{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T18:06:15Z","timestamp":1774029975244,"version":"3.50.1"},"reference-count":42,"publisher":"MDPI AG","issue":"24","license":[{"start":{"date-parts":[[2020,12,21]],"date-time":"2020-12-21T00:00:00Z","timestamp":1608508800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["JP19K23434"],"award-info":[{"award-number":["JP19K23434"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["JP17H01073"],"award-info":[{"award-number":["JP17H01073"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["JP20K21146"],"award-info":[{"award-number":["JP20K21146"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["JP16H06358"],"award-info":[{"award-number":["JP16H06358"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>X-ray single-grating interferometry was applied to conduct accurate wavefront corrections for hard X-ray nanofocusing mirrors. Systematic errors in the interferometer, originating from a grating, a detector, and alignment errors of the components, were carefully examined. Based on the measured wavefront errors, the mirror shapes were directly corrected using a differential deposition technique. The corrected X-ray focusing mirrors with a numerical aperture of 0.01 attained two-dimensionally diffraction-limited performance. The results of the correction indicate that the uncertainty of the wavefront measurement was less than \u03bb\/72 in root-mean-square value.<\/jats:p>","DOI":"10.3390\/s20247356","type":"journal-article","created":{"date-parts":[[2020,12,21]],"date-time":"2020-12-21T20:42:01Z","timestamp":1608583321000},"page":"7356","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["X-Ray Single-Grating Interferometry for Wavefront Measurement and Correction of Hard X-Ray Nanofocusing Mirrors"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5476-4327","authenticated-orcid":false,"given":"Jumpei","family":"Yamada","sequence":"first","affiliation":[{"name":"RIKEN SPring-8 Center, 1-1-1 Kouto, Sayo, Hyogo 679-5148, Japan"},{"name":"Division of Precision Engineering and Applied Physics, Graduate School of Engineering, Osaka University, 2-1 Yamada-oka, Suita, Osaka 565-0871, Japan"}]},{"given":"Takato","family":"Inoue","sequence":"additional","affiliation":[{"name":"Division of Precision Engineering and Applied Physics, Graduate School of Engineering, Osaka University, 2-1 Yamada-oka, Suita, Osaka 565-0871, Japan"}]},{"given":"Nami","family":"Nakamura","sequence":"additional","affiliation":[{"name":"Division of Precision Engineering and Applied Physics, Graduate School of Engineering, Osaka University, 2-1 Yamada-oka, Suita, Osaka 565-0871, Japan"}]},{"given":"Takashi","family":"Kameshima","sequence":"additional","affiliation":[{"name":"RIKEN SPring-8 Center, 1-1-1 Kouto, Sayo, Hyogo 679-5148, Japan"},{"name":"Japan Synchrotron Radiation Research Institute, 1-1-1 Kouto, Sayo, Hyogo 679-5148, Japan"}]},{"given":"Kazuto","family":"Yamauchi","sequence":"additional","affiliation":[{"name":"Division of Precision Engineering and Applied Physics, Graduate School of Engineering, Osaka University, 2-1 Yamada-oka, Suita, Osaka 565-0871, Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9567-9690","authenticated-orcid":false,"given":"Satoshi","family":"Matsuyama","sequence":"additional","affiliation":[{"name":"Division of Precision Engineering and Applied Physics, Graduate School of Engineering, Osaka University, 2-1 Yamada-oka, Suita, Osaka 565-0871, Japan"},{"name":"Department of Materials Physics, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa, Nagoya 464-8603, Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2472-1684","authenticated-orcid":false,"given":"Makina","family":"Yabashi","sequence":"additional","affiliation":[{"name":"RIKEN SPring-8 Center, 1-1-1 Kouto, Sayo, Hyogo 679-5148, Japan"},{"name":"Japan Synchrotron Radiation Research Institute, 1-1-1 Kouto, Sayo, Hyogo 679-5148, Japan"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"394206","DOI":"10.1088\/0953-8984\/23\/39\/394206","article-title":"Single-nanometer focusing of hard x-rays by Kirkpatrick\u2013Baez mirrors","volume":"23","author":"Yamauchi","year":"2011","journal-title":"J. Phys. Condens. Matter"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"19311","DOI":"10.1364\/OE.21.019311","article-title":"Sub-5 nm hard x-ray point focusing by a combined Kirkpatrick-Baez mirror and multilayer zone plate","volume":"21","author":"Robisch","year":"2013","journal-title":"Opt. Express"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"43624","DOI":"10.1038\/srep43624","article-title":"Interlaced zone plate optics for hard X-ray imaging in the 10 nm range","volume":"7","author":"Mohacsi","year":"2017","journal-title":"Sci. Rep."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"17162","DOI":"10.1038\/lsa.2017.162","article-title":"X-ray focusing with efficient high-NA multilayer Laue lenses","volume":"7","author":"Bajt","year":"2018","journal-title":"Light Sci. Appl."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"115610","DOI":"10.1088\/2040-8986\/abb9c2","article-title":"A ray-trace analysis of x-ray multilayer Laue lenses for nanometer focusing","volume":"22","author":"Chapman","year":"2020","journal-title":"J. Opt."