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Microscopic imaging and holography with hard X-rays using Fresnel zone-plates
15 June 2000
Optics Communications 180 Ž2000. 233–238 www.elsevier.comrlocateroptcom
Microscopic imaging and holography with hard X-rays using Fresnel zone-plates W. Leitenberger ) , T. Weitkamp, M. Drakopoulos, I. Snigireva, A. Snigirev European Synchrotron Radiation Facility ESRF, Experiments DiÕision, ID 22, BP220, F-38043 Grenoble Cedex, France Received 8 February 2000; received in revised form 12 April 2000; accepted 15 April 2000
Abstract The imaging properties of a Fresnel zone-plate ŽFZP. were used for magnified imaging of microobjects using hard X-rays. The experiments were done using 14 keV synchrotron radiation. The coherence properties of the radiation produced by an undulator allowed the recording of real images and holograms from an object in one single exposure. These images result from the positive and the negative first order diffracted beams respectively. The X-ray microscope worked at an X-ray magnification factor of 12 and could resolve structures of 0.3 mm in size. By going to slightly defocused conditions we obtained magnified images of the holographical nearfield diffraction pattern Žin-line holograms. of the object. q 2000 Elsevier Science B.V. All rights reserved. PACS: 07.85.y; 42.40; 41.50; 42.25 Keywords: X-ray microscopy; X-ray holography; Coherent X-rays; X-ray imaging; Fresnel zone-plate; Synchrotron radiation
1. Introduction There are in general several possibilities to achieve a lateral resolution below one micrometer in multikeV X-ray imaging. The traditional method is the recording of an X-ray absorption radiograph with a high-resolution detector and magnification afterwards. Common detectors are high-resolution X-ray films or thin scintillator screens in combination with an optical microscope projecting the image to a CCD camera. These techniques are resolution limited by the grain size of the film or the optical diffraction limit of the microscope and the response function of the scintillator w1x. Another approach to go to sub) Corresponding author. Tel.: q33-4-7688-2261; fax: q33-47688-2785; e-mail: [email protected]
micron resolution is the recording of a magnified image of an object by X-ray projection microscopy at a large distance from a point-like X-ray source w2,3x. X-ray lenses have been available for a few years that make direct image magnification possible. Such X-ray lenses are Bragg–Fresnel lenses w4,5x, Fresnel zone-plates ŽFZP. w6–9x or compound refractive lenses w10–12x. Microscopic X-ray imaging and also scanning X-ray microscopy has been demonstrated using all of these three types of X-ray optical devices. At lower photon energies Ž1 . . . 6 keV. spatial resolutions of a few hundred nanometers have been achieved with zone-plate microscopes w13–15x. While FZPs for imaging in the soft X-ray range usually have a zone height in the order of 200 nm and an outermost zone width down to 20 nm w16x, the FZPs suited for hard X-rays require a much
0030-4018r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 0 - 4 0 1 8 Ž 0 0 . 0 0 7 1 0 - 0
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W. Leitenberger et al.r Optics Communications 180 (2000) 233–238
larger zone height on the order of one micron to have enough efficiency and with it sufficient flux in the positive first order diffracted beam. The minimum outermost zone width which is achievable for FZPs for hard X-rays is nowadays between 0.1 and 0.2 mm at a zone height of about 1 mm w17x. Under the conditions used in the experiments they act nearly as phase zone plates. The lateral resolution of the microscopic techniques is limited by the numerical aperture of the imaging X-ray lens. In the case of an FZP the aperture is limited by the width of the outermost Fresnel zone. In real imaging with a lens each illuminated point of the object can be considered as the source of a laterally coherent wave and is thus projected sharply onto the image plane even if the object is illuminated with incoherent radiation. Contrary to this the formation of an in-line hologram of an object requires illumination with a coherent source because the waves emitted by each point of the object contributes to each point in the hologram. The spatial coherence length l s of a beam in a given experimental set-up represents the maximum distance of two object points in the object plane which can be coherently illuminated. It is given by l s s Dlru s with wavelength l, source size u s and source-to-object distance D w18,19x.
