Abstract

Recently we presented one-dimensional Angular-measurement-based Stitching Interferometry (ASI) technique for synchrotron mirror metrology coupling an autocollimator and a white light interferometer. In this work, we conduct a further study on the measurement repeatability of this technique under different conditions, e.g. different scanning time or lengths with/without system drift. The similarity between the angle measuring stitching technique in ASI and the slope integration technique in deflectometry is addressed. The analytic expression of the height repeatability is derived while the slope noise is a zero-mean uncorrelated additive noise. In addition, we use a set of typical stationary signals from the autocollimator and the white light interferometer in a real experiment to simulate numerous virtual scans for the numerical calculation of the measurement repeatability under different measurement conditions. The simulation result predicts a link between the measurement repeatability and the scanning time with a constant speed. Moreover, it indicates that the major factor affecting the repeatability of our current ASI system is the system drift error.

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

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References

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  1. P. Z. Takacs, S.-n. Qian, and J. Colbert, “Design of a long trace surface profiler,” Proc. SPIE 0749, 59–64 (1987).
    [Crossref]
  2. F. Siewert, T. Noll, T. Schlegel, T. Zeschke, and H. Lammert, “The nanometer optical component measuring machine: a new sub-nm topography measuring device for x-ray optics at BESSY,” AIP Conf. Proc. 705(1), 847–850 (2004).
    [Crossref]
  3. S. Qian and M. Idir, “Innovative nano-accuracy surface profiler for sub-50 nrad rms mirror test,” Proc. SPIE 9687, 96870D (2016).
    [Crossref]
  4. S. Qian and B. Gao, “Nano-accuracy measurement technology of optical-surface profiles,” Proc. SPIE 9687, 96870E (2016).
    [Crossref]
  5. 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]
  6. 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]
  7. 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-rayreflective optics,” Rev. Sci. Instruments 76(4), 045102 (2005).
    [Crossref]
  8. 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]
  9. M. Idir, K. Kaznatcheev, G. Dovillaire, J. Legrand, and R. Rungsawang, “A 2D high accuracy slope measuring system based on a stitching Shack Hartmann Optical head,” Opt. Express 22(3), 2770–2781 (2014).
    [Crossref] [PubMed]
  10. L. Huang, J. Xue, and M. Idir, “Controlling X-ray deformable mirrors during inspection,” J. Synchrotron Radiat. 23(6), 1348–1356 (2016).
    [Crossref] [PubMed]
  11. 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]
  12. L. Huang, M. Idir, C. Zuo, K. Kaznatcheev, L. Zhou, and A. Asundi, “Comparison of two-dimensional integration methods for shape reconstruction from gradient data,” Opt. Lasers Eng. 64, 1–11 (2015).
    [Crossref]
  13. W. H. Southwell, “Wave-front estimation from wave-front slope measurements,” J. Opt. Soc. Am. 70(8), 998–1006 (1980).
    [Crossref]
  14. L. Huang, J. Xue, B. Gao, C. Zuo, and M. Idir, “Zonal wavefront reconstruction in quadrilateral geometry for phase measuring deflectometry,” Appl. Opt. 56(18), 5139–5144 (2017).
    [Crossref] [PubMed]
  15. W. Li, T. Bothe, C. v. Kopylow, and W. P. O. Juptner, “Evaluation methods for gradient measurement techniques,” Proc. SPIE 5457, 300–311 (2004).
    [Crossref]
  16. C. B. Kreischer, “Retrace error: interferometry’s dark little secret,” Proc. SPIE 8884, 88840X (2013).
    [Crossref]
  17. 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]

2018 (1)

2017 (1)

2016 (4)

L. Huang, J. Xue, and M. Idir, “Controlling X-ray deformable mirrors during inspection,” J. Synchrotron Radiat. 23(6), 1348–1356 (2016).
[Crossref] [PubMed]

