High-resolution and high-sensitivity X-ray ptychographic coherent diffraction imaging using the CITIUS detector

Abstract

Ptychographic coherent diffraction imaging (PCDI) is a synchrotron X-ray microscopy technique that provides high spatial resolution and a wide field of view. To improve the performance of PCDI, the performance of the synchrotron radiation source and imaging detector should be improved. In this study, ptychographic diffraction pattern measurements using the CITIUS high-speed X-ray image detector and the corresponding image reconstruction are reported. X-rays with an energy of 6.5 keV were focused by total reflection focusing mirrors, and a flux of ∼2.6 × 10¹⁰ photons s⁻¹ was obtained at the sample plane. Diffraction intensity data were collected at up to ∼250 Mcounts s⁻¹ pixel⁻¹ without saturation of the detector. Measurements of tantalum test charts and silica particles and the reconstruction of phase images were performed. A resolution of ∼10 nm and a phase sensitivity of ∼0.01 rad were obtained. The CITIUS detector can be applied to the PCDI observation of various samples using low-emittance synchrotron radiation sources and to the stability evaluation of light sources.

Full text

research papers
J. Synchrotron Rad. (2023). 30 https://doi.org/10.1107/S1600577523004897 1of6
Received 9 March 2023
Accepted 5 June 2023
Edited by M. Yamamoto, RIKEN SPring-8
Center, Japan
Keywords: pychographic coherent diffraction
imaging; CITIUS.
High-resolution and high-sensitivity X-ray
ptychographic coherent diffraction imaging
using the CITIUS detector
Yukio Takahashi,
a,b,c
* Masaki Abe,
a,d
Hideshi Uematsu,
a,d
Shuntaro Takazawa,
a,d
Yuhei Sasaki,
a,d
Nozomu Ishiguro,
a,b,c
Kyosuke Ozaki,
c
Yoshiaki Honjo,
c
Haruki Nishino,
c,e
Kazuo Kobayashi,
c
Toshiyuki Nishiyama Hiraki,
c
Yasumasa Joti
c,e
and Takaki Hatsui
c
a
International Center for Synchrotron Radiation Innovation Smart (SRIS), Tohoku University, 2-1-1 Katahira,
Aoba-ku, Sendai 980-8577, Japan,
b
Institute of Multidisciplinary Research for Advanced Materials (IMRAM),
Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan,
c
RIKEN SPring-8 Center, 1-1-1 Kouto,
Sayo-cho, Sayo-gun, Hyogo 679-5148, Japan,
d
Department of Metallurgy, Materials Science and Materials
Processing, Graduate School of Engineering, Tohoku University, 6-6-2 Aoba-yama, Aoba-ku, Sendai 980-8579,
Japan, and
e
Japan Synchrotron Radiation Research Institute, 1-1-1 Kouto, Sayo-cho, Sayo-gun, Hyogo 679-5198,
Japan. *Correspondence e-mail: ytakahashi@tohoku.ac.jp
Ptychographic coherent diffraction imaging (PCDI) is a synchrotron X-ray
microscopy technique that provides high spatial resolution and a wide field of
view. To improve the performance of PCDI, the performance of the synchrotron
radiation source and imaging detector should be improved. In this study,
ptychographic diffraction pattern measurements using the CITIUS high-speed
X-ray image detector and the corresponding image reconstruction are reported.
X-rays with an energy of 6.5 keV were focused by total reflection focusing
mirrors, and a flux of 2.6 10
10
photons s
1
was obtained at the sample plane.
Diffraction intensity data were collected at up to 250 Mcounts s
1
pixel
1
without saturation of the detector. Measurements of tantalum test charts and
silica particles and the reconstruction of phase images were performed. A
resolution of 10 nm and a phase sensitivity of 0.01 rad were obtained. The
CITIUS detector can be applied to the PCDI observation of various samples
using low-emittance synchrotron radiation sources and to the stability
evaluation of light sources.
1. Introduction
Coherent diffraction imaging (CDI) is a lensless microscopy
technique that reconstructs a sample image by performing
iterative phase retrieval calculations on a computer based
on a two-dimensional diffraction pattern observed in the far
field when the sample is illuminated with coherent X-rays
(Chapman & Nugent, 2010; Miao et al., 2015). Ptychographic
CDI (PCDI) is a scanning-type CDI technique that can be
used to observe a spatially extended sample. Therefore, it can
be applied to various sample observations and probe char-
acterization (Rodenburg et al., 2007; Pfeiffer, 2018). Addi-
tionally, it has been applied in a wide range of research fields,
including biology (Giewekemeyer et al., 2010; Deng et al.,
2015), materials science (Shapiro et al., 2014; Hirose et al.,
2019) and devices (Holler et al., 2017), with a field of view on
the 10 mm scale and a spatial resolution of approximately
10 nm. Further improvement of PCDI performance is chal-
lenging.
The key performance characteristics of PCDI, such as
spatiotemporal resolution and sensitivity, are highly depen-
dent on the performance metrics of the synchrotron radiation
ISSN 1600-5775
Published under a CC BY 4.0 licence

