Abstract

A null lens moving back and forth relative to a point source can generate variable spherical aberration for flexible test of aspheres. Different from the previous methods, variable spherical aberration null theory was developed by us to optimize the null lens. The optimized null was a plano-convex singlet containing a high order even asphere. Its attractive advantages are the simple structure and the broad range of testable surfaces. Most concave prolate conic and near conic surfaces with k∙R value varying between 0 and about 70000mm and with smaller relative aperture than that determined by each k∙R value can be tested. The testable asphericity range is between 0 and about 230λ. Relations among these testable surfaces were revealed as different groups of equidistant surfaces. To explicitly show the ability of the null, the measurable surfaces range map that contains all parameters defining a conic surface was offered. A practical near-null test system using this null was established. Alignment, near-null data processing, and error sources are analyzed in detail. To verify the broad testable surfaces range, three surfaces with widely varying amounts of asphericity were tested. Cross tests were provided to verify the test system accuracy.

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

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  1. D. Malacara, Optical Shop Testing (Wiley, 2007).
  2. L. Huang, J. Xue, B. Gao, C. McPherson, J. Beverage, and M. Idir, “Modal phase measuring deflectometry,” Opt. Express 24(21), 24649–24664 (2016).
    [Crossref] [PubMed]
  3. H. Ren, F. Gao, and X. Jiang, “Least-squares method for data reconstruction from gradient data in deflectometry,” Appl. Opt. 55(22), 6052–6059 (2016).
    [Crossref] [PubMed]
  4. P. J. Groot, “Long-wavelength laser diode interferometer for surface flatness measurement,” Proc. SPIE 2248, 136–140 (1994).
    [Crossref]
  5. K. Creath, Y. Cheng, and J. Wyant, “Contouring aspheric surfaces using two-wavelength phase-shifting interferometry,” Int. J. Opt. 32(12), 1455–1464 (1985).
  6. S. Xue, S. Chen, D. Zhai, and F. Shi, “Quasi-absolute surface figure test with two orthogonal transverse spatial shifts,” Opt. Commun. 389, 133–143 (2017).
    [Crossref]
  7. J. E. Greivenkamp, “Sub-Nyquist interferometry,” Appl. Opt. 26(24), 5245–5258 (1987).
    [Crossref] [PubMed]
  8. E. Garbusi, C. Pruss, and W. Osten, “Interferometer for precise and flexible asphere testing,” Opt. Lett. 33(24), 2973–2975 (2008).
    [Crossref] [PubMed]
  9. X. Hou, F. Wu, L. Yang, and Q. Chen, “Experimental study on measurement of aspheric surface shape with complementary annular subaperture interferometric method,” Opt. Express 15(20), 12890–12899 (2007).
    [Crossref] [PubMed]
  10. 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]
  11. 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).
  12. S. Chen, S. Xue, Y. Dai, and S. Li, “Subaperture stitching test of large steep convex spheres,” Opt. Express 23(22), 29047–29058 (2015).
    [Crossref] [PubMed]
  13. 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]
  14. S. Chen, S. Xue, Y. Dai, and S. Li, “Subaperture stitching test of convex aspheres by using the reconfigurable optical null,” Opt. Laser Technol. 91, 175–184 (2017).
    [Crossref]
  15. 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 Ann. 59(1), 547–550 (2010).
    [Crossref]
  16. C. Pruss and H. Tiziani, “Dynamic null lens for aspheric testing using a membrane mirror,” Opt. Commun. 233(1), 15–19 (2004).
    [Crossref]
  17. Y. He, L. Huang, X. Hou, W. Fan, and R. Liang, “Modeling near-null testing method of a freeform surface with a deformable mirror compensator,” Appl. Opt. 56(33), 9132–9138 (2017).
    [Crossref] [PubMed]
  18. L. Huang, H. Choi, W. Zhao, L. R. Graves, and D. W. Kim, “Adaptive interferometric null testing for unknown freeform optics metrology,” Opt. Lett. 41(23), 5539–5542 (2016).
    [Crossref] [PubMed]
  19. L. Zhang, S. Zhou, D. Li, Y. Liu, T. He, B. Yu, and J. Li, “Pure adaptive interferometer for free form surfaces metrology,” Opt. Express 26(7), 7888–7898 (2018).
    [Crossref] [PubMed]
  20. K. Fuerschbach, K. P. Thompson, and J. P. Rolland, “Interferometric measurement of a concave, φ-polynomial, Zernike mirror,” Opt. Lett. 39(1), 18–21 (2014).
    [Crossref] [PubMed]
