Jpn. J. Appl. Phys. Vol. 38 (1999) pp. L 1556–L 1558
Part 2, No. 12B, 15 December 1999
c
°1999
Publication Board, Japanese Journal of Applied Physics
Development of an X-Ray Interferometer for High-Resolution
Phase-Contrast X-Ray Imaging
Keiichi H IRANO and Atsushi M OMOSE1
Institute of Materials Structure Science, High Energy Accelerator Research Organization, 1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan
1 Advanced Research Laboratory, Hitachi, Ltd., Hatoyama, Saitama 350-0395, Japan
(Received August 31, 1999; accepted for publication October 27, 1999)
An X-ray interferometer for high-resolution phase-contrast X-ray imaging was developed by thinning the central part of
the analyzer crystal of a triple Laue-case (LLL) X-ray interferometer. The interferometer was tested at beamline 47XU at the
SPring-8, and the improvement of the resolution of interference patterns was successfully observed for a plastic sphere of 1 mm
diameter.
KEYWORDS: phase contrast, X-ray interferometer, high resolution, synchrotron radiation
The recent development of phase-contrast X-ray imaging,
which detects phase shifts produced by a sample by means
of an X-ray interferometer, has opened up new possibilities
of observing the structures inside biological soft tissues.1, 2)
Because the interaction cross section of the X-ray phase shift
is about a thousand times larger than that of the X-ray absorption for light elements such as hydrogen, carbon, nitrogen and oxygen, the phase-contrast X-ray imaging has much
higher sensitivity for biological soft tissues than the conventional absorption-contrast X-ray imaging. Due to this advantage, phase-contrast X-ray imaging can resolve the structures
inside biological soft tissues without the need for staining and
without serious radiation exposure.
Phase-contrast X-ray imaging by means of the X-ray interferometer has been developed to phase-contrast X-ray computed tomography (CT).3) In phase-contrast X-ray CT, a
series of interference patterns is measured to generate appropriate CT input data, then the three-dimensional image is reconstructed by computer analysis of the interference patterns.
The best spatial resolution achieved to date is around 30 µm.
Although this resolution is sufficient for observing the macroscopic structures inside samples, it is insufficient for observing the microscopic structures inside them. To explore microscopic structures such as cells and defects, it is necessary to
improve the spatial resolution.
The spatial resolution of the reconstructed CT image is
closely related to that of the interference patterns. There are
three factors that affect the resolution of the interference patterns: the resolution of the X-ray area detector, the size of the
light source and the diffraction effect in the X-ray interferometer. The influence of the source size on the resolution is
estimated by
Rs ≈ sl/L ,
ometer.
Let us consider the mechanism leading to resolution deterioration caused by a triple Laue-case (LLL) X-ray interferometer. The LLL-type X-ray interferometer4) has three parallel
wafers as shown in Fig. 1. When the incident X-ray beam satisfies the diffraction condition, the Laue-case diffraction takes
place in each wafer. The first wafer (splitter) produces two
coherent beams, and, subsequently, the second (mirror) and
the third (analyzer) wafers recombine the interfering beams
and produce two outgoing beams. A sample is inserted in one
of the paths of coherent beams between the mirror and the
analyzer. Because of the phase shift caused by the sample,
interference patterns appear in the outgoing beams. At the
same time, X-rays are slightly refracted by the sample. Due
to this refraction, the incidence angle of the X-ray beam to the
analyzer slightly deviates from the diffraction condition. The
deviation angle, 1θ, is usually negligible, but in several cases
it amounts to several arcseconds. According to the dynamical
theory of X-ray diffraction,5) the direction of the energy flow
inside the analyzer is quite sensitive to the deviation angle,
1θ. If we assume that there is no absorption inside the analyzer, the angle between the direction of the energy flow and
the lattice plane is given by
Ã
!
√
W2 − W W2 + 1
−1
tan θB ,
(2)
2 = tan
√
1 + W2 − W W2 + 1
(1)
where s is the source size, L the distance from the source to
the sample and l the distance from the sample to the detector.
In our previous experiments carried out at beamline 14B
at the Photon Factory, the minimum fringe spacing detectable
was about 10 µm in the vertical direction (perpendicular to
the scattering plane of the interferometer) and 100 µm in the
horizontal direction. As a result, the spatial resolution was
anisotropic. The resolution due to the source size was estimated from eq. (1) to be about 1 µm vertically and 10 µm
horizontally. The resolution of the X-ray area detector was
12 µm. This indicates that the resolution deterioration in the
horizontal direction was mainly caused by the X-ray interfer-
Fig. 1. A schematic diagram of the setup for phase-contrast X-ray imaging.
The monochromatic X-ray beam is incident upon a LLL-type X-ray interferometer. A sample is inserted in one of the paths of the coherent beams
between the mirror and the analyzer of the interferometer. Interference
patterns in the O-beam or H-beam are observed with an X-ray area detector. For high-resolution X-ray imaging, the central part of the analyzer is
thinned by chemical etching.
L 1556
K. H IRANO and A. M OMOSE
Jpn. J. Appl. Phys. Vol. 38 (1999) Pt. 2, No. 12B
where
π V sin 2θB
1θ.
