Abstract

Data reduction in non-null tests is difficult due to the presence of retrace error. We propose a simple yet effective data reduction approach for aspheric testing in a non-null interferometer. The new approach gives figure error of the aspheric by just subtracting the theoretical wavefront and first-order errors from the real wavefront obtained in the non-null interferometer. Precise prediction of the theoretical wavefront can be achieved by accurate calibration of the partial compensation system. The approach can be considered a generalization of the traditional data processing method in null tests, and errors that may affect its accuracy are discussed. A set of experiments have been carried out to demonstrate its validity and feasibility.

© 2012 Optical Society of America

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References

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  3. B. Dörband and H. J. Tiziani, “Testing aspheric surfaces with computer-generated holograms: analysis of adjustment and shape errors,” Appl. Opt. 24, 2604–2611 (1985).
    [CrossRef]
  4. J. C. Wyant and V. P. Bennett, “Using computer generated holograms to test aspheric wavefronts,” Appl. Opt. 11, 2833–2839 (1972).
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  5. M. F. Küchel, “Interferometric measurement of rotationally symmetric aspheric surfaces,” Proc. SPIE 7389, 738916 (2009).
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  6. P. Murphy, J. Fleig, G. Forbes, D. Miladinovic, G. DeVries, and S. O’Donohue, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE 6293, 62930J (2006).
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  8. J. E. Greivenkamp and R. O. Gappinger, “Design of a non-null interferometer for aspheric wavefronts,” Appl. Opt. 43, 5143–5151 (2004).
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  9. J. Pfund, N. Lindlein, and J. Schwider, “Non-null testing of rotationally symmetric aspheres: a systematic error assessment,” Appl. Opt. 40, 439–446 (2001).
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  11. O. Kwon, J. C. Wyant, and C. R. Hayslett, “Rough surface interferometry at 10.6 µm,” Appl. Opt. 19, 1862–1869 (1980).
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  12. K. Creath, Y.-Y. Cheng, and J. C. Wyant, “Contouring aspheric surfaces using two-wavelength phase-shifting interferometry,” Opt. Acta 32, 1455–1464 (1985).
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  13. C. Tian, Y. Yang, Y. Luo, D. Liu, and Y. Zhuo, “Study on phase retrieval of a single closed fringe interferogram in radial shearing interferometer for aspheric test,” Proc. SPIE 7656, 765612 (2010).
    [CrossRef]
  14. J. E. Greivenkamp, “Sub-Nyquist interferometry,” Appl. Opt. 26, 5245–5258 (1987).
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  15. J. E. Greivenkamp, A. E. Lowman, and R. J. Palum, “Sub-Nyquist interferometry: implementation and measurement capability,” Opt. Eng. 35, 2962–2969 (1996).
    [CrossRef]
  16. R. E. Parks, C. J. Evans, P. J. Sullivan, L. Shao, and B. E. Loucks, “Measurements of the LIGO Pathfinder optics,” Proc. SPIE 3134, 95–111 (1997).
    [CrossRef]
  17. M. Tricard, G. Forbes, and P. Murphy, “Subaperture metrology technologies extend capabilities in optics manufacturing,” Proc. SPIE 5965, 59650B (2005).
    [CrossRef]
  18. A. E. Lowman and J. E. Greivenkamp, “Interferometer errors due to the presence of fringes,” Appl. Opt. 35, 6826–6828 (1996).
    [CrossRef]
  19. R. O. Gappinger and J. E. Greivenkamp, “Iterative reverse optimization procedure for calibration of aspheric wave-front measurements on a non-null interferometer,” Appl. Opt. 43, 5152–5161 (2004).
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  20. C. Tian, Y. Yang, T. Wei, and Y. Zhuo, “Non-null interferometer simulation for aspheric testing based on ray tracing,” Appl. Opt. 50, 3559–3569 (2011).
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  21. P. E. Murphy, T. G. Brown, and D. T. Moore, “Measurement and calibration of interferometric imaging aberrations,” Appl. Opt. 39, 6421–6429 (2000).
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  22. A. E. Lowman and J. E. Greivenkamp, “Interferometer-induced wavefront errors when testing in a non-null configuration,” Proc. SPIE 2004, 173–181 (1994).
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  23. C. Huang, “Propagation errors in precision Fizeau interferometry,” Appl. Opt. 32, 7016–7021 (1993).
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  24. P. E. Murphy, T. G. Brown, and D. T. Moore, “Interference imaging for aspheric surface testing,” Appl. Opt. 39, 2122–2129 (2000).
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    [CrossRef]
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    [CrossRef]