  21. L. Zhang, S. Zhou, D. Li, J. Li, and B. Yu, “Model-based adaptive non-null interferometry for freeform surface metrology,” Chin. Opt. Lett. 16(8), 081203 (2018).
    [Crossref]
  22. Z. Cao, L. Xuan, L. Hu, Y. Liu, Q. Mu, and D. Li, “Investigation of optical testing with a phase-only liquid crystal spatial light modulator,” Opt. Express 13(4), 1059–1065 (2005).
    [Crossref] [PubMed]
  23. J. Kacperski and M. Kujawinska, “Active, LCoS based laser interferometer for microelements studies,” Opt. Express 14(21), 9664–9678 (2006).
    [Crossref] [PubMed]
  24. M. Ares, S. Royo, I. Sergievskaya, and J. Riu, “Active optics null test system based on a liquid crystal programmable spatial light modulator,” Appl. Opt. 49(32), 6201–6206 (2010).
    [Crossref] [PubMed]
  25. M. T. Cashmore, S. R. Hall, and G. D. Love, “Traceable interferometry using binary reconfigurable holograms,” Appl. Opt. 53(24), 5353–5358 (2014).
    [Crossref] [PubMed]
  26. S. Xue, S. Chen, Z. Fan, and D. Zhai, “Adaptive wavefront interferometry for unknown free-form surfaces,” Opt. Express 26(17), 21910–21928 (2018).
    [Crossref] [PubMed]
  27. 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]
  28. C. Tian, Y. Yang, T. Wei, and Y. Zhuo, “Nonnull interferometer simulation for aspheric testing based on ray tracing,” Appl. Opt. 50(20), 3559–3569 (2011).
    [Crossref] [PubMed]
  29. J. Sullivan and J. Greivenkamp, “Design of partial nulls for testing of fast aspheric surfaces,” Proc. SPIE 6671, 66710W (2007).
    [Crossref]
  30. Q. Hao, T. Li, Y. Hu, S. Wang, Y. Ning, Y. Tan, and X. Zhang, “Vertex radius of curvature error measurement of aspheric surface based on slope asphericity in partial compensation interferometry,” Opt. Express 25(15), 18107–18121 (2017).
    [Crossref] [PubMed]
  31. R. S. Hilbert and M. P. Rimmer, “A variable refractive null Lens,” Appl. Opt. 9(4), 849–852 (1970).
    [Crossref] [PubMed]
  32. D. Shafer, “Zoom null lens,” Appl. Opt. 18(22), 3863–3865 (1979).
  33. H. Dall, “A null test for paraboloids,” J. Br. Astron. Assoc. 57, 201–205 (1947).
  34. R. T. Holleran, “An Algebraic Solution for the Small Lens Null Compensator,” Appl. Opt. 7(1), 137–144 (1968).
    [Crossref] [PubMed]
  35. J. Wyant and K. Creath, “Basic wavefront aberration theory,” in Applied Optics and Optical Engineering, R. Shannon and J. Wyant, eds. (Academic, 1992), pp. 31–34.
  36. T. Shi, “General interferometric aspheric testing with partial null lens,” Doctoral dissertation, Zhejiang University, China, 109–113 (2017).
  37. FOGALE nanotech, “Sensors & systems documentations,” http://www.fogale.fr/brochures.html
  38. L. Zhang, D. Liu, T. Shi, Y. Yang, and Y. Shen, “Practical and accurate method for aspheric misalignment aberrations calibration in non-null interferometric testing,” Appl. Opt. 52(35), 8501–8511 (2013).
    [Crossref] [PubMed]
  39. 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. Opt. 55(35), 9992–10001 (2016).
    [Crossref] [PubMed]
  40. C. Evans and J. B. Bryan, “Compensation for errors introduced by nonzero fringe densities in phase-measuring interferometers,” Ann. CIRP 42(1), 577–580 (1993).
    [Crossref]
  41. P. E. Murphy, T. G. Brown, and D. T. Moore, “Measurement and calibration of interferometric imaging aberrations,” Appl. Opt. 39(34), 6421–6429 (2000).
    [Crossref] [PubMed]
  42. R. O. Gappinger and J. E. Greivenkamp, “Iterative reverse optimization procedure for calibration of aspheric wave-front measurements on a nonnull interferometer,” Appl. Opt. 43(27), 5152–5161 (2004).
    [Crossref] [PubMed]
  43. C. Tian, Y. Yang, and Y. Zhuo, “Generalized data reduction approach for aspheric testing in a non-null interferometer,” Appl. Opt. 51(10), 1598–1604 (2012).
    [Crossref] [PubMed]
  44. 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. Opt. 53(24), 5538–5546 (2014).
    [Crossref] [PubMed]
  45. 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]
  46. T. Shi, D. Liu, Y. Zhou, T. Yan, Y. Yang, L. Zhang, J. Bai, Y. She, L. Miao, and W. Huang, “Practical retrace error correction in non-null aspheric testing: A comparison,” Opt. Commun. 383, 378–385 (2017).
    [Crossref]
  47. A. Offner, “A Null Corrector for Paraboloidal Mirrors,” Appl. Opt. 2(2), 153–156 (1963).
    [Crossref]
  48. S. Xue, S. Chen, Y. Tian, J. Lu, and H. Hu, “Verification and in situ calibration of large-aperture null correctors for convex aspheric mirrors,” Measurement 106, 79–87 (2017).
    [Crossref]