source used (e.g. coherent flux and stability) and the image
detector (e.g. photon count rate, sensitivity and area). Since
synchrotron radiation sources produce partially coherent light
in space and time, slits for generating virtual light sources
are necessary, in addition to monochromators. Additionally,
focusing devices play a significant role in forming high-inten-
sity coherent X-ray beams. Spatial resolution at a 10 nm level
has been achieved by PCDI using focusing devices such as
total reflection mirrors (Takahashi et al., 2011), Fresnel zone
plates (Vila-Comamala et al., 2011) and refractive lenses
(Schropp et al., 2012) thus far. Recent technological advances
in low-emittance storage rings have increased the coherent
flux available at new synchrotron facilities (Johansson et al.,
2021) and upgrades to existing facilities (Pacchioni, 2019).
Further performance improvements in PCDI are expected in
the near future.
In contrast, with regard to image detectors, the advent of
single-photon-counting pixel detectors such as EIGER
(Dinapoli et al., 2011) and Lambda (Pennicard et al., 2012) has
significantly improved the measurement throughput of PCDI
(Guizar-Sicairos et al., 2014; Wilke et al., 2014). However,
photon count rates have reached their limits of approximately
1 Mcounts s
1
pixel
1
because of pile-up challenges inherent
in photon-counting types, which necessitates the use of
attenuators (Wilke et al., 2013; Reinhardt et al., 2017). Inte-
grating-type detectors can operate regardless of the instanta-
neous count rate limitation (Hatsui & Graafsma, 2015). Tate et
al. (2013) reported the demonstration of a quasi-integrating-
type detector MM-PAD by implementing a mixed-mode in-
pixel circuitry. Additionally, high-flux PCDI using MM-PAD
has been reported (Giewekemeyer et al., 2014). One of the
other development programs to realize count rate beyond the
photon counting limit is CITIUS (Hatsui et al., in preparation),
which has native integrating-type pixels.
In this study, we first demonstrate high-spatial-resolution
and high-sensitivity PCDI using the CITIUS detector at
SPring-8. Furthermore, we conduct a quantitative evaluation
of the spatial resolution and sensitivity of PCDI.
2. Experimental
PCDI measurements were performed at the BL29XUL
beamline (Tamasaku et al., 2001) at SPring-8. Fig. 1 shows the
experimental setup. Synchrotron radiation emitted from an in-
vacuum undulator device was monochromated to 6.5 keV by a
Si (111) double-crystal monochromator, and the X-ray beam
was cut out with slits. The size of the light source in
synchrotron radiation was determined by the size of the
electron beam. The width of the Gaussian distribution defined
the size, which was 301 mm in the vertical (V) direction and
6mm in the horizontal (H) direction when all gaps of insertion
devices were opened. Based on the van Cittert–Zernike
theorem, the transverse coherence length at the slit position
was approximately 17 mm (H) 800 mm (V). The X-ray
beam was focused by Kirkpatrick–Baez (KB) optics (JTEC
Corporation) using total reflection mirrors located 45 m
downstream of the slits. The KB mirror design parameters are
summarized in Table 1. The aperture, positioned just in front
of the KB mirror, had a size of 270 mm (H) 315 mm (V)
adjusted to illuminate the entire effective area of the mirror.
The KB mirrors were housed in an acrylic chamber in a helium
gas atmosphere, with 5 mm-thick polyimide windows mounted
at the X-ray entrance and exit of the chamber. An ion
chamber was placed immediately after the acrylic chamber to
monitor incident X-ray intensities. The samples selected for
the evaluation of spatial resolution and sensitivity were
tantalum (Ta) test charts with thickness values of 200 nm
(XRESO-50, NTT Advanced Technology Corp.) and 6 nm
(GS20-2, NTT Advanced Technology Corp.) and silica parti-
cles (QSG-30, Shin-Etsu Chemical Co. Ltd) with a diameter of
approximately 30 nm which were dispersed on a 500 nm-thick
SiN membrane. The samples were positioned on piezo stages
at the location of a focal point in a vacuum chamber. A 25 mm-
thick polyimide window was mounted at the X-ray entrance of
the sample chamber. Spatial filters were placed in front of the
sample to eliminate parasitic scattering from the focusing
mirror (Takahashi et al., 2013). Silicon slits with a length of
100 mm per side were used as a spatial window. The CITIUS
detector used in this study has 840 kpixels and is composed
of three sensor modules. Each module has 384 728 pixels.
The CITIUS detector is mounted on a vacuum flange and
connected to the sample chamber through a flight tube, which
ensures there is no window between the sample and the
research papers
2of6 Yukio Takahashi et al. X-ray ptychographic coherent diffraction imaging J. Synchrotron Rad. (2023). 30
Figure 1
Experimental setup of the ptychographic measurement system with the
CITIUS detector.
Table 1
Parameter values for the KB mirrors.
Vertical focusing
mirror
Horizontal focusing
mirror
Glancing angle (mrad) 3.5 3.0
Mirror length (mm) 90 90
Focal length (m) 0.595 0.490

