in
the depletion layer form various types of event
patterns.
A mesh experiment is introduced to measure the
X-ray responsivity with subpixel resolution [3].
Using this method, we can specify the X-ray
landing position within the pixel for all X-ray
events [10,11]. Then, we developed a method of
directly measuring the charge cloud shape generated by X-ray photons [4]. Precise knowledge
of the cloud shape enables us to determine the
X-ray landing position with subpixel resolution
using split pixel events. In this paper, we report
experimental results for the improvement of the
position resolution of the CCD.
mine the mutual alignment between the mesh and
the CCD. In this way, we can obtain the CCD
pixel map for the X-ray responsivity. The detailed
explanation of the mesh experiment is given in the
literature [3,5]. The CCD pixel map obtained
shows the pixel structure convoluted with the
mesh hole shape. Therefore, the accuracy of the
pixel structure is limited by the mesh hole size.
Similarly, we can easily restrict the X-ray
landing position on the CCD with CCD-pixel-size
precision if we assume that the X-ray landing
position is somewhere inside the event pixel. In this
way, we can obtain the mesh hole map of the
X-ray transmission. The mesh hole map obtained
shows the mesh hole structure convoluted with the
CCD pixel shape. The CCD pixel shape is an exact
square. Thus, we can estimate the effective mesh
hole size [6]. Fig. 1 shows a mesh hole shape
convoluted with the CCD pixel shape. Since the
CCD pixel shape is much bigger than the mesh
hole shape, the result mainly reflects the CCD
pixel shape.
Once we determine the X-ray landing position
with subpixel resolution, we know what type of
X-ray events are generated according to the X-ray
landing position. This enables us to measure the
charge cloud shape generated by an X-ray photon.
2. Experimental setup and image restoration
The mesh experiment consists of three parts: a
parallel X-ray beam, a CCD operating in the
X-ray photon counting mode and a metal mesh
placed above the CCD. The CCD used has a 12 12 mm2 pixel size and was manufactured by
Hamamatsu Photonics Inc. We employed a gold
mesh of about 10 mm thickness with small holes of
about 2 mm diameter spaced 48 mm apart. These
parameters are each mesh dependent, and were
measured for the actual mesh by both using the
scanning electron microscopic images and measuring the X-ray transmission. Placing the mesh just
above the CCD, we can restrict the X-ray landing
position with mesh-hole-size precision, since the
raw data show a moire! pattern which comes from
the interaction between the periodically spaced
CCD pixels and periodically spaced mesh holes.
The moire! pattern enables us to precisely deter-
Fig. 1. Accuracy of the X-ray position determination based on
the event pixel method. Four shapes are shown separated by
48 mm; while the CCD pixel size is 12 12 mm2 :
H. Tsunemi et al. / Nuclear Instruments and Methods in Physics Research A 477 (2002) 155–160
The result is a convolution between the actual
charge cloud shape and the mesh hole shape [4].
Fig. 2 shows a charge cloud shape obtained in this
way using Ti–K X-rays (4:5 keV) [7]. It can be well
expressed by an axial symmetric Gaussian function of s ¼ 1:1 mm along the charge transfer
direction and s ¼ 1:5 mm perpendicular to it where
s is the standard deviation.
3. Determination of the X-ray landing position
inside the CCD
3.1. Methods of estimating the X-ray
landing position
When we detect X-ray events on the CCD, we
assume that the X-ray landing position is in the
event pixel. This is confirmed since the charge
cloud shape is well expressed by a Gaussian
function. There are three methods of estimating
the X-ray landing position for each X-ray event.
The simplest method, the ‘event pixel method’, is
to employ the center of the event pixel as the X-ray
landing position. It is obvious that the accuracy of
the position determination depends on the pixel
size which is shown in Fig. 1.
Fig. 2. Charge cloud shapes for Ti–K X-ray photons are shown
in a 12 12 mm2 square [7]. A linear contour is overlaid.
157
The second method, the ‘charge centroid method’, is to employ the center of gravity of the Xray event. Yoshita et al. [8] studied the relation
between the center of gravity of the X-ray events
and the actual X-ray landing position on the CCD.
They found that the center of gravity is a good
indicator of the X-ray landing position, although
they pointed out that the actual landing position
should be determined taking into account the
charge cloud shape. The third method that we
employ, the ‘cloud shape method’, is to calculate
the X-ray landing position based on the charge
cloud shape. We can calculate the X-ray landing
position so that the charge splits in such a way as
to reproduce the event pattern.
