PHASE IMAGING WITH AN X-RAY TALBOT INTERFEROMETER

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$Copyright JCPDS-Iteratioal Cetre for Diffractio Data 006 ISSN 1097-000 PHASE IMAGING WITH AN X-RAY TALBOT INTERFEROMETER 1 Atsushi Momose, a Wataru Yashiro, a Yoshihiro Takeda, b Yoshio Suzuki, c ad$

1 Copyright JCPDS-Iteratioal Cetre for Diffractio Data 006 ISSN PHASE IMAGING WITH AN X-RAY TALBOT INTERFEROMETER 1 Atsushi Momose, a Wataru Yashiro, a Yoshihiro Takeda, b Yoshio Suzuki, c ad Tadashi Hattori d a Departmet of Advaced Materials Scieces, Graduate School of Frotier Scieces, The Uiversity of Tokyo,5-1-5 Kashiwaoha, Kashiwa, Chiba , Japa. b Graduate School of Pure ad Applied Scieces, Uiversity of Tsukuba, Teodai, Tsukuba, Ibaraki , Japa. c JASRI/SPrig-8,Mikazuki, Hyogo , Japa. d Laboratory of Advaced Sciece ad Techology for Idustry, Uiversity of Hyogo, 3-1- Kouto, Kamigori, Hyogo , Japa. ABSTRACT X-ray Talbot iterferometry (XTI) is described as a ovel phase-sesitive X-ray imagig method. XTI uses two trasmissio gratigs, ad therefore i priciple it fuctios with coe-beam X-rays of a broad eergy bad width, allowig its istrumetatio with a compact X-ray source. Because a amplitude trasmissio gratig is eeded, X-ray lithography ad electrochemical gold platig were employed to fabricate a high-aspect-ratio patter. The performace of the phase imagig with XTI was tested usig sychrotro radiatio, ad its high sesitivity was demostrated by the observatio of biological tissues. INTRODUCTION Sice the middle of the 90 s, X-ray phase-sesitive imagig, icludig phase tomography, has attracted attetio, because the sesitivity i X-ray trasmissio imagig is much improved, compared with that of the covetioal method that relies o absorptio for cotrast geeratio. 1) I order to geerate a cotrast depedig o the shift of X-ray phase caused by a object, several techiques have bee developed so far. -4) A crystal X-ray iterferometer 5) was first used i this field, ) ad aother method usig crystals was also proposed to select refracted X-rays. 3) Because the methods use crystal optics uder the Bragg diffractio coditio, moochromatic X-ray plae wave is eeded. Bright X-ray source is therefore ecessary ad, as a matter of fact, sychrotro radiatio is used to record a image with a practical exposure time. Aother method 4) uses o optics provided that X-ray spatial coherece is sufficietly high. I this case, cotrast is geerated by Fresel diffractio, ad the cotrast outlies the surface of a object ad structural boudaries i it. Normally, the width of the outlies is several micros, ad therefore a high resolutio image detector is preferred to resolve them. This implies that sufficiet flux is eeded ito a small pixel. Bright X-ray source such as sychrotro radiatio is therefore maily used. Although a exceptio, which has bee commercialized i Japa, used a image detector with a pixel larger tha te micros, 6) the cotributio of the X-ray phase cotrast

$X-ray Aalysis. Sposored by the Iteratioal Cetre for Diffractio Data (ICDD).$ This documet is provided by ICDD i cooperatio with the authors ad preseters of

This documet is provided by ICDD i cooperatio with the authors ad preseters of

All copyrights for the documet are retaied by ICDD.

2 This documet was preseted at the Dever X-ray Coferece (DXC) o Applicatios of X-ray Aalysis. Sposored by the Iteratioal Cetre for Diffractio Data (ICDD). This documet is provided by ICDD i cooperatio with the authors ad preseters of the DXC for the express purpose of educatig the scietific commuity. All copyrights for the documet are retaied by ICDD. Usage is restricted for the purposes of educatio ad scietific research. DXC Website ICDD Website -

$Copyright JCPDS-Iteratioal Cetre for Diffractio Data 006 ISSN 1097-000 to the image quality is very limited, ad quatitative phase measuremet is ot carried out.$