2. Experimental In the experiments with the X-ray microscope a Fresnel zone plate made of gold was used. It was manufactured by X-ray lithography on a SiN substrate. Characteristic parameters are the following: height of the zones 1.5 mm, radius of the central zone 12.45 mm, width of the outermost zone 0.25 mm. The FZP has 620 zones giving a full aperture of 620 mm. At 14 keV the FZP has a focal length of f s 1.75 m and a calculated diffraction efficiency of 12%. To avoid radiation-induced corrosion during the experiments, the FZP was protected by a nitrogen gas atmosphere. The experimental arrangement of the microscope is shown in Fig. 1. The distances of the optical elements are determined by the parameters of the FZP and by the used wavelength. Large X-ray magnifications require large distances. The set-up re-
Fig. 1. Experimental set-up for X-ray microscopy. The geometrical ray paths for forming an real image and a hologram from the different diffraction orders of the Fresnel zone plate ŽFZP. are shown Žsee also Section 3.3..
quires access to the photon beam at two positions far enough apart from each other. The ESRF beamline ID22 offers two experimental stations of approximately 10 m length each and separated by another 10 m. Thus the lens and object could be mounted in the first station and the images were recorded in the second station, with a distance of more than 20 m between lens and detector. Moreover, the long distances of 44 m and 63 m between the undulator source and the centers of the two stations, the approximate source size ŽFWHM: u sv s 30 mm Žvertical. and u sh s 700 mm Žhorizontal.. and the polished vacuum windows ensure a high degree of beam coherence, opening up good possibilities of holographic imaging. A symmetric Si-111 fixed exit double-crystal monochromator was used to monochromatize the beam to an energy of E s 14 keV with a bandwidth of D lrl s 4 10y4 . Its fixed-exit design makes it possible to quickly change the focal length of the X-ray lens by varying the photon energy. A pair of slits at 37 m from the source matched the beam size to the aperture of the FZP. The test objects were placed at a distance of D s 40 m from the undulator source. No apertures for spatial filtering were inserted in the beam path, so that lateral coherence was exclusively determined by the primary source.
W. Leitenberger et al.r Optics Communications 180 (2000) 233–238
The positions of the object and image planes are related to the position of the lens by 1rf s 1rL1 q 1rL2 . In complete analogy with geometrical optics f denotes the focal length of the lens at the given wavelength l, and L1 and L2 are the object-to-lens and lens-to-image distances. Their values in the setup described here are: f s 1.85 m, L1 s 2.0 m, L2 s 24 m, resulting in a magnification of M s L2rL1 s 12. For tests of resolution and image quality a fine free-standing gold grid and a second FZP were used. The gold grid structure had 15 mm pitch and 3.5 mm width of the grid bars. One part of this grid carries a finer, 1-mm-pitch grid. The ‘test’ FZP was 200 mm in diameter, had a zone height of 1.15 mm and an outermost zone width of 0.3 mm. For holographic imaging a sample consisting of two crossed boron fibres, each 100 mm in diameter with a 15-mm-thick tungsten core, was used. This fibre contains with its tungsten core a strongly absorbing object and at the same time with boron a good phase object. All images shown here were recorded with high resolution X-ray film ŽKodak.. The film allows to record images of large sizes Ždiameter of 7 mm in the experiment. with a resolution of one micron and a optical magnification afterwards using a light microscope.
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they were placed in the object plane of the microscope in the first experimental station of the beamline. The gold mesh was used because its square structure, extending over the full size of the image, would reveal possible image distortions. The fine grid structure on it served as a first test structure for spatial resolution, its stripes being only 0.5 mm wide and having a periodicity of 1 mm. Fig. 2Ža. shows an image obtained on X-ray film. The area in the recording plane where an image can directly be seen without any background correction has a diameter of more than 5 mm. It corresponds to a diameter in the object plane of about 400 mm taking into account
3. Results The experimental results are discussed in the following three sections. These are firstly the test of the lateral resolution and the image quality by recording the positive first order real image. Secondly the object was moved slightly away from the FZP out of its optimum imaging conditions. The nearfield phase contrast image Žor Gabor in-line hologram. is transferred through the FZP. Finally we discussing the image formation of the first negative diffraction order Ždiverging. that yields an enlarged image of the farfield in-line hologram. 3.1. Magnification of real images The performance of the X-ray microscope in real imaging mode was tested with the gold mesh structure and the second FZP as well. For this purpose
Fig. 2. Ža. Image of the gold-mesh structure with 15 mm pitch, taken with the hard X-ray microscope at 14 keV, a magnification factor of 12 and recorded on high-resolution X-ray film. The center of the X-ray image at the upper right side of the figure is blackened by the zero-order beam passing undiffracted through the lens. No background correction has been applied. The enlarged detail in the upper part shows the grid bars Ž3 mm width. and the fine grid with 0.5 mm width. This structure has some small defects in it. Note that the substructure is visible even under the mesh wires. Žb. Image of a Fresnel zone plate taken with the X-ray microscope in the same geometry as the image of the gold mesh. The outermost zones have a width of 0.3 mm.
