We demonstrate a single shot two-dimensional grating-based X-ray phase-contrast imaging using a synchrotron radiation source. A checkerboard designed phase grating for π phase modulation at 17 keV and 35 keV, and a lattice-shaped amplitude grating with a high aspect ratio to shield X-rays up to 35 keV were fabricated. A Fourier analysis of Moiré fringe generated by the gratings was introduced to obtain the two-dimensional differential phase-contrast image with a single exposure. The results show that soft tissues and cartilages of a chicken wing sample are clearly seen with differential phase variation in two-dimensional directions. Using this method not only the whole of an object but also only an inner part of the object can be imaged.
© 2011 OSA
Conventional X-ray imaging has been widely used for medical imaging and non-destructive imaging. Since Röntgen found X-ray in 1895, X-ray imaging has been developed based on the absorption contrast. However, due to a large amount of the dose and the difficulty of imaging soft tissues, X-ray imaging is a limited tool for medical imaging. Since 1990s, the studies of X-ray phase-contrast imaging have been active using synchrotron radiation sources. The Bonse-Hart interferometer  using triple silicon single-crystal plates is able to image the phase of an object, but it requires parallel and monochromatic X-rays. The diffraction enhanced imaging (DEI) [2–4] is used to obtain the differential phase-contrast image using double or triple silicon single-crystal monochromators, and as a consequence the X-ray photons are lost by the monochromators. On the other hand, the propagation-based imaging [5-6] is a simple method that X-ray detector is kept as far away from an object as possible, but the obtained image is mainly governed by the absorption contrast with an edge enhancement. On the contrary to these three methods, the grating-based interferometer using the Talbot effect  is one of the promising methods to achieve a novel X-ray medical imaging modality using a conventional X-ray tube.
Momose’s [8-9] and Pfeiffer’s [10–12] groups have studied the grating-based X-ray phase-contrast imaging using a phase stepping technique. Their imaging method has an advantage of a high spatial resolution, but a disadvantage of requirement of multiple exposures at least three images. Recently, another phase retrieval approach was introduced to X-ray phase-contrast imaging by Momose et al.  to obtain the time resolved phase-contrast images using a white beam of synchrotron radiation source. They applied the Fourier transform phase retrieval for their study, but only one-dimensional differential phase-contrast image was obtained. On the other hand, Kottler et al.  have retrieved two-dimensional phase-contrast image via an algorism to combine x- and y-directional differential phase-contrast images using one-dimensional gratings. In their imaging method, however, a double number of exposures are required to obtain two-dimensional phase information due to the use of one-dimensional gratings with rotation. As a consequence, a multiple shot imaging increases the radiation dose and is not resistant to the movement of the object for medical applications. Recently, differential phase-contrast images were obtained by the refraction effect of X-rays using two-dimensional transmission gratings, a stack of two Bucky grids, by Wen et al. . A focal spot size of X-ray source is expected to be limited due to the separation of absorption and phase components in the image.
In this study we demonstrate a single shot two-dimensional grating-based X-ray phase-contrast imaging using a synchrotron radiation source. A checkerboard designed phase grating for π phase modulation and a lattice-shaped amplitude grating were positioned with a distance of the first Talbot position. Differential phase-contrast image was obtained by the Fourier analysis of Moiré fringe generated by the gratings on X-ray detector. The present imaging method includes obtaining the phase-contrast image and the absorption image in two-dimensional directions with a single exposure.
Figure 1 shows our experimental set up. It consists of a phase grating, an amplitude grating, and an X-ray detector. The phase grating has a structure of checkerboard with the height equivalent to π phase modulation at the set X-ray energy. Silicon is chosen for the phase grating because of the fabrication properties and the high transparency of X-rays. The lattice-shaped amplitude grating is used to shield X-rays partially and generate Moiré fringe. The amplitude grating is a fabricated silicon structure with filling of gold in order to shield X-rays. The amplitude grating is positioned along X-ray beams with a distance from the phase grating, called Talbot distance defined by the period of the phase grating and X-ray wavelength.