2018 (3)

2017 (7)

Q. Hao, T. Li, Y. Hu, S. Wang, Y. Ning, Y. Tan, and X. Zhang, “Vertex radius of curvature error measurement of aspheric surface based on slope asphericity in partial compensation interferometry,” Opt. Express 25(15), 18107–18121 (2017).
[Crossref] [PubMed]

S. Xue, S. Chen, D. Zhai, and F. Shi, “Quasi-absolute surface figure test with two orthogonal transverse spatial shifts,” Opt. Commun. 389, 133–143 (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]

S. Chen, S. Xue, Y. Dai, and S. Li, “Subaperture stitching test of convex aspheres by using the reconfigurable optical null,” Opt. Laser Technol. 91, 175–184 (2017).
[Crossref]

Y. He, L. Huang, X. Hou, W. Fan, and R. Liang, “Modeling near-null testing method of a freeform surface with a deformable mirror compensator,” Appl. Opt. 56(33), 9132–9138 (2017).
[Crossref] [PubMed]

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

S. Xue, S. Chen, Y. Tian, J. Lu, and H. Hu, “Verification and in situ calibration of large-aperture null correctors for convex aspheric mirrors,” Measurement 106, 79–87 (2017).
[Crossref]

2016 (4)

2015 (3)

2014 (4)

2013 (1)

2012 (1)

2011 (1)

2010 (2)

M. Ares, S. Royo, I. Sergievskaya, and J. Riu, “Active optics null test system based on a liquid crystal programmable spatial light modulator,” Appl. Opt. 49(32), 6201–6206 (2010).
[Crossref] [PubMed]

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 Ann. 59(1), 547–550 (2010).
[Crossref]

2009 (1)

2008 (1)

2007 (2)

2006 (1)

2005 (1)

2004 (2)

2000 (1)

1994 (1)

P. J. Groot, “Long-wavelength laser diode interferometer for surface flatness measurement,” Proc. SPIE 2248, 136–140 (1994).
[Crossref]

1993 (1)

C. Evans and J. B. Bryan, “Compensation for errors introduced by nonzero fringe densities in phase-measuring interferometers,” Ann. CIRP 42(1), 577–580 (1993).
[Crossref]

1987 (1)

1985 (1)

K. Creath, Y. Cheng, and J. Wyant, “Contouring aspheric surfaces using two-wavelength phase-shifting interferometry,” Int. J. Opt. 32(12), 1455–1464 (1985).

1979 (1)

1970 (1)

1968 (1)

1963 (1)

1947 (1)

H. Dall, “A null test for paraboloids,” J. Br. Astron. Assoc. 57, 201–205 (1947).

Ares, M.

Bai, J.

