Abstract

Aspherical surfaces can provide significant benefits to a wide variety of optical systems, but manufacturing high-precision aspherical surfaces has historically been limited by the ability to measure them. Null testing has always been the ideal method in aspherical measurement. However, in many cases, it is hard to realize null testing for complex surfaces, especially for convex surfaces in complicated forms. In this paper, we propose a hybrid compensation method combining a spherical mirror and a computer generated hologram (CGH) to achieve the null testing of the convex aspherical surface. Firstly, we introduce our self-developed mathematical models in the hybrid compensation method, including optics alignment model, distortion correction model and spherical surface error removing model. Then the performance of our proposed method is analyzed by a null testing experiment of an off-axis convex ellipsoid mirror. The experimental result shows that the proposed method can accomplish the hybrid compensation testing of convex aspherical surfaces effectively, and it can also bring much to the application of our method in convex aspherical surface testing.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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  22. J. H. Burge, “Fizeau interferometry for large convex surfaces,” Proc. SPIE 2536, 127–138 (1995).
    [Crossref]
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    [Crossref]

2019 (1)

2018 (4)

2017 (1)

2015 (2)

2014 (1)

2013 (2)

2012 (1)

C. Supranowitz, C.M. Fee, P. Murphy, G. Forbes, A. Kulawiec, and D. Miladinovic, “Asphere Metrology Using Variable Optical Null Technology,” Proc. SPIE 8416, 841604 (2012).
[Crossref]

2011 (1)

2010 (2)

A. Kulawiec, P. Murphy, and M.D. Marco, “Measurement of high-departure aspheres using subaperture stitching with the Variable Optical Null (VONTM),” Proc. SPIE 7655, 765512 (2010).

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

2009 (2)

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

M. B. Dubin, P. Su, and J. H. Burge, “Fizeau interferometer with spherical reference and CGH correction for measuring large convex aspheres,” Proc. SPIE 7426, 74260S (2009).
[Crossref]

2007 (1)

2003 (1)

P. Murphy, G. Forbes, J. Fleig, P. Dumas, and M. Tricard, “Stitching interferometry: a flexible solution for surface metrology,” Opt. Photonics News 14(5), 38–43 (2003).
[Crossref]

1995 (1)

J. H. Burge, “Fizeau interferometry for large convex surfaces,” Proc. SPIE 2536, 127–138 (1995).
[Crossref]

1994 (1)

O. Masashi, O. Katsuyuki, and T. Jumper, “Measurement of large plane surface shapes by connecting small-aperture interferograms,” Opt. Eng. 33(2), 608–613 (1994).
[Crossref]

1988 (1)

1982 (1)

Bai, J.

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. Opt. 49(1), 21–31 (2010).
[Crossref]

M. B. Dubin, P. Su, and J. H. Burge, “Fizeau interferometer with spherical reference and CGH correction for measuring large convex aspheres,” Proc. SPIE 7426, 74260S (2009).
[Crossref]

J. H. Burge, “Fizeau interferometry for large convex surfaces,” Proc. SPIE 2536, 127–138 (1995).
[Crossref]

Chang, H. S.

Chen, D. F.

Chen, Q.

Chen, S. Y.

Chen, Y. C.

Cheng, H. B.

Chong, S. Y.

Dai, Y. Y.

Du, H. B.

Dubin, M. B.

M. B. Dubin, P. Su, and J. H. Burge, “Fizeau interferometer with spherical reference and CGH correction for measuring large convex aspheres,” Proc. SPIE 7426, 74260S (2009).
[Crossref]

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(5), 38–43 (2003).
[Crossref]

Fee, C.M.

C. Supranowitz, C.M. Fee, P. Murphy, G. Forbes, A. Kulawiec, and D. Miladinovic, “Asphere Metrology Using Variable Optical Null Technology,” Proc. SPIE 8416, 841604 (2012).
[Crossref]

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(5), 38–43 (2003).
[Crossref]

Forbes, G.

C. Supranowitz, C.M. Fee, P. Murphy, G. Forbes, A. Kulawiec, and D. Miladinovic, “Asphere Metrology Using Variable Optical Null Technology,” Proc. SPIE 8416, 841604 (2012).
[Crossref]

P. Murphy, G. Forbes, J. Fleig, P. Dumas, and M. Tricard, “Stitching interferometry: a flexible solution for surface metrology,” Opt. Photonics News 14(5), 38–43 (2003).
[Crossref]

Ge, B. L.

Gu, F. F.

Guo, H. W.

Hao, Q.

Hou, X.

Hu, H. X.

Hu, Y.

Jumper, T.

O. Masashi, O. Katsuyuki, and T. Jumper, “Measurement of large plane surface shapes by connecting small-aperture interferograms,” Opt. Eng. 33(2), 608–613 (1994).
[Crossref]

Katsuyuki, O.