(3)
W = 2
λ re |P||Fh |
In eqs. (2) and (3), λ is the wavelength, P the polarization
factor, Fh the crystal structure factor, V the volume of the
unit cell, re the classical electron radius and θB the Bragg angle. For example, Fig. 2 shows the calculated angle, 2, for
the Laue-case Si 220 diffraction. The calculation conditions
are: λ = 0.7 Å and P = 1 (σ -polarization). In Fig. 2, the
calculated angle, 2, is about 25,000 times larger than the deviation angle, 1θ, inside the diffraction region. When the
X-ray beam exits the analyzer, it is positioned away from the
exit point for 1θ = 0 by
1l = t · | tan 2|,
L 1557
ples have complex three-dimensional structures, the blurring
effect remains to some extent. We consider that this is the
factor which limits the current spatial resolution of the phasecontrast X-ray CT.
When the refracted beam by the sample and the nonrefracted reference beam interfere, interference fringes are produced. The period of the interference fringes is given by
|λ/1θ|. Because the shift of the exit point must be smaller
than this period, 1θ should satisfy
1l < |λ/1θ|.
(5)
Figure 3 shows calculated 1l and |λ/1θ|. Calculations were
performed for t = 1 mm and t = 240 µm under the same
(4)
where t is the thickness of the analyzer. This shift of the exit
point distorts images and degrades coherence. As a result, the
visibility of the interference patterns decreases and the spatial
resolution degrades. Note that the shift does not occur in the
direction perpendicular to the scattering plane, and therefore,
this consideration is consistent with the anisotropic resolution
observed in our previous experiments. In the phase-contrast
X-ray CT, the rotation axis of a sample is set parallel to the
scattering plane. Then, a sectional image is reconstructed
on a plane perpendicular to the scattering plane, where the
blurring effect is minimum. However, because actual sam-
(a)
Fig. 2. Calculated 1θ-dependence of the angle, 2, for the Si 220 diffraction. Calculation conditions are: λ = 0.7 Å and P = 1 (σ -polarization).
(b)
Fig. 3. Calculated 1θ-dependence of the shift of the exit point for
t = 1 mm (solid) and t = 240 µm (broken line) and the period of interference fringes (dotted line). Calculations were performed under the
same conditions for Fig. 2.
Fig. 4. Phase-contrast images of a plastic sphere observed with an X-ray
zooming tube. The diameter of the plastic sphere was 1 mm. The thickness
of the analyzer was (a) 1 mm and (b) 240 µm. The horizontal direction is
perpendicular to the scattering plane.
L 1558
Jpn. J. Appl. Phys. Vol. 38 (1999) Pt. 2, No. 12B
conditions for Fig. 2. It is seen that the valid region for 1θ is
between −0.300 and +0.300 for t = 1 mm and between −0.600
and +0.600 for t = 240 µm. The valid region for 1θ is expanded by making the analyzer thinner.
To improve the resolution of interference patterns and to
broaden the valid region for 1θ, we fabricated the X-ray interferometer with a thin analyzer. At first we cut an LLL-type
X-ray interferometer from an FZ silicon ingot. The thickness
of the analyzer was about 500 µm. Then the whole interferometer was etched in the etchant for a few minutes to remove
the surface strained layer. The thickness of the analyzer after
the etching was about 400–450 µm. Finally the central part of
the analyzer was thinned down to 240 µm by chemical etching. The etchant consisted of a 5 : 1 : 1 HNO3 (65%), HF
(40%) and CH3 COOH (100%) mixture. Handling of the interferometer can be easily accomplished using the remaining
stable part at the rim of the analyzer.
We tested the X-ray interferometer by comparing it with
an X-ray interferometer with a 1-mm analyzer at beamline
47XU at the SPring-8 using 18.3-keV X-rays (λ = 0.68 Å).
A plastic sphere of 1 mm diameter was used as a test object
and the interference patterns were observed by means of an Xray zooming tube6) with the pixel size of 0.92 µm. Figure 4
shows the obtained interference patterns of the plastic sphere.
The thickness of the analyzer of the X-ray interferometer was
1 mm for Fig. 4(a) and 240 µm for Fig. 4(b). In Fig. 4(a)
the interference fringes are blurred and elongated in the direction parallel to the scattering plane. On the contrary, the
interference fringes are clear in all directions and circular in
Fig. 4(b). This result shows that the X-ray interferometer with
K. H IRANO and A. M OMOSE
a thinner analyzer can resolve smaller interference patterns
with smaller deformation. The small stains in Fig. 4(b) are
due to the roughness of the analyzer surface formed during
the chemical thinning process.
We are planning to develop phase-contrast microtomography using the interferometer proposed above.7) For this purpose, further thinning of the analyzer and improvement of the
surface finish quality are required. Because a sample which
causes lesser refraction can be observed with better resolution, the present phase-contrast X-ray imaging is suitable for
observing biological soft tissues. We expect that a spatial resolution below 10 µm would be achieved by thinning the analyzer below 100 µm.
This study was carried out with Special Coordination
Funds for Promoting Science and Technology from the Science and Technology Agency of the Japanese Government.
The experiments were performed under the approval of
SPring-8 committee 1999A0079-NOM-np.
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