S. Qian and M. Idir, “Innovative nano-accuracy surface profiler for sub-50 nrad rms mirror test,” Proc. SPIE 9687, 96870D (2016).
[Crossref]

S. Qian and B. Gao, “Nano-accuracy measurement technology of optical-surface profiles,” Proc. SPIE 9687, 96870E (2016).
[Crossref]

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)

L. Huang, M. Idir, C. Zuo, K. Kaznatcheev, L. Zhou, and A. Asundi, “Comparison of two-dimensional integration methods for shape reconstruction from gradient data,” Opt. Lasers Eng. 64, 1–11 (2015).
[Crossref]

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]

2014 (1)

2013 (1)

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

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-rayreflective optics,” Rev. Sci. Instruments 76(4), 045102 (2005).
[Crossref]

2004 (2)

F. Siewert, T. Noll, T. Schlegel, T. Zeschke, and H. Lammert, “The nanometer optical component measuring machine: a new sub-nm topography measuring device for x-ray optics at BESSY,” AIP Conf. Proc. 705(1), 847–850 (2004).
[Crossref]

W. Li, T. Bothe, C. v. Kopylow, and W. P. O. Juptner, “Evaluation methods for gradient measurement techniques,” Proc. SPIE 5457, 300–311 (2004).
[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, “Microstitching interferometry for x-ray reflective optics,” Rev. Sci. Instruments 74(5), 2894–2898 (2003).
[Crossref]

1987 (1)

P. Z. Takacs, S.-n. Qian, and J. Colbert, “Design of a long trace surface profiler,” Proc. SPIE 0749, 59–64 (1987).
[Crossref]

1980 (1)

Asundi, A.

L. Huang, M. Idir, C. Zuo, K. Kaznatcheev, L. Zhou, and A. Asundi, “Comparison of two-dimensional integration methods for shape reconstruction from gradient data,” Opt. Lasers Eng. 64, 1–11 (2015).
[Crossref]

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]

Bothe, T.

W. Li, T. Bothe, C. v. Kopylow, and W. P. O. Juptner, “Evaluation methods for gradient measurement techniques,” Proc. SPIE 5457, 300–311 (2004).
[Crossref]

Colbert, J.

P. Z. Takacs, S.-n. Qian, and J. Colbert, “Design of a long trace surface profiler,” Proc. SPIE 0749, 59–64 (1987).
[Crossref]

Dovillaire, G.

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-rayreflective 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]

Gao, B.

Haiyang, Q.

Handa, S.

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.

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]

L. Huang, J. Xue, B. Gao, C. Zuo, and M. Idir, “Zonal wavefront reconstruction in quadrilateral geometry for phase measuring deflectometry,” Appl. Opt. 56(18), 5139–5144 (2017).
[Crossref] [PubMed]

L. Huang, J. Xue, and M. Idir, “Controlling X-ray deformable mirrors during inspection,” J. Synchrotron Radiat. 23(6), 1348–1356 (2016).
[Crossref] [PubMed]

L. Huang, M. Idir, C. Zuo, K. Kaznatcheev, L. Zhou, and A. Asundi, “Comparison of two-dimensional integration methods for shape reconstruction from gradient data,” Opt. Lasers Eng. 64, 1–11 (2015).
[Crossref]

Idir, M.

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]

L. Huang, J. Xue, B. Gao, C. Zuo, and M. Idir, “Zonal wavefront reconstruction in quadrilateral geometry for phase measuring deflectometry,” Appl. Opt. 56(18), 5139–5144 (2017).
[Crossref] [PubMed]

L. Huang, J. Xue, and M. Idir, “Controlling X-ray deformable mirrors during inspection,” J. Synchrotron Radiat. 23(6), 1348–1356 (2016).
[Crossref] [PubMed]

S. Qian and M. Idir, “Innovative nano-accuracy surface profiler for sub-50 nrad rms mirror test,” Proc. SPIE 9687, 96870D (2016).
[Crossref]