detector sensor. It was located 2.44 m downstream of the
sample. The vacuum was evacuated from the port near the
sample to <1 Pa. The diffraction patterns from each sample
were collected with a step size of 150 nm and a perfect
grid of 17 17 scanning points with 1 s exposure per point.
For the Ta test charts with a thickness of 200 nm, the slit width
was varied from 10 mmto30mm in the horizontal direction
and from 30 mm to 150 mm in the vertical direction. For the
6 nm-thick Ta test charts and silica particles, the slit width was
30 mm (H) 150 mm (V).
3. Diffraction pattern of 200 nm-thick Ta test chart
Fig. 2(a) shows a diffraction pattern taken without a sample,
where only the intensity distribution of the direct beam can be
seen. The intensity around the direct beam was suppressed
by a spatial filter. Fig. 2(b) shows one of the ptychographic
diffraction patterns from the 200 nm-thick test chart and its
low spatial frequency range expansion. The slit width was
30 mm (H) 150 mm (V), and the flux at the sample position
was 2.6 10
10
photons s
1
. The maximum intensity per
pixel was 250 Mcounts s
1
. Fig. 2(c) shows the horizontal
intensity profile along the q
x
direction at q
z
= 0 with and
without the sample. Diffraction patterns were measured with
a high signal-to-noise ratio, and weak diffraction intensity
patterns were observed in the high-spatial-frequency range,
indicating a one-photon level of sensitivity and handling count
rates per pixel.
4. Image reconstruction
The diffraction patterns collected for this experiment consist
of 1225 pixels in the horizontal direction (q
x
) and 728 pixels in
the vertical direction (q
z
), which includes the gap between the
sensors. To ensure equal pixel dimensions, an image size of
1225 1225 pixels was used for the reconstruction, where a
value of 0 was assigned for 497 pixels in the high-q
z
region.
The image reconstruction of the 200 nm-thick Ta test chart
was performed using an extended ptychographical iterative
engine (ePIE) (Maiden & Rodenburg, 2009) extended to a
mixed-state model (Thibault & Menzel, 2013) and an algo-
rithm for lateral position correction using the gradient of
intensity patterns (Dwivedi et al., 2018), which is referred to as
the IG method in this paper. A function propagating 0.5 mm
downstream from a circular aperture of diameter 300 nm was
used as the initial probe function, and 700 iterations were
performed using three mixed-state probe modes. However,
the IG method did not perform well for the image recon-
struction of the 6 nm-thick Ta test chart and silica particles due
to weak scattering intensity from the sample. To address this,
the weak phase object approximation (Dierolf et al., 2010) and
orthogonal probe relaxation (OPR) (Odstrcil et al., 2016) were
used. Although less accurate than the IG method, OPR can
correct for irradiation position deviation by treating it as a
probe variation. The image reconstruction of the 6 nm-thick
Ta test chart and silica particles was performed using ePIE
with OPR extended to a mixed-state model (m-s OPR)
(Eschen et al., 2022). To reconstruct the image of the 6 nm-
thick Ta test chart and silica particles, the probe function
obtained from the reconstruction of the 200 nm-thick Ta test
chart with a slit size of 30 mm150 mm was used as the initial
probe function. Three mixed-state probe modes, each with
three eigenprobes, were utilized, and 540 iterations were
performed for the 6 nm-thick Ta test chart, while 740 itera-
tions were performed for the silica particles. In all recon-
structions, the initial object function had a real part of 1 and
an imaginary part of 0, and the pixel size of all reconstructed
images was 5.2 nm.
4.1. 200 nm-thick Ta test chart
Fig. 3(a) depicts the sample phase and probe intensity
images of the first mode in three mixed-state modes recon-
structed from the diffraction intensity patterns measured with
a slit width of 10 mm (H) 30 mm (V) (left) and 30 mm (H) 
150 mm (V) (right). Both images successfully reconstructed a
minimum structure of 50 nm in the sample. The probe inten-
sity distribution obtained with a slit size of 10 mm (H) 30 mm
(V) resembled that of the Fraunhofer diffraction intensity for
a rectangular aperture, and it was focused near the diffraction
limit. The focal spot size was measured to be 321 nm (H) 
428 nm (V) full width at half-maximum (FWHM). In contrast,
research papers
J. Synchrotron Rad. (2023). 30 Yukio Takahashi et al. X-ray ptychographic coherent diffraction imaging 3of6
Figure 2
(a) Diffraction pattern without the sample, showing overall (left) and an
enlarged view (right) of the low-spatial frequency region. (b) Diffraction
patterns of the 200 nm-thick test chart, showing overall (left) and an
enlarged view (right) of the low-spatial frequency region. (c) One-
dimensional intensity distribution of the diffraction patterns shown in (a)
and (b) along the q
x
direction at q
z
=0.

