Two-dimensional gratings-based phase-contrast imagingusing a conventional x-ray tube

Genta Sato,* Takeshi Kondoh, Hidenosuke Itoh, Soichiro Handa, Kimiaki Yamaguchi, Takashi Nakamura,Kentaro Nagai, Chidane Ouchi, Takayuki Teshima, Yutaka Setomoto, and Toru DenCorporate R&D Headquarters, Canon Inc., 3-30-2 Shimomaruko, Ohta-ku, Tokyo 146-8501, Japan

*Corresponding author: sato.genta@canon.co.jp

Received June 23, 2011; revised July 29, 2011; accepted August 3, 2011;posted August 5, 2011 (Doc. ID 149784); published September 8, 2011

A Talbot–Lau interferometer using two-dimensional gratings and a conventional x-ray tube has been used toinvestigate a phase-contrast imaging technique that is sensitive to phase gradients in two orthogonal directions.Fourier analysis of Moiré fringe patterns was introduced to obtain differential phase images and scattering imagesfrom a single exposure. Two-dimensional structures of plastic phantoms and characteristic features of soft tissuewere clearly obtained at 17:5 keV. The phase-stepping technique was also examined to investigate the spatial re-solution of different phase retrieval methods. In the presented setup we found that the choice of phase retrievalmethod made little difference in image blur, and a large effective source size was found to give a high intensityin the image plane. © 2011 Optical Society of AmericaOCIS codes: 340.7450, 110.6760, 170.7440.

X-ray phase-contrast imaging has attracted great atten-tion since 1990s. Because of a stronger interaction ofx ray with materials for phase shift compared to that forabsorption, various phase-sensitive x-ray imaging meth-ods have been developed [1–7]. In particular, a grating-based x-ray interferometer is one of the promisingmethods due to the advantages of high phase sensitivity,a large field of view, and utilization of polychromaticx rays. Momose et al. [4,5] and Pfeiffer and coworkers[6,7] have studied an x-ray Talbot interferometer usingone-dimensional (1-D) line gratings. However, to retrievethe phase image from a 1-D differential phase image, theyneed empty space outside the support of the object forthe meaningful phase value in integration because of lackof sensitivity to structures in the object oriented perpen-dicular to the grating lines. In order to overcome this dis-advantage, a few grating-based interferometers usinggratings that form a two-dimensional (2-D) structurehave been developed [8–10]. The systems developed byWen et al. [8] and Zanettle et al. [9] consist of 2-D struc-tured gratings formed by closely stacked double line grat-ings. Recently, genuine 2-D gratings were fabricated andinstalled in an x-ray Talbot interferometer, which wasimplemented at a synchrotron radiation source [10].An interferometer using genuine 2-D gratings providesan advantage for avoiding the phase mismatch in retrie-val caused by the misalignment of the closely stackedpair of line gratings.In order to apply our 2-D phase-contrast imaging tech-

nique for the laboratory use, we have introduced a 2-DTalbot–Lau interferometer [11] using a conventionalx-ray tube. In this Letter, we present phase-contrastimages of soft-tissue samples and the scattering imagesthat may be contributed by ultra small-angle scatteringfrom the objects. Raw images of plastic fibers were alsoobtained with two different effective source sizes ofx rays, and the differential phase images were retrievedby Fourier analysis and the phase-stepping technique toinvestigate the effect of the source size and phaseretrieval methods on the image blur.

Figure 1 shows a schematic setup of the Talbot–Lauinterferometer with 2-D gratings used in this study. Itconsists of a conventional x-ray tube, a source grating(G0), a phase grating (G1), an amplitude grating (G2),and an x-ray detector. G1 has a checkerboard structurewith the diagonal period p1 and the thickness equivalentto π phase shifting. G1 produces an interference distribu-tion of highly intense spots with a lattice pattern [10]. Theinterference pattern of the period ps ¼ M × p1=ð2Þ1=2 isobserved at the Talbot distance zT ¼ M × ð2m − 1Þp12=4λ, with the wavelength λ, the positive integer m, andthe magnification factor M according to the Fresnel scal-ing theorem [12]. G2 acts as an analyzer grating at theTalbot distance to generate a Moiré fringe. The periodof G2, p2, is chosen equal to the period of the interferencepattern. G0 is installed downstream from the x-ray tubeto create a set of virtual sources. The virtual sources forma lattice pattern with the period p0 ¼ ps × L=zT , where Lis the distance between G0 and G1. The x ray from theeach virtual source independently creates self-images,which are superimposed and intensified at G2.

