Abstract

In this work, we present one-dimensional stitching interferometry based on the angular measurement for high-precision mirror metrology. The tilt error introduced by the stage motion during the stitching process is measured by an extra angular measurement device. The local profile measured by the interferometer in a single field of view is corrected using the measured angle before the piston adjustment in the stitching process. Comparing to the classical software stitching technique, the angle measuring stitching technique is more reliable and accurate in profiling mirror surface at the nanometer level. Experimental results demonstrate the feasibility of the proposed stitching technique. Based on our measurements, the typical repeatability within 200 mm scanning range is 0.5 nm RMS or less.

© 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. J. Liang, D. R. Williams, and D. T. Miller, “Supernormal vision and high-resolution retinal imaging through adaptive optics,” J. Opt. Soc. Am. A 14(11), 2884–2892 (1997).
    [Crossref]
  2. L. J. Hornbeck, “Deformable-mirror spatial light modulators,” Proc. SPIE 1150, 86–104 (1990).
    [Crossref]
  3. J. B. Richard, A. Andrew, S. Liubov, and P. M. Adrian, “Design of the mirror optical systems for coherent diffractive imaging at the SPB/SFX instrument of the European XFEL,” J. Opt. 18(7), 074011 (2016).
    [Crossref]
  4. P. Z. Takacs, S.-n. Qian, and J. Colbert, “Design of a long trace surface profiler,” Proc. SPIE 0749, 59–64 (1987).
    [Crossref]
  5. 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]
  6. S. Qian and M. Idir, “Innovative nano-accuracy surface profiler for sub-50 nrad rms mirror test,” Proc. SPIE 9687, 96870D (2016).
    [Crossref]
  7. 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]
  8. R. Kudo, T. Kitayama, Y. Tokuta, H. Shiraji, M. Nakano, K. Yamamura, and K. Endo, “High-accuracy three-dimensional aspheric mirror measurement with nanoprofiler based on normal vector tracing method,” Opt. Lasers Eng. 98, 159–162 (2017).
    [Crossref]
  9. 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]
  10. A. Rommeveaux and R. Barrett, “Micro-stitching interferometry at the ESRF,” Nucl. Instruments Methods Phys. Res. Sect. A: Accel. Spectrometers, Detect. Assoc. Equip. 616(2–3), 183–187 (2010).
    [Crossref]
  11. 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]
  12. H. Ohashi, T. Tsumura, H. Okada, H. Mimura, T. Masunaga, Y. Senba, S. Goto, K. Yamauchi, and T. Ishikawa, “Microstitching interferometer and relative angle determinable stitching interferometer for half-meter-long x-ray mirror,” Proc. SPIE 6704, 670405 (2007).
    [Crossref]
  13. 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]
  14. 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. Instrum. Meth. Phys. Res. A 616(2–3), 203–206 (2010).
    [Crossref]
  15. 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]
  16. A. Wiegmann, M. Schulz, and C. Elster, “Absolute profile measurement of large moderately flat optical surfaces with high dynamic range,” Opt. Express 16(16), 11975–11986 (2008).
    [Crossref] [PubMed]
  17. 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]
  18. C. B. Kreischer, “Retrace error: interferometry’s dark little secret,” Proc. SPIE 8884, 88840X (2013).
    [Crossref]
  19. 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]

2017 (2)

R. Kudo, T. Kitayama, Y. Tokuta, H. Shiraji, M. Nakano, K. Yamamura, and K. Endo, “High-accuracy three-dimensional aspheric mirror measurement with nanoprofiler based on normal vector tracing method,” Opt. Lasers Eng. 98, 159–162 (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 (2)

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

J. B. Richard, A. Andrew, S. Liubov, and P. M. Adrian, “Design of the mirror optical systems for coherent diffractive imaging at the SPB/SFX instrument of the European XFEL,” J. Opt. 18(7), 074011 (2016).
[Crossref]

2015 (1)

2014 (1)

2013 (1)

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

2010 (2)

A. Rommeveaux and R. Barrett, “Micro-stitching interferometry at the ESRF,” Nucl. Instruments Methods Phys. Res. Sect. A: Accel. Spectrometers, Detect. Assoc. Equip. 616(2–3), 183–187 (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. Instrum. Meth. Phys. Res. A 616(2–3), 203–206 (2010).
[Crossref]

2008 (2)

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]

A. Wiegmann, M. Schulz, and C. Elster, “Absolute profile measurement of large moderately flat optical surfaces with high dynamic range,” Opt. Express 16(16), 11975–11986 (2008).
[Crossref] [PubMed]

2007 (1)

H. Ohashi, T. Tsumura, H. Okada, H. Mimura, T. Masunaga, Y. Senba, S. Goto, K. Yamauchi, and T. Ishikawa, “Microstitching interferometer and relative angle determinable stitching interferometer for half-meter-long x-ray mirror,” Proc. SPIE 6704, 670405 (2007).
[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]

2004 (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]

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]

1997 (1)

1990 (1)

L. J. Hornbeck, “Deformable-mirror spatial light modulators,” Proc. SPIE 1150, 86–104 (1990).
[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]

Adrian, P. M.

