Abstract

In this work, we proposed for stitching interferometry to use a triple-beam interferometer to measure both the distance and the tilt for all sub-apertures before the stitching process. The relative piston between two neighboring sub-apertures is then calculated by using the data in the overlapping area. Comparisons are made between our method, and the classical least-squares principle stitching method. Our method can improve the accuracy and repeatability of the classical stitching method when a large number of sub-aperture topographies are taken into account. Our simulations and experiments on flat and spherical mirrors indicate that our proposed method can decrease the influence of the interferometer error from the stitched result. The comparison of stitching system with Fizeau interferometry data is about 2 nm root mean squares and the repeatability is within ± 2.5 nm peak to valley.

© 2017 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Interferometer reference error suppression by the high-overlapping-density phase-stitching algorithm

Po-Chih Lin, Hung-Sheng Chang, Yi-Chun Chen, and Chao-Wen Liang
Appl. Opt. 53(29) H220-H226 (2014)

Non-null annular subaperture stitching interferometry for steep aspheric measurement

Lei Zhang, Chao Tian, Dong Liu, Tu Shi, Yongying Yang, Hanshuo Wu, and Yibing Shen
Appl. Opt. 53(25) 5755-5762 (2014)

Sub-aperture stitching interferometry using stereovision positioning technique

Pengfei Zhang, Hong Zhao, Xiang Zhou, and Jinjun Li
Opt. Express 18(14) 15216-15222 (2010)

References

  • View by:
  • |
  • |
  • |

  1. W. W. Chow and G. N. Lawrence, “Method for subaperture testing interferogram reduction,” Opt. Lett. 8(9), 468–470 (1983).
    [PubMed]
  2. J. G. Thunen and O. Y. Kwon, “Full aperture testing with subaperture test optics,” Proc. SPIE 0351, 19–27 (1983).
  3. C.-W. Liang, H.-S. Chang, P.-C. Lin, C.-C. Lee, and Y.-C. Chen, “Vibration modulated subaperture stitching interferometry,” Opt. Express 21(15), 18255–18260 (2013).
    [PubMed]
  4. S. Chen, Y. Dai, S. Li, X. Peng, and J. Wang, “Error reductions for stitching test of large optical flats,” Opt. Laser Technol. 44, 1543–1550 (2012).
  5. M. Bray, “Stitching interferometry–the long and winding road,” in International Optical Design Conference and Optical Fabrication and Testing (Optical Society of America, 2010), paper OMA5.
  6. 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, 32–38 (2006).
  7. A. Wiegmann, M. Stavridis, M. Walzel, F. Siewert, T. Zeschke, M. Schulz, and C. Elster, “Accuracy evaluation for sub-aperture interferometry measurements of a synchrotron mirror using virtual experiments,” Precis. Eng. 35, 183–190 (2011).
  8. G. A. Smith, C. Zhao, P. Su, and J. H. Burge, “Subaperture stitching performance estimation,” Proc. SPIE 8838, 88380D (2013).
  9. M. Bray, “Stitching interferometry and absolute surface shape metrology: similarities,” Proc. SPIE 4451, 375–383 (2001).
  10. F. Munteanu, “Self-calibrating lateral scanning white-light interferometer,” Appl. Opt. 49(12), 2371–2375 (2010).
    [PubMed]
  11. X. Jia, F. Xu, W. Xie, and T. Xing, “Analysis of absolute flatness testing in sub-stitching interferometer,” Proc. SPIE 9684, 968438 (2016).
  12. P. E. Murphy, G. W. Forbes, J. F. Fleig, D. Miladinovic, G. DeVries, and S. O’Donohue, “Recent advances in subaperture stitching interferometry,” in Frontiers in Optics (Optical Society of America, 2006), paper OFWC2.
  13. W. Deng, K. Wang, and J. Zhang, “Influence of alignment error and random noise on interferometry flat sub-aperture stitching,” Proc. SPIE 8417, 841715 (2012).
  14. A. Wiegmann, M. Stavridis, M. Walzel, F. Siewert, T. Zeschke, M. Schulz, and C. Elster, “Accuracy evaluation for sub-aperture interferometry measurements of a synchrotron mirror using virtual experiments,” Precis. Eng. 35, 183–190 (2011).
  15. 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. Instrum. 76, 045102 (2005).
  16. 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. Instrum. 74, 2894–2898 (2003).
  17. Y. Lu, F. Tang, X. Wang, Y. Li, X. Wan, F. Guo, and F. Dai, “A high-accuracy subaperture stitching system for nonflatness measurement of wafer stage mirror,” Proc. SPIE 9276, 927617 (2014).
  18. M. Schulz and C. Elster, “Traceable multiple sensor system for measuring curved surface profiles with high accuracy and high lateral resolution,” Opt. Eng. 45, 060503 (2006).
  19. 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).
    [PubMed]
  20. P. Murphy, G. Forbes, J. Fleig, P. Dumas, and M. Tricard, “Stitching interferometry: a flexible solution for surface metrology,” Opt. Photonics News 14, 38–43 (2003).