The three gratings in the interferometer were fabri-cated in a similar way to those presented in our previouspaper [10]. G1 was made of silicon and had a period ofp1 ¼ 8:49 μm. The height of the silicon structure was23 μm, which is equivalent to the π phase modulationof the x ray at 17:5keV. The gratings, G0 and G2, had

Fig. 1. Schematic setup of 2-D x-ray Talbot–Lau interferom-eter. The interferometer consists of a source grating (G0), acheckerboard designed phase grating (G1), and a lattice-shapedamplitude grating (G2). X rays generated by a conventionalx-ray tube are recorded by a detector behind G2.

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a lattice-shaped structure made of gold on silicon sub-strates. The structure of gold had a sufficient height toattenuate more than 80% of the x ray at 35 keV. G0and G2 had periods of p0 ¼ 22:11 μm and p2 ¼ 8:24 μm,respectively. The aperture size of G0 was 8 μm.The experiments were performed using a rotating

anode type x-ray tube (Rigaku Co., ultraX 18) with a tung-sten anode. Two types of effective source size, s ¼0:3mm and 0:1mm in FWHM, were used. The x-ray tubewas operated at an anode voltage of 35 kV, anode cur-rents of 90mA for s ¼ 0:3mm, and 20mA for s ¼0:1mm, respectively. G0 was placed 12 cm away fromthe x-ray focal spot. The distance between G0 and G1(L) and between G1 and G2 (zT ) were L ¼ 936mmand zT ¼ 348mm, respectively. The Moiré fringes weregenerated by slightly rotating G2 and were recordedusing an x-ray flat panel detector (Hamamatsu PhotonicsC9732DK) placed behind G2. Samples were placed imme-diately upstream of G1.Fourier analysis [13] of 2-D Moiré fringes was used to

extract the phase information. The period of the Moiréfringe, pM , was adjusted to 200 μm which is equivalentto four pixels of the detector. The Fourier transformmethod has the advantage that the differential phaseimages along two orthogonal directions can be obtainedfrom a single Moiré fringe image.To investigate the spatial resolution of the present in-

terferometer, a Moiré fringe image with nylon samples (arod of 500 μm in diameter, mesh of 200 and 120 μm indiameter) was captured using the effective source sizeof 0:3mm with an exposure time of 44 s. Figures. 2(a)and 2(b) show the differential phase images along thex and y directions, respectively, retrieved by the Fouriertransform method. Two types of nylon mesh and a nylonrod can be identified in the restored image. The spatialresolution of our setup can be estimated as 120 μm or lessfrom the finest structure in the nylon mesh. As shown inFig. 2(b), the structure oriented perpendicular to the dif-ferential direction of restored image in the nylon rod isnot visible. The interferometer using 2-D gratings givesphase information in two directions and helps to identifythe structure of the sample.We have also demonstrated imaging of soft tissues

using the present system. Figure 3 shows the imagesof a chicken’s bone including cartilage in a plastic cellfilled with water [Fig. 3(a)] and a tomato in air [Fig. 3(e)].An absorption image, the differential phase image, andthe scattering image of each sample were obtained.The scattering image was obtained by mapping the localvisibility reduction of the Moiré fringe caused by the

sample [9]. We calculated reduction of the visibility asthe decrease in the ratio of the first peak to the zeroth peakin Fourier space. Cartilage can be seen in the differentialphase image shown in Fig. 3(c), whereas the absorptionimage [Fig. 3(b)] does not show any such profile. Onthe other hand, the inner structure of the tomato is diffi-cult to image with differential phase [Fig. 3(g)] as well asabsorption contrast [Fig. 3(f)]. By contrast with these twotypes of images, the scattering image can show the placen-ta and the seeds of the tomato clearly, as shown in Fig. 3(h). It is considered that the fibrous structure is stronglyenhanced in the scattering image because ultra small-angle scattering frommicrostructures andnanostructuressmaller than the spatial resolution of the image dominatesthe scattering image [14]. Since the microstructure alsohas a preferred orientation, our 2-D interferometer hasadvantages in comparison with the 1-D interferometerin the case of the scattering images.

