Spectrochimica Acta Part B 62 (2007) 626 – 630
www.elsevier.com/locate/sab
Hard X-ray phase imaging and tomography using a grating interferometer ☆
C. David a,⁎, T. Weitkamp a,1 , F. Pfeiffer a , A. Diaz a , J. Bruder a , T. Rohbeck a , A. Groso a ,
O. Bunk a , M. Stampanoni a , P. Cloetens b
b
a
Paul Scherrer Institut, Villigen, Switzerland
European Synchrotron Radiation Facility, Grenoble, France
Received 6 January 2006; accepted 11 March 2007
Available online 16 March 2007
Abstract
An interferometric technique for hard X-rays is presented. It is based on two transmission gratings and a phase-stepping technique, and it
provides separate radiographs of the phase and absorption profiles of bulk samples. Tomographic reconstruction yields quantitative threedimensional maps of the X-ray refractive index and of the attenuation coefficient, with a spatial resolution down to a few microns. The method is
mechanically robust, it requires little monochromaticity, and can be scaled up to large fields of view. These are important prerequisites for use with
laboratory X-ray sources. Numerous applications ranging from wave front sensing to medical radiography are presently under investigation.
© 2007 Elsevier B.V. All rights reserved.
Keywords: Synchrotron radiation; Phase contrast; Radiography; Interferometry
1. Introduction
X-ray radiography and tomography are important methods
for the non-destructive investigation of bulk samples, as the
penetration depth of hard X-ray beams is rather high, and the
low level of diffuse scattering allows for the recording of sharp
projections of the attenuation coefficient. However, for such
important classes of samples as biological tissue, polymers, and
fiber composites, the use of conventional X-ray radiography is
limited because these objects show only weak absorption.
Therefore, X-ray radiographs or tomographic data sets with
sufficient amplitude contrast are often difficult to obtain. In
particular for medical applications such as mammography, a
high radiation dose is required.
The cross section for elastic scattering of hard X rays in matter,
which causes a phase shift of the wave passing through the object
of interest, is usually much greater than that for absorption. For
☆
This paper was presented at the “18th International Congress on X-ray
Optics and Microanalysis” (ICXOM-18) held in Frascati, Rome (Italy), 25–30
September 2005, and is published in the Special Issue of Spectrochimica Acta
Part B, dedicated to that conference.
⁎ Corresponding author. Tel.: 0041 56 310 3753; fax: 0041 56 310 2646.
E-mail address: christian.david@psi.ch (C. David).
1
Present address: ANKA Light Source, Forschungszentrum Karlsruhe, Germany.
0584-8547/$ - see front matter © 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.sab.2007.03.001
example, 17.5-keV X-rays that pass through a 50-μm-thick sheet
of biological tissue are attenuated by only a fraction of a percent,
while the phase shift is close to π. Recording the X-ray phase shift
rather than only the absorption thus has the potential of
substantially increased contrast. A variety of X-ray techniques
are employed to detect the phase contrast of a sample, i.e. to
convert it into an amplitude contrast in the image plane [1]. Some
techniques use the Fresnel diffraction of coherent hard X-rays at
the edges of a phase object to significantly improve the visibility of
an object in microradiography (see for example [2]). In first
approximation, the obtained intensity distribution is proportional to
the Laplacian of the refractive index distribution [3] and in certain
cases a reconstruction of a phase object from a single micrograph is
possible [4]. Quantitative information on arbitrary phase objects
can be obtained by numerically evaluating series of images
acquired with the detector placed at different distances from the
sample [5].