L. Huang, M. Idir, C. Zuo, K. Kaznatcheev, L. Zhou, and A. Asundi, “Comparison of two-dimensional integration methods for shape reconstruction from gradient data,” Opt. Lasers Eng. 64, 1–11 (2015).
[Crossref]

M. Idir, K. Kaznatcheev, G. Dovillaire, J. Legrand, and R. Rungsawang, “A 2D high accuracy slope measuring system based on a stitching Shack Hartmann Optical head,” Opt. Express 22(3), 2770–2781 (2014).
[Crossref] [PubMed]

Ishikawa, T.

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-rayreflective 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]

Juptner, W. P. O.

W. Li, T. Bothe, C. v. Kopylow, and W. P. O. Juptner, “Evaluation methods for gradient measurement techniques,” Proc. SPIE 5457, 300–311 (2004).
[Crossref]

Kaznatcheev, K.

L. Huang, M. Idir, C. Zuo, K. Kaznatcheev, L. Zhou, and A. Asundi, “Comparison of two-dimensional integration methods for shape reconstruction from gradient data,” Opt. Lasers Eng. 64, 1–11 (2015).
[Crossref]

M. Idir, K. Kaznatcheev, G. Dovillaire, J. Legrand, and R. Rungsawang, “A 2D high accuracy slope measuring system based on a stitching Shack Hartmann Optical head,” Opt. Express 22(3), 2770–2781 (2014).
[Crossref] [PubMed]

Kimura, T.

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]

Kopylow, C. v.

W. Li, T. Bothe, C. v. Kopylow, and W. P. O. Juptner, “Evaluation methods for gradient measurement techniques,” Proc. SPIE 5457, 300–311 (2004).
[Crossref]

Kreischer, C. B.

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

Lammert, H.

F. Siewert, T. Noll, T. Schlegel, T. Zeschke, and H. Lammert, “The nanometer optical component measuring machine: a new sub-nm topography measuring device for x-ray optics at BESSY,” AIP Conf. Proc. 705(1), 847–850 (2004).
[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]

Legrand, J.

Li, W.

W. Li, T. Bothe, C. v. Kopylow, and W. P. O. Juptner, “Evaluation methods for gradient measurement techniques,” Proc. SPIE 5457, 300–311 (2004).
[Crossref]

Matsuyama, S.

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-rayreflective optics,” Rev. Sci. Instruments 76(4), 045102 (2005).
[Crossref]

Mimura, H.

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-rayreflective 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-rayreflective 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]

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-rayreflective optics,” Rev. Sci. Instruments 76(4), 045102 (2005).
[Crossref]

Noll, T.

F. Siewert, T. Noll, T. Schlegel, T. Zeschke, and H. Lammert, “The nanometer optical component measuring machine: a new sub-nm topography measuring device for x-ray optics at BESSY,” AIP Conf. Proc. 705(1), 847–850 (2004).
[Crossref]

Qian, S.

S. Qian and M. Idir, “Innovative nano-accuracy surface profiler for sub-50 nrad rms mirror test,” Proc. SPIE 9687, 96870D (2016).
[Crossref]

S. Qian and B. Gao, “Nano-accuracy measurement technology of optical-surface profiles,” Proc. SPIE 9687, 96870E (2016).
[Crossref]

Qian, S.-n.

P. Z. Takacs, S.-n. Qian, and J. Colbert, “Design of a long trace surface profiler,” Proc. SPIE 0749, 59–64 (1987).
[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, 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-rayreflective 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]

Schlegel, T.

F. Siewert, T. Noll, T. Schlegel, T. Zeschke, and H. Lammert, “The nanometer optical component measuring machine: a new sub-nm topography measuring device for x-ray optics at BESSY,” AIP Conf. Proc. 705(1), 847–850 (2004).
[Crossref]

Siewert, F.