O. Masashi, O. Katsuyuki, and T. Jumper, “Measurement of large plane surface shapes by connecting small-aperture interferograms,” Opt. Eng. 33(2), 608–613 (1994).
[Crossref]

Kim, C. J.

Koliopoulos, C. L.

Kulawiec, A.

C. Supranowitz, C.M. Fee, P. Murphy, G. Forbes, A. Kulawiec, and D. Miladinovic, “Asphere Metrology Using Variable Optical Null Technology,” Proc. SPIE 8416, 841604 (2012).
[Crossref]

A. Kulawiec, P. Murphy, and M.D. Marco, “Measurement of high-departure aspheres using subaperture stitching with the Variable Optical Null (VONTM),” Proc. SPIE 7655, 765512 (2010).

Lawrence, G. N.

Li, K. X.

Li, S. Y.

Li, T. F.

Liang, C. W.

Lin, P. C.

Liu, D.

Liu, Y. M.

Luo, Y. J.

Marco, M.D.

A. Kulawiec, P. Murphy, and M.D. Marco, “Measurement of high-departure aspheres using subaperture stitching with the Variable Optical Null (VONTM),” Proc. SPIE 7655, 765512 (2010).

Masashi, O.

O. Masashi, O. Katsuyuki, and T. Jumper, “Measurement of large plane surface shapes by connecting small-aperture interferograms,” Opt. Eng. 33(2), 608–613 (1994).
[Crossref]

Miladinovic, D.

C. Supranowitz, C.M. Fee, P. Murphy, G. Forbes, A. Kulawiec, and D. Miladinovic, “Asphere Metrology Using Variable Optical Null Technology,” Proc. SPIE 8416, 841604 (2012).
[Crossref]

Murphy, P.

C. Supranowitz, C.M. Fee, P. Murphy, G. Forbes, A. Kulawiec, and D. Miladinovic, “Asphere Metrology Using Variable Optical Null Technology,” Proc. SPIE 8416, 841604 (2012).
[Crossref]

A. Kulawiec, P. Murphy, and M.D. Marco, “Measurement of high-departure aspheres using subaperture stitching with the Variable Optical Null (VONTM),” Proc. SPIE 7655, 765512 (2010).

P. Murphy, G. Forbes, J. Fleig, P. Dumas, and M. Tricard, “Stitching interferometry: a flexible solution for surface metrology,” Opt. Photonics News 14(5), 38–43 (2003).
[Crossref]

Nowick, K.

Parks, R. E.

Peng, J. Z.

Shen, Y. B.

Shi, T.

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. Opt. 49(1), 21–31 (2010).
[Crossref]

M. B. Dubin, P. Su, and J. H. Burge, “Fizeau interferometer with spherical reference and CGH correction for measuring large convex aspheres,” Proc. SPIE 7426, 74260S (2009).
[Crossref]

Supranowitz, C.

C. Supranowitz, C.M. Fee, P. Murphy, G. Forbes, A. Kulawiec, and D. Miladinovic, “Asphere Metrology Using Variable Optical Null Technology,” Proc. SPIE 8416, 841604 (2012).
[Crossref]

Tam, H.-Y.

Tan, Y. F.

Tian, C.

Tie, G. P.

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(5), 38–43 (2003).
[Crossref]

Wagner, K.

Wang, L.

Wang, S. P.

Wang, S. S.

Wang, X. K.

Wei, T.

Wen, Y. F.

Wu, C. C.

Wu, F.

Xue, S.

Yan, L. S.

Yang, L.

Yang, Y. Y.

Yu, Y. J.

Zeng, X. F.

Zhai, D. D.

Zhang, L.

Zhang, X. J.

Zhao, H.

Zhao, Z. X.

Zheng, L. G.

Zhong, J. G.

Zhou, D. M.

Zhuo, Y. M.

Appl. Opt. (8)

Opt. Eng. (1)

O. Masashi, O. Katsuyuki, and T. Jumper, “Measurement of large plane surface shapes by connecting small-aperture interferograms,” Opt. Eng. 33(2), 608–613 (1994).
[Crossref]

Opt. Express (9)

L. S. Yan, X. K. Wang, L. G. Zheng, X. F. Zeng, H. X. Hu, and X. J. Zhang, “Experimental study on subaperture testing with iterative triangulation algorithm,” Opt. Express 21(19), 22628–22644 (2013).
[Crossref]

Z. X. Zhao, H. Zhao, F. F. Gu, H. B. Du, and K. X. Li, “Non-null testing for aspheric surfaces using elliptical sub-aperture stitching technique,” Opt. Express 22(5), 5512–5520 (2014).
[Crossref]

