Abstract

Measurement of steep acylindrical surface has the difficulty with respect to its large localized slope, which may lead to irresolvable fringe densities in off-axis subapertures. To address this problem, we analyze the departure of off-axis acylindrical subapertures, and propose a measurement strategy by yawing the cylinder null. When the cylinder null is yawed with different angles, variable mounts of acylindrical wavefronts are generated to compensate most of the aberrations for different off-axis subapertures. Thus, the fringe densities are drastically reduced within the vertical dynamic range of interferometers. To connect all subaperture together, we also propose an acylindrical stitching approach. Experimental results demonstrate that an acylindrical lens with a departure of up to 81µm from the best-fitting cylinder can be measured using the proposed method. More importantly, it does not require an additional reconfigurable optical null, making the measurement system simple and inexpensive.

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

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References

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  4. P. Su, J. H. Burge, and R. E. Parks, “Application of maximum likelihood reconstruction of subaperture data for measurement of large flat mirrors,” Appl. Optics 49(1), 21–31 (2010).
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  6. P. Murphy, G. Forbes, J. Fleig, P. Dumas, and M. Tricard, “Stitching Interferometry: A Flexible Solution for Surface Metrology,” Optics and Photonics News 14, 38–43 (2003).
    [Crossref]
  7. P. Murphy, J. Fleig, F. Forbes, D. Miladinovic, G. DeVries, and S. O’Donohue, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE 6293, 62930J (2006).
    [Crossref]
  8. Z. Zhao, H. Zhao, F. Gu, H. Du, and K. Li, “Non-null testing for aspheric surfaces using elliptical sub-aperture stitching technique,” Opt. Express 22(5), 5512–5521 (2014).
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    [Crossref] [PubMed]
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    [Crossref]
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  13. D. Liu, T. Shi, L. Zhang, Y. Yang, S. Chong, and Y. Shen, “Reverse optimization reconstruction of aspheric figure error in a non-null interferometer,” Appl. Optics 53(24), 5538–5546 (2014)
    [Crossref]
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    [Crossref]
  23. T. Shi, D. Liu, Y. Zhou, T. Yan, Y. Yang, L. Zhang, J. Bai, Y. Shen, L. Miao, and W. Huang, “Practical retrace error correction in non-null aspheric testing: A comparison,” Opt. Commun. 383(15), 378–385 (2017).
    [Crossref]
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2017 (1)

T. Shi, D. Liu, Y. Zhou, T. Yan, Y. Yang, L. Zhang, J. Bai, Y. Shen, L. Miao, and W. Huang, “Practical retrace error correction in non-null aspheric testing: A comparison,” Opt. Commun. 383(15), 378–385 (2017).
[Crossref]

2016 (2)

Q. Hao, S. Wang, Y. Hu, H. Cheng, M. Chen, and T. Li, “Virtual interferometer calibration method of a non-null interferometer for freeform surface measurements,” Appl. Optics 55(35), 9992–10001 (2016).
[Crossref]

J. Peng, X. Liu, X. Peng, Y. Yu, and X. Li, “Selection of F/number in lattice design for stitching inferferometry of aspheric surface,” Proc. SPIE 10250, 1025010 (2016);

2015 (4)

2014 (5)

X. Wang, “Measurement of mild asphere by digital plane,” Chin. Opt. Lett. 12(s2), S21201 (2014).
[Crossref]

Z. Zhao, H. Zhao, F. Gu, H. Du, and K. Li, “Non-null testing for aspheric surfaces using elliptical sub-aperture stitching technique,” Opt. Express 22(5), 5512–5521 (2014).
[Crossref] [PubMed]

S. Chen, C. Zhao, Y. Dai, and S. Li, “Reconfigurable optical null based on counter-rotating Zernike plates for test of aspheres,” Opt. Express 22(2), 1381–1386 (2014).
[Crossref] [PubMed]

D. Liu, T. Shi, L. Zhang, Y. Yang, S. Chong, and Y. Shen, “Reverse optimization reconstruction of aspheric figure error in a non-null interferometer,” Appl. Optics 53(24), 5538–5546 (2014)
[Crossref]

L. Zhang, C. Tian, D. Liu, T. Shi, Y. Yang, H. Wu, and Y. Shen, “Non-null annular subaperture stitching interferometry for steep aspheric measurement,” Appl. Optics 53(25), 5755–5762 (2014)
[Crossref]