2011 (1)

2010 (1)

C. Tian, Y. Yang, Y. Luo, D. Liu, and Y. Zhuo, “Study on phase retrieval of a single closed fringe interferogram in radial shearing interferometer for aspheric test,” Proc. SPIE 7656, 765612 (2010).
[CrossRef]

2009 (4)

M. F. Küchel, “Interferometric measurement of rotationally symmetric aspheric surfaces,” Proc. SPIE 7389, 738916 (2009).
[CrossRef]

D. Liu, Y. Yang, Y. Luo, C. Tian, Y. Shen, and Y. Zhuo, “Non-null interferometric aspheric testing with partial null lens and reverse optimization,” Proc. SPIE 7426, 74260M (2009).
[CrossRef]

E. Garbusi and W. Osten, “Perturbation methods in optics: application to the interferometric measurement of surfaces,” J. Opt. Soc. Am. A 26, 2538–2549 (2009).
[CrossRef]

Y. Yang, D. Liu, G. Xin, C. Tian, Y. Luo, Y. Shen, and Y. Zhuo, “Research of precision interference locating method for a partial null compensator at aspheric testing,” Proc. SPIE 7426, 74260R (2009).
[CrossRef]

2008 (1)

2006 (1)

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

2005 (1)

M. Tricard, G. Forbes, and P. Murphy, “Subaperture metrology technologies extend capabilities in optics manufacturing,” Proc. SPIE 5965, 59650B (2005).
[CrossRef]

2004 (2)

2003 (1)

2002 (1)

S. Reichelt, C. Pruss, and H. J. Tiziani, “New design techniques and calibration methods for CGH-null testing of aspheric surfaces,” Proc. SPIE 4778, 158–168 (2002).
[CrossRef]

2001 (1)

2000 (2)

1997 (1)

R. E. Parks, C. J. Evans, P. J. Sullivan, L. Shao, and B. E. Loucks, “Measurements of the LIGO Pathfinder optics,” Proc. SPIE 3134, 95–111 (1997).
[CrossRef]

1996 (2)

A. E. Lowman and J. E. Greivenkamp, “Interferometer errors due to the presence of fringes,” Appl. Opt. 35, 6826–6828 (1996).
[CrossRef]

J. E. Greivenkamp, A. E. Lowman, and R. J. Palum, “Sub-Nyquist interferometry: implementation and measurement capability,” Opt. Eng. 35, 2962–2969 (1996).
[CrossRef]

1995 (1)

A. E. Lowman and J. E. Greivenkamp, “Modeling an interferometer for non-null testing of aspheres,” Proc. SPIE 2536, 139–147 (1995).
[CrossRef]

1994 (1)

A. E. Lowman and J. E. Greivenkamp, “Interferometer-induced wavefront errors when testing in a non-null configuration,” Proc. SPIE 2004, 173–181 (1994).
[CrossRef]

1993 (1)

1987 (1)

1985 (2)

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

B. Dörband and H. J. Tiziani, “Testing aspheric surfaces with computer-generated holograms: analysis of adjustment and shape errors,” Appl. Opt. 24, 2604–2611 (1985).
[CrossRef]

1980 (1)

1974 (1)

1972 (1)

1970 (1)

1966 (1)

H. H. Hopkins and H. J. Tiziani, “A theoretical and experimental study of lens centering errors and their influence on optical image quality,” Br. J. Appl. Phys. 17, 33 (1966).
[CrossRef]

Bennett, V. P.

Brangaccio, D. J.

Brown, T. G.

Bruning, J. H.

Cheng, Y.-Y.

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

Creath, K.

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

DeVries, G.

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

Dörband, B.

Evans, C. J.

R. E. Parks, C. J. Evans, P. J. Sullivan, L. Shao, and B. E. Loucks, “Measurements of the LIGO Pathfinder optics,” Proc. SPIE 3134, 95–111 (1997).
[CrossRef]

Fleig, J.

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

Forbes, G.

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

M. Tricard, G. Forbes, and P. Murphy, “Subaperture metrology technologies extend capabilities in optics manufacturing,” Proc. SPIE 5965, 59650B (2005).
[CrossRef]

Gallagher, J. E.

Gappinger, R. O.