The most sensitive method to measure the phase shifts
introduced to a wave front is interferometry. A set-up for a
Mach-Zehnder type interferometer operated in the hard X-ray
range was introduced by Bonse and Hart [6] about four decades
ago. It consists of three partially transmitting Bragg crystals used
as beam splitter and recombining elements. The incoming light
is split into two separated branches one of which passes through
C. David et al. / Spectrochimica Acta Part B 62 (2007) 626–630
the sample while the other serves as an unperturbed reference
beam. The two beams interfering at the exit of the interferometer
give an intensity distribution that represents the difference in
optical path and thus – if perfectly aligned – of the phase shift
caused by the object. Ando and Hosoya pioneered phase contrast
imaging with such a device in the early seventies [7], and more
recent set-ups have produced large numbers of excellent phase
contrast images and computer tomograms, e.g. of biological
specimens [8,9]. The main technical difficulty lies in the extreme
demands on the mechanical stability of the optical components,
as the relative positions of the optical components have to be
stable within a fraction of a lattice constant, i.e. to sub-Ångstrom
dimensions. Therefore, Bonse-Hart interferometers are very
difficult to handle especially when made big enough to
investigate large samples.
We developed a different kind of interferometer, in which the
interfering beams are not completely separated but merely
sheared by a small angle so that they pass through different,
closely spaced parts of the sample. The principle of this device
is depicted in Fig. 1. It consists of a phase grating G1 and an
absorption grating G2, a scheme which was first proposed by us
in 2002 [10]. The first grating acts as a beam splitter and divides
the incoming beam essentially into the two first diffraction
orders. Since the wavelength λ of the illuminating hard X-rays
(≈ 10− 10 m) is much smaller than the grating pitch (≈ 10− 6 m),
the angle between the two diffracted beams is very small.
Downstream of the beam-splitter grating, the diffracted beams
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interfere and form linear periodic fringe patterns with a
periodicity g that equals half the period of G1. Note that the
period and the lateral position of these fringes do not depend on
the wavelength of the X-rays. Perturbations of the incident wave
front, such as those induced by refraction on an object in the
beam, lead to local displacement of the fringes. However, since
the pitch of the phase grating (and thus the spacing of the
interference fringes) does not exceed a few microns, an area
detector placed in the detection plane will generally not have
sufficient resolution to resolve the fringes. Therefore, a grating
G2 with absorbing lines and the same periodicity and orientation
as the fringes is placed in the detection plane, immediately in
front of the detector. This analyzer grating acts as a transmission
mask for the detector and transforms local fringe position into
signal intensity variation. The detected signal profile thus
contains quantitative information about the phase gradient of
the object.
To separate this phase information from other contributions
to the signal, such as absorption in the sample, inhomogeneous
illumination or imperfections of the gratings, the phase-stepping
approach used in visible-light interferometry [11] was adapted
to this setup. We can derive two separate images of an object
following a process described in more detail in [12]. The first
one represents the amplitude contrast image that we would have
received with no interferometer in the beam. It contains
absorption contrast and in-line phase contrast caused by
diffraction on the edges of the sample. The intensity signal of
the second image is proportional to the phase shift gradient in
the object, which is why we call it the differential phase contrast
(DPC) image. The DPC image can be used to obtain the phase
profile of the object by a simple one-dimensional integration.
An example of an amplitude contrast image, a DPC image, and
a phase contrast image of a simple test object obtained with the
described method is shown in Fig. 2. One can already see a
significant enhancement of the contrast in the phase contrast
images. Moreover, it should be pointed out that a different
physical quantity is used for the image formation: while the
attenuation of the beam is related to the imaginary part of the
complex refractive index, the phase shift is related to its real
part.
2. Grating fabrication
Fig. 1. Principle of the X-ray grating interferometer. The first grating splits the
incoming wave into two waves which create a line pattern by interference. This
pattern is analyzed using a second grating. An object with a phase gradient in the
beam will act as a prism and slightly refract the beam, which in turn shifts the
interference pattern downstream of the object in lateral direction. The resulting
change in transmission through the analyzer grating depends on the sign and
strength of the phase gradient.
Obviously, the quality of the gratings used in such an
interferometer set-up is crucial. We use micro-fabrication
techniques to define the grating structures with sufficient
accuracy. It is essential that the two gratings have the correct
ratio of periods. For a plane incoming wave, the period of G2
should be two times smaller than that of G1, whereas for a
spherical incoming wave, a slight correction needs to be
included. Microlithography techniques need to be used to define
the grating line pattern on silicon substrates. The further
processing depends on the individual properties required: the
beam splitter grating G1 should have low absorbing structures
that introduce a phase shift of π to the passing X-ray waves,
whereas the analyzer grating G2 should have highly absorbing
lines.