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that the object is magnified by a factor of 12. The center of the image located at the upper right part of the figure is overexposed by the zero-order beam. This area has at least the size of the entrance aperture of 0.6 = 0.6 mm2 but it is enlarged to approximately 1mm diameter by the divergence of the beam. The recorded image has no distortions that means right angles are reproduced in the image, and the fine grid including defects in it can be seen. The second FZP was a test object with even finer structures. Fig. 2Žb. shows the image, on which the outermost zones of 0.3 mm width show up clearly. The exposure time for these images was 4 minutes. 3.2. Magnification of holograms This part of the experiment was aimed at testing whether it is possible to generate magnified real images of interference patterns of phase objects which are usually observable in a set-up for in-line holography w20,21x. Because of the small vertical undulator source size and the spatial vertical coherence length of l sv s 120 mm the object was coherently illuminated and horizontal interference fringes are visible. The sample was in an otherwise unaltered setup moved out of the object plane of the microscope in the direction away from the FZP. The intensity distribution of the wave in the object plane which is transferred trough the lens into the image plane changes with increased defocussing. It changes in the same way as the image in a conventional transmission radiograph with coherent illumination as the distance between object and detector is increased. The focused case gives an absorption radiograph while the defocused case gives a Gabor in-line hologram The feasibility of this experiment is shown using a boron fibre sample. In the well focused position shown in Fig. 3Ža. only a weak outline image of the border of the boron fibre and the tungsten core is visible. The boron shows almost no absorption contrast itself. The weak ‘outlining’ is due to a not completely accurate positioning of the object in the object plane. At larger distances from the correct object position in Fig. 3Žb. wider spaced interference fringes are observed in increased number. This effect is identical to the observations in direct recording of Gabor in-line holograms at different distances from
Fig. 3. Magnified X-ray image of two crossed boron fibres at the same energy of 14 keV but two different object distances L1. The enlarged part on the right shows the holographic interference fringes at the border of the boron. Ža. L1 s1.91 m. The bright bars at the left side and the lower side are the tungsten cores of 15 mm diameter each. Of the boron only the borders are enhanced by a few interference fringes. Žb. L1 s 2.06 m. A defocussing of 15 cm gives a near-field diffraction wave front in the image plane containing both absorption and phase contrast. A large number of horizontal interference fringes is visible due to the large transverse coherence length in vertical direction Žsmall undulator source size. whereas only one interference fringe is visible in the vertical direction. ŽThe field of view shifted to the upper right by about 15 mm with respect to Fig. 3Ža...
the sample w20x. The experiment shows that in-line holograms formed with coherent hard X-rays can be passed through an FZP microscope using real imaging to obtain magnification. 3.3. Holographic imaging The same coherence properties of the illuminating beam that allow the real imaging of in-line holograms ŽSection 3.2. make it possible to observe simultaneously a real and a holographic image. As
W. Leitenberger et al.r Optics Communications 180 (2000) 233–238
known from the theory of zone-plates each FZP acts simultaneously as a converging and a diverging lens. In addition to the positive converging first order diffracted portion which has been discussed in the previous two sections the negative diverging first order portion gives usually no image because it is acting as a diverging lens. In the experiment two crossed boron fibres were placed as a sample into the object plane of the X-ray microscope. The magnified image shown in Fig. 4 was recorded in the same way as described in Section 3.1. In the lower part one observes again the cross structure of the tungsten core. The boron shows no significant absorption contrast and the borders are only visible by a weak outline effect making it possible to distinguish the boron from the background as already shown in Fig. 3Ža.. In the upper part of Fig. 4 above the zero-order overexposed central spot, a hologram with many horizontal interference fringes is visible. This hologram is formed
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by interference of the negative first order diffracted wave which goes seemingly out of the virtual focal point yf Ž object waÕe . and the positive first order diffracted wave passing the lower part of the FZP as a reference waÕe Žsee Fig. 1.. The good visibility of horizontal interference fringes is due to the spatial coherence length of l sv s 120 mm in the vertical direction whereas in the horizontal direction the value is only l sh s 5 mm and no interference fringes are visible. More generally, the smaller the primary source is in a given dimension, the more pronounced the interference fringes perpendicular to this dimension will be. This effect does not appear in the widely used experimental set-up in soft X-ray microscopy using a central beamstop integrated into a condenser zone-plate which illuminates the sample w22x, because in this case the sample is in general not coherently illuminated. The hologram pattern and the real image are located on opposite sides of the optical axis, and they do not overlap. It is thus possible to record a real magnified image and a magnified holographic image of the object at a single shot. From the Fig. 4 and the different imaging properties in the horizontal and the vertical direction one sees quite well that real imaging using a FZP requires no coherent radiation while for forming a hologram the coherence conditions are decisive. In a further step of the experiment a small secondary source was formed by closing a pair the vertical slits 10 m upstream of the object down to 30 mm. This increases the spatial coherence in the horizontal direction to l sh s 30 mm. In addition to the horizontal fringes the recorded image showed also vertical interference fringes from the vertical fibre. However this image suffers from low intensity has a bad quality and is not suited for printed reproduction.
