Abstract

In this paper, a two-dimensional stitching interferometry system using two tiltmeters is proposed. During the scanning and the measurement, one tiltmeter stays with the interferometer and the other one is attached to the translation stage where the surface under test is placed. The differences of the x- and y-tilt readings between these two tiltmeters are recorded as the relative tilt between interferometer and surface under test. The relative tilt in both x- and y-directions are used to correct the surface tip/tilt of each subset, and then the piston is adjusted to get the final stitching surface map. As an example, a stitching result of a 125mm-long mirror surface is presented. The repeatability of our current stitching system is about 1.48 nm RMS. The stitching result is compared to the result of a one-dimensional angular-measurement-based stitching method to discuss the merits and limitation of the proposed method.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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  5. Y. Wen, H. Cheng, H.-Y. Tam, and D. Zhou, “Modified stitching algorithm for annular subaperture stitching interferometry for aspheric surfaces,” Appl. Opt. 52(23), 5686–5694 (2013).
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    [Crossref]
  7. M. Otsubo, K. Okada, and J. Tsujiuchi, “Measurement of large plane surface shapes by connecting small-aperture interferograms,” Opt. Eng. 33(2), 608–613 (1994).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  12. H. Yumoto, H. Mimura, T. Kimura, S. Handa, S. Matsuyama, Y. Sano, and K. Yamauchi, “Stitching interferometric metrology for steeply curved x-ray mirrors,” Surf. Interface Analysis 40(6–7), 1023–1027 (2008).
    [Crossref]
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    [Crossref] [PubMed]
  18. L. Huang, J. Xue, B. Gao, and M. Idir, “One-dimensional angular-measurement-based stitching interferometry,” Opt. Express 26(8), 9882–9892 (2018).
    [Crossref] [PubMed]
  19. G. Ehret, S. Laubach, and M. Schulz, “Flatness metrology based on small-angle deflectometric procedures with electronic tiltmeters,” Proc. SPIE 10326, 1032604 (2017).
    [Crossref]
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    [Crossref] [PubMed]

2018 (1)

2017 (2)

G. Ehret, S. Laubach, and M. Schulz, “Flatness metrology based on small-angle deflectometric procedures with electronic tiltmeters,” Proc. SPIE 10326, 1032604 (2017).
[Crossref]

J. Xue, L. Huang, B. Gao, K. Kaznatcheev, and M. Idir, “One-dimensional stitching interferometry assisted by a triple-beam interferometer,” Opt. Express 25(8), 9393–9405 (2017).
[Crossref] [PubMed]

2016 (1)

A. Vivo, B. Lantelme, R. Baker, and R. Barrett, “Stitching methods at the European Synchrotron Radiation Facility (ESRF),” Rev. Sci. Instruments 87(5), 051908 (2016).
[Crossref]

2015 (2)

H. Yiwei, X. Hou, Q. Haiyang, and W. Song, “Retrace error reconstruction based on point characteristic function,” Opt. Express 23(22), 28216–28223 (2015).
[Crossref] [PubMed]

J. Peng, Q. Wang, X. Peng, and Y. Yu, “Stitching interferometry of high numerical aperture cylindrical optics without using a fringe-nulling routine,” J. Opt. Soc. Am. A 33(11), 1964–1972 (2015).
[Crossref]

2014 (1)

2013 (3)

2010 (2)

H. Yumoto, H. Mimura, S. Handa, T. Kimura, S. Matsuyama, Y. Sano, H. Ohashi, K. Yamauchi, and T. Ishikawa, “Stitching-angle measurable microscopic-interferometer: Surface-figure metrology tool for hard X-ray nanofocusing mirrors with large curvature,” Nucl. Instruments Methods Phys. Res. Sect. A: Accel. Spectrometers, Detect. Assoc. Equip. 616, (2)203–206 (2010).
[Crossref]

T. Kimura, H. Ohashi, H. Mimura, D. Yamakawa, H. Yumoto, S. Matsuyama, T. Tsumura, H. Okada, T. Masunaga, Y. Senba, S. Goto, T. Ishikawa, and K. Yamauchi, “A stitching figure profiler of large X-ray mirrors using RADSI for subaperture data acquisition,” Nucl. Instruments Methods Phys. Res. Sect. A: Accel. Spectrometers, Detect. Assoc. Equip. 616, (2)229–232 (2010).
[Crossref]

2008 (1)

H. Yumoto, H. Mimura, T. Kimura, S. Handa, S. Matsuyama, Y. Sano, and K. Yamauchi, “Stitching interferometric metrology for steeply curved x-ray mirrors,” Surf. Interface Analysis 40(6–7), 1023–1027 (2008).
[Crossref]

