x-ray imaging microscope with a partial coherent illumination

X-ray imaging microscope with a partial coherent illumination

Akihisa Takeuchi*, Hidekazu Takano, Kentaro Uesugi and Yoshio Suzuki JASRI / Spring-8, Kouto 1-1 -1, Mikazuki-Tyo, Sayo-Gun, Hyogo 679-5 198, Japan

ABSTRACT An x-ray imaging microscopy experiment nas performed at the x-ray energ!- of 8 keV. A Fresnel zone plate (FZP) fabricated by electron-beam lithography technique was used as an objective. Material of the zone structure is tantalum. The experiment was done at the undulator beamline BL47XU of Spring-8. Undulator radiation u-as monochromatized by passing through a liquid nitrogen cooled Si 11 1 double crystal monochromator. In order to eliminate speckle-like background noise; a partial coherent illumination was introduced by using a -'beam diffuser" consisted of graphite powder. Beam spread of the illumination with the diffuser was about 35 p a d . A charge coupled device (CCD) camera coupled d h a phosphor screen and a microscope objective (x 12 or x 24) was used as an image detector. Converted pixel size with the x 24 lens was 0.5 pm. Magnitication of the x-ray microscope system was set to be 7.61 - 13. Pitch of0.6 pm (0.3 pm line and 0.3 pm space) pattern of the test chart \\.as resolvedd; and the outermost zone structure of the same type of FZP was obsemed. Imaging properties are also discussed by using Hopkins' optical imaging t h e o ~ .

Keywords: X-ray microscopy, Fresnel zone plate, ynchrotron radiation, partial coherent illumination

1 . INTRODUCTION Although it takes only about 10 years or less since the developments of hard x-rav micro-imaging have been started, spatial resolution has been already achieved sub-pm order and is now getting ahead of that of the visible light microscopy. Various types of hard x-ray optical devices have been developed mainly as focusing devices for generating x-ray microbeams. However, some types of them are started developing also as microscope objectives; e.g.; Fresnel zone plate (FZP)]-'; Bragg- Fresnel optics (BFO)', refractive lenses5. and Wolter type mirror' - * " , Also imaging microscope systems using these objectiiw have achieved pm order or sub-pm resolution.

Ad\.ent of the 3rd generation synchrotron radiation (SR) light source which supplies high flux density beam enables to design high-magnifkation and high-resolution x-ray microscope system. Howeverr; another property of SR source, highly- coherent beam, is unwelcome for the illumination of the imaging microscope. It is because images and backgrounds tend to be modulated by interference between the incident beam and the diffracted beam when highly-coherent beam is used for illumination. Moreover, if surface errors of the optical devices such as window; monochromator, and objective are not sufficiently small; images are deteriorated by speckle-like noise"- ". That is why the coherence as low as possible is proper for the illumination of the imaging microscope. Kagoshima et. al. perfomed incoherent illumination imaging at x-ray energy of 10 keV by scanning a condenser tm-o-dimensionally during exposure'. They also succeeded in widening the field of view with this method. However; because the original field of Tie\{- illuminated bj- condenser is small, this method needs a long exposure time for condenser scanning e l m if the photon flus is enough high. White et. al . showed a partial coherent illumination imaging in soft x-ray region by using a beam diffuser plate. In order to average out the effect of speckle caused by the diffuser plate itself, it was moved during exposure". In the hard x-ray region, An-aji et. al. used this method at 25 keV16. This method enables to use incident beam from the SR source directly, Hence not so long exposure time is needed if the transmittance of the diffuser is high. However; especially in the hard x-ray region, due to the lack of materials with large scattering angle, it is difficult to produce perfect incoherent illumination. Therefore the illumination is always obliged to be the partial coherent; however, which must be dificult in order to evaluate the precise imaging properties.