4. Conclusion
Fig. 4. Image of the crossed boron fibres at 14 keV. The real image in the lower part and the holographic image in the upper part were taken simultaneously Žfor details see text..
A hard X-ray microscope with a Fresnel zone-plate has been set up and used for magnified imaging in absorption and phase contrast. Structures of 0.3 mm size and thus below the optical diffraction limit could be clearly resolved with good image quality.
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By improved manufacturing technology FZPs with smaller outermost zone width were already manufactured. This will give an increased lateral resolution going beyond the 0.1 mm limit. It has also been shown that with a partially coherent synchrotron beam the positive and negative first diffraction orders of a Fresnel zone plate can be used for simultaneous real and holographic imaging. The high image quality and the simplicity of the setup puts the technique in a condition that is ready for applications. The absence of order-selecting apertures or a condensing element, the possibility of taking phasecontrast images and the possible use of the first diverging order of the zone plate to create holographic images without changes in the setup add to the flexibility of the method. A combination of the X-ray microscope with tomography can be envisioned. The linear pathway of an FZP optic simplifies the alignment and makes the whole arrangement more stable than others based on optical elements in reflection geometry such as mirrors or Bragg–Fresnel optics.
w3x w4x w5x w6x
w7x
w8x w9x w10x w11x w12x
w13x
Acknowledgements The zone plate was provided by the Advanced Photon Source through a collaboration with the Center for X-ray Lithography ŽUniv. of Wisconsin-Madison. and the Istituto di Elettronica dello Stato Solido ŽIESS-CNR, Italy.. The ‘test’ zone plate was provided by the IESS-CNR in Rome ŽItaly.. We are very grateful to A. Simionovici and J.M. Rigal for their assistance during the experiments. One of the authors ŽW.L.. was supported by a Marie-Curie-Fellowship of the European Commission.
w14x w15x w16x w17x
w18x w19x w20x
References w1x A. Koch, C. Raven, P. Spanne, A. Snigirev, J. Opt. Soc. Am. A 15 Ž1998. 1940–1951. w2x S. Di Fonzo, W. Jark, G. Soullie, ´ A. Cedola, S. Lago-
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marsino, P. Cloetens, C. Riekel, J. Synchrotron. Rad. 5 Ž1998. 376–378. T.E. Gureyev, S.W. Wilkins, J. Opt. Soc. Am. A 15 Ž1998. 579–585. V.V. Aristov, A.A. Snigirev, Y.A. Basov, A.Y. Nikulin, AIP Conf. Proc. No. 147 Ž1986. 253. A. Snigirev, I. Snigireva, P. Bosecke, S. Lequin, I. Sche¨ lokov, Opt. Commun. 135 Ž1997. 378. B. Lai, W. Yun, Y. Xiao, L. Yang, D. Legnini, Z. Cai, A. Krasnoperova, F. Cerrina, E. DiFabrizio, L. Grella, M. Gentili, Rev. Sci. Instrum. 66 Ž1995. 2287–2289. B. Lai, W. Yun, D. Legnini, Y. Xiao, J. Chrzas, J. Viccaro, V. White, S. Bajikar, D. Denton, F. Cerrina, E. Di Fabrizio, M. Gentili, L. Grella, M. Bacciocchi, Appl. Phys. Lett. 61 Ž1992. 1877. K. Saitoh, K. Inagawa, K. Kohra, C. Hayashi, Rev. Sci. Instrum. 60 Ž1989. 1519–1523. W.B. Yun, P.J. Viccaro, B. Lai, J. Chrzas, Rev. Sci. Instrum. 63 Ž1991. 582–585. A. Snigirev, V. Kohn, I. Snigireva, B. Lengeler, Nature 384 Ž1996. 49–51. B. Lengeler, J. Tuemmler, A. Snigirev, I. Snigireva, C. Raven, J. Appl. Phys. 84 Ž1998. 5855. B. Lengeler, C. Schroer, M. Richwin, J. Tuemmler, M. Drakopoulos, A. Snigirev, I. Snigireva, Appl. Phys. Lett. 74 Ž1999. 3924. B. Kaulich, S. Oestreich, S. Salome, R. Barret, J. Susini, T. Wilhein, D. Di Fabrizio, M. Gentili, P. Charalambous, Appl. Phys. Lett. 75 Ž1999. 4061–4063. Z.H. Levine, A.R. Kalukin, S.P. Frigo, I. McNulty, M. Kuhn, Appl. Phys. Lett. 74 Ž1999. 150–152. I. Mc Nulty, S.P. Frigo, C.C. Retsch et al., SPIE Proc. 3449 Ž1998. 67–74. S.J. Spector, C.J. Jacobson, D.M. Tenant, J. Vac. Sci. Technol. B. 19 Ž1997. 2872–2876. W. Yun, B. Lai, Z. Cai, J. Maser, D. Legnini, G. Gluskin, Z. Chen, A.A. Krasnoperova, Y. Vladimirsky, F. Cerrina, E. Di Fabrizio, M. Gentili, Rev. Sci. Instrum. 70 Ž1999. 2238–2241. D. Attwood, Soft X-rays and Extreme Ultraviolet Radiation, 1st ed., Cambridge University Press, 1999. M. Born, E. Wolf, Principles of Optic, 7th ed., Cambridge University Press, 1999. A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, I. Schelokov, Rev. Sci. Instrum. 66 Ž1995. 5486–5492. T.J. Davis, D. Gao, T.E. Gureyev, A.W. Stevenson, S.W. Wilkins, Nature 373 Ž1995. 595–598. B. Niemann, D. Rudolph, G. Schmahl, Appl. Opt. 15 Ž1976. 1883.
