Abstract

X-ray full-field microscopy is a promising method for nondestructive observation of opaque materials because it can attain a high resolution and wide field of view without sample scanning. We recently developed hard x-ray objective optics, which are key devices for full-field microscopy, based on total-reflection mirrors with high throughput and achromatic properties. The objective optics consist of two types of advanced Kirkpatrick–Baez mirrors configured as crossed one-dimensional Wolter type I and type III optics. The designed optics possessed magnification factors of 42–45 with a compact camera length of approximately 2 m. The hard x-ray full-field microscope based on this system was tested at the BL29XU beamline at SPring-8. We were able to resolve 100-nm periods (50-nm line widths) of a resolution test chart at a photon energy of 15 keV over 30 h, which demonstrated the remarkable stability of this system. The image quality was preserved over a wide photon energy range from 9 to 15 keV. A periodic dot pattern with dot diameters of 300 nm, formed on a 775-µm-thick Si substrate, was three-dimensionally visualized by computed tomography.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Hard x-ray microscopy provides distinctive capabilities, notably high resolution and nondestructive measurement. Among its many relevant methods [1,2], x-ray full-field microscopy, which directly forms a magnified image using objective optics, offers a straightforward technique to achieve a wide field of view and nanometer-scale resolution without requiring sample scanning or complex data analysis. Fresnel zone plates [3], compound refractive lenses [4], and normal-incident soft x-ray Schwarzchild mirrors [5] have been deployed widely for x-ray objective optics, whereas recent technological developments [68] have enabled designing a total-reflection hard x-ray mirror for objective optics. Mirror-based x-ray objective optics offer unique advantages, including high throughput and achromatic properties. These properties enable, for example, fast tomographic measurements using broadband x-ray beams. Furthermore, the achromatic property is advantageous for conducting high-resolution x-ray absorption fine structure (XAFS) imaging [9] by changing the incident wavelength, as well as for performing x-ray fluorescence (XRF) imaging [10] by discriminating photon energies of the formed image using energy dispersive detectors. These capabilities, which combine spectroscopy and microscopy (i.e., spectromicroscopy), enable three-dimensional (3D) mapping of the chemical information of opaque materials.

Previously, we developed mirror-based x-ray objective optics consisting of a pair of advanced Kirkpatrick–Baez (AKB) mirrors [11,12] based on a Wolter type I [13,14] geometry (AKB-I) for the hard x-ray full-field microscope (HXM), and successfully conducted high-resolution XAFS imaging [15] and XRF imaging [16]. However, the HXM based on AKB-I optics required a very long camera length of several tens of meters (e.g., 45 m in Ref. [15]) to obtain a sufficiently large magnification factor. Consequently, the applications of AKB-I optics are limited to synchrotron radiation (SR) facilities that have long experimental hutches.

This challenge can be resolved by installing a different type of AKB optics based on a Wolter type III [13] geometry (AKB-III), which has been previously investigated in a theoretical study, and a 1D focusing test [17,18]. AKB-III optics, comprising elliptical concave and hyperbolic convex mirrors, permit a large magnification factor with a short camera length. Although hard x-ray mirror optics have been developed with flat or concave shapes, an optimal combination of concave and convex mirrors improves practical usability and versatility of the mirror-based HXM, and makes compact SR-based and/or laboratory-based applications feasible.

This Letter reports the demonstration of newly designed mirror-based objective optics and of compact, achromatic, and high-resolution HXM. Hard x-ray objective mirrors combining AKB-I and AKB-III optics were developed with sufficient accuracy. Then, 2D and 3D imaging tests were performed at the SPring-8 SR facility.

 figure: Fig. 1.

Fig. 1. (a) Arrangement of the objective mirrors combining AKB-I and AKB-III optics. The “ell.” (“hyp.”) is an abbreviation of “ellipse” (“hyperbola”). (b) Cross sections of (a).