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1038\/nphys1457","article-title":"Breaking the 10 nm barrier in hard-X-ray focusing","volume":"6","author":"Mimura","year":"2010","journal-title":"Nat. Phys."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"18440","DOI":"10.1038\/s41598-018-35611-0","article-title":"Nanofocusing of X-ray free-electron laser using wavefront-corrected multilayer focusing mirrors","volume":"8","author":"Matsuyama","year":"2018","journal-title":"Sci. Rep."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"072503","DOI":"10.1143\/JJAP.48.072503","article-title":"Wavefront control system for phase compensation in hard X-ray optics","volume":"48","author":"Kimura","year":"2009","journal-title":"Jpn. J. Appl. Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"14623","DOI":"10.1038\/ncomms14623","article-title":"Perfect X-ray focusing via fitting corrective glasses to aberrated optics","volume":"8","author":"Seiboth","year":"2017","journal-title":"Nat. Commun."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1484","DOI":"10.1364\/OPTICA.6.001484","article-title":"Adaptable refractive correctors for x-ray optics","volume":"12","author":"Laundy","year":"2019","journal-title":"Optica"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"054101","DOI":"10.1063\/1.1857066","article-title":"X-ray wavefront analysis and optics characterization with a grating interferometer","volume":"86","author":"Weitkamp","year":"2005","journal-title":"Appl. Phys. Lett."},{"key":"ref_12","first-page":"161","article-title":"X-ray active mirror coupled with a Hartmann wavefront sensor","volume":"616","author":"Idir","year":"2006","journal-title":"Nucl. Instrum. Methods Phys. Res. A"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"158102","DOI":"10.1103\/PhysRevLett.108.158102","article-title":"Two-Dimensional X-Ray beam phase sensing","volume":"108","author":"Ziegler","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"886","DOI":"10.1107\/S1600577515005433","article-title":"X-ray pulse wavefront metrology using speckle tracking","volume":"22","author":"Berujon","year":"2015","journal-title":"J. Synchrotron Rad."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1105","DOI":"10.1107\/S160057751401323X","article-title":"Ronchi test for characterization of X-ray nanofocusing optics and beamlines","volume":"21","author":"Nilsson","year":"2014","journal-title":"J. Synchrotron Rad."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1256","DOI":"10.1016\/j.ultramic.2009.05.012","article-title":"An improved ptychographical phase retrieval algorithm for diffractive imaging","volume":"109","author":"Maiden","year":"2009","journal-title":"Ultramicroscopy"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1016\/j.ultramic.2010.01.004","article-title":"Ptychographic characterization of the wavefield in the focus of reflective hard X-ray optics","volume":"110","author":"Kewish","year":"2010","journal-title":"Ultramicroscopy"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"11552","DOI":"10.1364\/OE.22.011552","article-title":"Reconstruction of wave front and object for inline holography from a set of detection planes","volume":"22","author":"Hagemann","year":"2014","journal-title":"Opt. Express"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"498","DOI":"10.1107\/S160057751700128X","article-title":"Probe reconstruction for holographic X-ray imaging","volume":"24","author":"Hagemann","year":"2017","journal-title":"J. Synchrotron Rad."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3089","DOI":"10.1116\/1.588328","article-title":"Alignment of a multilayer-coated imaging system using extreme ultraviolet Foucault and Ronchi interferometric testing","volume":"13","author":"Ng","year":"1995","journal-title":"J. Vac. Sci. Technol. B"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2939","DOI":"10.1116\/1.1321290","article-title":"Extreme ultraviolet carrier-frequency shearing interferometry of a lithographic four-mirror optical system","volume":"18","author":"Naulleau","year":"2000","journal-title":"J. Vac. Sci. Technol. B"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"24977","DOI":"10.1364\/OE.20.024977","article-title":"Wavefront measurement for a hard-X-ray nanobeam using single-grating interferometry","volume":"20","author":"Matsuyama","year":"2012","journal-title":"Opt. Express"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"033603","DOI":"10.1117\/1.OE.52.3.033603","article-title":"Methodology for optimal in situ alignment and setting of bendable optics for nearly diffraction-limited focusing of soft x-rays","volume":"52","author":"Merthe","year":"2013","journal-title":"Opt. Eng."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1520","DOI":"10.1063\/1.2436354","article-title":"Wavefront metrology for EUV projection optics by soft X-ray interferometry in the NewSUBARU","volume":"879","author":"Niibe","year":"2007","journal-title":"AIP Conf. Proc."