3 Copyright JCPDS-Iteratioal Cetre for Diffractio Data 006 ISSN to the image quality is very limited, ad quatitative phase measuremet is ot carried out. The high sesitivity of X-ray phase-sesitive methods, which is potetially a thousad times larger tha that of absorptio-cotrast methods, has bee well demostrated so far usig sychrotro radiatio. However, their practical applicatios are ot progressig. This is because the istrumetatio of X-ray phase-sesitive techique with a compact X-ray source is ot as easy as with sychrotro radiatio sources. I order to avoid the drawback of the crystal X-ray optics, gratig optics is attractive. 7-11) We have proposed X-ray Talbot iterferometry (XTI), 8) which uses two trasmissio gratigs ad geerates a cotrast based o the Talbot effect, 1) as a ovel phase-sesitive imagig. Phase tomography is also attaied with XTI. 10,11) XTI fuctios with a coe beam of a broad eergy bad, ad therefore is compatible with a compact X-ray source. I additio, a X-ray image detector with a spatial resolutio as high as that required i the outlie-cotrast detectio is ot ecessary. A problem to be resolved to costruct a X-ray Talbot iterferometer is the fabricatio of a X-ray gratig with a high aspect ratio. For this purpose, we used X-ray lithography ad electrochemical gold platig. First, the priciple of XTI is described, ad the imagig results with XTI, which was prelimiarily carried out usig sychrotro radiatio, are preseted. Fially, we discuss the prospects of XTI for practical applicatios. PRINCIPLE X-ray Talbot Iterferometry XTI is based o the Talbot effect 1) i the X-ray regio, 13) which is kow as a self-imagig effect observed away from a object with a periodic structure, such as a gratig, uder coheret Fig. 1 Illustratio showig the Talbot effect i the case of plae-wave illumiatio. For a amplitude gratig, self-images are geerated at z = 0, d /λ, d /λ, ad so o, where d ad λ are the period of the gratig ad wavelegth, respectively. For a phase gratig, similar patters are observed at itermediate positios.

$Copyright JCPDS-Iteratioal Cetre for Diffractio Data 006 ISSN 1097-000 illumiatio.$

4 Copyright JCPDS-Iteratioal Cetre for Diffractio Data 006 ISSN illumiatio. The distaces z T betwee the object ad self-imagig plaes are determied by the light wavelegth λ ad the period d of the structure as show i Fig. 1. Whe a amplitude gratig is coheretly illumiated, z T = pd /λ, where p is a iteger. O the other had, for a phase gratig, o itesity cotrast is geerated at the positios give above. However, at the itermediate positios, z T = p + 1 d /, periodic patters are ( ) λ observed, which we cosider as self-images of the phase gratig. This self-image pheomeo is uderstood as a result of Fresel diffractio or multi-beam iterferece betwee diffractio orders caused by a gratig. Givig the complex trasmissio fuctio T(x, y) of a gratig with a Fourier series expasio as x T y) = a exp π i, (1) d Fig. Deformatio of a self-image caused by the refractio at a sample placed i frot of a gratig. 3 where a periodic structure is made alog the x-axis. Assumig uit-amplitude moochromatic plae-wave illumiatio, the field E(x, y, z) behid the gratig is give by E y, z) = a zλ x exp π i exp π i, () d d with paraxial approximatio. Thus, it ca be uderstood that the wave field becomes similar to T(x, y) at the specific distaces (z = z T ). Here, let s cosider a case that the wavefrot icidet to the gratig is deformed for istace due to the phase shift, or refractio, at a object placed i frot of the gratig as show i Fig.. The, E(x,y,z) is correspodigly deformed as zλ E y, z) a exp π i exp π i ( x zϕ x y) ), (3) d d = where λ Φ( x, y) ϕ x y) = (4) π x is the agle of beam deflectio i the x directio iduced by the phase shift Φ(x, y). Thus, if the deformed self-image is detected ad aalyzed, oe ca retrieve the wavefrot icidet upo the gratig. However, the period d is ormally too small to resolve with a covetioal image detector. Therefore, XTI uses aother gratig at the positio of the self-image as show i Fig. 3.