2006 (1)

C. Elster, I. Weingärtner, and M. Schulz, “Coupled distance sensor systems for high-accuracy topography measurement: Accounting for scanning stage and systematic sensor errors,” Precis. Eng. 30(1), 32–38 (2006).
[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, “Relative angle determinable stitching interferometry for hard x-ray reflective optics,” Rev. Sci. Instruments 76(4), 045102 (2005).
[Crossref]

2003 (3)

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, “Microstitching interferometry for x-ray reflective optics,” Rev. Sci. Instruments 74(5), 2894–2898 (2003).
[Crossref]

M. Schulz, I. Weingaertner, C. Elster, and J. Gerhardt, “Low- and mid-spatial-frequency component measurement for aspheres,” Proc. SPIE 5188, 287–295 (2003).
[Crossref]

P. Murphy, G. Forbes, J. Fleig, P. Dumas, and M. Tricard, “Stitching interferometry: a flexible solution for surface metrology,” Opt. Photonics News 14(5), 38–43 (2003).
[Crossref]

1999 (1)

M. Bray, “Stitching interferometry: how and why it works,” Proc. SPIE 3739, 259–273 (1999).
[Crossref]

1994 (1)

M. Otsubo, K. Okada, and J. Tsujiuchi, “Measurement of large plane surface shapes by connecting small-aperture interferograms,” Opt. Eng. 33(2), 608–613 (1994).
[Crossref]

Asundi, A. K.

Baker, R.

A. Vivo, B. Lantelme, R. Baker, and R. Barrett, “Stitching methods at the European Synchrotron Radiation Facility (ESRF),” Rev. Sci. Instruments 87(5), 051908 (2016).
[Crossref]

Barrett, R.

A. Vivo, B. Lantelme, R. Baker, and R. Barrett, “Stitching methods at the European Synchrotron Radiation Facility (ESRF),” Rev. Sci. Instruments 87(5), 051908 (2016).
[Crossref]

Bray, M.

M. Bray, “Stitching interferometry: how and why it works,” Proc. SPIE 3739, 259–273 (1999).
[Crossref]

Cheng, H.

Dovillaire, G.

Dumas, P.

P. Murphy, G. Forbes, J. Fleig, P. Dumas, and M. Tricard, “Stitching interferometry: a flexible solution for surface metrology,” Opt. Photonics News 14(5), 38–43 (2003).
[Crossref]

Ehret, G.

G. Ehret, S. Laubach, and M. Schulz, “Flatness metrology based on small-angle deflectometric procedures with electronic tiltmeters,” Proc. SPIE 10326, 1032604 (2017).
[Crossref]

Elster, C.

C. Elster, I. Weingärtner, and M. Schulz, “Coupled distance sensor systems for high-accuracy topography measurement: Accounting for scanning stage and systematic sensor errors,” Precis. Eng. 30(1), 32–38 (2006).
[Crossref]

M. Schulz, I. Weingaertner, C. Elster, and J. Gerhardt, “Low- and mid-spatial-frequency component measurement for aspheres,” Proc. SPIE 5188, 287–295 (2003).
[Crossref]

Endo, K.

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, “Relative angle determinable stitching interferometry for hard x-ray reflective optics,” Rev. Sci. Instruments 76(4), 045102 (2005).
[Crossref]

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, “Microstitching interferometry for x-ray reflective optics,” Rev. Sci. Instruments 74(5), 2894–2898 (2003).
[Crossref]

Fleig, J.

P. Murphy, G. Forbes, J. Fleig, P. Dumas, and M. Tricard, “Stitching interferometry: a flexible solution for surface metrology,” Opt. Photonics News 14(5), 38–43 (2003).
[Crossref]

Forbes, G.

P. Murphy, G. Forbes, J. Fleig, P. Dumas, and M. Tricard, “Stitching interferometry: a flexible solution for surface metrology,” Opt. Photonics News 14(5), 38–43 (2003).
[Crossref]

Gao, B.

Gerhardt, J.

M. Schulz, I. Weingaertner, C. Elster, and J. Gerhardt, “Low- and mid-spatial-frequency component measurement for aspheres,” Proc. SPIE 5188, 287–295 (2003).
[Crossref]

Goto, S.

T. Kimura, H. Ohashi, H. Mimura, D. Yamakawa, H. Yumoto, S. Matsuyama, T. Tsumura, H. Okada, T. Masunaga, Y. Senba, S. Goto, T. Ishikawa, and K. Yamauchi, “A stitching figure profiler of large X-ray mirrors using RADSI for subaperture data acquisition,” Nucl. Instruments Methods Phys. Res. Sect. A: Accel. Spectrometers, Detect. Assoc. Equip. 616, (2)229–232 (2010).
[Crossref]

Haiyang, Q.