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

Y. C. Chen, C. W. Liang, H. S. Chang, and P. C. Lin, “Reconstruction of reference error in high overlapping density subaperture stitching interferometry,” Opt. Express 26(22), 29123–29133 (2018).
[Crossref]

S. Xue, S. Y. Chen, and G. P. Tie, “Near-null interferometry using an aspheric null lens generating a broad range of variable spherical aberration for flexible test of aspheres,” Opt. Express 26(24), 31172–31189 (2018).
[Crossref]

J. Z. Peng, D. F. Chen, H. W. Guo, J. G. Zhong, and Y. J. Yu, “Variable optical null based on a yawing CGH for measuring steep acylindrical surface,” Opt. Express 26(16), 20306–20318 (2018).
[Crossref]

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]

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

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

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(5), 38–43 (2003).
[Crossref]

Proc. SPIE (4)

A. Kulawiec, P. Murphy, and M.D. Marco, “Measurement of high-departure aspheres using subaperture stitching with the Variable Optical Null (VONTM),” Proc. SPIE 7655, 765512 (2010).

C. Supranowitz, C.M. Fee, P. Murphy, G. Forbes, A. Kulawiec, and D. Miladinovic, “Asphere Metrology Using Variable Optical Null Technology,” Proc. SPIE 8416, 841604 (2012).
[Crossref]

J. H. Burge, “Fizeau interferometry for large convex surfaces,” Proc. SPIE 2536, 127–138 (1995).
[Crossref]

M. B. Dubin, P. Su, and J. H. Burge, “Fizeau interferometer with spherical reference and CGH correction for measuring large convex aspheres,” Proc. SPIE 7426, 74260S (2009).
[Crossref]

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Figures (26)

Fig. 1.
Fig. 1. Hybrid compensation with CGH and spherical mirror.
Fig. 2.
Fig. 2. Alignment process (step1 and step2)
Fig. 3.
Fig. 3. Alignment process (step3 and step4)
Fig. 4.
Fig. 4. Description of coordinate systems in testing
Fig. 5.
Fig. 5. Description of coordinate systems in alignment
Fig. 6.
Fig. 6. Distortion of a convex aspherical mirror with hybrid compensation: (a) uniform grid on the aspherical mirror on the test, (b) uniform grid mapping to the CGH
Fig. 7.
Fig. 7. Departure between ellipsoid mirror and best-fit sphere
Fig. 8.
Fig. 8. Design of testing path
Fig. 9.
Fig. 9. Residual error after compensated with spherical mirror
Fig. 10.
Fig. 10. Residual error after CGH compensation
Fig. 11.
Fig. 11. Diffractive regions distribution on CGH
Fig. 12.
Fig. 12. CGH used in the measurement
Fig. 13.
Fig. 13. Testing setup
Fig. 14.
Fig. 14. Test sphere with alignment interferometer (a) Interferogram before alignment between spherical mirror and alignment interferometer (b) Interferogram after alignment between spherical mirror and alignment interferometer
Fig. 15.
Fig. 15. Align CGH with alignment interferometer (a) Interferogram before alignment between spherical mirror, CGH and alignment interferometer (b) Interferogram after alignment between spherical mirror, CGH and alignment interferometer
Fig. 16.
Fig. 16. Align CGH with testing interferometer (a) Interferogram before alignment between spherical mirror, CGH and testing interferometer (b) Interferogram after alignment between spherical mirror, CGH and testing interferometer
Fig. 17.
Fig. 17. Align aspherical mirror (a) Interferogram before alignment between spherical mirror, CGH, testing interferometer and aspherical mirror (b) Interferogram after alignment between spherical mirror, CGH, testing interferometer and aspherical mirror
Fig. 18.
Fig. 18. Testing map of aspherical mirror
Fig. 19.
Fig. 19. Testing map of spherical mirror
Fig. 20.
Fig. 20. Area of spherical mirror used in the hybrid compensation testing
Fig. 21.
Fig. 21. Surface map of aspherical mirror after removing the error of spherical mirror
Fig. 22.
Fig. 22. Surface map of aspherical mirror after replacing the target pixels
Fig. 23.
Fig. 23. Subapertures design with CGH
Fig. 24.
Fig. 24. The layout of subaperture testing system
Fig. 25.
Fig. 25. Subaperture testing results
Fig. 26.
Fig. 26. Subaperture stitching map

Tables (2)

Tables Icon

Table 1. Summary of CGH regions

Tables Icon

Table 2. Description of CGH regions

Equations (4)

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

[ X i Y i 1 ] = T [ x y 1 ] ,
T = [ s cos θ s sin θ t x s sin θ s cos θ t y 0 0 1 ] ,
[ X i Y i ] = [ x i s cos θ y i s sin θ + t x x i s sin θ + y i s cos θ + t y ] ,
min = i = 1 N ( ( X i X i ) 2 + ( Y i Y i ) 2 ) ,

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