2016 (1)

X. Jia, F. Xu, W. Xie, and T. Xing, “Analysis of absolute flatness testing in sub-stitching interferometer,” Proc. SPIE 9684, 968438 (2016).

2014 (1)

Y. Lu, F. Tang, X. Wang, Y. Li, X. Wan, F. Guo, and F. Dai, “A high-accuracy subaperture stitching system for nonflatness measurement of wafer stage mirror,” Proc. SPIE 9276, 927617 (2014).

2013 (2)

C.-W. Liang, H.-S. Chang, P.-C. Lin, C.-C. Lee, and Y.-C. Chen, “Vibration modulated subaperture stitching interferometry,” Opt. Express 21(15), 18255–18260 (2013).
[PubMed]

G. A. Smith, C. Zhao, P. Su, and J. H. Burge, “Subaperture stitching performance estimation,” Proc. SPIE 8838, 88380D (2013).

2012 (2)

S. Chen, Y. Dai, S. Li, X. Peng, and J. Wang, “Error reductions for stitching test of large optical flats,” Opt. Laser Technol. 44, 1543–1550 (2012).

W. Deng, K. Wang, and J. Zhang, “Influence of alignment error and random noise on interferometry flat sub-aperture stitching,” Proc. SPIE 8417, 841715 (2012).

2011 (2)

A. Wiegmann, M. Stavridis, M. Walzel, F. Siewert, T. Zeschke, M. Schulz, and C. Elster, “Accuracy evaluation for sub-aperture interferometry measurements of a synchrotron mirror using virtual experiments,” Precis. Eng. 35, 183–190 (2011).

A. Wiegmann, M. Stavridis, M. Walzel, F. Siewert, T. Zeschke, M. Schulz, and C. Elster, “Accuracy evaluation for sub-aperture interferometry measurements of a synchrotron mirror using virtual experiments,” Precis. Eng. 35, 183–190 (2011).

2010 (1)

2008 (1)

2006 (2)

M. Schulz and C. Elster, “Traceable multiple sensor system for measuring curved surface profiles with high accuracy and high lateral resolution,” Opt. Eng. 45, 060503 (2006).

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, 32–38 (2006).

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. Instrum. 76, 045102 (2005).

2003 (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. Instrum. 74, 2894–2898 (2003).

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

2001 (1)

M. Bray, “Stitching interferometry and absolute surface shape metrology: similarities,” Proc. SPIE 4451, 375–383 (2001).

1983 (2)

W. W. Chow and G. N. Lawrence, “Method for subaperture testing interferogram reduction,” Opt. Lett. 8(9), 468–470 (1983).
[PubMed]

J. G. Thunen and O. Y. Kwon, “Full aperture testing with subaperture test optics,” Proc. SPIE 0351, 19–27 (1983).

Bray, M.

M. Bray, “Stitching interferometry and absolute surface shape metrology: similarities,” Proc. SPIE 4451, 375–383 (2001).

Burge, J. H.

G. A. Smith, C. Zhao, P. Su, and J. H. Burge, “Subaperture stitching performance estimation,” Proc. SPIE 8838, 88380D (2013).

Chang, H.-S.

Chen, S.

S. Chen, Y. Dai, S. Li, X. Peng, and J. Wang, “Error reductions for stitching test of large optical flats,” Opt. Laser Technol. 44, 1543–1550 (2012).

Chen, Y.-C.