T. Shi, D. Liu, Y. Zhou, T. Yan, Y. Yang, L. Zhang, J. Bai, Y. She, L. Miao, and W. Huang, “Practical retrace error correction in non-null aspheric testing: A comparison,” Opt. Commun. 383, 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).

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 Ann. 59(1), 547–550 (2010).
[Crossref]

Beverage, J.

Brown, T. G.

Bryan, J. B.

C. Evans and J. B. Bryan, “Compensation for errors introduced by nonzero fringe densities in phase-measuring interferometers,” Ann. CIRP 42(1), 577–580 (1993).
[Crossref]

Cao, Z.

Cashmore, M. T.

Chen, M.

Chen, Q.

Chen, S.

S. Xue, S. Chen, Z. Fan, and D. Zhai, “Adaptive wavefront interferometry for unknown free-form surfaces,” Opt. Express 26(17), 21910–21928 (2018).
[Crossref] [PubMed]

S. Xue, S. Chen, Y. Tian, J. Lu, and H. Hu, “Verification and in situ calibration of large-aperture null correctors for convex aspheric mirrors,” Measurement 106, 79–87 (2017).
[Crossref]

S. Xue, S. Chen, D. Zhai, and F. Shi, “Quasi-absolute surface figure test with two orthogonal transverse spatial shifts,” Opt. Commun. 389, 133–143 (2017).
[Crossref]

S. Chen, S. Xue, Y. Dai, and S. Li, “Subaperture stitching test of convex aspheres by using the reconfigurable optical null,” Opt. Laser Technol. 91, 175–184 (2017).
[Crossref]

S. Chen, S. Xue, Y. Dai, and S. Li, “Subaperture stitching test of large steep convex spheres,” Opt. Express 23(22), 29047–29058 (2015).
[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]

Cheng, H.

Cheng, Y.

K. Creath, Y. Cheng, and J. Wyant, “Contouring aspheric surfaces using two-wavelength phase-shifting interferometry,” Int. J. Opt. 32(12), 1455–1464 (1985).

Choi, H.

Chong, S.

Creath, K.

K. Creath, Y. Cheng, and J. Wyant, “Contouring aspheric surfaces using two-wavelength phase-shifting interferometry,” Int. J. Opt. 32(12), 1455–1464 (1985).

Dai, Y.

Dall, H.

H. Dall, “A null test for paraboloids,” J. Br. Astron. Assoc. 57, 201–205 (1947).

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 Ann. 59(1), 547–550 (2010).
[Crossref]

Evans, C.

C. Evans and J. B. Bryan, “Compensation for errors introduced by nonzero fringe densities in phase-measuring interferometers,” Ann. CIRP 42(1), 577–580 (1993).
[Crossref]

Fan, W.

Fan, Z.

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 Ann. 59(1), 547–550 (2010).
[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 Ann. 59(1), 547–550 (2010).
[Crossref]

Fuerschbach, K.

Gao, B.

Gao, F.

Gappinger, R. O.

Garbusi, E.

Ge, B.

Graves, L. R.

Greivenkamp, J.

J. Sullivan and J. Greivenkamp, “Design of partial nulls for testing of fast aspheric surfaces,” Proc. SPIE 6671, 66710W (2007).
[Crossref]

Greivenkamp, J. E.

Groot, P. J.

P. J. Groot, “Long-wavelength laser diode interferometer for surface flatness measurement,” Proc. SPIE 2248, 136–140 (1994).
[Crossref]

Haiyang, Q.

Hall, S. R.

Hao, Q.

He, T.

He, Y.

Hilbert, R. S.

Holleran, R. T.

Hou, X.

Hu, H.

S. Xue, S. Chen, Y. Tian, J. Lu, and H. Hu, “Verification and in situ calibration of large-aperture null correctors for convex aspheric mirrors,” Measurement 106, 79–87 (2017).
[Crossref]

Hu, L.

Hu, Y.

Huang, L.

Huang, W.

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

Idir, M.

Jiang, X.

Kacperski, J.

Kaznatcheev, K.

Kim, D. W.

Kujawinska, M.

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 Ann. 59(1), 547–550 (2010).
[Crossref]

Li, D.

Li, J.

Li, S.

Li, T.

Liang, R.

Liu, D.

Liu, Y.

Love, G. D.

Lu, J.