2012 (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).
[Crossref]

2010 (3)

P. Su, J. H. Burge, and R. E. Parks, “Application of maximum likelihood reconstruction of subaperture data for measurement of large flat mirrors,” Appl. Optics 49(1), 21–31 (2010).
[Crossref]

V. N. Mahajan, “Orthonormal aberration polynomials for anamorphic optical imaging systems with rectangular pupils,” Appl. Optics 49(36), 6924–6929 (2010).
[Crossref]

M. Tricard, A. Kulawiec, M. Bauer, G. Devries, J. Fleig, G. Forbes, D. Miladinovich, and P. Murphy, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Annals-Manuf. Techn. 59, 547–550 (2010).
[Crossref]

2009 (1)

2006 (3)

P. Murphy, J. Fleig, F. Forbes, D. Miladinovic, G. DeVries, and S. O’Donohue, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE 6293, 62930J (2006).
[Crossref]

S. Chen, S. Li, Y. Dai, and Z. Zheng, “Lattice design for subaperture stitching test of a concave paraboloid surface,” Appl. Optics 45(10), 2280–2286 (2006).
[Crossref]

S. Chen, S. Li, Y. Dai, and Z. Zheng, “Iterative algorithm for subaperture stitching test with spherical interferometers,” J. Opt. Soc. Am. A,  23(5), 1219–1226 (2006).
[Crossref]

2003 (2)

H. Guo and M. Chen, “Multiview connection technique for 360-deg three-dimensional measurement,” Opt. Eng. 42(4), 900–905 (2003).
[Crossref]

P. Murphy, G. Forbes, J. Fleig, P. Dumas, and M. Tricard, “Stitching Interferometry: A Flexible Solution for Surface Metrology,” Optics and Photonics News 14, 38–43 (2003).
[Crossref]

1994 (1)

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

Bai, J.

T. Shi, D. Liu, Y. Zhou, T. Yan, Y. Yang, L. Zhang, J. Bai, Y. Shen, L. Miao, and W. Huang, “Practical retrace error correction in non-null aspheric testing: A comparison,” Opt. Commun. 383(15), 378–385 (2017).
[Crossref]

L. Zhang, D. Liu, T. Shi, Y. Yang, S. Chong, B. Ge, Y. Shen, and J. Bai, “Aspheric subaperture stitching based on system modeling,” Opt. Express 23(15), 19176–19188 (2015).
[Crossref] [PubMed]

Bauer, M.

M. Tricard, A. Kulawiec, M. Bauer, G. Devries, J. Fleig, G. Forbes, D. Miladinovich, and P. Murphy, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Annals-Manuf. Techn. 59, 547–550 (2010).
[Crossref]

Burge, J. H.

P. Su, J. H. Burge, and R. E. Parks, “Application of maximum likelihood reconstruction of subaperture data for measurement of large flat mirrors,” Appl. Optics 49(1), 21–31 (2010).
[Crossref]

Chen, M.

Q. Hao, S. Wang, Y. Hu, H. Cheng, M. Chen, and T. Li, “Virtual interferometer calibration method of a non-null interferometer for freeform surface measurements,” Appl. Optics 55(35), 9992–10001 (2016).
[Crossref]

J. Peng, H. Xu, Y. Yu, and M. Chen, “Stitching interferometry for cylindrical optics with large angular aperture,” Meas. Sci. Technol. 26(1), 025204 (2015).
[Crossref]

H. Guo and M. Chen, “Multiview connection technique for 360-deg three-dimensional measurement,” Opt. Eng. 42(4), 900–905 (2003).
[Crossref]

Chen, S.

Cheng, H.

Q. Hao, S. Wang, Y. Hu, H. Cheng, M. Chen, and T. Li, “Virtual interferometer calibration method of a non-null interferometer for freeform surface measurements,” Appl. Optics 55(35), 9992–10001 (2016).
[Crossref]

Chong, S.

L. Zhang, D. Liu, T. Shi, Y. Yang, S. Chong, B. Ge, Y. Shen, and J. Bai, “Aspheric subaperture stitching based on system modeling,” Opt. Express 23(15), 19176–19188 (2015).
[Crossref] [PubMed]

D. Liu, T. Shi, L. Zhang, Y. Yang, S. Chong, and Y. Shen, “Reverse optimization reconstruction of aspheric figure error in a non-null interferometer,” Appl. Optics 53(24), 5538–5546 (2014)
[Crossref]

Dai, Y.