5 Copyright JCPDS-Iteratioal Cetre for Diffractio Data 006 ISSN The, moiré friges are observed by the superpositio of the gratig, which should be a amplitude oe, o the deformed self-image. Assumig that the gratigs have symmetric structures, the moiré patter I(x, y, z) is give by 4 I( x, y, z) = b z c + b z c π { yθ + zϕ y + χ} 0 ( ) 0 ( ) cos x ) d 1, (5) where b (z) ad c are the th Fourier coefficiets of the self-image of the first gratig ad the itesity trasmissio fuctio of the secod gratig, respectively. θ (<< 1) is the icliatio agle betwee the gratigs about the z axis, ad χ is the displacemet of oe gratig agaist the other i the x directio. Phase Measuremet For quatitative uderstadig, it is preferable to be able to obtai ϕ x (x, y) by measurig the moiré patter. We applied Fig. 3 Costitutio of X-ray Talbot iterferometer. the techique of phase-shiftig iterferometry for that purpose as described below. After multiple images are acquired by chagig the displacemet χ with a costat step of d/m (M: iteger), we calculate M π ik arg I k y, z) exp M = k 1 (6) = arg ( ), exp ( + (, ), ( 3) b z cc M π i yθ zϕ x x y M d where I k (x, y, z) is a moiré patter measured whe χ = kd/m. C,M is defied by C, M M = k 1 π ik M whe 1 = qm exp ( 1) = M 0 otherwise ( q :iteger). (7) If higher orders ( ) are egligible, eq. (6) reduces to arg M = k 1 I k π ik π y, z) exp = M d as i the case of two-beam iterferometry. { yθ + zϕ y) } x, (8)

$Copyright JCPDS-Iteratioal Cetre for Diffractio Data 006 ISSN 1097-000 We cosequetly could use eq.$ (8) as with the techique of phase-shiftig iterferometry. as described below.as idicated by eq. (7), some higher orders do ot cause systematic errors depedig o M eve whe b(z)c i eq.

(8) as with the techique of phase-shiftig iterferometry. as described below.as idicated by eq. (7), some higher orders do ot cause systematic errors depedig o M eve whe b(z)c i eq.

6 Copyright JCPDS-Iteratioal Cetre for Diffractio Data 006 ISSN We cosequetly could use eq. (8) Table 1 Orders that cause systematic errors i the because of the fact supportig its validity, determiatio of the differetial phase shift from eq. (8) as with the techique of phase-shiftig iterferometry. as described below.as idicated by eq. (7), some higher orders do ot cause systematic errors depedig o M eve whe b(z)c i eq. (6) have o-zero values.14) The coditios are listed i Table 1. If M = 3, the lowest order that will cause a systematic error is. However, sice eve orders ca be igored if the gratigs have 1:1 lie-ad-space (L&S) patters, fifth order is the lowest oe. It is otable that M = 5 is a suitable choice because the lowest order that will cause a systematic error is 9, the magitude of which is ormally very small. I additio, actual gratig patters are ot completely rectagular ad the spatial coherecy of X-rays that impige o the gratigs is ormally icomplete. These factors decrease higher orders ad cotribute to reducig errors i obtaiig ϕx(x, y) with eq. (8). Whe a sample is placed ad rotated i frot of the first gratig, phase tomography ca be performed usig the techique described above. ϕx(x, y) caused by the sample ca be obtaied by the subtractio procedure betwee two data measured with ad without the sample. The, the phase shift caused by the sample Φ(x, y) ca be calculated by itegratio as idicated by eq. (4). Givig the refractive idex with 1 δ (x, y, z), π (9) Φ y ) = δ y, z ) dz. λ Therefore, oe ca recostruct δ (x, y, z) from the Φ(x, y), which is called X-ray phase tomography. EXPERIMENTAL RESULTS Gratigs As metioed, the secod gratig should be a amplitude gratig. Therefore, the gratig patter should be sufficietly thick so that X-ray amplitude, or itesity, is modulated fully. We selected gold as a material for the gratig patter because its absorptio coefficiet is comparatively large. Nevertheless, the thickess should be more tha a few tes of micros. As for the gratig period, it should be smaller tha or comparable to Fig. 4 Image of scaig electro microscopy (SEM) of the amplitude gratig fabricated by X-ray lithography ad electrochemical platig of gold. 5