Garbusi, E.

Greivenkamp, J. E.

J. E. Greivenkamp and R. O. Gappinger, “Design of a non-null interferometer for aspheric wavefronts,” Appl. Opt. 43, 5143–5151 (2004).
[CrossRef]

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

J. E. Greivenkamp, A. E. Lowman, and R. J. Palum, “Sub-Nyquist interferometry: implementation and measurement capability,” Opt. Eng. 35, 2962–2969 (1996).
[CrossRef]

A. E. Lowman and J. E. Greivenkamp, “Interferometer errors due to the presence of fringes,” Appl. Opt. 35, 6826–6828 (1996).
[CrossRef]

A. E. Lowman and J. E. Greivenkamp, “Modeling an interferometer for non-null testing of aspheres,” Proc. SPIE 2536, 139–147 (1995).
[CrossRef]

A. E. Lowman and J. E. Greivenkamp, “Interferometer-induced wavefront errors when testing in a non-null configuration,” Proc. SPIE 2004, 173–181 (1994).
[CrossRef]

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

Hayslett, C. R.

Herriott, D. R.

Hopkins, H. H.

H. H. Hopkins and H. J. Tiziani, “A theoretical and experimental study of lens centering errors and their influence on optical image quality,” Br. J. Appl. Phys. 17, 33 (1966).
[CrossRef]

Huang, C.

Küchel, M. F.

M. F. Küchel, “Interferometric measurement of rotationally symmetric aspheric surfaces,” Proc. SPIE 7389, 738916 (2009).
[CrossRef]

Kwon, O.

Lindlein, N.

Liu, D.

C. Tian, Y. Yang, Y. Luo, D. Liu, and Y. Zhuo, “Study on phase retrieval of a single closed fringe interferogram in radial shearing interferometer for aspheric test,” Proc. SPIE 7656, 765612 (2010).
[CrossRef]

D. Liu, Y. Yang, Y. Luo, C. Tian, Y. Shen, and Y. Zhuo, “Non-null interferometric aspheric testing with partial null lens and reverse optimization,” Proc. SPIE 7426, 74260M (2009).
[CrossRef]

Y. Yang, D. Liu, G. Xin, C. Tian, Y. Luo, Y. Shen, and Y. Zhuo, “Research of precision interference locating method for a partial null compensator at aspheric testing,” Proc. SPIE 7426, 74260R (2009).
[CrossRef]

Loucks, B. E.

R. E. Parks, C. J. Evans, P. J. Sullivan, L. Shao, and B. E. Loucks, “Measurements of the LIGO Pathfinder optics,” Proc. SPIE 3134, 95–111 (1997).
[CrossRef]

Lowman, A. E.

J. E. Greivenkamp, A. E. Lowman, and R. J. Palum, “Sub-Nyquist interferometry: implementation and measurement capability,” Opt. Eng. 35, 2962–2969 (1996).
[CrossRef]

A. E. Lowman and J. E. Greivenkamp, “Interferometer errors due to the presence of fringes,” Appl. Opt. 35, 6826–6828 (1996).
[CrossRef]

A. E. Lowman and J. E. Greivenkamp, “Modeling an interferometer for non-null testing of aspheres,” Proc. SPIE 2536, 139–147 (1995).
[CrossRef]

A. E. Lowman and J. E. Greivenkamp, “Interferometer-induced wavefront errors when testing in a non-null configuration,” Proc. SPIE 2004, 173–181 (1994).
[CrossRef]

Luo, Y.

C. Tian, Y. Yang, Y. Luo, D. Liu, and Y. Zhuo, “Study on phase retrieval of a single closed fringe interferogram in radial shearing interferometer for aspheric test,” Proc. SPIE 7656, 765612 (2010).
[CrossRef]

D. Liu, Y. Yang, Y. Luo, C. Tian, Y. Shen, and Y. Zhuo, “Non-null interferometric aspheric testing with partial null lens and reverse optimization,” Proc. SPIE 7426, 74260M (2009).
[CrossRef]

Y. Yang, D. Liu, G. Xin, C. Tian, Y. Luo, Y. Shen, and Y. Zhuo, “Research of precision interference locating method for a partial null compensator at aspheric testing,” Proc. SPIE 7426, 74260R (2009).
[CrossRef]

Malacara, D.

D. Malacara, Optical Shop Testing, 3rd ed. (Wiley, 2007).

Miladinovic, D.