Chow, W. W.

Dai, F.

Y. Lu, F. Tang, X. Wang, Y. Li, X. Wan, F. Guo, and F. Dai, “A high-accuracy subaperture stitching system for nonflatness measurement of wafer stage mirror,” Proc. SPIE 9276, 927617 (2014).

Dai, Y.

S. Chen, Y. Dai, S. Li, X. Peng, and J. Wang, “Error reductions for stitching test of large optical flats,” Opt. Laser Technol. 44, 1543–1550 (2012).

Deng, W.

W. Deng, K. Wang, and J. Zhang, “Influence of alignment error and random noise on interferometry flat sub-aperture stitching,” Proc. SPIE 8417, 841715 (2012).

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, 38–43 (2003).

Elster, C.

A. Wiegmann, M. Stavridis, M. Walzel, F. Siewert, T. Zeschke, M. Schulz, and C. Elster, “Accuracy evaluation for sub-aperture interferometry measurements of a synchrotron mirror using virtual experiments,” Precis. Eng. 35, 183–190 (2011).

A. Wiegmann, M. Stavridis, M. Walzel, F. Siewert, T. Zeschke, M. Schulz, and C. Elster, “Accuracy evaluation for sub-aperture interferometry measurements of a synchrotron mirror using virtual experiments,” Precis. Eng. 35, 183–190 (2011).

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).
[PubMed]

M. Schulz and C. Elster, “Traceable multiple sensor system for measuring curved surface profiles with high accuracy and high lateral resolution,” Opt. Eng. 45, 060503 (2006).

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, 32–38 (2006).

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. Instrum. 76, 045102 (2005).

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. Instrum. 74, 2894–2898 (2003).

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, 38–43 (2003).

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, 38–43 (2003).

Guo, F.

Y. Lu, F. Tang, X. Wang, Y. Li, X. Wan, F. Guo, and F. Dai, “A high-accuracy subaperture stitching system for nonflatness measurement of wafer stage mirror,” Proc. SPIE 9276, 927617 (2014).

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-ray reflective optics,” Rev. Sci. Instrum. 76, 045102 (2005).

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. Instrum. 74, 2894–2898 (2003).

Jia, X.

X. Jia, F. Xu, W. Xie, and T. Xing, “Analysis of absolute flatness testing in sub-stitching interferometer,” Proc. SPIE 9684, 968438 (2016).

Kwon, O. Y.

J. G. Thunen and O. Y. Kwon, “Full aperture testing with subaperture test optics,” Proc. SPIE 0351, 19–27 (1983).

Lawrence, G. N.

Lee, C.-C.

Li, S.

S. Chen, Y. Dai, S. Li, X. Peng, and J. Wang, “Error reductions for stitching test of large optical flats,” Opt. Laser Technol. 44, 1543–1550 (2012).

Li, Y.

Y. Lu, F. Tang, X. Wang, Y. Li, X. Wan, F. Guo, and F. Dai, “A high-accuracy subaperture stitching system for nonflatness measurement of wafer stage mirror,” Proc. SPIE 9276, 927617 (2014).

Liang, C.-W.

Lin, P.-C.

Lu, Y.

Y. Lu, F. Tang, X. Wang, Y. Li, X. Wan, F. Guo, and F. Dai, “A high-accuracy subaperture stitching system for nonflatness measurement of wafer stage mirror,” Proc. SPIE 9276, 927617 (2014).

Matsuyama, S.

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. Instrum. 76, 045102 (2005).

Mimura, H.

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. Instrum. 76, 045102 (2005).

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. Instrum. 74, 2894–2898 (2003).

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. Instrum. 76, 045102 (2005).

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. Instrum. 74, 2894–2898 (2003).

Munteanu, F.

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, 38–43 (2003).

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. Instrum. 76, 045102 (2005).

Peng, X.

S. Chen, Y. Dai, S. Li, X. Peng, and J. Wang, “Error reductions for stitching test of large optical flats,” Opt. Laser Technol. 44, 1543–1550 (2012).

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. Instrum. 74, 2894–2898 (2003).

Sano, 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. Instrum. 76, 045102 (2005).

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. Instrum. 74, 2894–2898 (2003).

Schulz, M.