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Tables Icon

Table 1. Design Parameters for the Objective Mirror

Figure 1(a) shows a schematic diagram of the proposed objective mirrors. The mirrors closer to the sample are AKB-I optics arranged for vertical imaging, while the other mirror pair has AKB-III optics used for horizontal imaging. The design parameters of the mirrors are listed in Table 1. With an iridium coating, the maximum glancing incident angle is 4.4 mrad, which provides an upper limit for the photon energy of approximately 15 keV. The numerical apertures (NAs) in the vertical and horizontal directions are ${1.0} \times {{10}^{ - 3}}$ and correspond to a Rayleigh resolution of 50-nm full-width and a depth of field of 41 µm at 15 keV. Using this design, we estimated theoretical fields of view of 7.6 µm in vertical and 12.44 µm in horizontal directions (see Supplement 1). The magnification factors of objective optics are determined by the position of the principal planes that are formed by the intersections of the incident rays and the doubly reflected rays. The horizontal principal plane is shifted closer to the object owing to the geometry of the AKB-III optics [see Fig. 1(b)], and thus, a sufficiently large magnification factor could be attained even with the short distance between the object and the mirrors. As a result, we were able to achieve vertical and horizontal magnification factors of 42–45 with a compact camera length of approximately 2 m.

Mirror shapes were fabricated on Si (001) substrates using previously reported [68] ultra-precision machining and measurement methods, with an accuracy of 2 nm in peak-to-valley (PV) and a roughness of 0.25 nm in root-mean-square (rms) values. The elliptical and hyperbolic concave shapes for the AKB-I optics were fabricated on a single substrate to simplify the alignment procedure [15], which fixed the relative displacement and angle between them with sufficient accuracies of 0.2 µm and 1.3 μrad, respectively. Although a similar method cannot be applied to the AKB-III optics, we were able to stabilize the AKB-III optics using the following procedure. First, the two mirrors were aligned based on previously reported wavefront measurements [18]. Then, the mirrors were bonded to a Si substrate using an ultraviolet curing resin, as shown in Fig. 2(a). The wavefront error measured after the bonding was as small as 1.1 rad ($\lambda /{6}$) in PV and 0.37 rad ($\lambda /{17}$) in rms at a photon energy of 15 keV, caused mainly by the shape errors on the mirrors and not by alignment errors. Further details are provided in Supplement 1.

Using the developed objective mirrors, we performed 2D imaging tests. Figure 2(b) shows a schematic of the HXM setup installed in the second experimental hutch of beamline BL29XU at SPring-8. The samples and mirrors were placed in an air environment for a proof-of-concept study. A silicon attenuator (AT) was used to prevent possible mirror contamination due to interactions between the high-power x-ray beam and dust particles in the air [19]. A rotating diffuser was placed downstream from the AT to reduce unwanted speckles on the images [20]. After beam shaping with a 4D slit, a quasiparallel beam with divergence of ${12.5}\;({V})\;\unicode{x00B5}{\rm rad} \times {32.2}\;({ H})\;\unicode{x00B5}{\rm rad}$ was used to illuminate the samples. The objective mirrors, which were coated with a 15-nm chromium medium layer and a 130-nm iridium top layer, reflected the x-ray beam from the sample. Bright-field x-ray images were obtained using an x-ray camera {XSight Micron LC ($ \times {20}$) X-ray sCMOS camera from the RIGAKU corporation, with an effective pixel size of 0.325 µm and a detection area of ${666} \times {666}\;\unicode{x00B5}{\rm m}$ [21]}. The expected resolution determined by Abbe’s resolution criterion [22] of ${0.82}\lambda / {\rm NA}$ was 67.8-nm full-width at 15 keV, owing to the quasiparallel illumination without the condenser optics, as in this case.

 figure: Fig. 2.

Fig. 2. (a) Photograph of the developed objective mirrors. (b) Schematic drawing of the experimental setup.

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The measured reflectivity after the quadruple reflection was 69.2% at a photon energy of 10 keV, which agrees well with the theoretical value of 71.1% calculated for a surface and boundary roughness of 0.25-nm rms [23]. The same calculations at 15 keV resulted in a quadruple reflectivity of 45.4%. Figure 3(a) shows the x-ray images of a radial test pattern (XRESO-50HC, tantalum thickness 500 nm, NTT-AT) obtained just after the initial tuning of the objective mirrors and another obtained after 33.5 h. The images were acquired using a photon energy of 15 keV and an AT thickness of 0.25 mm with an exposure time of 30 s. In this condition, a photon flux at the camera of ${1.1} \times {{10}^{11}}\;{\rm photons}/{\rm s}$ was expected (see Supplement 1). To improve the contrast and signal-to-noise ratio, we applied the flat-field correction, by dividing the acquired sample image by an image of an empty area. The 100-nm periods (50-nm line widths) were resolved in both images, and image quality was preserved without any degradation, demonstrating the stability of this HXM.

 figure: Fig. 3.