S. Xue, S. Chen, Y. Tian, J. Lu, and H. Hu, “Verification and in situ calibration of large-aperture null correctors for convex aspheric mirrors,” Measurement 106, 79–87 (2017).
[Crossref]

Luo, Y.

McPherson, C.

Miao, L.

T. Shi, D. Liu, Y. Zhou, T. Yan, Y. Yang, L. Zhang, J. Bai, Y. She, L. Miao, and W. Huang, “Practical retrace error correction in non-null aspheric testing: A comparison,” Opt. Commun. 383, 378–385 (2017).
[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 Ann. 59(1), 547–550 (2010).
[Crossref]

Moore, D. T.

Mu, Q.

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 Ann. 59(1), 547–550 (2010).
[Crossref]

Murphy, P. E.

Ning, Y.

Offner, A.

Osten, W.

Pruss, C.

E. Garbusi, C. Pruss, and W. Osten, “Interferometer for precise and flexible asphere testing,” Opt. Lett. 33(24), 2973–2975 (2008).
[Crossref] [PubMed]

C. Pruss and H. Tiziani, “Dynamic null lens for aspheric testing using a membrane mirror,” Opt. Commun. 233(1), 15–19 (2004).
[Crossref]

Ren, H.

Rimmer, M. P.

Riu, J.

Rolland, J. P.

Royo, S.

Sergievskaya, I.

Shafer, D.

She, Y.

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

Shen, Y.

Shi, F.

S. Xue, S. Chen, D. Zhai, and F. Shi, “Quasi-absolute surface figure test with two orthogonal transverse spatial shifts,” Opt. Commun. 389, 133–143 (2017).
[Crossref]

Shi, T.

Song, W.

Sullivan, J.

J. Sullivan and J. Greivenkamp, “Design of partial nulls for testing of fast aspheric surfaces,” Proc. SPIE 6671, 66710W (2007).
[Crossref]

Tan, Y.

Thompson, K. P.

Tian, C.

Tian, Y.

S. Xue, S. Chen, Y. Tian, J. Lu, and H. Hu, “Verification and in situ calibration of large-aperture null correctors for convex aspheric mirrors,” Measurement 106, 79–87 (2017).
[Crossref]

Tiziani, H.

C. Pruss and H. Tiziani, “Dynamic null lens for aspheric testing using a membrane mirror,” Opt. Commun. 233(1), 15–19 (2004).
[Crossref]

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 Ann. 59(1), 547–550 (2010).
[Crossref]

Wang, L.

Wang, S.

Wei, T.

Wu, F.

Wyant, J.

K. Creath, Y. Cheng, and J. Wyant, “Contouring aspheric surfaces using two-wavelength phase-shifting interferometry,” Int. J. Opt. 32(12), 1455–1464 (1985).

Xuan, L.

Xue, J.

Xue, S.

S. Xue, S. Chen, Z. Fan, and D. Zhai, “Adaptive wavefront interferometry for unknown free-form surfaces,” Opt. Express 26(17), 21910–21928 (2018).
[Crossref] [PubMed]

S. Xue, S. Chen, Y. Tian, J. Lu, and H. Hu, “Verification and in situ calibration of large-aperture null correctors for convex aspheric mirrors,” Measurement 106, 79–87 (2017).
[Crossref]

S. Xue, S. Chen, D. Zhai, and F. Shi, “Quasi-absolute surface figure test with two orthogonal transverse spatial shifts,” Opt. Commun. 389, 133–143 (2017).
[Crossref]

S. Chen, S. Xue, Y. Dai, and S. Li, “Subaperture stitching test of convex aspheres by using the reconfigurable optical null,” Opt. Laser Technol. 91, 175–184 (2017).
[Crossref]

S. Chen, S. Xue, Y. Dai, and S. Li, “Subaperture stitching test of large steep convex spheres,” Opt. Express 23(22), 29047–29058 (2015).
[Crossref] [PubMed]

Yan, T.

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

Yang, L.

Yang, Y.

Yiwei, H.

Yu, B.

Zhai, D.