Recently we have developed a hard x-ra!- imaging microscope system with SR source; FZP objective and beam diffuser for partial coherence illumination. In this paper, 1t-e describe the estimation of imaging properties of this system using Hopkins' theoc, and compare the estimation nith the experimental data.

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X-Ray Micro- and Nano-Focusing: Applications and Techniques II, Ian McNulty, Editor,Proceedings of SPIE Vol. 4499 (2001) © 2001 SPIE · 0277-786X/01/$15.00 29

2. EXPERIMENTAL SETUP A schematic diagram of the experimental setup is s h o w in Figure 1 , The experiment was c a n i d out at the R & D beamline BL47XU of SP~ing-8. The system consists of a light source (undulator installed storage ring of SPiing-81, double crystal monochsomator, a beam diEuser, pinholes, a Fresnel zone plate objective; and an image detector.

.-

Figure 1. Schematic diagram of the experimental setup FZP Fresnel zone plate Magndcation was set to be from \i 7 61 (a = 181 rnm and b = 1379 mm) to \i 13 (a = 172 3 mm and b = 2240mm)

'In \.acuum hpe" 139 pole undulator radiation nas used as a light source X-sa! energ v as chosen to be 8 keV b! passing through a lq-N? cooled type Si 1 1 1 double cqstal monochsomator

The vertical spatial coherence at the experimental hutch of this beamline was measured to be about 80 ym at the X-ray enerR of 8 keV. In this case the angular deviation of the incident beam \vas about 1 - 2 p a d . As mentioned in previous chapter, illumination using such a highly-coherent beam deteriorates image properties. Therefore in order to decrease the coherence, a beam diffuser (graphite powder; grinded by mortar and pasted on a thin film) was installed just in front of the sample; and was rotated during the acquisition of the images to shade off the speckle-like noise from the diffuser itself15. Using this; the angular spread of illumination at the sample was about 35 krad in full width at half maximum (FWHM) as sh0n.n in Figure 2 . Transmittance was about 50 %.

A Fresnel zone plate (FZP) u as used as a microscope objective fabricated b) usmg electron-beam lithograph! technique at N

SEM image of the FZP is shown in Figure 3. This 14 as TT-AT (NipDon Telephone and Telegram Advanced

- --_- -_ _- -

> I

- 1- - - 2 5 0 - 2 0 0 -150 -100 -50 0 50 100 1 5 0 200 250

Bsam Dn srgsnce [ p d d ] - Figure 2. Intensit! distribution of the mcident beam nith the beam diffuser (graphite powder). clrcled dot measured data. sohd lme fitted b! two gaussians

0 5 pin

Figure 3. SEM image of around the o u t e m s t zone ofthe oblectire Fresnel zone plate

Proc. SPIE Vol. 449930

Technolog!-). The zone structure with outermost zone width of 0.25 pm \\-as made of 1 pm-thick tantalum. The diameter of FZP is 100 pm> number of zone is 100, and the focal length of the 1 ’’ order is 160 mm at the X-ray energy of 8 keV. A center beam stop (2 pm-thick gold) with diameter of 50 pm is deposited on the FZP. With the microbeam knife-edge scan test of the FZP; a focal spot size v-as measured to be 0.3 pm in FWHM which n-as almost equal to the diffraction limit”. In order to select only the h t - o r d e r diffraction of the FZP, a pinhole (100 pm in diameter)r); cross slits (opening size: 80 pm x 80 pm), and a center beam stop (gold wire: 200 pm in diameter) were installed in front of the sample, at the back focal plane and in fi-ont ofthe detector, respectively. And from the same reason, more than half of the field of view was blind by the center stop. Therefore the system is off-axis coniiguration in the vertical direction as shown in Figure 1 . Optical axis v-as shifted about 30 - 40 wm from the center ofthe FZP in the vertical direction.