Fig. 3. (a) X-ray images of the Siemens star obtained after the first tuning of mirrors and after 33.5 h. The exposures were for 30 s with a 0.25-mm Si attenuator whose transmittance was 57% at 15 keV. The minimum line width denotes 50 nm. (b) Results of the PSA. The “Ratio (V)” [“Ratio (H)”] in the graph means ratio between the “Vertical” (“Horizontal”) and the “Empty (V)” [“Empty (H)”]. The black dashed line indicates ratio of 1.0. The red and blue dashed lines indicate vertical and horizontal cutoff frequencies, corresponding to full periods of 71 and 87 nm, respectively. (c) Photon energy dependence between 9 and 15 keV. The exposures are for 30 s using a 0.25-mm Si attenuator for all images. The expected resolutions for 15, 12, and 9 keV are 67.8, 84.7, and 113.0 nm, respectively. The bars denote 2 µm.

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A power spectral density analysis (PSA), shown in Fig. 3(b), indicates that the cutoff frequencies of the microscope are approximately 71-nm full-width (35.5 nm half-width) in the vertical direction and 87-nm full-width (43.5 nm half-width) in the horizontal direction. The method and further description of the PSA are described in Supplement 1. Achromatic capabilities were investigated while decreasing the photon energy from 15 to 9 keV [Fig. 3(c)]. Although the resolutions varied, because of changes in the wavelength, images with consistent image quality were obtained at the same focal position, as expected.

An HXM with high penetration power should be suitable for observing the inner structures of thick and extended samples, such as integrated circuit devices. As a demonstration, a 300-nm-diameter tungsten dot pattern on a Si substrate with a thickness of 775 µm (National Metrology Institute of Japan) was observed. The pattern is a standard reference dedicated for scanning electron microscopes (SEMs). Although these nanostructures on the thick substrate have been rarely applied for high-resolution x-ray applications, we were able to visualize such thick samples at a photon energy of 15 keV, as shown in Fig. 4(a). It is noteworthy that the pattern, when rotated by 59.85 deg to correspond to a substrate absorption thickness of 1.54 mm, could be measured even at an exposure time of 10 s. Furthermore, computed tomography (CT) was applied. The dot pattern was rotated and observed at 0.45° intervals between 0° and 180°, except for the angular range of 72°–108° because of the low image contrast caused by substrate absorption. Note that the lack of side angle information and the absorption of the dot structures themselves generated the artifacts in the reconstructed images, which are common features in conventional CT reconstruction for these plate-like and highly absorptive samples. Sliced images of the 3D reconstruction results, which were calculated by a filtered back projection algorithm using a 15-nm voxel size, are shown in Fig. 4(b). Defects of dots with a slightly thin center regime were resolved. Although further investigations were needed for ensuring the defect structures, Kumagai et al. reported observation of similar defects using SEM [24] for smaller dot patterns that were manufactured by the same methods.

 figure: Fig. 4.

Fig. 4. (a) Images of dot patterns on a 775-µm Si substrate with rotation angles of 0° (left) and 59.85° (right) at an x-ray energy of 15 keV. The exposures are for 10 s. (b) In-plane sliced (left) and vertically sliced (right) images of the CT reconstruction. The bars denote 2 µm.

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In conclusion, we have successfully demonstrated that high-resolution and high-throughput HXM using mirror-based objective optics was achievable in a 2-m compact setup. To our knowledge, the obtained images showed the first imaging results using a Wolter type III optics configuration. The HXM possessed a wide-range achromaticity, which is strongly advantageous for the application of spectromicroscopy. Nanostructures on the thick opaque substrate were three-dimensionally visualized owing to the long-term stability and high penetration power of the HXM.

In this study, the iridium coating was adopted because of its high reflectivity at 15 keV. For a spectroscopic application, a coating material of rhodium or ruthenium can keep a high reflectivity in a wide range from 9 to 15 keV and avoid absorption edges of the iridium. The exposure times of 10–30 s in this study can be drastically shortened by a factor of 10–500 by utilizing condenser optics and a vacuum environment. Additionally, appropriate condenser optics will slightly enhance the theoretical resolution according to the resolution criterion in partially coherent illumination [25]. The resolution in the horizontal direction was degraded, as compared with the vertical direction, which was probably due to a slight alignment change in the bonded AKB-III optics. We assume that the resins expanded because of humidity during the two months between the bonding experiment and the imaging test. This issue can be mitigated by optimizing the bonding methods. Alternatively, precise alignment control using a mechanical aligner can be considered. The theoretical resolution will be improved by a factor of two to five by installing a multilayer technique [26], which was utilized for hard x-ray ${7} \times {8}\;{{\rm nm}^2}$ focusing mirrors [27], at the cost of reduced achromaticity. However, an energy bandwidth of 500–900 eV ($\Delta { E}/{ E}$ of 3%–11%) and an angular acceptance of 0.4–1.1 mrad are achievable in the multilayer reflection, which are sufficient for AKB microscopic applications in polychromatic laboratory x-ray sources.