S. Xue, S. Chen, Z. Fan, and D. Zhai, “Adaptive wavefront interferometry for unknown free-form surfaces,” Opt. Express 26(17), 21910–21928 (2018).
[Crossref] [PubMed]

S. Xue, S. Chen, D. Zhai, and F. Shi, “Quasi-absolute surface figure test with two orthogonal transverse spatial shifts,” Opt. Commun. 389, 133–143 (2017).
[Crossref]

Zhang, L.

Zhang, X.

Zhao, C.

Zhao, W.

Zhou, S.

Zhou, Y.

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

Zhuo, Y.

Ann. CIRP (1)

C. Evans and J. B. Bryan, “Compensation for errors introduced by nonzero fringe densities in phase-measuring interferometers,” Ann. CIRP 42(1), 577–580 (1993).
[Crossref]

Appl. Opt. (16)

P. E. Murphy, T. G. Brown, and D. T. Moore, “Measurement and calibration of interferometric imaging aberrations,” Appl. Opt. 39(34), 6421–6429 (2000).
[Crossref] [PubMed]

R. O. Gappinger and J. E. Greivenkamp, “Iterative reverse optimization procedure for calibration of aspheric wave-front measurements on a nonnull interferometer,” Appl. Opt. 43(27), 5152–5161 (2004).
[Crossref] [PubMed]

C. Tian, Y. Yang, and Y. Zhuo, “Generalized data reduction approach for aspheric testing in a non-null interferometer,” Appl. Opt. 51(10), 1598–1604 (2012).
[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. Opt. 53(24), 5538–5546 (2014).
[Crossref] [PubMed]

L. Zhang, D. Liu, T. Shi, Y. Yang, and Y. Shen, “Practical and accurate method for aspheric misalignment aberrations calibration in non-null interferometric testing,” Appl. Opt. 52(35), 8501–8511 (2013).
[Crossref] [PubMed]

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. Opt. 55(35), 9992–10001 (2016).
[Crossref] [PubMed]

A. Offner, “A Null Corrector for Paraboloidal Mirrors,” Appl. Opt. 2(2), 153–156 (1963).
[Crossref]

H. Ren, F. Gao, and X. Jiang, “Least-squares method for data reconstruction from gradient data in deflectometry,” Appl. Opt. 55(22), 6052–6059 (2016).
[Crossref] [PubMed]

J. E. Greivenkamp, “Sub-Nyquist interferometry,” Appl. Opt. 26(24), 5245–5258 (1987).
[Crossref] [PubMed]

Y. He, L. Huang, X. Hou, W. Fan, and R. Liang, “Modeling near-null testing method of a freeform surface with a deformable mirror compensator,” Appl. Opt. 56(33), 9132–9138 (2017).
[Crossref] [PubMed]

M. Ares, S. Royo, I. Sergievskaya, and J. Riu, “Active optics null test system based on a liquid crystal programmable spatial light modulator,” Appl. Opt. 49(32), 6201–6206 (2010).
[Crossref] [PubMed]

M. T. Cashmore, S. R. Hall, and G. D. Love, “Traceable interferometry using binary reconfigurable holograms,” Appl. Opt. 53(24), 5353–5358 (2014).
[Crossref] [PubMed]

C. Tian, Y. Yang, T. Wei, and Y. Zhuo, “Nonnull interferometer simulation for aspheric testing based on ray tracing,” Appl. Opt. 50(20), 3559–3569 (2011).
[Crossref] [PubMed]

R. S. Hilbert and M. P. Rimmer, “A variable refractive null Lens,” Appl. Opt. 9(4), 849–852 (1970).
[Crossref] [PubMed]

D. Shafer, “Zoom null lens,” Appl. Opt. 18(22), 3863–3865 (1979).

R. T. Holleran, “An Algebraic Solution for the Small Lens Null Compensator,” Appl. Opt. 7(1), 137–144 (1968).
[Crossref] [PubMed]

Chin. Opt. Lett. (1)

CIRP Ann. (1)

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 Ann. 59(1), 547–550 (2010).
[Crossref]

Int. J. Opt. (1)

K. Creath, Y. Cheng, and J. Wyant, “Contouring aspheric surfaces using two-wavelength phase-shifting interferometry,” Int. J. Opt. 32(12), 1455–1464 (1985).