Devries, G.

M. Tricard, A. Kulawiec, M. Bauer, G. Devries, J. Fleig, G. Forbes, D. Miladinovich, and P. Murphy, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Annals-Manuf. Techn. 59, 547–550 (2010).
[Crossref]

P. Murphy, J. Fleig, F. Forbes, D. Miladinovic, G. DeVries, and S. O’Donohue, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE 6293, 62930J (2006).
[Crossref]

Du, H.

Dumas, P.

P. Murphy, G. Forbes, J. Fleig, P. Dumas, and M. Tricard, “Stitching Interferometry: A Flexible Solution for Surface Metrology,” Optics and Photonics News 14, 38–43 (2003).
[Crossref]

Fleig, J.

M. Tricard, A. Kulawiec, M. Bauer, G. Devries, J. Fleig, G. Forbes, D. Miladinovich, and P. Murphy, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Annals-Manuf. Techn. 59, 547–550 (2010).
[Crossref]

P. Murphy, J. Fleig, F. Forbes, D. Miladinovic, G. DeVries, and S. O’Donohue, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE 6293, 62930J (2006).
[Crossref]

P. Murphy, G. Forbes, J. Fleig, P. Dumas, and M. Tricard, “Stitching Interferometry: A Flexible Solution for Surface Metrology,” Optics and Photonics News 14, 38–43 (2003).
[Crossref]

Forbes, F.

P. Murphy, J. Fleig, F. Forbes, D. Miladinovic, G. DeVries, and S. O’Donohue, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE 6293, 62930J (2006).
[Crossref]

Forbes, G.

M. Tricard, A. Kulawiec, M. Bauer, G. Devries, J. Fleig, G. Forbes, D. Miladinovich, and P. Murphy, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Annals-Manuf. Techn. 59, 547–550 (2010).
[Crossref]

P. Murphy, G. Forbes, J. Fleig, P. Dumas, and M. Tricard, “Stitching Interferometry: A Flexible Solution for Surface Metrology,” Optics and Photonics News 14, 38–43 (2003).
[Crossref]

Ge, B.

Gu, F.

Guo, H.

H. Guo and M. Chen, “Multiview connection technique for 360-deg three-dimensional measurement,” Opt. Eng. 42(4), 900–905 (2003).
[Crossref]

Hao, Q.

Q. Hao, S. Wang, Y. Hu, H. Cheng, M. Chen, and T. Li, “Virtual interferometer calibration method of a non-null interferometer for freeform surface measurements,” Appl. Optics 55(35), 9992–10001 (2016).
[Crossref]

Hu, Y.

Q. Hao, S. Wang, Y. Hu, H. Cheng, M. Chen, and T. Li, “Virtual interferometer calibration method of a non-null interferometer for freeform surface measurements,” Appl. Optics 55(35), 9992–10001 (2016).
[Crossref]

Huang, W.

T. Shi, D. Liu, Y. Zhou, T. Yan, Y. Yang, L. Zhang, J. Bai, Y. Shen, L. Miao, and W. Huang, “Practical retrace error correction in non-null aspheric testing: A comparison,” Opt. Commun. 383(15), 378–385 (2017).
[Crossref]

Kulawiec, A.

M. Tricard, A. Kulawiec, M. Bauer, G. Devries, J. Fleig, G. Forbes, D. Miladinovich, and P. Murphy, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Annals-Manuf. Techn. 59, 547–550 (2010).
[Crossref]

Li, K.

Li, S.

Li, T.

Q. Hao, S. Wang, Y. Hu, H. Cheng, M. Chen, and T. Li, “Virtual interferometer calibration method of a non-null interferometer for freeform surface measurements,” Appl. Optics 55(35), 9992–10001 (2016).
[Crossref]

Li, X.

J. Peng, X. Liu, X. Peng, Y. Yu, and X. Li, “Selection of F/number in lattice design for stitching inferferometry of aspheric surface,” Proc. SPIE 10250, 1025010 (2016);

Liu, D.