We anticipate that, with further advancements, an HXM using mirror-based objective optics that can attain a resolution of approximately 10 nm in 2D and approximately 20 nm in 3D will be utilized widely for various scientific investigations, not only in SR and x-ray free-electron laser facilities, but in laboratories as well.

Funding

Japan Society for the Promotion of Science (JP16H06358, JP17H01073, JP26286077); Adaptable and Seamless Technology Transfer Program through Target-Driven R and D (AS2915035S).

Acknowledgment

The authors acknowledge Kentaro Hata, Takato Inoue, and Hiroyuki Yamaguchi for their support during the experiments. The use of beamline BL29XU at SPring-8 was supported by RIKEN. One of the authors (J. Y.) would like to acknowledge the SACLA research support program for graduate students and the special postdoctoral researcher program of RIKEN.

Disclosures

The authors declare no conflicts of interest.

 

See Supplement 1 for supporting content.

REFERENCES

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3. W. Chao, P. Fischer, T. Tyliszczak, S. Rekawa, E. Anderson, and P. Naulleau, Opt. Express 20, 9777 (2012). [CrossRef]  

4. A. Barannikov, M. Polikarpov, P. Ershov, V. Bessonov, K. Abrashitova, I. Snigireva, V. Yunkin, G. Bourenkov, T. Schneider, A. A. Fedyanin, and A. Snigirev, J. Synchrotron Radiat. 26, 714 (2019). [CrossRef]  

5. I. A. Artioukov, A. V. Vinogradov, V. E. Asadchikov, Y. S. Kas’yanov, R. V. Serov, A. I. Fedorenko, V. V. Kondratenko, and S. A. Yulin, Opt. Lett. 20, 2451 (1995). [CrossRef]  

6. K. Yamauchi, H. Mimura, K. Inagaki, and Y. Mori, Rev. Sci. Instrum. 73, 4028 (2002). [CrossRef]  

7. K. Yamauchi, K. Yamamura, H. Mimura, Y. Sano, A. Saito, K. Ueno, K. Endo, A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, and Y. Mori, Rev. Sci. Instrum. 74, 2894 (2003). [CrossRef]  

8. H. Mimura, H. Yumoto, S. Matsuyama, K. Yamamura, Y. Sano, K. Ueno, K. Endo, Y. Mori, M. Yabashi, K. Tamasaku, Y. Nishino, T. Ishikawa, and K. Yamauchi, Rev. Sci. Instrum. 76, 045102 (2005). [CrossRef]  

9. F. Meirer, J. Cabana, Y. Liu, A. Mehta, J. C. Andrews, and P. Pianetta, J. Synchrotron Rad. 18, 773 (2011). [CrossRef]  

10. M. Hoshino, T. Ishino, T. Namiki, N. Yamada, N. Watanabe, and S. Aoki, Rev. Sci. Instrum. 78, 073706 (2007). [CrossRef]  

11. R. Kodama, Y. Katori, T. Iwai, N. Ikeda, Y. Kato, and K. Takeshi, Opt. Lett. 21, 132 (1996). [CrossRef]  

12. R. Sauneuf, J. M. Dalmasso, T. Jalinaud, J. P. LeBreton, D. Schirmann, J. P. Marioge, F. Bridou, G. Tissot, and J. Y. Clotaire, Rev. Sci. Instrum. 68, 3412 (1997). [CrossRef]  

13. H. Wolter, Ann. Phys. 445, 94 (1952).

14. S. Egawa, H. Motoyama, A. Iwasaki, G. Yamaguchi, T. Kume, K. Yamanouchi, and H. Mimura, Opt. Lett. 45, 515 (2020). [CrossRef]  

15. S. Matsuyama, S. Yasuda, J. Yamada, H. Okada, Y. Kohmura, M. Yabashi, T. Ishikawa, and K. Yamauchi, Sci. Rep. 7, 46358 (2017). [CrossRef]  