Handa, S.

H. Yumoto, H. Mimura, S. Handa, T. Kimura, S. Matsuyama, Y. Sano, H. Ohashi, K. Yamauchi, and T. Ishikawa, “Stitching-angle measurable microscopic-interferometer: Surface-figure metrology tool for hard X-ray nanofocusing mirrors with large curvature,” Nucl. Instruments Methods Phys. Res. Sect. A: Accel. Spectrometers, Detect. Assoc. Equip. 616, (2)203–206 (2010).
[Crossref]

H. Yumoto, H. Mimura, T. Kimura, S. Handa, S. Matsuyama, Y. Sano, and K. Yamauchi, “Stitching interferometric metrology for steeply curved x-ray mirrors,” Surf. Interface Analysis 40(6–7), 1023–1027 (2008).
[Crossref]

Hou, X.

Huang, L.

Idir, M.

Ishikawa, T.

T. Kimura, H. Ohashi, H. Mimura, D. Yamakawa, H. Yumoto, S. Matsuyama, T. Tsumura, H. Okada, T. Masunaga, Y. Senba, S. Goto, T. Ishikawa, and K. Yamauchi, “A stitching figure profiler of large X-ray mirrors using RADSI for subaperture data acquisition,” Nucl. Instruments Methods Phys. Res. Sect. A: Accel. Spectrometers, Detect. Assoc. Equip. 616, (2)229–232 (2010).
[Crossref]

H. Yumoto, H. Mimura, S. Handa, T. Kimura, S. Matsuyama, Y. Sano, H. Ohashi, K. Yamauchi, and T. Ishikawa, “Stitching-angle measurable microscopic-interferometer: Surface-figure metrology tool for hard X-ray nanofocusing mirrors with large curvature,” Nucl. Instruments Methods Phys. Res. Sect. A: Accel. Spectrometers, Detect. Assoc. Equip. 616, (2)203–206 (2010).
[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, “Relative angle determinable stitching interferometry for hard x-ray reflective optics,” Rev. Sci. Instruments 76(4), 045102 (2005).
[Crossref]

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, “Microstitching interferometry for x-ray reflective optics,” Rev. Sci. Instruments 74(5), 2894–2898 (2003).
[Crossref]

Kaznatcheev, K.

Kimura, T.

T. Kimura, H. Ohashi, H. Mimura, D. Yamakawa, H. Yumoto, S. Matsuyama, T. Tsumura, H. Okada, T. Masunaga, Y. Senba, S. Goto, T. Ishikawa, and K. Yamauchi, “A stitching figure profiler of large X-ray mirrors using RADSI for subaperture data acquisition,” Nucl. Instruments Methods Phys. Res. Sect. A: Accel. Spectrometers, Detect. Assoc. Equip. 616, (2)229–232 (2010).
[Crossref]

H. Yumoto, H. Mimura, S. Handa, T. Kimura, S. Matsuyama, Y. Sano, H. Ohashi, K. Yamauchi, and T. Ishikawa, “Stitching-angle measurable microscopic-interferometer: Surface-figure metrology tool for hard X-ray nanofocusing mirrors with large curvature,” Nucl. Instruments Methods Phys. Res. Sect. A: Accel. Spectrometers, Detect. Assoc. Equip. 616, (2)203–206 (2010).
[Crossref]

H. Yumoto, H. Mimura, T. Kimura, S. Handa, S. Matsuyama, Y. Sano, and K. Yamauchi, “Stitching interferometric metrology for steeply curved x-ray mirrors,” Surf. Interface Analysis 40(6–7), 1023–1027 (2008).
[Crossref]

Kreischer, C. B.

C. B. Kreischer, “Retrace error: interferometry’s dark little secret,” Proc. SPIE 8884, 88840X (2013).
[Crossref]

Lantelme, B.

A. Vivo, B. Lantelme, R. Baker, and R. Barrett, “Stitching methods at the European Synchrotron Radiation Facility (ESRF),” Rev. Sci. Instruments 87(5), 051908 (2016).
[Crossref]

Laubach, S.

G. Ehret, S. Laubach, and M. Schulz, “Flatness metrology based on small-angle deflectometric procedures with electronic tiltmeters,” Proc. SPIE 10326, 1032604 (2017).
[Crossref]

Legrand, J.

Masunaga, T.

T. Kimura, H. Ohashi, H. Mimura, D. Yamakawa, H. Yumoto, S. Matsuyama, T. Tsumura, H. Okada, T. Masunaga, Y. Senba, S. Goto, T. Ishikawa, and K. Yamauchi, “A stitching figure profiler of large X-ray mirrors using RADSI for subaperture data acquisition,” Nucl. Instruments Methods Phys. Res. Sect. A: Accel. Spectrometers, Detect. Assoc. Equip. 616, (2)229–232 (2010).
[Crossref]

Matsuyama, S.