The image detector consists of a single crystal phosphor screen (Lu2Si05: Ce; <10 pm in thickness), a microscope objecti1.e (x 12 or x 24) and a cooled charge coupled device (CCD) camera (Figure 4(a); Hamamatsu Photonics K. K.: Japan). Pixel size ofthe CCD camera is 12 pm x 12 pm and number of pixel is 1000 (H) x 1018 (V). Therefore the converted pixel size of the detector system is 1 pm x 1 pm or 0.5 pm x 0.5 pm. The point spread functions of the detector with both microscope objectives are measured, and in each case FWHM is found to be about 2 pixels**. Modulation transfer function (MTF) ofthe detector obtained from the Fourier transform ofthe point spread hnction data is shown in Figure 4(b).

Magnification of the X-ra! microscope system n as set to be 7 61 - 13 A tantalum test chart (0 5 pm thickness) nas used as a sample It n as designed for evaluation of the imaging properties such as the spatial resolution and MTF It vas also fabricated b> usmg the electron-beam lithography technique at NTT-AT

1

0.8

0.6 I- = 0.4

0.2

0

U

0 200 400 600 800 1000 1200 1400 Spatial Frequency [Ip/rnrn]

Hgure 4. Image detector”EkamMonitorAA50 (Hammatsu Photonics KK , Japan) (a) photograph and schemtic dramlng of the optical SJ stem (b) Modulation transfer function (MTF) obtamed from the Illeasured pomt spread function data, (black h e . rmcroscope oblecti1.e oful2. gra! h e . o f d 4 ) ’ -

3. IMAGING PROPERTIES OF PARTIAL COHERENT ILLUMINATION SYSTEM In order to estimate the imaging properties of this experimental setup, it is necessar!. to consider the effect of the partial coherent illumination because the graphite beam diffuser cannot supply incoherent illumination. The MTF for the partial coherent illumination is calculated with supposing the object has a periodic transmittance distribution like a sine wave. For simpli*; let us consider only one direction ofthe imaging properties.

From Hopkins’ optical imaging theon-, one-dimensional intensity distribution of the image with partial coherent illumination microscope ?stem is expressed as following equation with omitting con~tant’~.

Proc. SPIE Vol. 4499 31

where T ( s ) is a Fourier transform ofthe amplitude transmittance of the object. C(s:s') is a transmission cross-coefficient of the system; expressed as

n h a e S = sAf, . S'= s' i f , fi is the focal length of the oblectil e P, ( 1 1 v) is the pupil function of the oblectir e. and P2 (i1.v)

is the eEectn e source or the pupil function ofthe condenser

In this estimation, let us assume that the amplitude transmittance of the oblect is approximated as one-dimensional cosine M ave function given as

( 3 , 1 2

t ( Y ) =- (1 + ucos(2mr)) ,

nhere a is assumed as real number supposing the object is an absorbing material

In the case of the on-focus unagmg. PI (1 , . v) is real number Therefore from Eqs (1 ) - ( 3 ) , n e get

On the other hand from Eq (31, intensity transmittance ofthe object is

Therefore the MTF can be represented as the fkquency response function comparmg Eq (4) and Eq (5).

('mu - 0 m m - ('mm - 0 m m ) - R ( s ) = - (Zmsx -Omm ) + ( Z m m -Omm) Z ( l / s ) + Z ( l / 2 s ) + 2 0 ( 1 / 2 s )

Z(1/ s) - Z(1/ 2s)

C(s.0) U

1 + - (C(s: 3 ) +C(s:-s) - 2 ) 4

If the absorption of the oblect is small ( u << 1 ). n e can consider R ( s ) = C(s.0) This approumation can be normall! applied for tine structures near the difiaction limit