T. Shi, D. Liu, Y. Zhou, T. Yan, Y. Yang, L. Zhang, J. Bai, Y. Shen, L. Miao, and W. Huang, “Practical retrace error correction in non-null aspheric testing: A comparison,” Opt. Commun. 383(15), 378–385 (2017).
[Crossref]

L. Zhang, D. Liu, T. Shi, Y. Yang, S. Chong, B. Ge, Y. Shen, and J. Bai, “Aspheric subaperture stitching based on system modeling,” Opt. Express 23(15), 19176–19188 (2015).
[Crossref] [PubMed]

L. Zhang, C. Tian, D. Liu, T. Shi, Y. Yang, H. Wu, and Y. Shen, “Non-null annular subaperture stitching interferometry for steep aspheric measurement,” Appl. Optics 53(25), 5755–5762 (2014)
[Crossref]

D. Liu, T. Shi, L. Zhang, Y. Yang, S. Chong, and Y. Shen, “Reverse optimization reconstruction of aspheric figure error in a non-null interferometer,” Appl. Optics 53(24), 5538–5546 (2014)
[Crossref]

D. Liu, Y. Yang, C. Tian, Y. Luo, and L. Wang, “Practical methods for retrace error correction in nonnull aspheric testing,” Opt. Express 17(9), 7025–7035 (2009)
[Crossref] [PubMed]

Liu, X.

J. Peng, X. Liu, X. Peng, Y. Yu, and X. Li, “Selection of F/number in lattice design for stitching inferferometry of aspheric surface,” Proc. SPIE 10250, 1025010 (2016);

Luo, Y.

Mahajan, V. N.

V. N. Mahajan, “Orthonormal aberration polynomials for anamorphic optical imaging systems with rectangular pupils,” Appl. Optics 49(36), 6924–6929 (2010).
[Crossref]

Miao, L.

T. Shi, D. Liu, Y. Zhou, T. Yan, Y. Yang, L. Zhang, J. Bai, Y. Shen, L. Miao, and W. Huang, “Practical retrace error correction in non-null aspheric testing: A comparison,” Opt. Commun. 383(15), 378–385 (2017).
[Crossref]

Miladinovic, D.

P. Murphy, J. Fleig, F. Forbes, D. Miladinovic, G. DeVries, and S. O’Donohue, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE 6293, 62930J (2006).
[Crossref]

Miladinovich, D.

M. Tricard, A. Kulawiec, M. Bauer, G. Devries, J. Fleig, G. Forbes, D. Miladinovich, and P. Murphy, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Annals-Manuf. Techn. 59, 547–550 (2010).
[Crossref]

Murphy, P.

M. Tricard, A. Kulawiec, M. Bauer, G. Devries, J. Fleig, G. Forbes, D. Miladinovich, and P. Murphy, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Annals-Manuf. Techn. 59, 547–550 (2010).
[Crossref]

P. Murphy, J. Fleig, F. Forbes, D. Miladinovic, G. DeVries, and S. O’Donohue, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE 6293, 62930J (2006).
[Crossref]

P. Murphy, G. Forbes, J. Fleig, P. Dumas, and M. Tricard, “Stitching Interferometry: A Flexible Solution for Surface Metrology,” Optics and Photonics News 14, 38–43 (2003).
[Crossref]

O’Donohue, S.

P. Murphy, J. Fleig, F. Forbes, D. Miladinovic, G. DeVries, and S. O’Donohue, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE 6293, 62930J (2006).
[Crossref]

Okada, K.

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

Otsubo, M.

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

Parks, R. E.

P. Su, J. H. Burge, and R. E. Parks, “Application of maximum likelihood reconstruction of subaperture data for measurement of large flat mirrors,” Appl. Optics 49(1), 21–31 (2010).
[Crossref]

Peng, J.

J. Peng, X. Liu, X. Peng, Y. Yu, and X. Li, “Selection of F/number in lattice design for stitching inferferometry of aspheric surface,” Proc. SPIE 10250, 1025010 (2016);

J. Peng, H. Xu, Y. Yu, and M. Chen, “Stitching interferometry for cylindrical optics with large angular aperture,” Meas. Sci. Technol. 26(1), 025204 (2015).
[Crossref]

J. Peng, Q. Wang, X. Peng, and Y. Yu, “Stitching interferometry of high numerical aperture cylindrical optics without using a fringe-nulling routine,” J. Opt. Soc. Am. A 32(11), 1964–1972 (2015).
[Crossref]

Peng, X.

J. Peng, X. Liu, X. Peng, Y. Yu, and X. Li, “Selection of F/number in lattice design for stitching inferferometry of aspheric surface,” Proc. SPIE 10250, 1025010 (2016);

J. Peng, Q. Wang, X. Peng, and Y. Yu, “Stitching interferometry of high numerical aperture cylindrical optics without using a fringe-nulling routine,” J. Opt. Soc. Am. A 32(11), 1964–1972 (2015).
[Crossref]

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).
[Crossref]

Shen, Y.