T. Kimura, H. Ohashi, H. Mimura, D. Yamakawa, H. Yumoto, S. Matsuyama, T. Tsumura, H. Okada, T. Masunaga, Y. Senba, S. Goto, T. Ishikawa, and K. Yamauchi, “A stitching figure profiler of large X-ray mirrors using RADSI for subaperture data acquisition,” Nucl. Instruments Methods Phys. Res. Sect. A: Accel. Spectrometers, Detect. Assoc. Equip. 616, (2)229–232 (2010).
[Crossref]

H. Yumoto, H. Mimura, S. Handa, T. Kimura, S. Matsuyama, Y. Sano, H. Ohashi, K. Yamauchi, and T. Ishikawa, “Stitching-angle measurable microscopic-interferometer: Surface-figure metrology tool for hard X-ray nanofocusing mirrors with large curvature,” Nucl. Instruments Methods Phys. Res. Sect. A: Accel. Spectrometers, Detect. Assoc. Equip. 616, (2)203–206 (2010).
[Crossref]

H. Yumoto, H. Mimura, T. Kimura, S. Handa, S. Matsuyama, Y. Sano, and K. Yamauchi, “Stitching interferometric metrology for steeply curved x-ray mirrors,” Surf. Interface Analysis 40(6–7), 1023–1027 (2008).
[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, “Relative angle determinable stitching interferometry for hard x-ray reflective optics,” Rev. Sci. Instruments 76(4), 045102 (2005).
[Crossref]

Mimura, H.

T. Kimura, H. Ohashi, H. Mimura, D. Yamakawa, H. Yumoto, S. Matsuyama, T. Tsumura, H. Okada, T. Masunaga, Y. Senba, S. Goto, T. Ishikawa, and K. Yamauchi, “A stitching figure profiler of large X-ray mirrors using RADSI for subaperture data acquisition,” Nucl. Instruments Methods Phys. Res. Sect. A: Accel. Spectrometers, Detect. Assoc. Equip. 616, (2)229–232 (2010).
[Crossref]

H. Yumoto, H. Mimura, S. Handa, T. Kimura, S. Matsuyama, Y. Sano, H. Ohashi, K. Yamauchi, and T. Ishikawa, “Stitching-angle measurable microscopic-interferometer: Surface-figure metrology tool for hard X-ray nanofocusing mirrors with large curvature,” Nucl. Instruments Methods Phys. Res. Sect. A: Accel. Spectrometers, Detect. Assoc. Equip. 616, (2)203–206 (2010).
[Crossref]

H. Yumoto, H. Mimura, T. Kimura, S. Handa, S. Matsuyama, Y. Sano, and K. Yamauchi, “Stitching interferometric metrology for steeply curved x-ray mirrors,” Surf. Interface Analysis 40(6–7), 1023–1027 (2008).
[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, “Relative angle determinable stitching interferometry for hard x-ray reflective optics,” Rev. Sci. Instruments 76(4), 045102 (2005).
[Crossref]

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, “Microstitching interferometry for x-ray reflective optics,” Rev. Sci. Instruments 74(5), 2894–2898 (2003).
[Crossref]

Mori, Y.

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, “Relative angle determinable stitching interferometry for hard x-ray reflective optics,” Rev. Sci. Instruments 76(4), 045102 (2005).
[Crossref]

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, “Microstitching interferometry for x-ray reflective optics,” Rev. Sci. Instruments 74(5), 2894–2898 (2003).
[Crossref]

Murphy, P.

P. Murphy, G. Forbes, J. Fleig, P. Dumas, and M. Tricard, “Stitching interferometry: a flexible solution for surface metrology,” Opt. Photonics News 14(5), 38–43 (2003).
[Crossref]

Nishino, Y.

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, “Relative angle determinable stitching interferometry for hard x-ray reflective optics,” Rev. Sci. Instruments 76(4), 045102 (2005).
[Crossref]

Ohashi, H.