In x-ray imaging, generally, the finite size of the x-raysource affects the sharpness of images. The effectivesource size of an x-ray tube in the Talbot–Lau interferom-eter also gives rise to blur in images. The relationship be-tween the effective source size and the blur of theretrieved image can be explained by the projected sourcesize on the detector in the present interferometer. To in-vestigate the effect of the projected source size on the blursize of the image on the detector, we chose two differenteffective source sizes of s ¼ 0:3 and 0:1mm in order to ob-tain differential phase images of the nylonmesh of 200 μmin diameter. The analysis with the phase-stepping tech-nique [4–7] was also performed to compare the spatialresolution with that obtained by the Fourier transformmethod. The phase stepping was performed by movingG0 over one period and in six steps in each direction with-out Moiré fringes. The exposure times in total are 44 and198 s with the effective source size of 0.3 and 0:1mm, re-spectively. The projected source size,w, is approximatelyexpressed as w ¼ szT=L (FWHM). The projected sourcesize used in the present interferometer is calculated to be111 μm for s ¼ 0:3mm and 37 μm for s ¼ 0:1mm.

Fig. 2. Differential phase images along (a) the x direction and(b) the y-direction retrieved by Fourier analysis of a single 2-DMoiré fringe.

Fig. 3. (Color online) Comparison of x-ray images of (a) carti-lage on a chicken’s bone and (e) a tomato. The cartilage isshown clearly in (c) the differential phase image comparedto (b) the absorption and (d) the scattering images. The innerstructure of the tomato can be seen in (h) the scattering image,whereas (f) the absorption and (g) the differential phase imagesdo not show any profiles.

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Figure 4 shows the differential phase images and aver-aged line profiles of each image retrieved by the Fouriertransform method and the phase-stepping technique witheffective source sizes of s ¼ 0:3 and 0:1mm. As can beseen from the line profiles of Figs. 4(a) and 4(b), thereis no significant difference between the two phaseretrieval methods in the case of s ¼ 0:3mm. Becausethe projected source size in the case of s ¼ 0:3mm isw ∼ 111 μm, which is larger than the used pixel size of50 μm, the spatial resolution is expected to be limitedby the projected source size.By contrast with this, in the case of s ¼ 0:1mm, the

spatial resolution of the differential phase image re-trieved by the phase-stepping technique was higher thanthat obtained by Fourier transform method shown inFigs. 4(c) and 4(d). The spatial resolution in the phase-stepping technique was improved by reduction of theprojected source size from 111 μm (s ¼ 0:3mm) to37 μm (s ¼ 0:1mm). In the case of the Fourier transformmethod, however, a small effective source size did notincrease the spatial resolution because the spatial reso-lution is limited by the clipping window width for the firstpeak in the Fourier space [13]. From our investigations itis found that the choice of either phase retrieval methoddoes not affect the spatial resolution in our experimentalsetup that consists of an effective source size of 0:3mmand a detector pixel size of 50 μm.It is important to reduce the exposure time in a Talbot–

Lau interferometer with a conventional x-ray tube toeliminate the movement artifacts for objects relating tomedical applications. A large effective source size is ne-cessary to give a large number of photons with a low bril-liance x-ray source, which results in short exposure time.

As mentioned above, the spatial resolution of the differ-ential phase image obtained with a large effective sourcesize x-ray tube is not affected by phase retrieval methods.However, the phase-stepping technique requires scan-ning in two orthogonal directions to obtain the 2-D phaseinformation. If the scanning direction is misaligned,phase mismatch may occur in the reconstruction ofphase images. The Fourier transform method can avoidsuch misalignment because the 2-D phase information isobtained from a single Moiré fringe pattern image.

We have demonstrated a 2-D grating-based interferom-eter using a conventional x-ray tube installed at our la-boratory. We introduced a 2-D lattice-shaped sourcegrating for use with the x-ray tube that had a large effec-tive source size in the present interferometer. The 2-Dinformation of phase and scattering were retrieved byFourier analysis of Moiré fringes. Choice of either theFourier transform method or the phase-stepping techni-que did not affect the spatial resolution in our setup thatconsists of a large effective source size of 0:3mm and adetector pixel size of 50 μm. The 2-D Talbot–Lau inter-ferometer using a conventional x-ray tube permits us toimage biological samples in various medical applications.

The authors gratefully acknowledge Mr. MasanobuHasegawa and Mr. Naoki Kohara (both Canon, Inc.)for helpful discussions.

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Fig. 4. (top) Differential phase images and (bottom) sectionprofiles of a nylon mesh sample of 200 μm in diameter, retrievedby (a) [(c)] Fourier analysis and by (b) [(d)] phase-steppingtechnique with effective source size of 0:3mm (0:1mm) andan exposure time of 44 s (198 s) in total.

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