3.2. Comparison between the charge centroid
method and the cloud shape method
There are several event patterns generated by
X-ray photons. The event pixel method is applicable to any event pattern, whereas the position
accuracy is limited by the CCD pixel size. The twopixel-split events can yield detailed positional
information along the split direction but little
information perpendicular to it. If we must
determine the X-ray landing position in both
X and Y directions, we must used split pixel
events in both directions. In practice, we used 3and 4-pixel-split events which are sure to occur in
the four corners of the pixel [5,6] and calculated
the center of gravity and also estimated the X-ray
landing position using the charge cloud shape. In
this calculation, we simply assume that the charge
cloud shape is well expressed by a point-symmetric
Gaussian function of s ¼ 1:3 mm; for simplicity.
The actual cloud shapes measured are slightly
distorted but this does not seriously affect our
results.
We calculated the relation between the mesh
hole center through which the X-ray photon
entered and the estimated X-ray landing position
in the pixel. The results using the charge centroid
method are shown in Fig. 3 and those using the
cloud shape method are shown in Fig. 4. The
horizontal axis shows the position of the mesh hole
center on the CCD pixel. At 0, the mesh hole
center just coincides with the pixel boundary to the
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H. Tsunemi et al. / Nuclear Instruments and Methods in Physics Research A 477 (2002) 155–160
Fig. 3. Relationship between the mesh hole center and the estimated X-ray landing position based on the charge centroid method.
Left: the horizontal direction. Right: the vertical direction. Unit is given in pixel size; see text.
Fig. 4. Same as for Fig. 3 but based on the cloud shape method.
neighboring pixel. Since the physical situation
is symmetrical with respect to the center of
the pixel, the horizontal axis starts and ends at
half the pixel size. The vertical axis shows the
estimated X-ray landing position inside the pixel.
Since we only employed 3- and 4-pixel-split events,
all the events used appear only near the pixel
boundary.
It is clear that the charge centroid method does
not yield the precise landing position. This is due
to the fact that the charge centroid method can
produce the correct answer only when the charge
cloud size is comparable to or larger than the CCD
pixel size. The data spread along the horizontal
axis in Fig. 4 is a result of the finite size of the mesh
hole.
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H. Tsunemi et al. / Nuclear Instruments and Methods in Physics Research A 477 (2002) 155–160
Fig. 5. Accuracy of position determination for the charge centroid method (left) and for the cloud shape method (right). The four
peaks in both figures are separated by 48 mm:
As we explained briefly in Section 2, we can
reconstruct the mesh hole shape using the X-ray
landing position determined by either the charge
centroid method or the cloud shape method. Fig. 5
shows the convolution between the point spread
function (PSF) of the two methods and the mesh
hole shape. We analyzed the PSF and summarize
its results in Table 1.
4. Discussion and conclusion
We confirmed that the cloud shape method
yields better results than the charge centroid
method or the event pixel method. The position
accuracy of this method shown in Fig. 5 is
s ¼ 1:170:1 mm: If we exclude the effect of
the finite size of the mesh hole, we obtain
s ¼ 1:070:1 mm for the cloud shape method
which is smaller than that of the charge cloud.
The charge cloud size depends on the depth at
which the photoabsorption occurs. The actual
charge cloud size shows scatter up to a few mm;
and the charge cloud size employed is the average
of various X-ray events. This will produce some
ambiguity in determining the X-ray landing
position.
Table 1
s (mm) of the results of the two methods using Ti–K X-raysa
Method
Charge centroid
Cloud shape
Data (Fig. 5)
PSFb
2:470:1
2:370:1
1:170:1
1:070:1
a
b
Note: Quoted errors are 90% confidence level.
Excluding the effect of mesh hole.
The cloud shape method will work well only
when X-rays produce split events. Taking into
account the measured charge cloud size, the CCD
pixel size of 6 mm square will be small enough to
make most X-ray events split pixel events so that
we can improve the position resolution over the
entire area. The single-pixel events are produced
when the landing position is somewhat away from
the pixel boundary so that all the charge is
collected into one pixel. Therefore, we can improve
the landing position for single-pixel events to
slightly better than the pixel size. The detailed
analysis for all X-ray events will be carried out
elsewhere.
We measured the final charge cloud shape
generated by Ti–K X-ray photons (4:5 keV). Then
we applied our results to improve the position
determination. The cloud shape method intro-
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H. Tsunemi et al. / Nuclear Instruments and Methods in Physics Research A 477 (2002) 155–160
duced here shows a PSF of s ¼ 1:0 mm: This
method yields more than twofold better results
than the charge centroid method. Our method is
applied only for split pixel events, whereas there is
some improvement in the position determination
for single-pixel events. It will be effective for the
Chandra ACIS since its image quality is better
than the CCD pixel size [9].
Acknowledgements
The authors are grateful to all members of the
CCD team in Osaka University. They also thank
Mr. K. Miyaguchi of Hamamatsu Photonics Inc.
for technical support. This research is partially
supported by Kurata Research Grant, the Grandin-Aid for Scientific Research by the Ministry of
Education, Culture, Sports, Science and Technology of Japan (13440062).
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