The principle of the present imaging method is the following. The X-rays are modulated with π phase by the phase grating and generate a self-image at the position of Talbot distance where the amplitude grating is arranged. Following the Talbot effect the self-image is created by the interference of diffracted X-rays from the phase grating. The intensity of the self-image generated at the position (x, y) of the wavefront and the distance from the phase grating, z, can be written as
Here, ψ is a Fourier series expansion coefficient of the period of phase grating, nx and ny are the counting number, PG1 is the period of phase grating, Φ is the phase of object, and λ is the wavelength of X-ray.
The intensity of Moiré fringe generated by the amplitude grating at the position of (x, y, z) is written by
It is necessary for the grating-based X-ray phase-contrast imaging that the self-image transforms to Moiré fringe by introducing the amplitude grating due to a low spatial resolution of conventional X-ray detectors compared to the self-image. Two-dimensional Moiré fringe is generated by the combination of the self-image and the slightly rotated amplitude grating with the same period of the self-image. The wavefront of X-rays through an object placed upstream of the phase grating is deformed by the phase shift of the object. This phase shift can be detected by the change of Moiré fringe on the X-ray detector.
The Fourier spectra are obtained by the Fourier transform of Moiré fringe. The spectrum at the center (the 0th spectrum) is attributed to an absorption component of X-rays, and the carrier frequency spectrum (the 1st spectrum) includes the phase information. To retrieve the phase information we compute the inverse Fourier transform of the carrier frequency spectrum with the surrounding region. The differential phase-contrast images with horizontal and vertical directions are obtained by the above-mentioned phase retrieval method. The Fourier transform of the intensity of Moiré fringe is written by
The technique has some advantages. This method uniquely determines the phase integrated from the differential phase-contrast images, whereas the phase stepping approach requires the origin of the integration. The present imaging method is able to obtain the phase-contrast image of an object bigger than the field of view, whereas the phase stepping method requires a space out of the object.
3. Experimental details
The experiments were performed with monochromatic X-rays of 17.5 and 35 keV at BL-20B2 of SPring-8, Japan. It is a nearly parallel X-ray beam reaching at the distance of 206 meters from the radiation-emitted point. We used an X-ray beam with a dimension of 16 mm by 24 mm shaped from the original beam size 50 mm by 300 mm using a double slits system. The X-rays were monochromatized by double single crystals of silicon (111).
The phase gratings were fabricated by a process including photolithography, and deep etching into silicon. The checkerboard designed phase grating [Fig. 3(a) ] with the period of 11.4 μm and the height of 23 μm for π phase modulation was prepared for the experiment with X-ray of 17.5 keV. The phase grating with the height of 46 μm was fabricated for the 35 keV use. The filling of gold by the electroplating was added to the fabrication process of the phase grating to fabricate the amplitude grating. The lattice-shaped amplitude grating with the period of 8.24 μm and the height of 100 μm was successfully fabricated as shown in Fig. 3(b) and (c). Many silicon pillars, whose cross section is a square 4μm on a side, are two-dimensionally arranged in the amplitude grating. The height of the gold is able to block X-rays up to 47 keV with a shielding rate of 80%.
The distance between the phase grating and the amplitude grating was set to 459 mm for 17.5 keV, and 921 mm for 35 keV corresponding to the 1st Talbot distance, respectively. The images were recorded with a fluorescent-screen lens-coupling system, Hamamatsu C4742-95HR combined with AA60 lens system. X-rays passing through the object are transformed into a visible light by the fluorescent screen. The images on the screen are read by a cooled CCD camera with a high numerical aperture lens. The module consists of an array of 4000 (H) × 2624 (V) pixels with a pixel size of 6.0 µm. We used this detector with binned pixels and the pixel size is 12 µm.