16. S. Matsuyama, J. Yamada, Y. Kohmura, M. Yabashi, T. Ishikawa, and K. Yamauchi, Opt. Express 27, 18318 (2019). [CrossRef]  

17. J. Yamada, S. Matsuyama, Y. Sano, and K. Yamauchi, Appl. Opt. 56, 967 (2017). [CrossRef]  

18. J. Yamada, S. Matsuyama, Y. Sano, Y. Kohmura, M. Yabashi, T. Ishikawa, and K. Yamauchi, Opt. Express 27, 3429 (2019). [CrossRef]  

19. H. Ohashi, Y. Senba, H. Yumoto, T. Koyama, T. Miura, and H. Kishimoto, AIP Conf. Proc. 1741, 040023 (2016). [CrossRef]  

20. K. V. Falch, C. Detlefs, M. S. Christensen, D. Panganin, and R. Mathiesen, Opt. Express 27, 20311 (2019). [CrossRef]  

21. J. Salplachta, T. Zikmund, M. Horvath, Y. Takeda, K. Omote, L. Pina, and J. Kaiser, in 9th Conference on Industrial Computed Tomography (iCT) (2019).

22. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 2001).

23. L. G. Paratt, Phys. Rev. 95, 359 (1954). [CrossRef]  

24. K. Kumagai and A. Kurokawa, Microsc. Microanal. 22, 448 (2016). [CrossRef]  

25. H. H. Hopkins and P. M. Barham, Proc. Phys. Soc. B 63, 737 (1950). [CrossRef]  

26. S. Matsuyama, J. Yamada, K. Hata, Y. Kohmura, M. Yabashi, T. Ishikawa, and K. Yamauchi, Microsc. Microanal. 24, 284 (2018). [CrossRef]  

27. K. Yamauchi, H. Mimura, T. Kimura, H. Yumoto, S. Handa, S. Matsuyama, K. Arima, Y. Sano, K. Yamamura, K. Inagaki, H. Nakamori, J. Kim, K. Tamasaku, Y. Nishino, M. Yabashi, and T. Ishikawa, J. Phys. Condens. Matter 23, 394206 (2011). [CrossRef]  

References

  • View by:

  1. A. Skdinawat and D. Attwood, Nat. Photonics 4, 840 (2010).
    [Crossref]
  2. H. N. Chapman and K. A. Nugent, Nat. Photonics 4, 833 (2010).
    [Crossref]
  3. W. Chao, P. Fischer, T. Tyliszczak, S. Rekawa, E. Anderson, and P. Naulleau, Opt. Express 20, 9777 (2012).
    [Crossref]
  4. A. Barannikov, M. Polikarpov, P. Ershov, V. Bessonov, K. Abrashitova, I. Snigireva, V. Yunkin, G. Bourenkov, T. Schneider, A. A. Fedyanin, and A. Snigirev, J. Synchrotron Radiat. 26, 714 (2019).
    [Crossref]
  5. I. A. Artioukov, A. V. Vinogradov, V. E. Asadchikov, Y. S. Kas’yanov, R. V. Serov, A. I. Fedorenko, V. V. Kondratenko, and S. A. Yulin, Opt. Lett. 20, 2451 (1995).
    [Crossref]
  6. K. Yamauchi, H. Mimura, K. Inagaki, and Y. Mori, Rev. Sci. Instrum. 73, 4028 (2002).
    [Crossref]
  7. K. Yamauchi, K. Yamamura, H. Mimura, Y. Sano, A. Saito, K. Ueno, K. Endo, A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, and Y. Mori, Rev. Sci. Instrum. 74, 2894 (2003).
    [Crossref]
  8. H. Mimura, H. Yumoto, S. Matsuyama, K. Yamamura, Y. Sano, K. Ueno, K. Endo, Y. Mori, M. Yabashi, K. Tamasaku, Y. Nishino, T. Ishikawa, and K. Yamauchi, Rev. Sci. Instrum. 76, 045102 (2005).
    [Crossref]
  9. F. Meirer, J. Cabana, Y. Liu, A. Mehta, J. C. Andrews, and P. Pianetta, J. Synchrotron Rad. 18, 773 (2011).
    [Crossref]
  10. M. Hoshino, T. Ishino, T. Namiki, N. Yamada, N. Watanabe, and S. Aoki, Rev. Sci. Instrum. 78, 073706 (2007).
    [Crossref]
  11. R. Kodama, Y. Katori, T. Iwai, N. Ikeda, Y. Kato, and K. Takeshi, Opt. Lett. 21, 132 (1996).
    [Crossref]
  12. R. Sauneuf, J. M. Dalmasso, T. Jalinaud, J. P. LeBreton, D. Schirmann, J. P. Marioge, F. Bridou, G. Tissot, and J. Y. Clotaire, Rev. Sci. Instrum. 68, 3412 (1997).
    [Crossref]
  13. H. Wolter, Ann. Phys. 445, 94 (1952).
  14. S. Egawa, H. Motoyama, A. Iwasaki, G. Yamaguchi, T. Kume, K. Yamanouchi, and H. Mimura, Opt. Lett. 45, 515 (2020).
    [Crossref]
  15. S. Matsuyama, S. Yasuda, J. Yamada, H. Okada, Y. Kohmura, M. Yabashi, T. Ishikawa, and K. Yamauchi, Sci. Rep. 7, 46358 (2017).
    [Crossref]
  16. S. Matsuyama, J. Yamada, Y. Kohmura, M. Yabashi, T. Ishikawa, and K. Yamauchi, Opt. Express 27, 18318 (2019).
    [Crossref]
  17. J. Yamada, S. Matsuyama, Y. Sano, and K. Yamauchi, Appl. Opt. 56, 967 (2017).
    [Crossref]
  18. J. Yamada, S. Matsuyama, Y. Sano, Y. Kohmura, M. Yabashi, T. Ishikawa, and K. Yamauchi, Opt. Express 27, 3429 (2019).
    [Crossref]
  19. H. Ohashi, Y. Senba, H. Yumoto, T. Koyama, T. Miura, and H. Kishimoto, AIP Conf. Proc. 1741, 040023 (2016).
    [Crossref]
  20. K. V. Falch, C. Detlefs, M. S. Christensen, D. Panganin, and R. Mathiesen, Opt. Express 27, 20311 (2019).
    [Crossref]
  21. J. Salplachta, T. Zikmund, M. Horvath, Y. Takeda, K. Omote, L. Pina, and J. Kaiser, in 9th Conference on Industrial Computed Tomography (iCT) (2019).
  22. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 2001).
  23. L. G. Paratt, Phys. Rev. 95, 359 (1954).
    [Crossref]
  24. K. Kumagai and A. Kurokawa, Microsc. Microanal. 22, 448 (2016).
    [Crossref]
  25. H. H. Hopkins and P. M. Barham, Proc. Phys. Soc. B 63, 737 (1950).
    [Crossref]
  26. S. Matsuyama, J. Yamada, K. Hata, Y. Kohmura, M. Yabashi, T. Ishikawa, and K. Yamauchi, Microsc. Microanal. 24, 284 (2018).
    [Crossref]
  27. K. Yamauchi, H. Mimura, T. Kimura, H. Yumoto, S. Handa, S. Matsuyama, K. Arima, Y. Sano, K. Yamamura, K. Inagaki, H. Nakamori, J. Kim, K. Tamasaku, Y. Nishino, M. Yabashi, and T. Ishikawa, J. Phys. Condens. Matter 23, 394206 (2011).
    [Crossref]

2020 (1)

2019 (4)

2018 (1)

S. Matsuyama, J. Yamada, K. Hata, Y. Kohmura, M. Yabashi, T. Ishikawa, and K. Yamauchi, Microsc. Microanal. 24, 284 (2018).
[Crossref]

2017 (2)

J. Yamada, S. Matsuyama, Y. Sano, and K. Yamauchi, Appl. Opt. 56, 967 (2017).
[Crossref]

S. Matsuyama, S. Yasuda, J. Yamada, H. Okada, Y. Kohmura, M. Yabashi, T. Ishikawa, and K. Yamauchi, Sci. Rep. 7, 46358 (2017).
[Crossref]

2016 (2)

K. Kumagai and A. Kurokawa, Microsc. Microanal. 22, 448 (2016).
[Crossref]

H. Ohashi, Y. Senba, H. Yumoto, T. Koyama, T. Miura, and H. Kishimoto, AIP Conf. Proc. 1741, 040023 (2016).
[Crossref]

2012 (1)

2011 (2)