A. Wiegmann, M. Stavridis, M. Walzel, F. Siewert, T. Zeschke, M. Schulz, and C. Elster, “Accuracy evaluation for sub-aperture interferometry measurements of a synchrotron mirror using virtual experiments,” Precis. Eng. 35, 183–190 (2011).

A. Wiegmann, M. Stavridis, M. Walzel, F. Siewert, T. Zeschke, M. Schulz, and C. Elster, “Accuracy evaluation for sub-aperture interferometry measurements of a synchrotron mirror using virtual experiments,” Precis. Eng. 35, 183–190 (2011).

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).
[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, 32–38 (2006).

M. Schulz and C. Elster, “Traceable multiple sensor system for measuring curved surface profiles with high accuracy and high lateral resolution,” Opt. Eng. 45, 060503 (2006).

Siewert, F.

A. Wiegmann, M. Stavridis, M. Walzel, F. Siewert, T. Zeschke, M. Schulz, and C. Elster, “Accuracy evaluation for sub-aperture interferometry measurements of a synchrotron mirror using virtual experiments,” Precis. Eng. 35, 183–190 (2011).

A. Wiegmann, M. Stavridis, M. Walzel, F. Siewert, T. Zeschke, M. Schulz, and C. Elster, “Accuracy evaluation for sub-aperture interferometry measurements of a synchrotron mirror using virtual experiments,” Precis. Eng. 35, 183–190 (2011).

Smith, G. A.

G. A. Smith, C. Zhao, P. Su, and J. H. Burge, “Subaperture stitching performance estimation,” Proc. SPIE 8838, 88380D (2013).

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. Instrum. 74, 2894–2898 (2003).

Stavridis, M.

A. Wiegmann, M. Stavridis, M. Walzel, F. Siewert, T. Zeschke, M. Schulz, and C. Elster, “Accuracy evaluation for sub-aperture interferometry measurements of a synchrotron mirror using virtual experiments,” Precis. Eng. 35, 183–190 (2011).

A. Wiegmann, M. Stavridis, M. Walzel, F. Siewert, T. Zeschke, M. Schulz, and C. Elster, “Accuracy evaluation for sub-aperture interferometry measurements of a synchrotron mirror using virtual experiments,” Precis. Eng. 35, 183–190 (2011).

Su, P.

G. A. Smith, C. Zhao, P. Su, and J. H. Burge, “Subaperture stitching performance estimation,” Proc. SPIE 8838, 88380D (2013).

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. Instrum. 76, 045102 (2005).

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. Instrum. 74, 2894–2898 (2003).

Tang, F.

Y. Lu, F. Tang, X. Wang, Y. Li, X. Wan, F. Guo, and F. Dai, “A high-accuracy subaperture stitching system for nonflatness measurement of wafer stage mirror,” Proc. SPIE 9276, 927617 (2014).

Thunen, J. G.

J. G. Thunen and O. Y. Kwon, “Full aperture testing with subaperture test optics,” Proc. SPIE 0351, 19–27 (1983).

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, 38–43 (2003).

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. Instrum. 76, 045102 (2005).

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. Instrum. 74, 2894–2898 (2003).

Walzel, M.

A. Wiegmann, M. Stavridis, M. Walzel, F. Siewert, T. Zeschke, M. Schulz, and C. Elster, “Accuracy evaluation for sub-aperture interferometry measurements of a synchrotron mirror using virtual experiments,” Precis. Eng. 35, 183–190 (2011).

A. Wiegmann, M. Stavridis, M. Walzel, F. Siewert, T. Zeschke, M. Schulz, and C. Elster, “Accuracy evaluation for sub-aperture interferometry measurements of a synchrotron mirror using virtual experiments,” Precis. Eng. 35, 183–190 (2011).

Wan, X.

Y. Lu, F. Tang, X. Wang, Y. Li, X. Wan, F. Guo, and F. Dai, “A high-accuracy subaperture stitching system for nonflatness measurement of wafer stage mirror,” Proc. SPIE 9276, 927617 (2014).

Wang, J.

S. Chen, Y. Dai, S. Li, X. Peng, and J. Wang, “Error reductions for stitching test of large optical flats,” Opt. Laser Technol. 44, 1543–1550 (2012).