Using Eq (6). MTF of the FZP under the same condition a ith the experimental setup is calculated In the calculation the pupil function ofthe oblectir e P, (11.v) is set as

where I ; is the radius of the objective and E ) is the obstruction ratio of the objective. l i d and v,, are the off-axis distance of hoiizontal direction and of vertical direction; respectively In this case, i i = 50 [pm], = 0.5, and off-axis parameters are i l d = 0 and vd = 37.5 [pm] (the pupil is shifted 314 times of the radius of objective in the lmtical direction). Therefore the horizontal direction comsponds to the normal to the off-axis direction, and the vertical direction corresponds to the parallel to it. As the effective source P2 ( Z I , ~ ) , profile of the beam divergence distribution fitted with two Gaussians s h o m in Figure 2 is used. The reason whl- fitting curve is used is in order to decrease the noise in the high frequency region. Two- dimensional maps of PI (21,v) and P2 TI;^) are shown in Figure 5(a) and Figure 5(b); respectively. Figure 6 shows calculated


MTFs with these parameters. For comparison; MTFs of both coherent illumination and incoherent illumination are also shoim Because of the off-axis system; imaging properties are different bet\\-een veitical direction and horizontal direction. Hence MTF in each direction is shown independently.

figure 5. Trio-dimensional mppmg of the pupd function (a) Pupil function of the oblectixe FZP P, (~/.v). (b) Effect11 e source function ofthe illummation VI ith graphite beamdiffuser P2(u.v)

1

0.8

,0.6 k 2 0.4

0.2

0

LL 0.6 k.

0.4

0.2

0 0 1000 2000 30 0 4000 0 1000 2000 3000 4000

Spatial Frequency [Ip/mrn? Spatial Frequency [lp/mrnI

Figure 6. Modulation transfer fimction (MTF) of the objective FZP for coherent lllurmnation (broken gray), mcoherent illurnmation (sohd gray). and dlumlnation nith graphite beam dlfhser (soM black) (a) ln horlzontal drection, (b) m T ertical direction

Schematic drawing of the effective domain of integration for the transmission cross-coefficient C(s:0) (Eq. ( 2 ) ) is shown in Figure 7 . The effecti1.e domain of integration is determined with the common area between the effective source (P2); the pupil functions of FZP ( P I ) shifted by s/ifi; and the complex conjugate ofP1 (PI’) shifted by s ‘id (here, PI = PI’; and s ’ = 0); as shown shaded in the figure. In order to calculate the horizontal MTF; PI is shifted along u-axis (Figure 7(a)). And in the case ofthe Itrtical MTF; P I is shifted along v-axis (Figure 7(b)).

As the horizontal MTF, if the radius of P2 is small (coherence is high) such as the illumination with the graphite diffuser; as shown in Figure 7(a) P2 does not overlap the obstructed area of P I . Hence as shown in Figure 6(a); the frequency response becomes monotonously smaller as the spatial frequency becomes higher, without response enhancing in the higher frequency region typically seen in the annular aperture sj-stem (see MTF of incoherent illumination in Figure 6). The response becomes zero at the spatial frequency of 2500 line pair / mm. This value corresponds to the spatial resolution of 0.4 pm> which is not achieved at the diffraction limit of the objective (0.3 pm). It is because the diameter of P I does not full!- used due to the off- axis configuration and due to small P2. Therefore large P2 (lower coherence) is preferable for high resolution.

On the other hand, as the vertical direction, it is evident from Figure 7@) that the obstructed area of P I must pass through P2. Therefore as shown in Figure 6(b); response peak exists in the high frequency region and becomes more conspicuous as the coherence becomes higher. In the case of the illumination \n-ith diffuser; response peak n.ith almost 100 % is separated to


lon-er frequent!- region (up to 1000 Ip /mm) and higher frequency region (2000 - 4000 lp imm). And there is almost no response in the middle region of 1000 - 2000 Ip /mm Therefore the spatial resolution achieves 0.25 pm; howeverr; the sti-uctures of 0.5 - 1 pm pitch cannot be resolved. It is evident that it is due to the effect of the annular apei-ture of the objecti1.e. If the radius of P2 is smaller than that of obstructed area of PI; non-response area exists in the middle frequency region like this case.