when the slit size was increased to 30 mm (H) 150 mm (V),
the vertical direction exhibited a larger geometric reduction
size compared with the diffraction-limited focusing size. The
measured focal spot size was found to be 343 nm (H) 
900 nm (V) at the FWHM. The spatial resolution was eval-
uated using the phase retrieval transfer function (PRTF)
(Chapman et al., 2006), averaged over the 17 17 scan
positions. Since only pixel values containing diffraction data
were used, spatial frequency regions higher than 0.057 nm
1
were valid only for the horizontal direction. The slit-width
dependence of the PRTF curve is shown in Fig. 3(b), indi-
cating that spatial resolution improves with increasing slit
width. When the slit size was 30 mm (H) 150 mm (V), the
corresponding flux was approximately 2.6 10
10
photons s
1
,
achieving a better full-period spatial resolution than 10.5 nm
for the horizontal direction. Furthermore, line profiles for
each image were analyzed, as shown in Fig. 3(d) with resolu-
tions of approximately 16 nm and 12 nm for slit sizes of
10 mm (H) 30 mm (V) and 30 mm (H) 150 mm (V),
respectively.
Table 2 provides a summary of the flux, beam size at the
sample position, and the percentage of each mode in the three
mixed-state modes for each slit size. As the slit size expands,
the first mode’s percentage decreases while higher-order mode
percentages increase. It has been reported that increasing the
number of photons in the first mode can improve spatial
resolution (Burdet et al., 2016). This trend is consistent with
our findings. As the slit size increases, the step size of the
diffraction intensity pattern measurement remains constant,
leading to an increased beam overlap ratio. In addition to the
heightened flux of the first mode, the increased overlap rate
may also enhance the convergence of phase retrieval calcu-
lations (Bunk et al., 2008) and contribute to the improved
resolution. The spatial coherence length should be sufficiently
coherent in the vertical direction for the 150 mmsize.
However, the reduced flux of the first modes can be due to
vibrations in the monochromator’s first crystal. When the slit
size is 30 mm (H) 150 mm (V), the reconstructed image
exhibits line artifacts not observed in the 10 mm (H) 30 mm
(V) configuration, and the slightly poorer phase quantification
is likely attributable to the monochromator’s vibration. The
exact cause of this phenomenon remains unclear.
4.2. 6 nm-thick Ta test chart and silica particles
Fig. 4(a) displays the reconstructed image of the 6 nm-thick
Ta test chart. A minimum structure of 20 nm can be resolved.
However, line artifacts, also observed in the 200 nm-thick Ta
test chart, are present, with additional artifacts visible in the
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4of6 Yukio Takahashi et al. X-ray ptychographic coherent diffraction imaging J. Synchrotron Rad. (2023). 30
Table 2
Flux, beam size at the sample position, and percentage of each mode in
the three mixed-state modes for varying slit sizes.
Probe size of first
mode (nm)
Percentage of
mixed-state mode
Slit size
(H V) (mm)
Flux
(photons s
1
) H V 1st 2nd 3rd
30 150 2.6 10
10
343 900 69.7 18.4 11.9
30 100 1.7 10
10
328 582 68.4 19.9 11.7
20 150 1.6 10
10
337 928 69.0 22.9 8.1
20 100 1.0 10
10
320 652 82.2 10.4 7.4
10 150 5.2 10
10
330 958 74.1 20.0 5.9
10 100 3.4 10
9
317 660 75.3 21.1 3.6
10 50 1.5 10
9
322 449 76.4 18.4 5.2
10 30 6.5 10
8
321 428 86.3 8.8 4.9
Figure 3
(a) Reconstructed phase images (top) and probe intensity images of the first mode in three mixed-state modes (bottom) of a 200 nm test chart at slit
widths of 10 mm (H) 30 mm (V) (left) and 30 mm (H) 150 mm (V) (right). (b) Dependence of the phase retrieval transfer function of the
reconstructed image of the 200 nm-thick test chart on slit width. (c) Line profiles along the colored lines in the reconstructed images of (a). The FWHM
values, obtained by fitting with the error function, are also displayed.