T. Kimura, H. Ohashi, H. Mimura, D. Yamakawa, H. Yumoto, S. Matsuyama, T. Tsumura, H. Okada, T. Masunaga, Y. Senba, S. Goto, T. Ishikawa, and K. Yamauchi, “A stitching figure profiler of large X-ray mirrors using RADSI for subaperture data acquisition,” Nucl. Instruments Methods Phys. Res. Sect. A: Accel. Spectrometers, Detect. Assoc. Equip. 616, (2)229–232 (2010).
[Crossref]

H. Yumoto, H. Mimura, S. Handa, T. Kimura, S. Matsuyama, Y. Sano, H. Ohashi, K. Yamauchi, and T. Ishikawa, “Stitching-angle measurable microscopic-interferometer: Surface-figure metrology tool for hard X-ray nanofocusing mirrors with large curvature,” Nucl. Instruments Methods Phys. Res. Sect. A: Accel. Spectrometers, Detect. Assoc. Equip. 616, (2)203–206 (2010).
[Crossref]

Okada, H.

T. Kimura, H. Ohashi, H. Mimura, D. Yamakawa, H. Yumoto, S. Matsuyama, T. Tsumura, H. Okada, T. Masunaga, Y. Senba, S. Goto, T. Ishikawa, and K. Yamauchi, “A stitching figure profiler of large X-ray mirrors using RADSI for subaperture data acquisition,” Nucl. Instruments Methods Phys. Res. Sect. A: Accel. Spectrometers, Detect. Assoc. Equip. 616, (2)229–232 (2010).
[Crossref]

Okada, K.

M. Otsubo, K. Okada, and J. Tsujiuchi, “Measurement of large plane surface shapes by connecting small-aperture interferograms,” Opt. Eng. 33(2), 608–613 (1994).
[Crossref]

Otsubo, M.

M. Otsubo, K. Okada, and J. Tsujiuchi, “Measurement of large plane surface shapes by connecting small-aperture interferograms,” Opt. Eng. 33(2), 608–613 (1994).
[Crossref]

Peng, J.

J. Peng, Q. Wang, X. Peng, and Y. Yu, “Stitching interferometry of high numerical aperture cylindrical optics without using a fringe-nulling routine,” J. Opt. Soc. Am. A 33(11), 1964–1972 (2015).
[Crossref]

Peng, X.

J. Peng, Q. Wang, X. Peng, and Y. Yu, “Stitching interferometry of high numerical aperture cylindrical optics without using a fringe-nulling routine,” J. Opt. Soc. Am. A 33(11), 1964–1972 (2015).
[Crossref]

Rungsawang, R.

Saito, A.

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, “Microstitching interferometry for x-ray reflective optics,” Rev. Sci. Instruments 74(5), 2894–2898 (2003).
[Crossref]

Sano, Y.

H. Yumoto, H. Mimura, S. Handa, T. Kimura, S. Matsuyama, Y. Sano, H. Ohashi, K. Yamauchi, and T. Ishikawa, “Stitching-angle measurable microscopic-interferometer: Surface-figure metrology tool for hard X-ray nanofocusing mirrors with large curvature,” Nucl. Instruments Methods Phys. Res. Sect. A: Accel. Spectrometers, Detect. Assoc. Equip. 616, (2)203–206 (2010).
[Crossref]

H. Yumoto, H. Mimura, T. Kimura, S. Handa, S. Matsuyama, Y. Sano, and K. Yamauchi, “Stitching interferometric metrology for steeply curved x-ray mirrors,” Surf. Interface Analysis 40(6–7), 1023–1027 (2008).
[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, “Relative angle determinable stitching interferometry for hard x-ray reflective optics,” Rev. Sci. Instruments 76(4), 045102 (2005).
[Crossref]

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, “Microstitching interferometry for x-ray reflective optics,” Rev. Sci. Instruments 74(5), 2894–2898 (2003).
[Crossref]

Schulz, M.

G. Ehret, S. Laubach, and M. Schulz, “Flatness metrology based on small-angle deflectometric procedures with electronic tiltmeters,” Proc. SPIE 10326, 1032604 (2017).
[Crossref]

C. Elster, I. Weingärtner, and M. Schulz, “Coupled distance sensor systems for high-accuracy topography measurement: Accounting for scanning stage and systematic sensor errors,” Precis. Eng. 30(1), 32–38 (2006).
[Crossref]

M. Schulz, I. Weingaertner, C. Elster, and J. Gerhardt, “Low- and mid-spatial-frequency component measurement for aspheres,” Proc. SPIE 5188, 287–295 (2003).
[Crossref]

Senba, Y.

T. Kimura, H. Ohashi, H. Mimura, D. Yamakawa, H. Yumoto, S. Matsuyama, T. Tsumura, H. Okada, T. Masunaga, Y. Senba, S. Goto, T. Ishikawa, and K. Yamauchi, “A stitching figure profiler of large X-ray mirrors using RADSI for subaperture data acquisition,” Nucl. Instruments Methods Phys. Res. Sect. A: Accel. Spectrometers, Detect. Assoc. Equip. 616, (2)229–232 (2010).
[Crossref]

Song, W.

Souvorov, A.