Figure 7. Schemtic drawing ofthe effective d o m i n of integration (shown shaded) for the transmission cross- coefficient C(s:0) for the off-axis imaging s!'stem with an annular pupil objective. (a) horizontalMTF (normal to the off-axis direction); (b) vertical MTF (parallel to the off-axis direction). P,: pupil function of objective; P,: effectiire source function.

4. RESULTS

4.1 Comparison with coherent illumination In older to compae the coherent illumlnation and the partial coherent illummation mith beam diffuser, a spoke patterned tantalum test chart \\as used as the object Figure 8(a) shows the Y-IBJ image obtained vithout beam diffuse1 (m this condition the coherence of the illumination n a s not actual17 perfect) Eyposure time \\as 50 sec Center of the shoun a e a correspond to be at about 30 pm away in vertical direction from the ob,iective axis. In this beamline; surfaces of optical devices such as monochromator and Be windows are carefully polished, and the ob,iective FZP was fabricated in good condition. Therefore &pica1 speckle-lke noise was not seen. However; it can be clearly seen that the background n-as deteriorated and the image \\-as modulated by interference pattern. This phenomenon is more typicall!- in the vertical direction because the coherence is higher in this direction. Figure S(b) represents the s- ra!- image of the same ob.ject obtained with the graphite beam diffuser. Exposure time \\-as 100 sec. The background noise and the modulation of the image decrease eTidentl1- due to the decline of the coherence. However. because the coherence still remains in the illumination, the effect of the edge-enhance is still seen.

Figure 8. X-ra! image o f a spoke test pattem (Ta. 0 5 pm thickness), (a) coherent Illurnation, (b) partial coherent dlumlnation (v ith graphite beamdlffuser)


4.2 Estimation of the MTF For comparison I\ ith the calculated value ofthe MTF as shonn in Figure 6. evpeiimental \ d u e of the MTF is measured using a tantalum test chart uith periodical patterns as the sample As shoun 111 Figure 9(a). this sample consists of rectangular periodical patterns with i.zious pitches from 0.1 pm (1 0000 lp imm). Therefore by measuring the image contrast of each pitch pattern, experimental 1.alue of MTF can be plotted. X-ray image obtained \vith this system is shown in Figure 9(b). Exposure time was 100 sec. As shown in this figure, image properties are different between the vei-tical direction and the horizontal direction. As the horizontal direction, images of up to 0.6 pm pitch v-ere resolved. As the vertical direction, although 0.4 pm pitch patterns were resolved, 0.6 pm - 1.0 pm pitch patterns were not. Figure 10(a) and (b) represent the intensity profile obtained from the x-ray images of the test chart. And Figure 10(c) and (d) show the experimental value of MTF (plot) measured from the profile data (a) and (b), respectively. In each graph, solid line represents the calculated MTF using Eq.

Material: Ta, 0.5 pi thick Transnuttanoe at 8 key: 0.875 Supporting membrane: Pitch0.1 pn 8

Pitch 0.2 pn Si3 N1,2 pn thick

Pitch 0.4 pn

Pltch0.6 pn '

Pitch 0.8 p (0.4 p line & 0.4 p space)

(a> (b> Figure 9. Ta test chart for MTF masuremnt (a) schematic dravmg and parameters, (b) X-ray imge .

0.8

1

0.8 0 5 1 0 1 5 20

Position [p]

I

0.8

u 0.6 I- 5.

0.4

0.2

0

* Measured Data FZP (with @-white cMFuser) ~

I FZP + Detector -2 -___--

0 1000 2000 3 00 4000 Spatlal Frequency [b/mm!