F. Meirer, J. Cabana, Y. Liu, A. Mehta, J. C. Andrews, and P. Pianetta, J. Synchrotron Rad. 18, 773 (2011).
[Crossref]

K. Yamauchi, H. Mimura, T. Kimura, H. Yumoto, S. Handa, S. Matsuyama, K. Arima, Y. Sano, K. Yamamura, K. Inagaki, H. Nakamori, J. Kim, K. Tamasaku, Y. Nishino, M. Yabashi, and T. Ishikawa, J. Phys. Condens. Matter 23, 394206 (2011).
[Crossref]

2010 (2)

A. Skdinawat and D. Attwood, Nat. Photonics 4, 840 (2010).
[Crossref]

H. N. Chapman and K. A. Nugent, Nat. Photonics 4, 833 (2010).
[Crossref]

2007 (1)

M. Hoshino, T. Ishino, T. Namiki, N. Yamada, N. Watanabe, and S. Aoki, Rev. Sci. Instrum. 78, 073706 (2007).
[Crossref]

2005 (1)

H. Mimura, H. Yumoto, S. Matsuyama, K. Yamamura, Y. Sano, K. Ueno, K. Endo, Y. Mori, M. Yabashi, K. Tamasaku, Y. Nishino, T. Ishikawa, and K. Yamauchi, Rev. Sci. Instrum. 76, 045102 (2005).
[Crossref]

2003 (1)

K. Yamauchi, K. Yamamura, H. Mimura, Y. Sano, A. Saito, K. Ueno, K. Endo, A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, and Y. Mori, Rev. Sci. Instrum. 74, 2894 (2003).
[Crossref]

2002 (1)

K. Yamauchi, H. Mimura, K. Inagaki, and Y. Mori, Rev. Sci. Instrum. 73, 4028 (2002).
[Crossref]

1997 (1)

R. Sauneuf, J. M. Dalmasso, T. Jalinaud, J. P. LeBreton, D. Schirmann, J. P. Marioge, F. Bridou, G. Tissot, and J. Y. Clotaire, Rev. Sci. Instrum. 68, 3412 (1997).
[Crossref]

1996 (1)

R. Kodama, Y. Katori, T. Iwai, N. Ikeda, Y. Kato, and K. Takeshi, Opt. Lett. 21, 132 (1996).
[Crossref]

1995 (1)

1954 (1)

L. G. Paratt, Phys. Rev. 95, 359 (1954).
[Crossref]

1952 (1)

H. Wolter, Ann. Phys. 445, 94 (1952).

1950 (1)

H. H. Hopkins and P. M. Barham, Proc. Phys. Soc. B 63, 737 (1950).
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K. Yamauchi, K. Yamamura, H. Mimura, Y. Sano, A. Saito, K. Ueno, K. Endo, A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, and Y. Mori, Rev. Sci. Instrum. 74, 2894 (2003).
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R. Sauneuf, J. M. Dalmasso, T. Jalinaud, J. P. LeBreton, D. Schirmann, J. P. Marioge, F. Bridou, G. Tissot, and J. Y. Clotaire, Rev. Sci. Instrum. 68, 3412 (1997).
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H. Mimura, H. Yumoto, S. Matsuyama, K. Yamamura, Y. Sano, K. Ueno, K. Endo, Y. Mori, M. Yabashi, K. Tamasaku, Y. Nishino, T. Ishikawa, and K. Yamauchi, Rev. Sci. Instrum. 76, 045102 (2005).
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S. Matsuyama, J. Yamada, Y. Kohmura, M. Yabashi, T. Ishikawa, and K. Yamauchi, Opt. Express 27, 18318 (2019).
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J. Yamada, S. Matsuyama, Y. Sano, and K. Yamauchi, Appl. Opt. 56, 967 (2017).
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S. Matsuyama, S. Yasuda, J. Yamada, H. Okada, Y. Kohmura, M. Yabashi, T. Ishikawa, and K. Yamauchi, Sci. Rep. 7, 46358 (2017).
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K. Yamauchi, H. Mimura, T. Kimura, H. Yumoto, S. Handa, S. Matsuyama, K. Arima, Y. Sano, K. Yamamura, K. Inagaki, H. Nakamori, J. Kim, K. Tamasaku, Y. Nishino, M. Yabashi, and T. Ishikawa, J. Phys. Condens. Matter 23, 394206 (2011).
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K. Yamauchi, H. Mimura, K. Inagaki, and Y. Mori, Rev. Sci. Instrum. 73, 4028 (2002).
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H. Mimura, H. Yumoto, S. Matsuyama, K. Yamamura, Y. Sano, K. Ueno, K. Endo, Y. Mori, M. Yabashi, K. Tamasaku, Y. Nishino, T. Ishikawa, and K. Yamauchi, Rev. Sci. Instrum. 76, 045102 (2005).
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Ann. Phys. (1)