F. Siewert, T. Noll, T. Schlegel, T. Zeschke, and H. Lammert, “The nanometer optical component measuring machine: a new sub-nm topography measuring device for x-ray optics at BESSY,” AIP Conf. Proc. 705(1), 847–850 (2004).
[Crossref]

Song, W.

Southwell, W. H.

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]

Takacs, P. Z.

P. Z. Takacs, S.-n. Qian, and J. Colbert, “Design of a long trace surface profiler,” Proc. SPIE 0749, 59–64 (1987).
[Crossref]

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-rayreflective 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]

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-rayreflective 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]

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-rayreflective 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]

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-rayreflective 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, 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-rayreflective 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.

Yumoto, H.

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-rayreflective optics,” Rev. Sci. Instruments 76(4), 045102 (2005).
[Crossref]

Zeschke, T.

F. Siewert, T. Noll, T. Schlegel, T. Zeschke, and H. Lammert, “The nanometer optical component measuring machine: a new sub-nm topography measuring device for x-ray optics at BESSY,” AIP Conf. Proc. 705(1), 847–850 (2004).
[Crossref]

Zhou, L.

L. Huang, M. Idir, C. Zuo, K. Kaznatcheev, L. Zhou, and A. Asundi, “Comparison of two-dimensional integration methods for shape reconstruction from gradient data,” Opt. Lasers Eng. 64, 1–11 (2015).
[Crossref]

Zuo, C.

L. Huang, J. Xue, B. Gao, C. Zuo, and M. Idir, “Zonal wavefront reconstruction in quadrilateral geometry for phase measuring deflectometry,” Appl. Opt. 56(18), 5139–5144 (2017).
[Crossref] [PubMed]

L. Huang, M. Idir, C. Zuo, K. Kaznatcheev, L. Zhou, and A. Asundi, “Comparison of two-dimensional integration methods for shape reconstruction from gradient data,” Opt. Lasers Eng. 64, 1–11 (2015).
[Crossref]

AIP Conf. Proc. (1)

F. Siewert, T. Noll, T. Schlegel, T. Zeschke, and H. Lammert, “The nanometer optical component measuring machine: a new sub-nm topography measuring device for x-ray optics at BESSY,” AIP Conf. Proc. 705(1), 847–850 (2004).
[Crossref]

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

J. Synchrotron Radiat. (1)

L. Huang, J. Xue, and M. Idir, “Controlling X-ray deformable mirrors during inspection,” J. Synchrotron Radiat. 23(6), 1348–1356 (2016).
[Crossref] [PubMed]

Opt. Express (3)

Opt. Lasers Eng. (1)

L. Huang, M. Idir, C. Zuo, K. Kaznatcheev, L. Zhou, and A. Asundi, “Comparison of two-dimensional integration methods for shape reconstruction from gradient data,” Opt. Lasers Eng. 64, 1–11 (2015).
[Crossref]

Proc. SPIE (5)

P. Z. Takacs, S.-n. Qian, and J. Colbert, “Design of a long trace surface profiler,” Proc. SPIE 0749, 59–64 (1987).
[Crossref]

S. Qian and M. Idir, “Innovative nano-accuracy surface profiler for sub-50 nrad rms mirror test,” Proc. SPIE 9687, 96870D (2016).
[Crossref]

S. Qian and B. Gao, “Nano-accuracy measurement technology of optical-surface profiles,” Proc. SPIE 9687, 96870E (2016).
[Crossref]

W. Li, T. Bothe, C. v. Kopylow, and W. P. O. Juptner, “Evaluation methods for gradient measurement techniques,” Proc. SPIE 5457, 300–311 (2004).
[Crossref]

C. B. Kreischer, “Retrace error: interferometry’s dark little secret,” Proc. SPIE 8884, 88840X (2013).
[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-rayreflective 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 (8)