Wang, K.

W. Deng, K. Wang, and J. Zhang, “Influence of alignment error and random noise on interferometry flat sub-aperture stitching,” Proc. SPIE 8417, 841715 (2012).

Wang, X.

Y. Lu, F. Tang, X. Wang, Y. Li, X. Wan, F. Guo, and F. Dai, “A high-accuracy subaperture stitching system for nonflatness measurement of wafer stage mirror,” Proc. SPIE 9276, 927617 (2014).

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, 32–38 (2006).

Wiegmann, A.

A. Wiegmann, M. Stavridis, M. Walzel, F. Siewert, T. Zeschke, M. Schulz, and C. Elster, “Accuracy evaluation for sub-aperture interferometry measurements of a synchrotron mirror using virtual experiments,” Precis. Eng. 35, 183–190 (2011).

A. Wiegmann, M. Stavridis, M. Walzel, F. Siewert, T. Zeschke, M. Schulz, and C. Elster, “Accuracy evaluation for sub-aperture interferometry measurements of a synchrotron mirror using virtual experiments,” Precis. Eng. 35, 183–190 (2011).

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).
[PubMed]

Xie, W.

X. Jia, F. Xu, W. Xie, and T. Xing, “Analysis of absolute flatness testing in sub-stitching interferometer,” Proc. SPIE 9684, 968438 (2016).

Xing, T.

X. Jia, F. Xu, W. Xie, and T. Xing, “Analysis of absolute flatness testing in sub-stitching interferometer,” Proc. SPIE 9684, 968438 (2016).

Xu, F.

X. Jia, F. Xu, W. Xie, and T. Xing, “Analysis of absolute flatness testing in sub-stitching interferometer,” Proc. SPIE 9684, 968438 (2016).

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. Instrum. 76, 045102 (2005).

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. Instrum. 74, 2894–2898 (2003).

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. Instrum. 76, 045102 (2005).

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. Instrum. 74, 2894–2898 (2003).

Yamauchi, 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. Instrum. 76, 045102 (2005).

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. Instrum. 74, 2894–2898 (2003).

Yumoto, H.

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. Instrum. 76, 045102 (2005).

Zeschke, T.

A. Wiegmann, M. Stavridis, M. Walzel, F. Siewert, T. Zeschke, M. Schulz, and C. Elster, “Accuracy evaluation for sub-aperture interferometry measurements of a synchrotron mirror using virtual experiments,” Precis. Eng. 35, 183–190 (2011).

A. Wiegmann, M. Stavridis, M. Walzel, F. Siewert, T. Zeschke, M. Schulz, and C. Elster, “Accuracy evaluation for sub-aperture interferometry measurements of a synchrotron mirror using virtual experiments,” Precis. Eng. 35, 183–190 (2011).

Zhang, J.

W. Deng, K. Wang, and J. Zhang, “Influence of alignment error and random noise on interferometry flat sub-aperture stitching,” Proc. SPIE 8417, 841715 (2012).

Zhao, C.

G. A. Smith, C. Zhao, P. Su, and J. H. Burge, “Subaperture stitching performance estimation,” Proc. SPIE 8838, 88380D (2013).

Appl. Opt. (1)

Opt. Eng. (1)

M. Schulz and C. Elster, “Traceable multiple sensor system for measuring curved surface profiles with high accuracy and high lateral resolution,” Opt. Eng. 45, 060503 (2006).

Opt. Express (2)

Opt. Laser Technol. (1)

S. Chen, Y. Dai, S. Li, X. Peng, and J. Wang, “Error reductions for stitching test of large optical flats,” Opt. Laser Technol. 44, 1543–1550 (2012).

Opt. Lett. (1)

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, 38–43 (2003).

Precis. Eng. (3)

A. Wiegmann, M. Stavridis, M. Walzel, F. Siewert, T. Zeschke, M. Schulz, and C. Elster, “Accuracy evaluation for sub-aperture interferometry measurements of a synchrotron mirror using virtual experiments,” Precis. Eng. 35, 183–190 (2011).

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, 32–38 (2006).

A. Wiegmann, M. Stavridis, M. Walzel, F. Siewert, T. Zeschke, M. Schulz, and C. Elster, “Accuracy evaluation for sub-aperture interferometry measurements of a synchrotron mirror using virtual experiments,” Precis. Eng. 35, 183–190 (2011).