center of the magnified image. These artifacts are believed to
result from the angular oscillation of the monochromator.
Fig. 4(b) presents the histogram of the phase distribution
corresponding to Fig. 4(a). The histogram was fit using a
composite function comprising two Gaussian functions. Phase
resolution was determined by measuring the standard devia-
tion () of the Gaussian fit, as defined by Putkunz et al. (2014).
Based on this definition, the phase resolution of the current
image is superior to 0.006 rad, which, to our knowledge,
represents the finest phase resolution achieved by PCDI thus
far. Moreover, the interval at the peak top position is
0.016 rad. The theoretical value of the 6 nm-thick Ta phase
shift for 6.5 keV X-rays is 0.012 rad. The minor discrepancy of
approximately 0.004 rad from the theoretical value is thought
to be a reconstruction error caused by the m-s OPR method.
Figs. 4(c) and 4(d) show the field-emission scanning electron
microscopy (FE-SEM) and reconstructed phase images of the
silica particles with a diameter of 30 nm, respectively, indi-
cating that the sample image is reconstructed at the same
position as the FE-SEM image. Fig. 4(e) shows the cross-
sectional profile of the particle in Fig. 4(d). The phase shift
of the 30 nm silica particles for 6.5 keV X-rays was estimated
to be 0.0089 rad, indicating that a similar phase shift was
reconstructed. The present results are comparable with the
best sensitivity reported to date (Lima et al., 2013) and are of a
high standard for spatial resolution. Fig. 4( f) presents the
PRTF curves for the reconstructed images of the 6 nm-thick
test chart and the silica particles. Based on the 1/e criterion,
the respective resolutions are determined to be 18.7 nm
and 29.9 nm.
5. Conclusion
In this study, PCDI measurements were performed using
the high-speed X-ray imaging detector CITIUS at SPring-8
BL29XUL, in which 6.5 keV X-rays were focused by total
reflection focusing mirrors, and a flux of 2.6 10
10
photons
s
1
was obtained at the sample plane. Diffraction intensity
data were collected at up to 250 Mcounts s
1
pixel
1
with
out saturation of the detector. With a spatial resolution of
research papers
J. Synchrotron Rad. (2023). 30 Yukio Takahashi et al. X-ray ptychographic coherent diffraction imaging 5of6
Figure 4
(a) Reconstructed phase and magnified image of the 6 nm-thick Ta test chart. (b) Histogram of the phase distribution in (a), fit with a composite function
consisting of two Gaussian functions. (c) FE-SEM image of silica particles with an approximate diameter of 30 nm. (d) Ptychographic phase and
magnified images corresponding to the same field of view as in (c). (e) Cross-sectional profile of the red dotted line in (d). ( f) Phase retrieval transfer
function for the reconstructed images of the 6 nm-thick Ta test chart and silica particles.

>10.5 nm, 200 nm-thick Ta test chart phase images were
reconstructed. Additionally, the phase images of the 6 nm-
thick Ta test chart with a minimum size of 20 nm and silica
particles with a diameter of 30 nm have been reconstructed,
which are extremely weak phase objects with a phase shift
of 0.01 rad. The present results show a high standard of
reconstruction with high spatial resolution and high sensitivity.
The CITIUS detector will be an indispensable imaging device
for sample observation in various fields using low-emittance
synchrotron radiation sources.
Acknowledgements
The authors would like to thank Mr Yasuhiko Inagaki and
Mr Kunihiko Fujiwara for the mechanical development of the
CITIUS detector that was used in this study.
Funding information
This work was supported by the Japan Society for the
Promotion of Science (JSPS) KAKENHI (Grant Nos.
JP22KJ0302, JP22KJ0301, JP22K05296, JP23KJ0137 and
JP23H05403), and Ministry of Education, Culture, Sports,
Science and Technology of Japan (MEXT) program: ‘Data
Creation and Utilization-Type Material Research and Devel-
opment’ project (Grant No. JPMXP1122712807).
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