T. Shi, D. Liu, Y. Zhou, T. Yan, Y. Yang, L. Zhang, J. Bai, Y. Shen, L. Miao, and W. Huang, “Practical retrace error correction in non-null aspheric testing: A comparison,” Opt. Commun. 383(15), 378–385 (2017).
[Crossref]

L. Zhang, D. Liu, T. Shi, Y. Yang, S. Chong, B. Ge, Y. Shen, and J. Bai, “Aspheric subaperture stitching based on system modeling,” Opt. Express 23(15), 19176–19188 (2015).
[Crossref] [PubMed]

L. Zhang, C. Tian, D. Liu, T. Shi, Y. Yang, H. Wu, and Y. Shen, “Non-null annular subaperture stitching interferometry for steep aspheric measurement,” Appl. Optics 53(25), 5755–5762 (2014)
[Crossref]

D. Liu, T. Shi, L. Zhang, Y. Yang, S. Chong, and Y. Shen, “Reverse optimization reconstruction of aspheric figure error in a non-null interferometer,” Appl. Optics 53(24), 5538–5546 (2014)
[Crossref]

Shi, T.

T. Shi, D. Liu, Y. Zhou, T. Yan, Y. Yang, L. Zhang, J. Bai, Y. Shen, L. Miao, and W. Huang, “Practical retrace error correction in non-null aspheric testing: A comparison,” Opt. Commun. 383(15), 378–385 (2017).
[Crossref]

L. Zhang, D. Liu, T. Shi, Y. Yang, S. Chong, B. Ge, Y. Shen, and J. Bai, “Aspheric subaperture stitching based on system modeling,” Opt. Express 23(15), 19176–19188 (2015).
[Crossref] [PubMed]

L. Zhang, C. Tian, D. Liu, T. Shi, Y. Yang, H. Wu, and Y. Shen, “Non-null annular subaperture stitching interferometry for steep aspheric measurement,” Appl. Optics 53(25), 5755–5762 (2014)
[Crossref]

D. Liu, T. Shi, L. Zhang, Y. Yang, S. Chong, and Y. Shen, “Reverse optimization reconstruction of aspheric figure error in a non-null interferometer,” Appl. Optics 53(24), 5538–5546 (2014)
[Crossref]

Su, P.

P. Su, J. H. Burge, and R. E. Parks, “Application of maximum likelihood reconstruction of subaperture data for measurement of large flat mirrors,” Appl. Optics 49(1), 21–31 (2010).
[Crossref]

Tian, C.

L. Zhang, C. Tian, D. Liu, T. Shi, Y. Yang, H. Wu, and Y. Shen, “Non-null annular subaperture stitching interferometry for steep aspheric measurement,” Appl. Optics 53(25), 5755–5762 (2014)
[Crossref]

D. Liu, Y. Yang, C. Tian, Y. Luo, and L. Wang, “Practical methods for retrace error correction in nonnull aspheric testing,” Opt. Express 17(9), 7025–7035 (2009)
[Crossref] [PubMed]

Tricard, M.

M. Tricard, A. Kulawiec, M. Bauer, G. Devries, J. Fleig, G. Forbes, D. Miladinovich, and P. Murphy, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Annals-Manuf. Techn. 59, 547–550 (2010).
[Crossref]

P. Murphy, G. Forbes, J. Fleig, P. Dumas, and M. Tricard, “Stitching Interferometry: A Flexible Solution for Surface Metrology,” Optics and Photonics News 14, 38–43 (2003).
[Crossref]

Tsujiuchi, J.

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

Wang, J.

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L. Zhang, C. Tian, D. Liu, T. Shi, Y. Yang, H. Wu, and Y. Shen, “Non-null annular subaperture stitching interferometry for steep aspheric measurement,” Appl. Optics 53(25), 5755–5762 (2014)
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T. Shi, D. Liu, Y. Zhou, T. Yan, Y. Yang, L. Zhang, J. Bai, Y. Shen, L. Miao, and W. Huang, “Practical retrace error correction in non-null aspheric testing: A comparison,” Opt. Commun. 383(15), 378–385 (2017).
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D. Liu, T. Shi, L. Zhang, Y. Yang, S. Chong, and Y. Shen, “Reverse optimization reconstruction of aspheric figure error in a non-null interferometer,” Appl. Optics 53(24), 5538–5546 (2014)
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J. Peng, X. Liu, X. Peng, Y. Yu, and X. Li, “Selection of F/number in lattice design for stitching inferferometry of aspheric surface,” Proc. SPIE 10250, 1025010 (2016);

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Zhang, L.