1

0.8

u 0.6

0.4 5

0.2

0 0 1000 2000 3000 4000 5000

Spatial Frequency [!p/mml

Figure 10. Intensit\ protile o f the X-ra\ image ofrectangular penodic test pattern shovn m Figure 9 (a) m honzontal direction and (b) m \ertical dlrection (c). (d) MTF obtalned from the proflle data (a) and (b), respectn el\


(6); and including additional consideration such as

where R ( s ) is the MTF calculated from Eq. (6) (represented by gray line in Figure 10(c). (d)); R , (s) is the MTF of the detector (Figure 4(b)), and .\I is the mapitication ratio of the x-ray microscope tem. It is evident that the calculated \ d u e of MTF has a good agreement to the measured \ d u e in each direction. As the spatial frequency is higher, the response becomes more deteriorated b!- the detector. Hence in the vertical MTF the response peak in the higher frequency decreases extremely. In order to increase the response in the higher frequency region, magnification should be larger. As shon-n in Figure 6; it is necessarJ- much lo\ver coherent illumination to lessen the difference of imaging properties between the horizontal direction and the vertical direction: to achieve the horizontal spatial resolution to the diffraction limit, and to increase the response of middle ikequency range in the \wtical direction.

Figure 1 l(a) shows a calculated MTF in the case of the pupil function is shifted 314 times of the radius in both horizontal and vertical directions from the axis. This corresponds to the MTF for an object with 45 degree inclined structure. This MTF gives a good response in the middle frequency range due to the influence of the horizontal MTF (Figure lO(c)); and also in the higher frequencJ- range good response remains due to the inthence of the vertical MTF (Figure 10(d)). Figure 11 (b) s h o w an s-ra!- image of a FZP whose parameters are same as the objective. Center of the shown area correspond to be at about 30 pm a n a y from the objective axis in both directions. All of the zone structure from inner (-0.5 pm width; -1 .0 pm pitch) to outermost (0.25 pm width: -0.5 pm pitch) can be obsenwi that is impossible for onlh- the vertical MTF or for only the horizontal MTF

1

0.8

u 0.6 + I

0.4

0.2

0

r

0 1000 2000 3000 4000 Spatial Frequency [Ip/rnm]

Figure 11 (a) Calculated MTF 1 ~ 1 the case of the oblectir e pupd function is shfied Yil t ims of the radius m both dlrection (b) X-ra\ image of a FZP. ahose parameters are same as that of the oblecti\ e FZP Center ofthe shonn area is located a t same o f f - a m distance between honzontaldlrection and I ertical drection

REFERENCES B. Lai, W. Yun, Y. Xiao, L. Yang, D. Legnini; Z. Cai; A. Krasnopero\.a, F. Cerrina, E. DiFabrizio, L. Grella and M. Gentili, "Development of a hard x-ray imaging microscope," Rev. Sci. Instrum. 66 (1 995) No. 2; 2287. M. An-aji; Y. Suzuki. A. Takeuchi, N. Kamijo; S. Tamura; M. Yasumoto and Y. Kohmura; "Imaging Hard X-Ray Microscopy with a Multilayer Fresnel Zone Plate," Proc. J 7th bit . Coi$ ~ ~ - R a y r Z f i c i a s c o ~ ~ , Bedyley, Califoniia; 1999 (American Inst. Phys., 2000) p.545. Y, Kagoshima, T. Ibuki, K. Takai; Y. Yokoyama, N. Miymoto, Y. Tsusaka and J. Matsui, "500-nm-Resolution 10keV X-Ray Imaging Transmission Microscope with Tantalum Phase Zone Plate," Jpn. J. Appl. Phys. 39 (2000) 433 A. Snigii-ev, I. Snigireva, P. Boeske, S. Lequien and I. SchelokoI~, '-High energy X-ray phase contrast microscopy using a circular Bragg-Fresnel lens;" Opt. Commun. 135 (1 997) 378.