Proc. SPIE (6)

G. A. Smith, C. Zhao, P. Su, and J. H. Burge, “Subaperture stitching performance estimation,” Proc. SPIE 8838, 88380D (2013).

M. Bray, “Stitching interferometry and absolute surface shape metrology: similarities,” Proc. SPIE 4451, 375–383 (2001).

J. G. Thunen and O. Y. Kwon, “Full aperture testing with subaperture test optics,” Proc. SPIE 0351, 19–27 (1983).

X. Jia, F. Xu, W. Xie, and T. Xing, “Analysis of absolute flatness testing in sub-stitching interferometer,” Proc. SPIE 9684, 968438 (2016).

W. Deng, K. Wang, and J. Zhang, “Influence of alignment error and random noise on interferometry flat sub-aperture stitching,” Proc. SPIE 8417, 841715 (2012).

Y. Lu, F. Tang, X. Wang, Y. Li, X. Wan, F. Guo, and F. Dai, “A high-accuracy subaperture stitching system for nonflatness measurement of wafer stage mirror,” Proc. SPIE 9276, 927617 (2014).

Rev. Sci. Instrum. (2)

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. Instrum. 76, 045102 (2005).

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. Instrum. 74, 2894–2898 (2003).

Other (2)

P. E. Murphy, G. W. Forbes, J. F. Fleig, D. Miladinovic, G. DeVries, and S. O’Donohue, “Recent advances in subaperture stitching interferometry,” in Frontiers in Optics (Optical Society of America, 2006), paper OFWC2.

M. Bray, “Stitching interferometry–the long and winding road,” in International Optical Design Conference and Optical Fabrication and Testing (Optical Society of America, 2010), paper OMA5.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (14)

Fig. 1
Fig. 1

Scheme of the 1D sub-aperture stitching system with the TBI. The SUT is fixed on the linear stage.

Fig. 2
Fig. 2

The simulated mirror under test. (a) height mirror map, (b) height profile along the center line.

Fig. 3
Fig. 3

An example of simulated measurement error for one sub-aperture. (a) measurement noise, (b) center line profile along x-direction in (a), (c) retrace error, (d) center line profile along x-direction in (c).

Fig. 4
Fig. 4

Stitching results and errors. The upper image is the stitched profile, the center plot shows the stitched and true profile, and the lower image is the stitching error. (a) SSI-TBI, (b) SSI-LS.

Fig. 5
Fig. 5

The accuracy and repeatability of SSI-TBI with 10 scans were simulated in different STD of angular measurement errors. (a) without retrace errors, (b) with retrace errors.

Fig. 6
Fig. 6

The accuracy and repeatability of SSI-LS with 10 scans were simulated in different STD of stage errors. (a) without retrace errors, (b) with retrace errors.

Fig. 7
Fig. 7

SSI-TBI experimental setup.

Fig. 8
Fig. 8

One hour stability test of SIOS TBI. (a) distance, (b) tilt.

Fig. 9
Fig. 9

Sub-aperture profiles with two scans in three mirror positions. (a) left side, (b) center, (c) right side.

Fig. 10
Fig. 10

A flat mirror was measured along the central line. (a) SSI-TBI, (b) SSI-LS, (c) Fizeau interferometer.

Fig. 11
Fig. 11

Comparison of three methods. (a) profiles, (b) Stitching error.

Fig. 12
Fig. 12

Calculated repeatability using the profiles of 10 scans (a) SSI-TBI, (c) SSI-LS.

Fig. 13
Fig. 13

A spherical mirror was measured along the central line. (a) SSI-TBI, (b) SSI-LS, (c) Fizeau interferometer, (d) Comparison of the measured profiles from SSI-TBI and SSI-LS and Fizeau.

Fig. 14
Fig. 14

The stable process of SIOS TBI is needed about 1 hour. (a) distance, (b) tilt.

Equations (4)

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

X n = d n +x n=1,2,,N
Z n = z n + p n + t n x n=1,2,,N
p n ={ 0 n=1 Z n - Z n-1 ¯ n1
z=a x 4 +b x 2 ,