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C. David et al. / Spectrochimica Acta Part B 62 (2007) 626–630
Fig. 2. X-ray micrographs of a test sample consisting of 100 μm and 200 μm diameter polystyrene spheres attached to a 350 mm diameter piece of polyacryl filament.
(a) Amplitude contrast image, (b) differential phase contrast (DPC) image, (c) phase contrast image. The field of view is approximately 1 mm × 1 mm. The images were
taken at the tomography end station of beamline 4S of the Swiss Light Source using 17.5 keV radiation.
We use silicon as the phase shifting material for the beam
splitter gratings. The structure height to obtain the required
phase shift is proportional to the photon energy used. For
17.5 keV, a height of 22 μm is optimum. The period of our beam
splitter gratings is close to 4 μm resulting in very high aspect
ratios of the structures. The top part of Fig. 3 shows a cross
section of such a grating. The structures are made by wet
chemical etching in potassium hydroxide solution. As substrates, we use 250 μm thick silicon wafers with ⟨110⟩
orientation. The grating patterns are exposed using a high
precision electron beam lithography process [13]. The orienta-
tion of the lines is along the ⟨112⟩ direction with a precision of
better than 0.1°, this results in an anisotropic etching with
vertical side walls. This process is also used for the fabrication
of linear Fresnel zone plates, more details can be found in [14].
The fabrication of the analyzer gratings is even more
challenging. Firstly, the period has to be two times smaller, i.e.
2 μm, and secondly, no simple etching process exists to pattern
highly absorbing materials with high aspect rations. The
structure height again depends on the photon energy, at
17.5 keV using gold as absorbing material, a structure height
of 10 μm is desirable for a high contrast of the DPC signal.
We first pattern a silicon grating using the method described
above. Then, the gaps of the grating are filled with gold by
electro-deposition. Using a shadow evaporation process and
selective wet etching, it is possible to let the gold grow from the
bottom of the silicon grooves [15], as any deposition on the side
walls or the silicon ridges would result in an incomplete filling
of the grooves. The lower part of Fig. 3 shows a cross section of
a gold-filled silicon grating fabricated by the described process.
3. Experimental results
In the setup used at various synchrotron beamlines, the
gratings are mounted into a holder unit, which has motorized
actuators for translation perpendicular to the grating lines and
rotation about the beam axis. The inter-grating distance is fixed
to typically a few centimeters, and the interferometer is mounted
directly onto an X-ray CCD camera. The gratings are then
aligned with the lines parallel to each other using a moiré
technique. The setup is very robust, it requires no special
precautions to reduce vibrations, mechanical drift, etc.
3.1. Phase contrast radiography
Fig. 3. Scanning electron micrographs of cross sections through the
interferometer gratings. (a) Silicon beam splitter grating with 4 mm grating
period and 22 μm high structures, (b) analyzer grating with 2 μm period
consisting of a silicon grating filled with gold by electroplating.
The method was applied to image an animal organ, a rat
heart, which was placed in a container filled with a 4% aqueous
formalin solution. The imaging of such a sample is very
challenging, as the sample and the surrounding medium have
very similar absorption and phase shift. Fig. 4 shows the
amplitude image and DPC image, as well as an image of the
projected phase shift of the sample. The phase image is again
the result of a numerical integration of the DPC image. The
C. David et al. / Spectrochimica Acta Part B 62 (2007) 626–630
629
Fig. 4. X-ray micrographs of a rat heart placed in a formalin solution. (a) Amplitude contrast image, (b) differential phase contrast (DPC) image, (c) phase contrast
image. The field of view is approximately 15 mm × 25 mm. The images were taken at beamline ID19 of the European Synchrotron Radiation Facility using 17.5 keV
radiation.
images are stitched together from two frames as the used X-ray
camera was too small to cover the whole sample. In amplitude
contrast, only some fatty tissue in the upper half of the image is
visible, whereas the complete organ with many details can be
seen in the DPC and the phase image. Note that the gray scale of
the DPC image and the phase contrast image are quantitative, as
can be seen from the units of the grayscale bar.