$Copyright JCPDS-Iteratioal Cetre for Diffractio Data 006 ISSN 1097-000 Fig. 5 Moiré patters ad their frige visibilities observed with 0.65-Å X-rays varyig the distace betwee the gratigs.$

7 Copyright JCPDS-Iteratioal Cetre for Diffractio Data 006 ISSN Fig. 5 Moiré patters ad their frige visibilities observed with 0.65-Å X-rays varyig the distace betwee the gratigs. the X-ray spatial coherece legth, which is several micros typically, ad as a result a patter of a high aspect ratio must be fabricated. Covetioal lithographic techiques do ot meet this demad, ad therefore we applied X-ray lithography. The sychrotro radiatio beamlie 11 of NewSUBARU, Japa, which is dedicated to LIGA (Lithographite Galvaoformug Abformug) process fabricatio, was used. A 30-µm X-ray resist film (MAX001, Nagase ChemteX Co.,LTD) was spi-coated o a 00-µm Si wafer with a 0.5-µm Ti layer, ad the a 4-µm L&S resist patter (d = 8 µm) was fabricated by X-ray exposure. Fially, Au lies were formed by electrochemical platig betwee the resist lies, which were retaied after the platig to support the Au lies (Fig. 4).15) The height of the Au lies was early 30 µm, ad the effective area of the gratig was 0 mm 0 mm. The first gratig for XTI also had a gold patter, but its thickess was much thier tha that of the secod. The thickess was experimetally evaluated to be optimal for X-rays aroud 0.65 Å as a π/ phase gratig. Performace of XTI A X-ray Talbot iterferometer was arraged at the beamlie 0XU of SPrig-8, Japa, where Fig. 6 Visibility of moiré friges as a fuctio of X-ray wavelegth. The distace betwee the gratigs was set to be d /λ. 6

$Copyright JCPDS-Iteratioal Cetre for Diffractio Data 006 ISSN 1097-000 Fig.$

8 Copyright JCPDS-Iteratioal Cetre for Diffractio Data 006 ISSN Fig. 7 Result of phase tomography with XTI obtaied with 1-Å sychrotro X-rays for a rabbit liver with VX cacer: (a) oe of differetial phase maps, (b) recostructed phase tomogram, ad (c) three-dimesioal rederig view of a part of recostructed data set. The grayscale of (a) idicates the beam deflectio agle caused by the refractio at the sample, ad that of (b) idicates the refractive idex differece. udulator X-rays were available at 45 m from the source poit. Figure 5 shows moiré patters observed with 0.65-Å X-rays with their visibilities as a fuctio of the distace betwee the gratigs. The moiré friges were geerated by settig θ = 1.3º. At z = d /λ, which was the best positio for XTI with a π/ phase gratig, the frige visibility exceeded 0.8. Icreasig the distace, the visibility miimized at z d /λ ad agai icreased, idicatig that this pheomeo occurred by the Talbot effect. The Fourier-trasform of the moiré patter at the best coditio is also show i Fig. 5. Spots of 0th, 1st, ad 3rd orders existed, ad higher orders ad eve orders were ot detected. This result assured that our selectio of 5 for M was reasoable for the experimets of phase tomography preseted below. Next, keepig the coditio z = d /λ, the visibility was plotted as a fuctio of λ (Fig. 6). This result shows that the Talbot iterferometer fuctioed i a wide eergy rage; the visibility was over 0.3 eve at 0.4 Å. Phase tomography The X-ray Talbot iterferometer was used for the tomographic observatio of biological soft tissues. A sample was fixed o the tip of a rotatio rod ad immersed i formali filled i a cell. The measuremet of ϕx(x, y) was repeated at each agular positio of sample rotatio with a step of 0.7º over 180º. Images were recorded with a CCD-based X-ray image detector whose effective pixel size was 4.34 µm. A piece of rabbit liver with cacer (VX) was first observed with 1.0-Å X-rays. Cacerous lesio depicted with a lower grayscale value was clearly differetiated from a ormal tissue as show i Fig. 7. Furthermore, the bright area see i the cacerous lesio was ecrosis. This feature is comparable to the observatio result16) by phase tomography usig a crystal X-ray iterferometer. 7