J. Br. Astron. Assoc. (1)

H. Dall, “A null test for paraboloids,” J. Br. Astron. Assoc. 57, 201–205 (1947).

Measurement (1)

S. Xue, S. Chen, Y. Tian, J. Lu, and H. Hu, “Verification and in situ calibration of large-aperture null correctors for convex aspheric mirrors,” Measurement 106, 79–87 (2017).
[Crossref]

Opt. Commun. (3)

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

S. Xue, S. Chen, D. Zhai, and F. Shi, “Quasi-absolute surface figure test with two orthogonal transverse spatial shifts,” Opt. Commun. 389, 133–143 (2017).
[Crossref]

C. Pruss and H. Tiziani, “Dynamic null lens for aspheric testing using a membrane mirror,” Opt. Commun. 233(1), 15–19 (2004).
[Crossref]

Opt. Express (13)

X. Hou, F. Wu, L. Yang, and Q. Chen, “Experimental study on measurement of aspheric surface shape with complementary annular subaperture interferometric method,” Opt. Express 15(20), 12890–12899 (2007).
[Crossref] [PubMed]

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]

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).

S. Chen, S. Xue, Y. Dai, and S. Li, “Subaperture stitching test of large steep convex spheres,” Opt. Express 23(22), 29047–29058 (2015).
[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]

L. Huang, J. Xue, B. Gao, C. McPherson, J. Beverage, and M. Idir, “Modal phase measuring deflectometry,” Opt. Express 24(21), 24649–24664 (2016).
[Crossref] [PubMed]

Z. Cao, L. Xuan, L. Hu, Y. Liu, Q. Mu, and D. Li, “Investigation of optical testing with a phase-only liquid crystal spatial light modulator,” Opt. Express 13(4), 1059–1065 (2005).
[Crossref] [PubMed]

J. Kacperski and M. Kujawinska, “Active, LCoS based laser interferometer for microelements studies,” Opt. Express 14(21), 9664–9678 (2006).
[Crossref] [PubMed]

L. Zhang, S. Zhou, D. Li, Y. Liu, T. He, B. Yu, and J. Li, “Pure adaptive interferometer for free form surfaces metrology,” Opt. Express 26(7), 7888–7898 (2018).
[Crossref] [PubMed]

S. Xue, S. Chen, Z. Fan, and D. Zhai, “Adaptive wavefront interferometry for unknown free-form surfaces,” Opt. Express 26(17), 21910–21928 (2018).
[Crossref] [PubMed]

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]

Q. Hao, T. Li, Y. Hu, S. Wang, Y. Ning, Y. Tan, and X. Zhang, “Vertex radius of curvature error measurement of aspheric surface based on slope asphericity in partial compensation interferometry,” Opt. Express 25(15), 18107–18121 (2017).
[Crossref] [PubMed]

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]

Opt. Laser Technol. (1)

S. Chen, S. Xue, Y. Dai, and S. Li, “Subaperture stitching test of convex aspheres by using the reconfigurable optical null,” Opt. Laser Technol. 91, 175–184 (2017).
[Crossref]

Opt. Lett. (3)

Proc. SPIE (2)

J. Sullivan and J. Greivenkamp, “Design of partial nulls for testing of fast aspheric surfaces,” Proc. SPIE 6671, 66710W (2007).
[Crossref]

P. J. Groot, “Long-wavelength laser diode interferometer for surface flatness measurement,” Proc. SPIE 2248, 136–140 (1994).
[Crossref]

Other (4)

D. Malacara, Optical Shop Testing (Wiley, 2007).

J. Wyant and K. Creath, “Basic wavefront aberration theory,” in Applied Optics and Optical Engineering, R. Shannon and J. Wyant, eds. (Academic, 1992), pp. 31–34.

T. Shi, “General interferometric aspheric testing with partial null lens,” Doctoral dissertation, Zhejiang University, China, 109–113 (2017).