5 . Y. Kohmura. M. An-a.ii; Y. Suzuki. T. Ishikan-a; Y . I . Dudchk, N. N. Kolchei,sky and F. F. Komarov, "X-ray focusing test and x-ray imaging test by a microcapillar? x-ray lens at an undulator beamline;" Rev. Sci. Instrum. 70 (1999) No. 11,4161,

6 . B. Lengeler, C . Schroer, J. Tummler, B. Benner, M. Richwin; A. Snigirev, I . Snigireva and M. Drakopoulos, "Imaging bl- parabolic refractive lenses in the hard x-ray range," J. Synchrotron Rad. 6 (1 999) 1 153

7. S. Aoki, "Axisymmetric Grazing Incidence Optics for an X-Ray Microscope and Microprobe," *Y-ray i\lici.oscopy ZI, ed. D. Sayre; M. Homells, J. Kirz and H. Rarback; (Springer Series in Optical Sciences. Springer-Verlag, Berlin. 1987); p. 102.

8. J. H. Underwood; A. C . Thomson, Y. Wu and R. D. Giauque, "X-ray microprobe using multiplayer mirrors;" Appl. Opt. 25 (1986) No. 1 1 , 1730.

9. A. Takeuchi, S. Aoki, K. Yamamoto, H. Takano; N. Watanabe and M. Ando, "Full-field x-ray iluorescence imaging microscope nith a Wolter mirror," Re\.. Sci. Instrum. 71 (2000) No. 3; 1279.

10. A. TBeuchi, K. Uesugi. Y. Suzuki and S. Aoki; "Hard X-Ray Microtomography Using X-Ray Imaging Optics ? ' ' Jpn. J. Appl. Phys. 40 (200 1) 1499.

1 1 . A. Snigirev, I. Snigire\.a, V. G. Kohn and S. M. Kuznetsov; "On the requirements to the instrumentation for the new generation ofthe synchrotron radiation sources. Beryllium windows;" Nucl. Instrum. Methods A 370 (1 996) 634.

12. A. Som70rov, I. Snigireva and A. Snigirev; "MIRROR SURFACE CHARACTERIZATION BY TOPOGRAPHY

13, Y.Suzuki, A.Momose and H.Sugiyama; "Characterization of windows and filters for coherent X-ray beamlines" J. SynchrotronRad. 5 (1998) 596.

14. N. Watanabe, S. Aoki, H. Takano, K. Yamamoto, A. Takeuchi, H. Tsubaki and T. Aota, "Phase-contrast Hard X-Ray Imaging Microscope with Wolter Mirror Optics," Proc. 17th hit . Coi$ .Y-Ray Microscopy, Beikeley; California, 1999 (American Inst. Phys.; 2000) p.84.

15. D. L . White, 0. R. Wood 11, J. E. Bjorkholm, S. Spector, A. A. MacDowell and B. LaFontaine, --Modulation of the coherence ofundulator radiation," Rev. Sci. Instrum. 66 (1 995) 1930.

16. M. Awa,ji: Y. Suzuki, A. Takeuchi; H. Takano, N. Kamijo; S. Tamura and M. Yasumoto, "X-ray imaging microscopy at 25 keV with Fresnel zone plate optics", to be published in Nucl. Instrum. Meths. A, Proc. 7& hit. Coi$ S ~ ~ C ~ O ~ ~ . O H Radiation Iiisfr71nieiitatioii (2000).

17. Y. Suzuki, A. Takeuchi, H. Takano, T. Ohigashi and H. Takenaka, "Diffraction-Limited Microbeam with Fresnel Zone Plate Optics in Hard X-Ray Regions," 5pn. 5. Appl. Phys. 40 (200 1) 1508.

18. H. Takano; Y. Suzuki. K. Uesugi, A. Takeuchi and N. Yagi, ..Point spread function measurement of imaging detectors with an x-ray microbeam," to be published in Proc. SPIE (200 1 ).

19. H. H. Hopkins; "On the diffraction theory of optical images," Proc. R. SOC. A 217 (1953) 408.

WITH COHERENT X-RAYS," Pi*oc. SPIE 3113 (1997) 476.


x-ray imaging microscope with a partial coherent illumination

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