Optics Communications 180 Ž2000. 233–238 www.elsevier.comrlocateroptcom
Microscopic imaging and holography with hard X-rays using Fresnel zone-plates W. Leitenberger ) , T. Weitkamp, M. Drakopoulos, I. Snigireva, A. Snigirev European Synchrotron Radiation Facility ESRF, Experiments DiÕision, ID 22, BP220, F-38043 Grenoble Cedex, France Received 8 February 2000; received in revised form 12 April 2000; accepted 15 April 2000
Abstract The imaging properties of a Fresnel zone-plate ŽFZP. were used for magnified imaging of microobjects using hard X-rays. The experiments were done using 14 keV synchrotron radiation. The coherence properties of the radiation produced by an undulator allowed the recording of real images and holograms from an object in one single exposure. These images result from the positive and the negative first order diffracted beams respectively. The X-ray microscope worked at an X-ray magnification factor of 12 and could resolve structures of 0.3 mm in size. By going to slightly defocused conditions we obtained magnified images of the holographical nearfield diffraction pattern Žin-line holograms. of the object. q 2000 Elsevier Science B.V. All rights reserved. PACS: 07.85.y; 42.40; 41.50; 42.25 Keywords: X-ray microscopy; X-ray holography; Coherent X-rays; X-ray imaging; Fresnel zone-plate; Synchrotron radiation
1. Introduction There are in general several possibilities to achieve a lateral resolution below one micrometer in multikeV X-ray imaging. The traditional method is the recording of an X-ray absorption radiograph with a high-resolution detector and magnification afterwards. Common detectors are high-resolution X-ray films or thin scintillator screens in combination with an optical microscope projecting the image to a CCD camera. These techniques are resolution limited by the grain size of the film or the optical diffraction limit of the microscope and the response function of the scintillator w1x. Another approach to go to sub) Corresponding author. Tel.: q33-4-7688-2261; fax: q33-47688-2785; e-mail: [email protected]
micron resolution is the recording of a magnified image of an object by X-ray projection microscopy at a large distance from a point-like X-ray source w2,3x. X-ray lenses have been available for a few years that make direct image magnification possible. Such X-ray lenses are Bragg–Fresnel lenses w4,5x, Fresnel zone-plates ŽFZP. w6–9x or compound refractive lenses w10–12x. Microscopic X-ray imaging and also scanning X-ray microscopy has been demonstrated using all of these three types of X-ray optical devices. At lower photon energies Ž1 . . . 6 keV. spatial resolutions of a few hundred nanometers have been achieved with zone-plate microscopes w13–15x. While FZPs for imaging in the soft X-ray range usually have a zone height in the order of 200 nm and an outermost zone width down to 20 nm w16x, the FZPs suited for hard X-rays require a much
0030-4018r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 0 - 4 0 1 8 Ž 0 0 . 0 0 7 1 0 - 0
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W. Leitenberger et al.r Optics Communications 180 (2000) 233–238
larger zone height on the order of one micron to have enough efficiency and with it sufficient flux in the positive first order diffracted beam. The minimum outermost zone width which is achievable for FZPs for hard X-rays is nowadays between 0.1 and 0.2 mm at a zone height of about 1 mm w17x. Under the conditions used in the experiments they act nearly as phase zone plates. The lateral resolution of the microscopic techniques is limited by the numerical aperture of the imaging X-ray lens. In the case of an FZP the aperture is limited by the width of the outermost Fresnel zone. In real imaging with a lens each illuminated point of the object can be considered as the source of a laterally coherent wave and is thus projected sharply onto the image plane even if the object is illuminated with incoherent radiation. Contrary to this the formation of an in-line hologram of an object requires illumination with a coherent source because the waves emitted by each point of the object contributes to each point in the hologram. The spatial coherence length l s of a beam in a given experimental set-up represents the maximum distance of two object points in the object plane which can be coherently illuminated. It is given by l s s Dlru s with wavelength l, source size u s and source-to-object distance D w18,19x.