Fig. 1
Fig. 1 The 1D ASI setup consists of an angular measurement device (e.g. an autocollimator with a flat mirror mounted on the stage) and an interferometer measuring local profiles of the SUT.
Fig. 2
Fig. 2 The slope and height values are usually connected by a finite difference expression in IOS (a), while the relations between tilt-corrected profiles are established by the piston calculated inside overlapping region in AMS (b).
Fig. 3
Fig. 3 Similar global height profiles (c) with comparable repeatability (d) can be obtained by the AMS with subset profiles after tilt correction (a) or by the IOS with the corresponding slopes (b).
Fig. 4
Fig. 4 Real temperature, AC angle and WLI tilt data in a 24-hour stationary test in our current ASI measurement environment. AC readings are averaged over 7 seconds.
Fig. 5
Fig. 5 By using the real 24-hour stationary data, 96 sets of 15 mins virtual scans are simulated: (a) slope discrepancies of these 96 repeating measurements, (b) slope repeatability of each scan, (c) spectrum of the slope profiles, (d) amplitudes of the lowest frequency component, (e) height discrepancies, and (f) height repeatability of each scan.
Fig. 6
Fig. 6 The repeatability of 70 actual ASI scans. (a) Height discrepancies from the mean value, and (b) the height repeatability in RMS.
Fig. 7
Fig. 7 Virtual scans by using (a) real experimental data, (b) virtual data with little drift, and (c) virtual data with no drift. Their corresponding height repeatability for a 15 mins scans (d)–(f) and 30 mins scans (g)–(i), respectively.
Fig. 8
Fig. 8 The average height repeatability is getting larger along with the scanning time increasing under different drift conditions. The scanning speed is based on the current ASI speed.

Equations (16)

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h n ( x ) = φ n ( x ) t n x .
z n ( x ) = h n ( x ) + Δ h n ¯ .
s = z + e s + e r ,
z B z A = ! s A + s B 2 Δ x ,
Δ z ¯ = d / 2 d / 2 z a ( x ) z b ( x ) d x d = n = 0 a n b n n + 1 x n + 1 | d / 2 d / 2 d = n = 0 a n b n n + 1 ( d 2 ) n , n = 0 , 2 , 4
z B z A = Δ z ¯ + n = 0 b n ( Δ x 2 ) n n = 0 a n ( Δ x 2 ) n = ( a 1 + b 1 ) Δ x 2 + n = 2 a n b n n + 1 ( d 2 ) n + n = 2 b n ( Δ x 2 ) n n = 2 a n ( Δ x 2 ) n .
z B z A a 1 + b 1 2 Δ x .
σ s 2 = 1 L L / 2 L / 2 | n s ( x ) | 2 d x .
σ s 2 = 1 L | F s ( u ) | 2 d u = 1 L N 2 Δ u N 2 Δ u | F s ( u ) | 2 d u .
σ s 2 = 1 L N 2 Δ u N 2 Δ u | F s ( u ) | 2 d u 1 L N 2 Δ u N 2 Δ u A 2 d u = N Δ u L A 2 = N L 2 A 2 .
| F z ( u ) | = | F s ( u ) | 2 π | u | A 2 π | u | = σ s Δ x N 2 π | u | .
σ z 2 = 1 L N 2 Δ u N 2 Δ u | F s ( u ) | 2 d u = 1 L ( σ s Δ x N 2 π ) 2 N 2 Δ u N 2 Δ u | u | 2 d u .
σ z 2 = 2 L ( σ s Δ x N 2 π ) 2 Δ u N 2 Δ u u 2 d u .
σ z 2 = 2 L ( σ s Δ x N 2 π ) 2 ( 1 Δ u 2 N Δ u ) .
σ z 2 = σ s 2 Δ x 2 ( N 2 ) 2 π 2 .
σ z = 2 σ s 2 π Δ x ( L 2 Δ x ) 2 σ s 2 π Δ x L , when L 2 Δ x .

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