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, “Microstitching interferometry for x-ray reflective optics,” Rev. Sci. Instruments 74(5), 2894–2898 (2003).
[Crossref]

Tam, H.-Y.

Tamasaku, K.

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, “Relative angle determinable stitching interferometry for hard x-ray reflective optics,” Rev. Sci. Instruments 76(4), 045102 (2005).
[Crossref]

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, “Microstitching interferometry for x-ray reflective optics,” Rev. Sci. Instruments 74(5), 2894–2898 (2003).
[Crossref]

Tricard, M.

P. Murphy, G. Forbes, J. Fleig, P. Dumas, and M. Tricard, “Stitching interferometry: a flexible solution for surface metrology,” Opt. Photonics News 14(5), 38–43 (2003).
[Crossref]

Tsujiuchi, J.

M. Otsubo, K. Okada, and J. Tsujiuchi, “Measurement of large plane surface shapes by connecting small-aperture interferograms,” Opt. Eng. 33(2), 608–613 (1994).
[Crossref]

Tsumura, T.

T. Kimura, H. Ohashi, H. Mimura, D. Yamakawa, H. Yumoto, S. Matsuyama, T. Tsumura, H. Okada, T. Masunaga, Y. Senba, S. Goto, T. Ishikawa, and K. Yamauchi, “A stitching figure profiler of large X-ray mirrors using RADSI for subaperture data acquisition,” Nucl. Instruments Methods Phys. Res. Sect. A: Accel. Spectrometers, Detect. Assoc. Equip. 616, (2)229–232 (2010).
[Crossref]

Ueno, K.

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, “Relative angle determinable stitching interferometry for hard x-ray reflective optics,” Rev. Sci. Instruments 76(4), 045102 (2005).
[Crossref]

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, “Microstitching interferometry for x-ray reflective optics,” Rev. Sci. Instruments 74(5), 2894–2898 (2003).
[Crossref]

Vivo, A.

A. Vivo, B. Lantelme, R. Baker, and R. Barrett, “Stitching methods at the European Synchrotron Radiation Facility (ESRF),” Rev. Sci. Instruments 87(5), 051908 (2016).
[Crossref]

Wang, Q.

J. Peng, Q. Wang, X. Peng, and Y. Yu, “Stitching interferometry of high numerical aperture cylindrical optics without using a fringe-nulling routine,” J. Opt. Soc. Am. A 33(11), 1964–1972 (2015).
[Crossref]

Weingaertner, I.

M. Schulz, I. Weingaertner, C. Elster, and J. Gerhardt, “Low- and mid-spatial-frequency component measurement for aspheres,” Proc. SPIE 5188, 287–295 (2003).
[Crossref]

Weingärtner, I.

C. Elster, I. Weingärtner, and M. Schulz, “Coupled distance sensor systems for high-accuracy topography measurement: Accounting for scanning stage and systematic sensor errors,” Precis. Eng. 30(1), 32–38 (2006).
[Crossref]

Wen, Y.

Xue, J.

Yabashi, M.

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, “Relative angle determinable stitching interferometry for hard x-ray reflective optics,” Rev. Sci. Instruments 76(4), 045102 (2005).
[Crossref]

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, “Microstitching interferometry for x-ray reflective optics,” Rev. Sci. Instruments 74(5), 2894–2898 (2003).
[Crossref]

Yamakawa, D.

T. Kimura, H. Ohashi, H. Mimura, D. Yamakawa, H. Yumoto, S. Matsuyama, T. Tsumura, H. Okada, T. Masunaga, Y. Senba, S. Goto, T. Ishikawa, and K. Yamauchi, “A stitching figure profiler of large X-ray mirrors using RADSI for subaperture data acquisition,” Nucl. Instruments Methods Phys. Res. Sect. A: Accel. Spectrometers, Detect. Assoc. Equip. 616, (2)229–232 (2010).
[Crossref]

Yamamura, K.

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, “Relative angle determinable stitching interferometry for hard x-ray reflective optics,” Rev. Sci. Instruments 76(4), 045102 (2005).
[Crossref]

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, “Microstitching interferometry for x-ray reflective optics,” Rev. Sci. Instruments 74(5), 2894–2898 (2003).
[Crossref]

Yamauchi, K.