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

Moore, D. T.

Murphy, P.

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

M. Tricard, G. Forbes, and P. Murphy, “Subaperture metrology technologies extend capabilities in optics manufacturing,” Proc. SPIE 5965, 59650B (2005).
[CrossRef]

Murphy, P. E.

O’Donohue, S.

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

Osten, W.

Palum, R. J.

J. E. Greivenkamp, A. E. Lowman, and R. J. Palum, “Sub-Nyquist interferometry: implementation and measurement capability,” Opt. Eng. 35, 2962–2969 (1996).
[CrossRef]

Parks, R. E.

R. E. Parks, C. J. Evans, P. J. Sullivan, L. Shao, and B. E. Loucks, “Measurements of the LIGO Pathfinder optics,” Proc. SPIE 3134, 95–111 (1997).
[CrossRef]

Pfund, J.

Pruss, C.

Reichelt, S.

S. Reichelt, C. Pruss, and H. J. Tiziani, “Absolute interferometric test of aspheres by use of twin computer-generated holograms,” Appl. Opt. 42, 4468–4479 (2003).
[CrossRef]

S. Reichelt, C. Pruss, and H. J. Tiziani, “New design techniques and calibration methods for CGH-null testing of aspheric surfaces,” Proc. SPIE 4778, 158–168 (2002).
[CrossRef]

Rimmer, M.

Rosenfeld, D. P.

Schwider, J.

Shao, L.

R. E. Parks, C. J. Evans, P. J. Sullivan, L. Shao, and B. E. Loucks, “Measurements of the LIGO Pathfinder optics,” Proc. SPIE 3134, 95–111 (1997).
[CrossRef]

Shen, Y.

D. Liu, Y. Yang, Y. Luo, C. Tian, Y. Shen, and Y. Zhuo, “Non-null interferometric aspheric testing with partial null lens and reverse optimization,” Proc. SPIE 7426, 74260M (2009).
[CrossRef]

Y. Yang, D. Liu, G. Xin, C. Tian, Y. Luo, Y. Shen, and Y. Zhuo, “Research of precision interference locating method for a partial null compensator at aspheric testing,” Proc. SPIE 7426, 74260R (2009).
[CrossRef]

Sullivan, P. J.

R. E. Parks, C. J. Evans, P. J. Sullivan, L. Shao, and B. E. Loucks, “Measurements of the LIGO Pathfinder optics,” Proc. SPIE 3134, 95–111 (1997).
[CrossRef]

Tian, C.

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

C. Tian, Y. Yang, Y. Luo, D. Liu, and Y. Zhuo, “Study on phase retrieval of a single closed fringe interferogram in radial shearing interferometer for aspheric test,” Proc. SPIE 7656, 765612 (2010).
[CrossRef]

D. Liu, Y. Yang, Y. Luo, C. Tian, Y. Shen, and Y. Zhuo, “Non-null interferometric aspheric testing with partial null lens and reverse optimization,” Proc. SPIE 7426, 74260M (2009).
[CrossRef]

Y. Yang, D. Liu, G. Xin, C. Tian, Y. Luo, Y. Shen, and Y. Zhuo, “Research of precision interference locating method for a partial null compensator at aspheric testing,” Proc. SPIE 7426, 74260R (2009).
[CrossRef]

Tiziani, H. J.

S. Reichelt, C. Pruss, and H. J. Tiziani, “Absolute interferometric test of aspheres by use of twin computer-generated holograms,” Appl. Opt. 42, 4468–4479 (2003).
[CrossRef]

S. Reichelt, C. Pruss, and H. J. Tiziani, “New design techniques and calibration methods for CGH-null testing of aspheric surfaces,” Proc. SPIE 4778, 158–168 (2002).
[CrossRef]

B. Dörband and H. J. Tiziani, “Testing aspheric surfaces with computer-generated holograms: analysis of adjustment and shape errors,” Appl. Opt. 24, 2604–2611 (1985).
[CrossRef]

H. H. Hopkins and H. J. Tiziani, “A theoretical and experimental study of lens centering errors and their influence on optical image quality,” Br. J. Appl. Phys. 17, 33 (1966).
[CrossRef]

Tricard, M.

M. Tricard, G. Forbes, and P. Murphy, “Subaperture metrology technologies extend capabilities in optics manufacturing,” Proc. SPIE 5965, 59650B (2005).
[CrossRef]

Wei, T.