J. B. Richard, A. Andrew, S. Liubov, and P. M. Adrian, “Design of the mirror optical systems for coherent diffractive imaging at the SPB/SFX instrument of the European XFEL,” J. Opt. 18(7), 074011 (2016).
[Crossref]

Andrew, A.

J. B. Richard, A. Andrew, S. Liubov, and P. M. Adrian, “Design of the mirror optical systems for coherent diffractive imaging at the SPB/SFX instrument of the European XFEL,” J. Opt. 18(7), 074011 (2016).
[Crossref]

Barrett, R.

A. Rommeveaux and R. Barrett, “Micro-stitching interferometry at the ESRF,” Nucl. Instruments Methods Phys. Res. Sect. A: Accel. Spectrometers, Detect. Assoc. Equip. 616(2–3), 183–187 (2010).
[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.

Elster, C.

A. Wiegmann, M. Schulz, and C. Elster, “Absolute profile measurement of large moderately flat optical surfaces with high dynamic range,” Opt. Express 16(16), 11975–11986 (2008).
[Crossref] [PubMed]

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]

Endo, K.

R. Kudo, T. Kitayama, Y. Tokuta, H. Shiraji, M. Nakano, K. Yamamura, and K. Endo, “High-accuracy three-dimensional aspheric mirror measurement with nanoprofiler based on normal vector tracing method,” Opt. Lasers Eng. 98, 159–162 (2017).
[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]

Gao, B.

Goto, S.

H. Ohashi, T. Tsumura, H. Okada, H. Mimura, T. Masunaga, Y. Senba, S. Goto, K. Yamauchi, and T. Ishikawa, “Microstitching interferometer and relative angle determinable stitching interferometer for half-meter-long x-ray mirror,” Proc. SPIE 6704, 670405 (2007).
[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. Instrum. Meth. Phys. Res. A 616(2–3), 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]

Hornbeck, L. J.

L. J. Hornbeck, “Deformable-mirror spatial light modulators,” Proc. SPIE 1150, 86–104 (1990).
[Crossref]

Hou, X.

Huang, L.

Idir, M.

Ishikawa, T.

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. Instrum. Meth. Phys. Res. A 616(2–3), 203–206 (2010).
[Crossref]

H. Ohashi, T. Tsumura, H. Okada, H. Mimura, T. Masunaga, Y. Senba, S. Goto, K. Yamauchi, and T. Ishikawa, “Microstitching interferometer and relative angle determinable stitching interferometer for half-meter-long x-ray mirror,” Proc. SPIE 6704, 670405 (2007).
[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.

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. Instrum. Meth. Phys. Res. A 616(2–3), 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]

Kitayama, T.

R. Kudo, T. Kitayama, Y. Tokuta, H. Shiraji, M. Nakano, K. Yamamura, and K. Endo, “High-accuracy three-dimensional aspheric mirror measurement with nanoprofiler based on normal vector tracing method,” Opt. Lasers Eng. 98, 159–162 (2017).
[Crossref]

Kreischer, C. B.

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

Kudo, R.

R. Kudo, T. Kitayama, Y. Tokuta, H. Shiraji, M. Nakano, K. Yamamura, and K. Endo, “High-accuracy three-dimensional aspheric mirror measurement with nanoprofiler based on normal vector tracing method,” Opt. Lasers Eng. 98, 159–162 (2017).
[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]

Legrand, J.

Liang, J.

Liubov, S.

J. B. Richard, A. Andrew, S. Liubov, and P. M. Adrian, “Design of the mirror optical systems for coherent diffractive imaging at the SPB/SFX instrument of the European XFEL,” J. Opt. 18(7), 074011 (2016).
[Crossref]

Masunaga, T.

H. Ohashi, T. Tsumura, H. Okada, H. Mimura, T. Masunaga, Y. Senba, S. Goto, K. Yamauchi, and T. Ishikawa, “Microstitching interferometer and relative angle determinable stitching interferometer for half-meter-long x-ray mirror,” Proc. SPIE 6704, 670405 (2007).
[Crossref]

Matsuyama, 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. Instrum. Meth. Phys. Res. A 616(2–3), 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]

Miller, D. T.

Mimura, H.