FOGALE nanotech, “Sensors & systems documentations,” http://www.fogale.fr/brochures.html

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Figures (16)

Fig. 1
Fig. 1 Principle of Dall test.
Fig. 2
Fig. 2 Measurable surfaces kR value variation with l for every fixed s value.
Fig. 3
Fig. 3 Measurable conic surfaces range of the spherical singlet type VSAN.
Fig. 4
Fig. 4 Approximation of an aspherical singlet by a combination of aspherical plate and spherical singlet.
Fig. 5
Fig. 5 Comparison of measurable conic surfaces range of the HOEA singlet type VSAN with that of the spherical singlet type VSAN.
Fig. 6
Fig. 6 Near-null test system utilizing HOEA singlet type VSAN.
Fig. 7
Fig. 7 Misalignment interferograms for aligning VSAN. (a) The interferogram without misalignments. (b) and (c) show the interferograms when the VSAN tilts around y and x axis, respectively. (d) and (e) show the interferograms when the VSAN translates along x and y axis, respectively.
Fig. 8
Fig. 8 Experiment layout of near-null test utilizing HOEA singlet type VSAN for 1# surface.
Fig. 9
Fig. 9 Comparison of the experimental and theoretical wavefronts. (a) and (c) are experimental and theoretical interferograms, respectively. (b) and (d) are corresponding phase maps, respectively.
Fig. 10
Fig. 10 Comparison of (a) near-null test utilizing HOEA singlet VSAN test result, and (b) null test result for 1# surface.
Fig. 11
Fig. 11 Experiment layouts of autocollimation test for 1# surface.
Fig. 12
Fig. 12 Comparison of test results for 2# surface. (a) Near-null test utilizing HOEA singlet VSAN test result, (b) autocollimation test result, (c) point to point difference map for the two methods.
Fig. 13
Fig. 13 Experiment layouts of (a) near-null test utilizing HOEA singlet VSAN, and (b) autocollimation test for 2# surface.
Fig. 14
Fig. 14 Comparison of (a) near-null test utilizing HOEA singlet VSAN test result, and (b) null test result for 3# surface.
Fig. 15
Fig. 15 Design of the Offner null for null test of 3# surface. (a) Optical layout, (b) the residual wavefront error.
Fig. 16
Fig. 16 Experiment layouts of (a) near-null test utilizing HOEA singlet VSAN, and (b) null test for 3# surface.

Tables (3)

Tables Icon

Table 1 Parameters of HOEA surface.

Tables Icon

Table 2 Typical testable surfaces of the HOEA singlet type VSAN.

Tables Icon

Table 3 Near-null test of the test surfaces with HOEA singlet type VSAN.

Equations (16)

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

S I (sn) = h 4 φ 3 P,
φ=(n1)(1/ r 1 1/ r 2 ).
P= n 2 (n2)+2 n (n1) 2 + 3nm(n1)4m n(n1)(1m) + (3n+2) m 2 n (1m) 2 .
S I (sn) = φ 3 P s 4 u 4 .
S I (c) =2kR u 4 .
S I (c) +2 S I (sn) =0.
kR= φ 3 P s 4 .
k t = k 0 R 0 /( R 0 +t),
g 4 = φ 3 P= 5.303 r 1 3 .
z (HOEA) = c 1 h 2 1+ 1(k+1) c 1 2 h 2 + A 4 h 4 + A 6 h 6 + A 8 h 8 + A 10 h 10 +... = c 1 h 2 2 + (1+k+ a 4 ) c 1 3 2 2 2! h 4 + 13 (1+k+ a 6 ) 2 c 1 5 2 3 3! h 6 + 135 (1+k+ a 8 ) 3 c 1 7 2 4 4! h 8 +.... = c 1 h 2 2 + (1+α) c 1 3 2 2 2! h 4 + 13(1+β) c 1 5 2 3 3! h 6 + 135(1+χ) c 1 7 2 4 4! h 8 +...
z (S) = c 1 r 2 1+ 1 c 1 2 r 2 = c 1 h 2 2 + 1 c 1 3 h 4 2 2 2! + 13 c 1 5 h 6 2 3 3! + 135 c 1 7 h 8 2 4 4! +.
Δz= z (HOEA) z (S) = α c 1 3 2 2 2! h 4 + 13β c 1 5 2 3 3! h 6 + 135χ c 1 7 2 4 4! h 8 +...,
ΔW= (n1)α c 1 3 2 2 2! h 4 .
Δ S I =(n1)α c 1 3 h 4 =(n1)α c 1 3 s 4 u 4 .
S I (hoean) = S I (sn) +Δ S I = φ 3 P s 4 u 4 +(n1)α c 1 3 s 4 u 4 .
kR=[ φ 3 P+(n1)α c 1 3 ] s 4 ,

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