White, A. D.

Wyant, J. C.

Xin, G.

Y. Yang, D. Liu, G. Xin, C. Tian, Y. Luo, Y. Shen, and Y. Zhuo, “Research of precision interference locating method for a partial null compensator at aspheric testing,” Proc. SPIE 7426, 74260R (2009).
[CrossRef]

Yang, Y.

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

C. Tian, Y. Yang, Y. Luo, D. Liu, and Y. Zhuo, “Study on phase retrieval of a single closed fringe interferogram in radial shearing interferometer for aspheric test,” Proc. SPIE 7656, 765612 (2010).
[CrossRef]

D. Liu, Y. Yang, Y. Luo, C. Tian, Y. Shen, and Y. Zhuo, “Non-null interferometric aspheric testing with partial null lens and reverse optimization,” Proc. SPIE 7426, 74260M (2009).
[CrossRef]

Y. Yang, D. Liu, G. Xin, C. Tian, Y. Luo, Y. Shen, and Y. Zhuo, “Research of precision interference locating method for a partial null compensator at aspheric testing,” Proc. SPIE 7426, 74260R (2009).
[CrossRef]

Zhuo, Y.

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

C. Tian, Y. Yang, Y. Luo, D. Liu, and Y. Zhuo, “Study on phase retrieval of a single closed fringe interferogram in radial shearing interferometer for aspheric test,” Proc. SPIE 7656, 765612 (2010).
[CrossRef]

D. Liu, Y. Yang, Y. Luo, C. Tian, Y. Shen, and Y. Zhuo, “Non-null interferometric aspheric testing with partial null lens and reverse optimization,” Proc. SPIE 7426, 74260M (2009).
[CrossRef]

Y. Yang, D. Liu, G. Xin, C. Tian, Y. Luo, Y. Shen, and Y. Zhuo, “Research of precision interference locating method for a partial null compensator at aspheric testing,” Proc. SPIE 7426, 74260R (2009).
[CrossRef]

Appl. Opt. (15)

S. Reichelt, C. Pruss, and H. J. Tiziani, “Absolute interferometric test of aspheres by use of twin computer-generated holograms,” Appl. Opt. 42, 4468–4479 (2003).
[CrossRef]

B. Dörband and H. J. Tiziani, “Testing aspheric surfaces with computer-generated holograms: analysis of adjustment and shape errors,” Appl. Opt. 24, 2604–2611 (1985).
[CrossRef]

J. C. Wyant and V. P. Bennett, “Using computer generated holograms to test aspheric wavefronts,” Appl. Opt. 11, 2833–2839 (1972).
[CrossRef]

J. E. Greivenkamp and R. O. Gappinger, “Design of a non-null interferometer for aspheric wavefronts,” Appl. Opt. 43, 5143–5151 (2004).
[CrossRef]

J. Pfund, N. Lindlein, and J. Schwider, “Non-null testing of rotationally symmetric aspheres: a systematic error assessment,” Appl. Opt. 40, 439–446 (2001).
[CrossRef]

O. Kwon, J. C. Wyant, and C. R. Hayslett, “Rough surface interferometry at 10.6 µm,” Appl. Opt. 19, 1862–1869 (1980).
[CrossRef]

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

A. E. Lowman and J. E. Greivenkamp, “Interferometer errors due to the presence of fringes,” Appl. Opt. 35, 6826–6828 (1996).
[CrossRef]

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

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

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

C. Huang, “Propagation errors in precision Fizeau interferometry,” Appl. Opt. 32, 7016–7021 (1993).
[CrossRef]

P. E. Murphy, T. G. Brown, and D. T. Moore, “Interference imaging for aspheric surface testing,” Appl. Opt. 39, 2122–2129 (2000).
[CrossRef]

M. Rimmer, “Analysis of perturbed lens systems,” Appl. Opt. 9, 533–537 (1970).
[CrossRef]

J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Appl. Opt. 13, 2693–2703 (1974).
[CrossRef]

Br. J. Appl. Phys. (1)

H. H. Hopkins and H. J. Tiziani, “A theoretical and experimental study of lens centering errors and their influence on optical image quality,” Br. J. Appl. Phys. 17, 33 (1966).
[CrossRef]

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

Opt. Acta (1)

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

Opt. Eng. (1)

J. E. Greivenkamp, A. E. Lowman, and R. J. Palum, “Sub-Nyquist interferometry: implementation and measurement capability,” Opt. Eng. 35, 2962–2969 (1996).
[CrossRef]