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. Instrum. Meth. Phys. Res. A 616(2–3), 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. Ohashi, T. Tsumura, H. Okada, H. Mimura, T. Masunaga, Y. Senba, S. Goto, K. Yamauchi, and T. Ishikawa, “Microstitching interferometer and relative angle determinable stitching interferometer for half-meter-long x-ray mirror,” Proc. SPIE 6704, 670405 (2007).
[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]

Nakano, M.

R. Kudo, T. Kitayama, Y. Tokuta, H. Shiraji, M. Nakano, K. Yamamura, and K. Endo, “High-accuracy three-dimensional aspheric mirror measurement with nanoprofiler based on normal vector tracing method,” Opt. Lasers Eng. 98, 159–162 (2017).
[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]

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]

Ohashi, H.

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. Instrum. Meth. Phys. Res. A 616(2–3), 203–206 (2010).
[Crossref]

H. Ohashi, T. Tsumura, H. Okada, H. Mimura, T. Masunaga, Y. Senba, S. Goto, K. Yamauchi, and T. Ishikawa, “Microstitching interferometer and relative angle determinable stitching interferometer for half-meter-long x-ray mirror,” Proc. SPIE 6704, 670405 (2007).
[Crossref]

Okada, H.

H. Ohashi, T. Tsumura, H. Okada, H. Mimura, T. Masunaga, Y. Senba, S. Goto, K. Yamauchi, and T. Ishikawa, “Microstitching interferometer and relative angle determinable stitching interferometer for half-meter-long x-ray mirror,” Proc. SPIE 6704, 670405 (2007).
[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]

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]

Richard, J. B.

J. B. Richard, A. Andrew, S. Liubov, and P. M. Adrian, “Design of the mirror optical systems for coherent diffractive imaging at the SPB/SFX instrument of the European XFEL,” J. Opt. 18(7), 074011 (2016).
[Crossref]

Rommeveaux, A.

A. Rommeveaux and R. Barrett, “Micro-stitching interferometry at the ESRF,” Nucl. Instruments Methods Phys. Res. Sect. A: Accel. Spectrometers, Detect. Assoc. Equip. 616(2–3), 183–187 (2010).
[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. Instrum. Meth. Phys. Res. A 616(2–3), 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]

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]

Schulz, M.

A. Wiegmann, M. Schulz, and C. Elster, “Absolute profile measurement of large moderately flat optical surfaces with high dynamic range,” Opt. Express 16(16), 11975–11986 (2008).
[Crossref] [PubMed]

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]

Senba, Y.

H. Ohashi, T. Tsumura, H. Okada, H. Mimura, T. Masunaga, Y. Senba, S. Goto, K. Yamauchi, and T. Ishikawa, “Microstitching interferometer and relative angle determinable stitching interferometer for half-meter-long x-ray mirror,” Proc. SPIE 6704, 670405 (2007).
[Crossref]

Shiraji, H.

R. Kudo, T. Kitayama, Y. Tokuta, H. Shiraji, M. Nakano, K. Yamamura, and K. Endo, “High-accuracy three-dimensional aspheric mirror measurement with nanoprofiler based on normal vector tracing method,” Opt. Lasers Eng. 98, 159–162 (2017).
[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.

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-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]

Tokuta, Y.

R. Kudo, T. Kitayama, Y. Tokuta, H. Shiraji, M. Nakano, K. Yamamura, and K. Endo, “High-accuracy three-dimensional aspheric mirror measurement with nanoprofiler based on normal vector tracing method,” Opt. Lasers Eng. 98, 159–162 (2017).
[Crossref]

Tsumura, T.

H. Ohashi, T. Tsumura, H. Okada, H. Mimura, T. Masunaga, Y. Senba, S. Goto, K. Yamauchi, and T. Ishikawa, “Microstitching interferometer and relative angle determinable stitching interferometer for half-meter-long x-ray mirror,” Proc. SPIE 6704, 670405 (2007).
[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]

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]

Wiegmann, A.

Williams, D. R.

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]

Yamamura, K.

R. Kudo, T. Kitayama, Y. Tokuta, H. Shiraji, M. Nakano, K. Yamamura, and K. Endo, “High-accuracy three-dimensional aspheric mirror measurement with nanoprofiler based on normal vector tracing method,” Opt. Lasers Eng. 98, 159–162 (2017).
[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]

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. Instrum. Meth. Phys. Res. A 616(2–3), 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. Ohashi, T. Tsumura, H. Okada, H. Mimura, T. Masunaga, Y. Senba, S. Goto, K. Yamauchi, and T. Ishikawa, “Microstitching interferometer and relative angle determinable stitching interferometer for half-meter-long x-ray mirror,” Proc. SPIE 6704, 670405 (2007).
[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.

Yumoto, H.