H. Yumoto, H. Mimura, S. Handa, T. Kimura, S. Matsuyama, Y. Sano, H. Ohashi, K. Yamauchi, and T. Ishikawa, “Stitching-angle measurable microscopic-interferometer: Surface-figure metrology tool for hard X-ray nanofocusing mirrors with large curvature,” Nucl. Instruments Methods Phys. Res. Sect. A: Accel. Spectrometers, Detect. Assoc. Equip. 616, (2)203–206 (2010).
[Crossref]

T. Kimura, H. Ohashi, H. Mimura, D. Yamakawa, H. Yumoto, S. Matsuyama, T. Tsumura, H. Okada, T. Masunaga, Y. Senba, S. Goto, T. Ishikawa, and K. Yamauchi, “A stitching figure profiler of large X-ray mirrors using RADSI for subaperture data acquisition,” Nucl. Instruments Methods Phys. Res. Sect. A: Accel. Spectrometers, Detect. Assoc. Equip. 616, (2)229–232 (2010).
[Crossref]

H. Yumoto, H. Mimura, T. Kimura, S. Handa, S. Matsuyama, Y. Sano, and K. Yamauchi, “Stitching interferometric metrology for steeply curved x-ray mirrors,” Surf. Interface Analysis 40(6–7), 1023–1027 (2008).
[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, “Relative angle determinable stitching interferometry for hard x-ray reflective optics,” Rev. Sci. Instruments 76(4), 045102 (2005).
[Crossref]

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, “Microstitching interferometry for x-ray reflective optics,” Rev. Sci. Instruments 74(5), 2894–2898 (2003).
[Crossref]

Yiwei, H.

Yu, Y.

J. Peng, Q. Wang, X. Peng, and Y. Yu, “Stitching interferometry of high numerical aperture cylindrical optics without using a fringe-nulling routine,” J. Opt. Soc. Am. A 33(11), 1964–1972 (2015).
[Crossref]

Yumoto, H.

T. Kimura, H. Ohashi, H. Mimura, D. Yamakawa, H. Yumoto, S. Matsuyama, T. Tsumura, H. Okada, T. Masunaga, Y. Senba, S. Goto, T. Ishikawa, and K. Yamauchi, “A stitching figure profiler of large X-ray mirrors using RADSI for subaperture data acquisition,” Nucl. Instruments Methods Phys. Res. Sect. A: Accel. Spectrometers, Detect. Assoc. Equip. 616, (2)229–232 (2010).
[Crossref]

H. Yumoto, H. Mimura, S. Handa, T. Kimura, S. Matsuyama, Y. Sano, H. Ohashi, K. Yamauchi, and T. Ishikawa, “Stitching-angle measurable microscopic-interferometer: Surface-figure metrology tool for hard X-ray nanofocusing mirrors with large curvature,” Nucl. Instruments Methods Phys. Res. Sect. A: Accel. Spectrometers, Detect. Assoc. Equip. 616, (2)203–206 (2010).
[Crossref]

H. Yumoto, H. Mimura, T. Kimura, S. Handa, S. Matsuyama, Y. Sano, and K. Yamauchi, “Stitching interferometric metrology for steeply curved x-ray mirrors,” Surf. Interface Analysis 40(6–7), 1023–1027 (2008).
[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, “Relative angle determinable stitching interferometry for hard x-ray reflective optics,” Rev. Sci. Instruments 76(4), 045102 (2005).
[Crossref]

Zhou, D.

Appl. Opt. (2)

J. Opt. Soc. Am. A (1)

J. Peng, Q. Wang, X. Peng, and Y. Yu, “Stitching interferometry of high numerical aperture cylindrical optics without using a fringe-nulling routine,” J. Opt. Soc. Am. A 33(11), 1964–1972 (2015).
[Crossref]

Nucl. Instruments Methods Phys. Res. Sect. A: Accel. Spectrometers, Detect. Assoc. Equip. (2)

T. Kimura, H. Ohashi, H. Mimura, D. Yamakawa, H. Yumoto, S. Matsuyama, T. Tsumura, H. Okada, T. Masunaga, Y. Senba, S. Goto, T. Ishikawa, and K. Yamauchi, “A stitching figure profiler of large X-ray mirrors using RADSI for subaperture data acquisition,” Nucl. Instruments Methods Phys. Res. Sect. A: Accel. Spectrometers, Detect. Assoc. Equip. 616, (2)229–232 (2010).
[Crossref]

H. Yumoto, H. Mimura, S. Handa, T. Kimura, S. Matsuyama, Y. Sano, H. Ohashi, K. Yamauchi, and T. Ishikawa, “Stitching-angle measurable microscopic-interferometer: Surface-figure metrology tool for hard X-ray nanofocusing mirrors with large curvature,” Nucl. Instruments Methods Phys. Res. Sect. A: Accel. Spectrometers, Detect. Assoc. Equip. 616, (2)203–206 (2010).
[Crossref]

Opt. Eng. (1)

M. Otsubo, K. Okada, and J. Tsujiuchi, “Measurement of large plane surface shapes by connecting small-aperture interferograms,” Opt. Eng. 33(2), 608–613 (1994).
[Crossref]