2. Experimental In the experiments with the X-ray microscope a Fresnel zone plate made of gold was used. It was manufactured by X-ray lithography on a SiN substrate. Characteristic parameters are the following: height of the zones 1.5 mm, radius of the central zone 12.45 mm, width of the outermost zone 0.25 mm. The FZP has 620 zones giving a full aperture of 620 mm. At 14 keV the FZP has a focal length of f s 1.75 m and a calculated diffraction efficiency of 12%. To avoid radiation-induced corrosion during the experiments, the FZP was protected by a nitrogen gas atmosphere. The experimental arrangement of the microscope is shown in Fig. 1. The distances of the optical elements are determined by the parameters of the FZP and by the used wavelength. Large X-ray magnifications require large distances. The set-up re-
Fig. 1. Experimental set-up for X-ray microscopy. The geometrical ray paths for forming an real image and a hologram from the different diffraction orders of the Fresnel zone plate ŽFZP. are shown Žsee also Section 3.3..
quires access to the photon beam at two positions far enough apart from each other. The ESRF beamline ID22 offers two experimental stations of approximately 10 m length each and separated by another 10 m. Thus the lens and object could be mounted in the first station and the images were recorded in the second station, with a distance of more than 20 m between lens and detector. Moreover, the long distances of 44 m and 63 m between the undulator source and the centers of the two stations, the approximate source size ŽFWHM: u sv s 30 mm Žvertical. and u sh s 700 mm Žhorizontal.. and the polished vacuum windows ensure a high degree of beam coherence, opening up good possibilities of holographic imaging. A symmetric Si-111 fixed exit double-crystal monochromator was used to monochromatize the beam to an energy of E s 14 keV with a bandwidth of D lrl s 4 10y4 . Its fixed-exit design makes it possible to quickly change the focal length of the X-ray lens by varying the photon energy. A pair of slits at 37 m from the source matched the beam size to the aperture of the FZP. The test objects were placed at a distance of D s 40 m from the undulator source. No apertures for spatial filtering were inserted in the beam path, so that lateral coherence was exclusively determined by the primary source.
W. Leitenberger et al.r Optics Communications 180 (2000) 233–238
The positions of the object and image planes are related to the position of the lens by 1rf s 1rL1 q 1rL2 . In complete analogy with geometrical optics f denotes the focal length of the lens at the given wavelength l, and L1 and L2 are the object-to-lens and lens-to-image distances. Their values in the setup described here are: f s 1.85 m, L1 s 2.0 m, L2 s 24 m, resulting in a magnification of M s L2rL1 s 12. For tests of resolution and image quality a fine free-standing gold grid and a second FZP were used. The gold grid structure had 15 mm pitch and 3.5 mm width of the grid bars. One part of this grid carries a finer, 1-mm-pitch grid. The ‘test’ FZP was 200 mm in diameter, had a zone height of 1.15 mm and an outermost zone width of 0.3 mm. For holographic imaging a sample consisting of two crossed boron fibres, each 100 mm in diameter with a 15-mm-thick tungsten core, was used. This fibre contains with its tungsten core a strongly absorbing object and at the same time with boron a good phase object. All images shown here were recorded with high resolution X-ray film ŽKodak.. The film allows to record images of large sizes Ždiameter of 7 mm in the experiment. with a resolution of one micron and a optical magnification afterwards using a light microscope.