The raw image of a Teflon rod and a polyamide rod was captured at 17.5 keV with an exposure time of 1.5 seconds. The differential phase-contrast image [Fig. 4(b) ] was calculated from the inverse Fourier transform of the 1st Fourier spectrum of the raw image. Compared to the absorption image [Fig. 4(a)] retrieved from the 0th Fourier spectrum, the polyamide rod having a very low X-ray absorption can be clearly seen in the differential phase-contrast image [Fig. 4(b)]. We can also identify a double layered structure of the polyamide rod from Fig. 4(b). The polyamide rod is filled with the material and the boundary of the double layered structure in the rod is invisible. The line profile of the polyamide rod shows the double layered structure more clearly with double gaps equivalent to 0.05 rad/μm differential phase variation as shown in Fig. 4(c).
A chicken wing was chosen as a biological sample with a simple reason of easy handling. The field of view was limited to 12 mm by 12mm due to the active area of the amplitude grating. The chicken wing was fixed on an acrylic plate by polyimide tapes without any wrapping. The absorption image was taken with the sample as close as possible to the detector, that is called contact image. Figure 5 shows the differential phase-contrast image and the contact image of a joint part of the chicken wing sample at 17.5 keV with an exposure time of 1.5 seconds. Some soft tissues between bones can be clearly seen in the differential phase-contrast image [Fig. 5(a)] compared with the contact image [Fig. 5(b)].
The present imaging method has an advantage in the scene of an object bigger than the field of view such as the image shown in Fig. 5. The grating-based X-ray phase-contrast imaging using one-dimensional gratings requires a space out of an object for the starting phase value in integration. The fringe analysis method used in the present study does not need any space out of an object, i.e. the phase-contrast image of an object filled in the field of view can be retrieved.
Cartilage is one of the most difficult parts of human bodies to be imaged in conventionalX-ray imaging. A cartilage of chicken wing can be seen in the differential phase-contrast image shown in Fig. 6 , whereas the contact image does not show any profile. The cartilage is more clearly identified at 17.5 keV [Fig. 6(a)] with comparison of the image at 35 keV [Fig. 6(b)]. It is considered that this is mainly caused by the difference of refractive index calculated from the composition of cartilage. The calculated refractive index of the cartilage is 7.98 x 10−6 at 17.5 keV and 2.04 x 10−6 at 35 keV. From these refractive indices the phase shift of cartilage is 0.716 rad/μm at 17.5 keV, 0.362 rad/μm at 35 keV, respectively.
A full image of the chicken wing sample was obtained from 99 individual differential phase-contrast images using an image stitching technology shown in Fig. 7(a) . The detailed texture of bones and soft tissues were imaged with differential phase variation. Another way of showing the differential phase-contrast image was also examined. The image shown in Fig. 7(b) has information of two-dimensional differential phase of the sample. The square-root of sum of squares of the differential phase-contrast image in x- and y-directions was calculated. The texture of the chicken wing sample was clearly observed with an edge enhancement. This is one of the most important features of our two-dimensional grating-based X-ray phase-contrast imaging. In addition, the present imaging method can avoid the artifact and the phase mismatch that may be happened if the misalignment of the gratings or the movement of an object in one-dimensional phase stepping approach with a double exposures.
We have demonstrated a single shot two-dimensional grating-based X-ray phase-contrast imaging using a synchrotron radiation source. We used a checkerboard designed phase grating and a lattice-shaped amplitude grating in Talbot interferometer to obtain two-dimensional phase information of the object. The Fourier analysis of Moiré fringe formed by the gratings was introduced to obtain the differential phase-contrast images with a single exposure. The present imaging method has advantages of reducing exposure times and retrieving the phase-contrast image of an object bigger than the field of view. Some soft tissues and cartilages of a chicken wing can be clearly imaged with differential phase variation in two-dimensional directions. This demonstration results show a high potential application of the present imaging system for medical imaging.
The authors gratefully acknowledge Mr. Masanobu Hasegawa and Mr. Naoki Kohara (both Canon Inc.) for helpful discussions, and Dr. Peter Fletcher and Dr. Stephen Hardy for image processing (both Canon Information Systems Research Australia), and Mr. Kentaro Uesugi and Dr. Masato Hoshino (both SPring-8) for technical supports. The synchrotron radiation experiments were performed at the BL-20B2 in the SPring-8 with the approval of the Japan Synchrotron Radiation Research Institute (JASRI) (Proposal No. 2009A1952).
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