Opt. Lett. (1)

Proc. SPIE (10)

C. Tian, Y. Yang, Y. Luo, D. Liu, and Y. Zhuo, “Study on phase retrieval of a single closed fringe interferogram in radial shearing interferometer for aspheric test,” Proc. SPIE 7656, 765612 (2010).
[CrossRef]

M. F. Küchel, “Interferometric measurement of rotationally symmetric aspheric surfaces,” Proc. SPIE 7389, 738916 (2009).
[CrossRef]

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

A. E. Lowman and J. E. Greivenkamp, “Modeling an interferometer for non-null testing of aspheres,” Proc. SPIE 2536, 139–147 (1995).
[CrossRef]

R. E. Parks, C. J. Evans, P. J. Sullivan, L. Shao, and B. E. Loucks, “Measurements of the LIGO Pathfinder optics,” Proc. SPIE 3134, 95–111 (1997).
[CrossRef]

M. Tricard, G. Forbes, and P. Murphy, “Subaperture metrology technologies extend capabilities in optics manufacturing,” Proc. SPIE 5965, 59650B (2005).
[CrossRef]

A. E. Lowman and J. E. Greivenkamp, “Interferometer-induced wavefront errors when testing in a non-null configuration,” Proc. SPIE 2004, 173–181 (1994).
[CrossRef]

Y. Yang, D. Liu, G. Xin, C. Tian, Y. Luo, Y. Shen, and Y. Zhuo, “Research of precision interference locating method for a partial null compensator at aspheric testing,” Proc. SPIE 7426, 74260R (2009).
[CrossRef]

S. Reichelt, C. Pruss, and H. J. Tiziani, “New design techniques and calibration methods for CGH-null testing of aspheric surfaces,” Proc. SPIE 4778, 158–168 (2002).
[CrossRef]

D. Liu, Y. Yang, Y. Luo, C. Tian, Y. Shen, and Y. Zhuo, “Non-null interferometric aspheric testing with partial null lens and reverse optimization,” Proc. SPIE 7426, 74260M (2009).
[CrossRef]

Other (3)

D. Malacara, Optical Shop Testing, 3rd ed. (Wiley, 2007).

TRIOPTICS, SpectroMaster, http://www.trioptics.com/spectromaster/description.php .

TRIOPTICS, Spherometers, http://www.trioptics.com/spherometers/description.php .

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Figures (6)

Fig. 1.
Fig. 1.

System layout of the non-null interferometer. PZT, piezoelectric transmitter; BS, beam splitter; PCS, partial compensation system.

Fig. 2.
Fig. 2.

Comparison of the experimental and theoretical wavefronts for dpa=951.344mm. (a) and (c) experimental and theoretical interferograms, respectively. (b) and (d) corresponding wavefronts Wdet and Wtest.

Fig. 3.
Fig. 3.

Comparison of the testing results. First row, 2-D and 3-D phase maps of the figure error by the non-null interferometer with the proposed method; second row, figure error by the autocollimation method; third row, 2-D and 3-D difference maps of the two results.

Fig. 4.
Fig. 4.

Repeatability verification. (a) One of the phase-shifting interferograms. (b) Reconstructed figure error. (c) Difference between (b) and the first row of Fig. 3.

Fig. 5.
Fig. 5.

Influence of the decenter of the aspheric to the final testing results. First row, recorded interferograms for xd=0.20, 0.40, 0.60mm; second row, corresponding figure error of the aspheric; third row, differences between second row of this figure and first row of Fig. 3.

Fig. 6.
Fig. 6.

Changes of c4 and c9 with respect to the errors of (a) refractive index, (b) thickness, (c) r1, (d) r2, and (e) dpa of the PCS, respectively. The vertical axes are all in the unit of wavelength.

Tables (1)

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Table 1. Impacts of Maximum Possible Calibration Errors of the PCS on the Theoretical Wavefronta

Equations (6)

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Wdet=WtestWref,
Wdet=WtestWref,
ΔW=WtestWtest=Wdet+WrefWtestWdetWtest,
Wasp=12{ΔW[A+Bx+Cy+D(x2+y2)]H},
Wasp12{(WdetWtest)[A+Bx+Cy+D(x2+y2)]}.
Wsp12{Wdet[A+Bx+Cy+D(x2+y2)]},

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