$Copyright JCPDS-Iteratioal Cetre for Diffractio Data 006 ISSN 1097-000 Fig. 8 Result of phase tomography with XTI obtaied with 0.4-Å sychrotro X-rays for a mouse tail.$

9 Copyright JCPDS-Iteratioal Cetre for Diffractio Data 006 ISSN Fig. 8 Result of phase tomography with XTI obtaied with 0.4-Å sychrotro X-rays for a mouse tail. Two tomograms across the itervertebral disc (a) ad boe (b), the positios of which are idicated by arrows i a sagital view (c), are preseted. Because the X-ray Talbot iterferometer fuctioed with 0.4-Å X-rays as suggested by Fig. 6, a mouse tail cotaiig a boe was observed at this wavelegth (Fig. 8). The advatage of usig higher-eergy X-rays is that ot oly soft tissues but also cartilage ad boe are imaged i the same view, while a boe geerates a more marked phase chage at its surface i the lower eergy regio, causig errors i the measuremet of Φ(x, y). As show i Fig. 8, soft-tissue structures are depicted with a cartilage (itervertebral disc) ad a boe i the same tomogram. DISCUSSIONS Performace of XTI Phase tomograms map the refractive idex differece i samples. The detectio limit of the refractive idex differece was estimated by the stadard deviatio i a uiform area of a tomogram; the stadard deviatio of the surroudig formali regio of the tomogram show i Fig. 7 was calculated to be Because the refractive idex differece is approximately proportioal to the mass desity, the stadard deviatio ca be coverted to the detectio limit of desity variatio, which is calculated to be 1.0 mg/cm3 because the refractive idex of water is for 1.0-Å X-rays. This is comparable to the value attaiable by the phase tomography with a crystal X-ray iterferometer. Because roughly 1% of X-rays icidet to the crystal X-ray iterferometer cotribute to iterferece ad impige o a sample, the X-ray dose o the sample is much lower tha that by XTI. However, uder the compariso o the assumptio of the same X-ray source, XTI rivals the crystal X-ray iterferometry for the samples, such as polymer materials,17) to which the radiatio damage is ot as crucial as to biological samples. The spatial resolutio is limited by the period of the gratig i priciple. We evaluated the resolutio by the full width at half maximum (FWHM) of the differetial cotrast profile across the sample surface of the tomogram. From Figs. 7 ad 8, 14 µm ad 16 µm were obtaied, respectively. The resolutio was slightly worse whe higher-eergy X-rays were used. This is explaied by the fact that the distace betwee the gratigs was larger for higher-eergy X-rays. 8

10 Copyright JCPDS-Iteratioal Cetre for Diffractio Data 006 ISSN Prospects I this paper, the performace of XTI was demostrated usig sychrotro radiatio. However, because XTI fuctios with coe-beam X-rays of a broad eergy bad width i priciple, the compatibility of XTI with a laboratory X-ray source is promisig. I this case, the distace betwee two gratigs should be z T = R λ 1 ( p + ) Rd 1 ( p + ) d for a phase gratig, where R is the distace from a source to the first gratig, whose period is d. The period of the secod gratig d is give by d = d( R + z ) T / R. Although spherical gratigs are ideal for XTI with a coe beam, plae gratigs are available provided that R is sufficietly larger tha the size of the field of view. Therefore, the techology developed to fabricate the gratig used i the preset work is trasferred to coe-beam XTI although the aspect ratio ad effective area should be further improved particularly for cliical applicatios. The details of the desig cocept of coe-beam XTI will be described elsewhere. 18) What kids of X-ray sources are available for coe-beam XTI? Sice XTI is based o the Talbot effect, the spatial coherece legth l, which is defied to be l = λr /( πσ ) where σ is the source size, is desirable to be comparable to or larger tha d. The smaller σ is, the higher the frige visibility is. At the same time, a sufficiet flux is eeded for imagig with a practical exposure time. Thus, a brilliat X-ray source is required, ad covetioal X-ray geerators do ot meet these demads. Therefore, a breakthrough is eeded i the developmet of ew compact X-ray sources, such as a table-top sychrotro. 19) As for a image detector, XTI does ot require a spatial resolutio for resolvig the gratig patter. Therefore, a variety of X-ray image detectors would match with XTI. Here, it should be oted that a image detector i combiatio with the two gratigs ca be cosidered as a phase-sesitive image detector. I this sese, XTI is a breakthrough for the developmet of the first X-ray wavefrot sesor. (10) 9 SUMMARY The priciple of XTI was described with phase imagig results with it. The key for the costructio of a X-ray Talbot iterferometer is the fabricatio of amplitude gratig, because a high-aspect-ratio patter must be formed. We fabricated a gold gratig by meas of X-ray lithography ad electrochemical platig. The X-ray Talbot iterferometer with the gold gratig fuctioed with sychrotro X-rays dow to 0.4 Å wavelegth. Provided that a gratig with a higher aspect ratio ad a wider effective area is fabricated, XTI is a attractive cadidate for practical X-ray phase imagig, such as cliical diagoses, because XTI has a advatage that coe-beam X-rays of a broad eergy bad width are available, allowig the compatibility with a