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"967","DOI":"10.1364\/OPTICA.5.000967","article-title":"High-accuracy wavefront sensing for x-ray free electron lasers","volume":"5","author":"Liu","year":"2018","journal-title":"Optica"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"043106","DOI":"10.1063\/1.5026440","article-title":"Systematic-error-free wavefront measurement using an X-ray single-grating interferometer","volume":"89","author":"Inoue","year":"2018","journal-title":"Rev. Sci. Instrum."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"254","DOI":"10.1107\/S1600577519017107","article-title":"X-ray free-electron laser wavefront sensing using the fractional Talbot effect","volume":"27","author":"Liu","year":"2020","journal-title":"J. Synchrotron Rad."},{"key":"ref_28","unstructured":"Yamada, J., Matsuyama, S., Inoue, T., Nakamura, N., Osaka, T., Inoue, I., Inubushi, Y., Tono, K., Yumoto, H., and Koyama, T. (2019, January 23\u201327). Development of XFEL sub-10 nm focusing mirrors at SACLA: Wavefront-corrected multilayer KB system and upgrade to advanced KB system. Proceedings of the RIAO-OPTILAS-MOPM 2019, Cancun, Mexico."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1019","DOI":"10.1002\/sia.2812","article-title":"Highly accurate differential deposition for X-ray reflective optics","volume":"40","author":"Handa","year":"2008","journal-title":"Surf. Interface Anal."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"180801","DOI":"10.1103\/PhysRevLett.103.180801","article-title":"Hard-X-ray phase-difference microscopy using a Fresnel zone plate and a transmission grating","volume":"103","author":"Yashiro","year":"2009","journal-title":"Phys. Rev. Lett."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1364\/JOSA.72.000156","article-title":"Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry","volume":"72","author":"Takeda","year":"1982","journal-title":"J. Opt. Soc. Am."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"2693","DOI":"10.1364\/AO.13.002693","article-title":"Digital wavefront measuring interferometer for testing optical surfaces and lenses","volume":"13","author":"Bruning","year":"1974","journal-title":"Appl. Opt."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"3631","DOI":"10.1364\/AO.24.003631","article-title":"Electrooptic holography and its application to hologram interferometry","volume":"24","author":"Setson","year":"1985","journal-title":"Appl. Opt."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"5254","DOI":"10.1143\/JJAP.45.5254","article-title":"Phase tomography by X-ray talbot interferometry for biological imaging","volume":"45","author":"Momose","year":"2006","journal-title":"Jpn. J. Appl. Phys."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"L89","DOI":"10.1143\/JJAP.46.L89","article-title":"X-ray phase imaging with single phase grating","volume":"3","author":"Takeda","year":"2007","journal-title":"Jpn. J. Appl. Phys."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2025","DOI":"10.1364\/JOSAA.25.002025","article-title":"Efficiency of capturing a phase image using cone-beam x-ray Talbot interferometry","volume":"8","author":"Yashiro","year":"2008","journal-title":"J. Opt. Soc. Am. A."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.optlaseng.2014.07.002","article-title":"Comparison of two-dimensional integration methods for shape reconstruction from gradient data","volume":"64","author":"Huang","year":"2015","journal-title":"Opt. Laser. Eng."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1117\/12.411621","article-title":"1-km beamline at SPring-8","volume":"4145","author":"Ishikawa","year":"2001","journal-title":"Proc. SPIE"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"5698","DOI":"10.1364\/AO.51.005698","article-title":"Noniterative boundary-artifact-free wavefront reconstruction from its derivatives","volume":"23","author":"Bon","year":"2012","journal-title":"Appl. Opt."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"967","DOI":"10.1364\/AO.56.000967","article-title":"Simulation of concave\u2013convex imaging mirror system for development of a compact and achromatic full-field x-ray microscope","volume":"56","author":"Yamada","year":"2017","journal-title":"Appl. Opt."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"3429","DOI":"10.1364\/OE.27.003429","article-title":"Compact reflective imaging optics in hard X-ray region based on concave and convex mirrors","volume":"27","author":"Yamada","year":"2019","journal-title":"Opt. Express"},{"key":"ref_42","unstructured":"Born, M., and Wolf, E. (2001). Principles of Optics, Cambridge University Press. [7th ed.]."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/24\/7356\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:48:09Z","timestamp":1760179689000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/24\/7356"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,21]]},"references-count":42,"journal-issue":{"issue":"24","published-online":{"date-parts":[[2020,12]]}},"alternative-id":["s20247356"],"URL":"https:\/\/doi.org\/10.3390\/s20247356","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,12,21]]}}}