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. Instrum. Meth. Phys. Res. A 616(2–3), 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]

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]

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]

J. Opt. (1)

J. B. Richard, A. Andrew, S. Liubov, and P. M. Adrian, “Design of the mirror optical systems for coherent diffractive imaging at the SPB/SFX instrument of the European XFEL,” J. Opt. 18(7), 074011 (2016).
[Crossref]

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

Nucl. Instrum. Meth. Phys. Res. A (1)

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. Instrum. Meth. Phys. Res. A 616(2–3), 203–206 (2010).
[Crossref]

Nucl. Instruments Methods Phys. Res. Sect. A: Accel. Spectrometers, Detect. Assoc. Equip. (1)

A. Rommeveaux and R. Barrett, “Micro-stitching interferometry at the ESRF,” Nucl. Instruments Methods Phys. Res. Sect. A: Accel. Spectrometers, Detect. Assoc. Equip. 616(2–3), 183–187 (2010).
[Crossref]

Opt. Express (4)

Opt. Lasers Eng. (1)

R. Kudo, T. Kitayama, Y. Tokuta, H. Shiraji, M. Nakano, K. Yamamura, and K. Endo, “High-accuracy three-dimensional aspheric mirror measurement with nanoprofiler based on normal vector tracing method,” Opt. Lasers Eng. 98, 159–162 (2017).
[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 (5)

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

H. Ohashi, T. Tsumura, H. Okada, H. Mimura, T. Masunaga, Y. Senba, S. Goto, K. Yamauchi, and T. Ishikawa, “Microstitching interferometer and relative angle determinable stitching interferometer for half-meter-long x-ray mirror,” Proc. SPIE 6704, 670405 (2007).
[Crossref]

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

L. J. Hornbeck, “Deformable-mirror spatial light modulators,” Proc. SPIE 1150, 86–104 (1990).
[Crossref]

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

Rev. Sci. Instruments (2)

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 (12)

Fig. 1
Fig. 1 The 1D ASI setup is composed of an angular measurement device (e.g. an autocollimator with a flat mirror mounted on the translation stage) and an interferometer measuring local profiles of the SUT which travels with a translation stage.
Fig. 2
Fig. 2 The 1D ASI instrument used in our work is composed of a WLI, an AC with a flat mirror, and a linear stage on a granite vibration isolation table inside an enclosure.
Fig. 3
Fig. 3 The laser spots on the CCD are much more stable in position after the laser alignment.
Fig. 4
Fig. 4 The RMSE of WLI reduces with the increase of the average measurement number.
Fig. 5
Fig. 5 By lengthening the averaging time, the RMS values of the angular measurement become smaller in our measurement environment.
Fig. 6
Fig. 6 The raw data from 1D ASI include the local profiles from the WLI (a) and the autocollimator-measured tilt introduced by the stage pitch (b).
Fig. 7
Fig. 7 The stitched profiles with best fitted spheres removed by trusting the stage (a), pure software stitching (b), and AMS(c), and their height discrepancies from their own average profiles (d–f) as well as the histogram of the discrepancy RMS (g–i), respectively.
Fig. 8
Fig. 8 The sub-nanometer RMS repeatability is demonstrated with 10 scans by 1D ASI.
Fig. 9
Fig. 9 A flat mirror is measured by ASI. (a) Results of a flat mirror measured by ASI are close to other measurement results from different metrology instruments, and (b) the discrepancies of the absolute shape profiles measured by ASI in different mirror orientations on different dates.
Fig. 10
Fig. 10 Typical measurement raw data of the elliptical cylindrical mirror from 1D ASI: the local profiles from the WLI (a) and the autocollimator-measured tilt introduced by the stage pitch (b).
Fig. 11
Fig. 11 The residuals after the best fit of the particular ellipse removed with the same p, q, θ in Eq. (6). (a) The RMS values of the discrepancies from their average values of A↦B scans (b) and B↦A scans (c), respectively.
Fig. 12
Fig. 12 Results of the elliptical mirror measured by different instruments are compared. (a) Measurement results of the 1D ASI in both A↦B and B↦A orientations are compared with the results from the NSP and Osaka University, and (b) taking the residual of Osaka University as a reference, the discrepancies of NSP, ASI A↦B and ASI B↦A residuals are compared. All the differences are less than 2 nm RMS.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

t = tan ( α ) .
h n ( x ) = φ n ( x ) t n x .
Δ h n ¯ = { 0 n = 1 h n 1 ( x ) h n ( x ) ¯ n > 1 .
z n ( x ) = h n ( x ) + Δ h n ¯ .
( x + p cos θ ) 2 + ( z p sin θ ) 2 + ( x q cos θ ) 2 + ( z q sin θ ) 2 = p + q ,
{ p = 45.170 [ m ] q = 331.92 [ mm ] θ = 2.8 [ mrad ] .

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