11 Copyright JCPDS-Iteratioal Cetre for Diffractio Data 006 ISSN compact X-ray source. ACKNOWLEDGEMENTS We appreciate the biological samples show i Figs. 7 ad 8 provided by Drs. J. Wu ad T. Takeda (Uiv. Tsukuba, Japa). The experimets usig sychrotro radiatio were performed uder the approval of SPrig-8 committee 005A036-NM-p. This study was fiacially supported by the project Developmet of System ad Techology for Advaced Measuremet ad Aalysis of Japa Sciece ad Techology Agecy (JST). REFERENCES 1) A. Momose, Jp. J. Appl. Phys. 44 (005) ) A. Momose, Nucl. Istrum. & Methods A 35 (1995) 6. 3) T. J. Davis, D. Gao, T. E. Gureyev, A. W. Steveso, ad S. W. Wilkis, Nature 373 (1995) ) A. Sigirev, I. Sigireva, V. Koh, S. Kuzetsov, I. Schelokov, Rev. Sci. Istrum. 66 (1995) ) U. Bose ad M. Hart, Appl. Phys. Lett. 6 (1965) ) (Japaese); A. Ishisaka, H. Ohara, ad C. Hoda, Opt. Rev. 7 (000) ) C. David, B. Nöhammer, H. H. Solak, ad E. Ziegler, Appl. Phys. Lett. 81 (00) ) A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, ad Y. Suzuki, Jp. J. Appl. Phys. 4 (003) L866. 9) T. Weitkamp, B. Nöhammer, A. Diaz, ad C. David, Appl. Phys. Lett. 86 (005) ) A. Momose, S. Kawamoto, I. Koyama, Y. Suzuki: SPIE Proc (004) ) T. Weitkamp, A. Daiz, ad C. David, Optics Express 13 (005) ) H. F. Talbot, Phil. Mag. 9 (1836) ) P. Cloetes, J. P. Guigay, C. De Martio, ad J. Baruchel, Opt. Lett. (1997) ) K. A. Stetso ad W. R. Brohisky, Appl. Opt. 4 (1985) ) M. Matsumoto, K. Takiguchi, M. Taaka, Y. Huabiki, H. Takeda, A. Momose, Y. Utsumi, ad T Hattori, High Aspect Ratio Micro Structure Techology Workshop 005, pp ) A. Momose, T. Takeda, Y. Itai, ad K. Hirao, Nature Med. (1996) ) A. Momose, A. Fujii, H. Kadowaki, ad H. Jiai, Macromelecules 38 (005) ) W. Yashiro, Y. Takeda, ad A. Momose, i preparatio. 19) Y. Yamada, AIP Proc. 716 (004) 1.

Optics. n n. sin. 1. law of rectilinear propagation 2. law of reflection = 3. law of refraction

$Optics. n n. sin. 1. law of rectilinear propagation 2. law of reflection = 3. law of refraction$ Optics What is light? Visible electromagetic radiatio Geometrical optics (model) Light-ray: extremely thi parallel light beam Usig this model, the explaatio of several optical pheomea ca be give as the