235
they were placed in the object plane of the microscope in the first experimental station of the beamline. The gold mesh was used because its square structure, extending over the full size of the image, would reveal possible image distortions. The fine grid structure on it served as a first test structure for spatial resolution, its stripes being only 0.5 mm wide and having a periodicity of 1 mm. Fig. 2Ža. shows an image obtained on X-ray film. The area in the recording plane where an image can directly be seen without any background correction has a diameter of more than 5 mm. It corresponds to a diameter in the object plane of about 400 mm taking into account
3. Results The experimental results are discussed in the following three sections. These are firstly the test of the lateral resolution and the image quality by recording the positive first order real image. Secondly the object was moved slightly away from the FZP out of its optimum imaging conditions. The nearfield phase contrast image Žor Gabor in-line hologram. is transferred through the FZP. Finally we discussing the image formation of the first negative diffraction order Ždiverging. that yields an enlarged image of the farfield in-line hologram. 3.1. Magnification of real images The performance of the X-ray microscope in real imaging mode was tested with the gold mesh structure and the second FZP as well. For this purpose
Fig. 2. Ža. Image of the gold-mesh structure with 15 mm pitch, taken with the hard X-ray microscope at 14 keV, a magnification factor of 12 and recorded on high-resolution X-ray film. The center of the X-ray image at the upper right side of the figure is blackened by the zero-order beam passing undiffracted through the lens. No background correction has been applied. The enlarged detail in the upper part shows the grid bars Ž3 mm width. and the fine grid with 0.5 mm width. This structure has some small defects in it. Note that the substructure is visible even under the mesh wires. Žb. Image of a Fresnel zone plate taken with the X-ray microscope in the same geometry as the image of the gold mesh. The outermost zones have a width of 0.3 mm.
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that the object is magnified by a factor of 12. The center of the image located at the upper right part of the figure is overexposed by the zero-order beam. This area has at least the size of the entrance aperture of 0.6 = 0.6 mm2 but it is enlarged to approximately 1mm diameter by the divergence of the beam. The recorded image has no distortions that means right angles are reproduced in the image, and the fine grid including defects in it can be seen. The second FZP was a test object with even finer structures. Fig. 2Žb. shows the image, on which the outermost zones of 0.3 mm width show up clearly. The exposure time for these images was 4 minutes. 3.2. Magnification of holograms This part of the experiment was aimed at testing whether it is possible to generate magnified real images of interference patterns of phase objects which are usually observable in a set-up for in-line holography w20,21x. Because of the small vertical undulator source size and the spatial vertical coherence length of l sv s 120 mm the object was coherently illuminated and horizontal interference fringes are visible. The sample was in an otherwise unaltered setup moved out of the object plane of the microscope in the direction away from the FZP. The intensity distribution of the wave in the object plane which is transferred trough the lens into the image plane changes with increased defocussing. It changes in the same way as the image in a conventional transmission radiograph with coherent illumination as the distance between object and detector is increased. The focused case gives an absorption radiograph while the defocused case gives a Gabor in-line hologram The feasibility of this experiment is shown using a boron fibre sample. In the well focused position shown in Fig. 3Ža. only a weak outline image of the border of the boron fibre and the tungsten core is visible. The boron shows almost no absorption contrast itself. The weak ‘outlining’ is due to a not completely accurate positioning of the object in the object plane. At larger distances from the correct object position in Fig. 3Žb. wider spaced interference fringes are observed in increased number. This effect is identical to the observations in direct recording of Gabor in-line holograms at different distances from
Fig. 3. Magnified X-ray image of two crossed boron fibres at the same energy of 14 keV but two different object distances L1. The enlarged part on the right shows the holographic interference fringes at the border of the boron. Ža. L1 s1.91 m. The bright bars at the left side and the lower side are the tungsten cores of 15 mm diameter each. Of the boron only the borders are enhanced by a few interference fringes. Žb. L1 s 2.06 m. A defocussing of 15 cm gives a near-field diffraction wave front in the image plane containing both absorption and phase contrast. A large number of horizontal interference fringes is visible due to the large transverse coherence length in vertical direction Žsmall undulator source size. whereas only one interference fringe is visible in the vertical direction. ŽThe field of view shifted to the upper right by about 15 mm with respect to Fig. 3Ža...