Opt. Express (4)

Opt. Photonics News (1)

P. Murphy, G. Forbes, J. Fleig, P. Dumas, and M. Tricard, “Stitching interferometry: a flexible solution for surface metrology,” Opt. Photonics News 14(5), 38–43 (2003).
[Crossref]

Precis. Eng. (1)

C. Elster, I. Weingärtner, and M. Schulz, “Coupled distance sensor systems for high-accuracy topography measurement: Accounting for scanning stage and systematic sensor errors,” Precis. Eng. 30(1), 32–38 (2006).
[Crossref]

Proc. SPIE (4)

M. Bray, “Stitching interferometry: how and why it works,” Proc. SPIE 3739, 259–273 (1999).
[Crossref]

M. Schulz, I. Weingaertner, C. Elster, and J. Gerhardt, “Low- and mid-spatial-frequency component measurement for aspheres,” Proc. SPIE 5188, 287–295 (2003).
[Crossref]

C. B. Kreischer, “Retrace error: interferometry’s dark little secret,” Proc. SPIE 8884, 88840X (2013).
[Crossref]

G. Ehret, S. Laubach, and M. Schulz, “Flatness metrology based on small-angle deflectometric procedures with electronic tiltmeters,” Proc. SPIE 10326, 1032604 (2017).
[Crossref]

Rev. Sci. Instruments (3)

A. Vivo, B. Lantelme, R. Baker, and R. Barrett, “Stitching methods at the European Synchrotron Radiation Facility (ESRF),” Rev. Sci. Instruments 87(5), 051908 (2016).
[Crossref]

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, “Microstitching interferometry for x-ray reflective optics,” Rev. Sci. Instruments 74(5), 2894–2898 (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, “Relative angle determinable stitching interferometry for hard x-ray reflective optics,” Rev. Sci. Instruments 76(4), 045102 (2005).
[Crossref]

Surf. Interface Analysis (1)

H. Yumoto, H. Mimura, T. Kimura, S. Handa, S. Matsuyama, Y. Sano, and K. Yamauchi, “Stitching interferometric metrology for steeply curved x-ray mirrors,” Surf. Interface Analysis 40(6–7), 1023–1027 (2008).
[Crossref]

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Figures (9)

Fig. 1
Fig. 1 The 2D stitching is fulfilled by adjusting the piston level of the neighboring subsets after the tilt correction assisted by the tilt measurement.
Fig. 2
Fig. 2 The sketch of the 2D TSI system includes an interferometer which measures the height map of each subset, a translation stage, and two tiltmeters which measures the relative tilts in x- and y-directions between the interferometer and mirror under test during the scans.
Fig. 3
Fig. 3 The actual 2D TSI setup in the experiment includes a white light interferometer, a translation stage, and two tiltmeters. In addition, an autocollimator coupled with a reflective mirror is used to compose a 1D ASI for comparison purpose.
Fig. 4
Fig. 4 Typical differential signals of x-tilt between the two tiltmeters during numbers of repeating scans (a) and typical x-tilt signals in a single scan period with 31 sub-aperture views (b).
Fig. 5
Fig. 5 Typical data from tiltmeters and WLI: The differential signals of x-tilt (a) and y-tilt (b) between the two tiltmeters in a single scan, and (c-g) five typical WLI-measured height results across the mirror under test.
Fig. 6
Fig. 6 Comparing to 16 repeating software stitching results (a), 16 repeating TSI stitching results (b) are much more repeatable. The stitching discrepancies by TSI (d) are much lower than those by software stitching (c). The plot (e) is an enlarged view of the same data in (d).
Fig. 7
Fig. 7 Comparing the x-tilt signals measured by the tiltmeters and the AC (a), we can find the repeatability of the x-tilt measured by the tiltmeters used in our experiment (b) is worse than that of the used AC (c).
Fig. 8
Fig. 8 The central line of the 2D TSI result (a) is compared with the 1D ASI result (b). The difference between TSI and ASI profiles is mainly a power term (c). The residuals from TSI and ASI after removing the best fit of the target ellipse (d) are compared by showing the discrepancy of their fitting residuals (e).
Fig. 9
Fig. 9 The residuals of 16 repeating 2D TSI and 1D ASI scans clearly demonstrate that the repeatability of the TSI with the used tiltmeter under the measuring condition is worse than the repeatability of the ASI with the used AC, which is consistent with the repeatability of the tilt measurement results in Fig. 7.

Tables (1)

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Table 1 Parameters of the target ellipse.

Equations (2)

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T n + 1 = M n + 1 t x x t y y .
S n + 1 = T n + 1 p .

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