T. Shi, D. Liu, Y. Zhou, T. Yan, Y. Yang, L. Zhang, J. Bai, Y. Shen, L. Miao, and W. Huang, “Practical retrace error correction in non-null aspheric testing: A comparison,” Opt. Commun. 383(15), 378–385 (2017).
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L. Zhang, D. Liu, T. Shi, Y. Yang, S. Chong, B. Ge, Y. Shen, and J. Bai, “Aspheric subaperture stitching based on system modeling,” Opt. Express 23(15), 19176–19188 (2015).
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D. Liu, T. Shi, L. Zhang, Y. Yang, S. Chong, and Y. Shen, “Reverse optimization reconstruction of aspheric figure error in a non-null interferometer,” Appl. Optics 53(24), 5538–5546 (2014)
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Zhao, H.

Zhao, Z.

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Appl. Optics (6)

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S. Chen, S. Li, Y. Dai, and Z. Zheng, “Lattice design for subaperture stitching test of a concave paraboloid surface,” Appl. Optics 45(10), 2280–2286 (2006).
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Chin. Opt. Lett. (1)

X. Wang, “Measurement of mild asphere by digital plane,” Chin. Opt. Lett. 12(s2), S21201 (2014).
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M. Tricard, A. Kulawiec, M. Bauer, G. Devries, J. Fleig, G. Forbes, D. Miladinovich, and P. Murphy, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Annals-Manuf. Techn. 59, 547–550 (2010).
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Meas. Sci. Technol. (1)

J. Peng, H. Xu, Y. Yu, and M. Chen, “Stitching interferometry for cylindrical optics with large angular aperture,” Meas. Sci. Technol. 26(1), 025204 (2015).
[Crossref]

Opt. Commun. (1)

T. Shi, D. Liu, Y. Zhou, T. Yan, Y. Yang, L. Zhang, J. Bai, Y. Shen, L. Miao, and W. Huang, “Practical retrace error correction in non-null aspheric testing: A comparison,” Opt. Commun. 383(15), 378–385 (2017).
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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).
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Optics and Photonics News (1)

P. Murphy, G. Forbes, J. Fleig, P. Dumas, and M. Tricard, “Stitching Interferometry: A Flexible Solution for Surface Metrology,” Optics and Photonics News 14, 38–43 (2003).
[Crossref]

Proc. SPIE (2)

P. Murphy, J. Fleig, F. Forbes, D. Miladinovic, G. DeVries, and S. O’Donohue, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE 6293, 62930J (2006).
[Crossref]

J. Peng, X. Liu, X. Peng, Y. Yu, and X. Li, “Selection of F/number in lattice design for stitching inferferometry of aspheric surface,” Proc. SPIE 10250, 1025010 (2016);

Other (1)

Encoding and fabrication report: CGH cylinder null H80F3C, Tech. Rep. C1437, (Diffraction International, 2014).

Supplementary Material (1)

NameDescription
» Visualization 1       Changes of the subaperture interferogram when measuring the acylindrical surface without and with a yawing CGH cylinder null.

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Figures (12)