H. Wolter, Ann. Phys. 445, 94 (1952).

Appl. Opt. (1)

J. Phys. Condens. Matter (1)

K. Yamauchi, H. Mimura, T. Kimura, H. Yumoto, S. Handa, S. Matsuyama, K. Arima, Y. Sano, K. Yamamura, K. Inagaki, H. Nakamori, J. Kim, K. Tamasaku, Y. Nishino, M. Yabashi, and T. Ishikawa, J. Phys. Condens. Matter 23, 394206 (2011).
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K. Yamauchi, H. Mimura, K. Inagaki, and Y. Mori, Rev. Sci. Instrum. 73, 4028 (2002).
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K. Yamauchi, K. Yamamura, H. Mimura, Y. Sano, A. Saito, K. Ueno, K. Endo, A. Souvorov, M. Yabashi, K. Tamasaku, T. Ishikawa, and Y. Mori, Rev. Sci. Instrum. 74, 2894 (2003).
[Crossref]

H. Mimura, H. Yumoto, S. Matsuyama, K. Yamamura, Y. Sano, K. Ueno, K. Endo, Y. Mori, M. Yabashi, K. Tamasaku, Y. Nishino, T. Ishikawa, and K. Yamauchi, Rev. Sci. Instrum. 76, 045102 (2005).
[Crossref]

M. Hoshino, T. Ishino, T. Namiki, N. Yamada, N. Watanabe, and S. Aoki, Rev. Sci. Instrum. 78, 073706 (2007).
[Crossref]

R. Sauneuf, J. M. Dalmasso, T. Jalinaud, J. P. LeBreton, D. Schirmann, J. P. Marioge, F. Bridou, G. Tissot, and J. Y. Clotaire, Rev. Sci. Instrum. 68, 3412 (1997).
[Crossref]

Sci. Rep. (1)

S. Matsuyama, S. Yasuda, J. Yamada, H. Okada, Y. Kohmura, M. Yabashi, T. Ishikawa, and K. Yamauchi, Sci. Rep. 7, 46358 (2017).
[Crossref]

Other (2)

J. Salplachta, T. Zikmund, M. Horvath, Y. Takeda, K. Omote, L. Pina, and J. Kaiser, in 9th Conference on Industrial Computed Tomography (iCT) (2019).

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 2001).

Supplementary Material (1)

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Supplement 1       Supplemental document for providing additional information

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Figures (4)

Fig. 1.
Fig. 1. (a) Arrangement of the objective mirrors combining AKB-I and AKB-III optics. The “ell.” (“hyp.”) is an abbreviation of “ellipse” (“hyperbola”). (b) Cross sections of (a).
Fig. 2.
Fig. 2. (a) Photograph of the developed objective mirrors. (b) Schematic drawing of the experimental setup.
Fig. 3.
Fig. 3. (a) X-ray images of the Siemens star obtained after the first tuning of mirrors and after 33.5 h. The exposures were for 30 s with a 0.25-mm Si attenuator whose transmittance was 57% at 15 keV. The minimum line width denotes 50 nm. (b) Results of the PSA. The “Ratio (V)” [“Ratio (H)”] in the graph means ratio between the “Vertical” (“Horizontal”) and the “Empty (V)” [“Empty (H)”]. The black dashed line indicates ratio of 1.0. The red and blue dashed lines indicate vertical and horizontal cutoff frequencies, corresponding to full periods of 71 and 87 nm, respectively. (c) Photon energy dependence between 9 and 15 keV. The exposures are for 30 s using a 0.25-mm Si attenuator for all images. The expected resolutions for 15, 12, and 9 keV are 67.8, 84.7, and 113.0 nm, respectively. The bars denote 2 µm.
Fig. 4.
Fig. 4. (a) Images of dot patterns on a 775-µm Si substrate with rotation angles of 0° (left) and 59.85° (right) at an x-ray energy of 15 keV. The exposures are for 10 s. (b) In-plane sliced (left) and vertically sliced (right) images of the CT reconstruction. The bars denote 2 µm.

Tables (1)

Tables Icon

Table 1. Design Parameters for the Objective Mirror

Metrics