the sample w20x. The experiment shows that in-line holograms formed with coherent hard X-rays can be passed through an FZP microscope using real imaging to obtain magnification. 3.3. Holographic imaging The same coherence properties of the illuminating beam that allow the real imaging of in-line holograms ŽSection 3.2. make it possible to observe simultaneously a real and a holographic image. As
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known from the theory of zone-plates each FZP acts simultaneously as a converging and a diverging lens. In addition to the positive converging first order diffracted portion which has been discussed in the previous two sections the negative diverging first order portion gives usually no image because it is acting as a diverging lens. In the experiment two crossed boron fibres were placed as a sample into the object plane of the X-ray microscope. The magnified image shown in Fig. 4 was recorded in the same way as described in Section 3.1. In the lower part one observes again the cross structure of the tungsten core. The boron shows no significant absorption contrast and the borders are only visible by a weak outline effect making it possible to distinguish the boron from the background as already shown in Fig. 3Ža.. In the upper part of Fig. 4 above the zero-order overexposed central spot, a hologram with many horizontal interference fringes is visible. This hologram is formed
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by interference of the negative first order diffracted wave which goes seemingly out of the virtual focal point yf Ž object waÕe . and the positive first order diffracted wave passing the lower part of the FZP as a reference waÕe Žsee Fig. 1.. The good visibility of horizontal interference fringes is due to the spatial coherence length of l sv s 120 mm in the vertical direction whereas in the horizontal direction the value is only l sh s 5 mm and no interference fringes are visible. More generally, the smaller the primary source is in a given dimension, the more pronounced the interference fringes perpendicular to this dimension will be. This effect does not appear in the widely used experimental set-up in soft X-ray microscopy using a central beamstop integrated into a condenser zone-plate which illuminates the sample w22x, because in this case the sample is in general not coherently illuminated. The hologram pattern and the real image are located on opposite sides of the optical axis, and they do not overlap. It is thus possible to record a real magnified image and a magnified holographic image of the object at a single shot. From the Fig. 4 and the different imaging properties in the horizontal and the vertical direction one sees quite well that real imaging using a FZP requires no coherent radiation while for forming a hologram the coherence conditions are decisive. In a further step of the experiment a small secondary source was formed by closing a pair the vertical slits 10 m upstream of the object down to 30 mm. This increases the spatial coherence in the horizontal direction to l sh s 30 mm. In addition to the horizontal fringes the recorded image showed also vertical interference fringes from the vertical fibre. However this image suffers from low intensity has a bad quality and is not suited for printed reproduction.
4. Conclusion
Fig. 4. Image of the crossed boron fibres at 14 keV. The real image in the lower part and the holographic image in the upper part were taken simultaneously Žfor details see text..
A hard X-ray microscope with a Fresnel zone-plate has been set up and used for magnified imaging in absorption and phase contrast. Structures of 0.3 mm size and thus below the optical diffraction limit could be clearly resolved with good image quality.
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By improved manufacturing technology FZPs with smaller outermost zone width were already manufactured. This will give an increased lateral resolution going beyond the 0.1 mm limit. It has also been shown that with a partially coherent synchrotron beam the positive and negative first diffraction orders of a Fresnel zone plate can be used for simultaneous real and holographic imaging. The high image quality and the simplicity of the setup puts the technique in a condition that is ready for applications. The absence of order-selecting apertures or a condensing element, the possibility of taking phasecontrast images and the possible use of the first diverging order of the zone plate to create holographic images without changes in the setup add to the flexibility of the method. A combination of the X-ray microscope with tomography can be envisioned. The linear pathway of an FZP optic simplifies the alignment and makes the whole arrangement more stable than others based on optical elements in reflection geometry such as mirrors or Bragg–Fresnel optics.
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Acknowledgements The zone plate was provided by the Advanced Photon Source through a collaboration with the Center for X-ray Lithography ŽUniv. of Wisconsin-Madison. and the Istituto di Elettronica dello Stato Solido ŽIESS-CNR, Italy.. The ‘test’ zone plate was provided by the IESS-CNR in Rome ŽItaly.. We are very grateful to A. Simionovici and J.M. Rigal for their assistance during the experiments. One of the authors ŽW.L.. was supported by a Marie-Curie-Fellowship of the European Commission.
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