Fig. 1
Fig. 1 Coordinate transformation between the off-axis subaperture and the central subaperture.
Fig. 2
Fig. 2 Sketch map of the simulation model.
Fig. 3
Fig. 3 Simulated phase map of off-axis subaperture (a) and its expansion coefficients by using the 2D Legendre polynomials (b).
Fig. 4
Fig. 4 Diffracted wavefronts when the CGH cylinder null was set at normal position (a) and was yawed with a certain angle (b).
Fig. 5
Fig. 5 Simulated interferograms of off-axis subapertures before (a–c) and after (d–f) yawing cylinder null when measuring acylindrical lens.
Fig. 6
Fig. 6 The expansion coefficients of the aberrations induced by yawing the CGH cylinder null (a), and the relationship between the coma and the yaw angle of the CGH cylinder null (b).
Fig. 7
Fig. 7 Photograph of the experimental system (a), and the subaperture layout (b).
Fig. 8
Fig. 8 Picture of the tested acylindrical lens (a) and its departure (b).
Fig. 9
Fig. 9 Interferograms measured at the off-axis subapertures before (a–d) and after (e–h) yawing the CGH cylinder null.
Fig. 10
Fig. 10 Two stitching results obtained by yawing the cylinder null and the test acylindrical lens was set with different misalignment errors. (a) The first stitching result, (b) the second stitching result.
Fig. 11
Fig. 11 Comparison between the 3D profilometer and the proposed method: (a) 3D view of the result measured by the Talysurf PGI Freeform, (b) 3D view of the stitching result obtained by proposed method.
Fig. 12
Fig. 12 Misalignment errors of the CGH cylinder null during the yawing process. (a) The center axis of the CGH deviates from the yawing axis with a lateral deviation, (b) the center axis of the CGH deviates from the yawing axis with a longitudinal deviation.

Tables (1)

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Table 1 Nominal motion parameters of off-axis subapertures.

Equations (13)

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y 2 2 R z + ( k + 1 ) z 2 = 0 .
( y c o s α z s i n α + y 0 ) 2 2 R ( y s i n α + z c o s α + z 0 ) + ( k + 1 ) ( y s i n α + z c o s α + z 0 ) 2 = 0 .
z z s = m 0 + m 1 y + m 2 y 2 + m 3 y 3 ,
[ x y z ] = [ s u r r b f + φ + Δ ϕ r t s v ( r r b f + φ + Δ ϕ ) 2 y 2 ] ,
[ X Y Z 1 ] = [ 1 0 0 0 0 c o s ( α ) s i n ( α ) 0 0 s i n ( α ) cos ( α ) 0 0 0 0 1 ] [ x y z 1 ] + [ 0 y c z c 1 ] ,
[ X ρ Θ ] = [ X Y 2 + Z 2 arctan ( Y ρ ) ] .
W ( U , V ) = W 0 ( U , V ) + a + b U + c V + d U V + e U 2 + f U W ( U , V )
W i ( U , V ) = W 0 i ( U , V ) + a i + b i U + c i V + d i U V + e i U 2 + f i U W i ( U , V ) , W j ( U , V ) = W 0 j ( U , V ) + a j + b j U + c j V + d j U V + e j U 2 + f j U W j ( U , V ) .
i = 1 N j = 1 N i j { [ W 0 i ( U , V ) + a i + b i U + c i V + d i U V + e i U 2 + f i U w i ( U , V ) ] [ W 0 j ( U , V ) + a j + b j U + c j V + d j U V + e j U 2 + f j U w j ( U , V ) ] } 2 m i n
z = a y + ( b 2 y 2 + b 1 y + b 0 ) 1 / 2 + c ,
a = ( k c o s α s i n α ) / ( 1 + k c o s α 2 ) , b 2 = [ ( k + 1 ) ( s i n 4 α + c o s 4 α ) + 2 c o s 2 α s i n 2 α ] / ( 1 + k c o s 2 α ) , b 1 = 2 [ ( R z 0 ( k + 1 ) ) s i n 3 α y 0 ( k + 1 ) c o s 3 α + ( R z 0 ( k + 1 ) ) c o s 2 α s i n α + y 0 ( k + 1 ) c o s α s i n 2 α ] / ( 1 + k c o s 2 α ) , b 0 = [ ( R y 0 ( k + 1 ) ) c o s 2 α + ( 2 R ( k + 1 ) z 0 ) s i n 2 α + 2 y 0 ( R ( k + 1 ) z 0 ) c o s α s i n α ] / ( 1 + k c o s 2 α ) , c = [ R c o s α z 0 c o s α + y 0 s i n α k z 0 c o s α ] / ( 1 + k c o s 2 α ) .
z = a y + b 0 ( 1 + 1 / 2 ( b 2 / b 0 y 2 + b 1 / b 0 y ) 1 / 4 ( b 2 / b 0 y 2 + b 1 / b 0 y ) 2 + ) + c = b 0 + c + ( a + b 1 / 2 ) y + ( b 2 / 2 b 1 2 / ( 4 b 2 ) ) y 2 ( b 1 b 2 ) / ( 2 b 0 ) y 3 b 2 2 / ( 4 b 0 ) y 4 + .
z z s = m 0 + m 1 y + m 2 y 2 + m 3 y 3

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