3.2. Phase contrast tomography
As mentioned before, the phase gradient images can be used
to obtain phase images by integration. As the method yields
quantitative information, a set of projections taken from an
object under different viewing angles can be used to obtain a 3dimensional map of the real part ™ of the complex refractive
index n = 1 − ™ + i® for each voxel. Fig. 5 shows a small spider
sitting on a loop of fishing line. This three-dimensional densityprojection rendering of the refractive-index distribution reveals
Fig. 5. Tomographic reconstruction of the phase shift caused by a small spider.
The field of view is approximately 1.4 mm × 1.4 mm. The data were acquired at
beamline ID19 of the European Synchrotron Radiation Facility using 14.4 keV
photon energy.
details of the internal structure of the animal that would be
difficult to access with other techniques. Note the fine details
inside the joints of the spider's legs. The spatial resolution is a
few micrometers.
3.3. Wave front sensing
The grating interferometer is very sensitive to minute
deflections of an X-ray wave front. In case of the described
radiography and tomography experiments, this is caused by
refraction on phase gradients in the object. The high sensitivity
of the method can also be used to monitor wave front distortions
of synchrotron radiation to characterize the source itself or
optical components. We have successfully applied this method
to map out the errors of X-ray multilayer mirrors [16] simply by
placing the interferometer directly behind the mirror. It was
possible to detect slope errors with a sensitivity better than
100 nrad, which is below the fabrication tolerances of state-ofthe-art mirror fabrication. A similar experiment was performed
to reveal the fabrication errors of Beryllium refractive X-ray
Fig. 6. Silicon beam splitter grating with a size of 64 mm × 64 mm fabricated by
photolithography.
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C. David et al. / Spectrochimica Acta Part B 62 (2007) 626–630
lenses. Besides the extreme sensitivity, the method has the great
advantage that it can be used in-situ, meaning when the optical
element is mounted in its operating environment including the
heat load of the synchrotron radiation.
4. Conclusion and outlook
We have demonstrated how an interferometer consisting of
two microstructured gratings can be used to record differential
phase contrast images and phase contrast images in the hard Xray range. Especially for light, low absorbing materials, the
contrast can be enhanced significantly. The image formation
process can also be used to acquire data sets suitable for a
tomographic reconstruction of the X-ray refractive index inside
an object. In addition, the interferometer can detect very small
wave front distortions in the X-ray range, which makes it useful
for the in-situ testing of X-ray optical elements.
Besides applications in materials science, and non-destructive testing, our future work will focus on the further
development of the technique for medical diagnostics. Mammography appears to be one of the most promising applications, as
the photon energies used in breast imaging are low compared to
other medical radiography techniques, the absorption contrast
between healthy tissue and a breast tumor is usually very small,
and the reduction of the applied radiation dose is a significant
issue.
This will require two major development steps. Firstly, the
field of view of the interferometer – and thus the gratings – has
to be scaled up from its present size of a few millimeters to
many centimeters. It is therefore no longer efficient to use slow
and expensive electron beam lithography for the grating
fabrication. We have therefore developed a photolithography
process that enables us to fabricate interferometer gratings over
large areas. Fig. 6 shows a photograph of a 64 mm × 64 mm
silicon beam splitter grating fabricated at the Laboratory for
Micro- and Nanotechnology. The size is at present limited by
the used 100 mm diameter wafers, but there is no fundamental
problem to transfer the process to the 300 mm diameter
substrates presently used in semiconductor industry.
The second development step is to transfer the technique
away from the synchrotron to X-ray tube sources. Unlike a
synchrotron, such sources provide too little flux to be used with
a monochromator, and the radiation is much less collimated. We
have demonstrated [12] that the grating interferometer technique can be used with broad-band X-rays and divergent
radiation. These properties make the presented phase contrast
imaging technique most promising for medical applications.
Acknowledgements
We would like to thank B. Haas, F. Glaus, and E. Deckardt of
the LMN for help in the microlithography processes. We are
also indebted to various staff members of the European
Synchrotron Radiation Facility ESRF and the Swiss Light
Source SLS.
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