Abstract

We present the use of a computer-generated hologram (CGH) to test the mid-spatial frequency error of a large aperture long-focal-length lens. In order to verify this test approach, a 450 mm × 450 mm reflective CGH is designed and fabricated for testing the 440 mm × 440 mm spatial filter lens. Both 0th and 1st order diffraction wavefront of CGH are measured, and the 0th order diffraction wavefront is used to calibrate the substrate error. The mid-spatial frequency wavefront error caused by the CGH fabrication errors are evaluated using the binary linear grating model and power spectral density (PSD) theory. Experimental results and error analysis show that the CGH test approach is also feasible for the measurement of mid-spatial frequency error, and the measurement accuracy of PSD1 can reach 0.8832 nm RMS.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. P. A. Baisden, L. J. Atherton, R. A. Hawley, T. A. Land, J. A. Menapace, P. E. Miller, M. J. Runkel, M. L. Spaeth, C. J. Stolz, T. I. Suratwala, P. J. Wegner, and L. L. Wong, “Large Optics for the National Ignition Facility,” Fusion Sci. Technol. 69(1), 295–351 (2016).
    [Crossref]
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    [Crossref]
  3. T. G. Parham, T. J. McCarville, and M. A. Johnson, “Focal length measurements for the National Ignition Facility large lenses,” Optical Fabrication and Testing (OFT 2002) paper: OWD8 http://www.opticsinfobase.org/abstract.cfm?URI=OFT-2002-OWD8.
  4. C. Jin, S. Liu, Y. Zhou, X. Xu, C. Wei, and J. Shao, “Study on measurement of medium and low spatial wavefront errors of long focal length lens,” Chin. Opt. Lett. 12(A02), S21203 (2014).
    [Crossref]
  5. L. Yan, D. Zhu, X. Zeng, M. Li, X. Wang, and D. Ma, “Experimental study on hybrid compensation testing of an off-axis convex ellipsoid surface,” Opt. Express 27(20), 27546–27561 (2019).
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    [Crossref]
  8. X. Wei, Y. He, K. Xu, B. Gao, Q. L and, and L. Chai, “Computer-generated holograms for precision optical testing,” Proc. SPIE 9684, 96842C (2016).
    [Crossref]
  9. J.-P. Cui, N. Zhang, J. Liu, D.-L. Wu, H. Xu, D.-Y. Yan, and P. Ma, “Testing the transmitted wavefront of large aperture and long-focal-length lens with computer-generated hologram,” Opt. Express 26(21), 28067–28077 (2018).
    [Crossref]
  10. J. M. Elson and J. M. Bennett, “Calculation of the power spectral density from surface profile data,” Appl. Opt. 34(1), 201–208 (1995).
    [Crossref]
  11. D. M. Aikens, C. R. Wolfe, and J. K. Lawson, “The use of Power Spectral Density (PSD) functions in specifying optics for the National Ignition Facility,” Proc. SPIE 2576, 281–292 (1995).
    [Crossref]
  12. P. Zhou and J. H. Burge, “Optimal design of computer-generated holograms to minimize sensitivity to fabrication errors,” Opt. Express 15(23), 15410–15417 (2007).
    [Crossref]
  13. N. Lindlein, “Analysis of the disturbing diffraction orders of computer-generated holograms used for testing optical aspherics,” Appl. Opt. 40(16), 2698–2708 (2001).
    [Crossref]
  14. Y. He, X. Hou, F. Wu, X. Ma, and R. Liang, “Analysis of spurious diffraction orders of computer-generated hologram in symmetric aspheric metrology,” Opt. Express 25(17), 20556–20572 (2017).
    [Crossref]
  15. Y. C. Chang, P. Zhou, and J. H. Burge, “Analysis of phase sensitivity for binary computer generated holograms,” Appl. Opt. 45(18), 4223–4234 (2006).
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    [Crossref]

2019 (1)

2018 (2)

2017 (1)

2016 (2)

X. Wei, Y. He, K. Xu, B. Gao, Q. L and, and L. Chai, “Computer-generated holograms for precision optical testing,” Proc. SPIE 9684, 96842C (2016).
[Crossref]

P. A. Baisden, L. J. Atherton, R. A. Hawley, T. A. Land, J. A. Menapace, P. E. Miller, M. J. Runkel, M. L. Spaeth, C. J. Stolz, T. I. Suratwala, P. J. Wegner, and L. L. Wong, “Large Optics for the National Ignition Facility,” Fusion Sci. Technol. 69(1), 295–351 (2016).
[Crossref]

2014 (1)

C. Jin, S. Liu, Y. Zhou, X. Xu, C. Wei, and J. Shao, “Study on measurement of medium and low spatial wavefront errors of long focal length lens,” Chin. Opt. Lett. 12(A02), S21203 (2014).
[Crossref]

2013 (1)

C. Zhao and J. H. Burge, “Optical testing with computer generated holograms: comprehensive error analysis,” Proc. SPIE 8838, 88380H (2013).
[Crossref]

2007 (1)

2006 (1)

2003 (1)

2001 (1)

1995 (3)

J. K. Lawson, C. R. Wolfe, K. R. Manes, J. B. Trenholme, D. M. Aikens, and R. E. English, “Specification of optical components using the power spectral density function,” Proc. SPIE 2536, 38–50 (1995).
[Crossref]

J. M. Elson and J. M. Bennett, “Calculation of the power spectral density from surface profile data,” Appl. Opt. 34(1), 201–208 (1995).
[Crossref]

D. M. Aikens, C. R. Wolfe, and J. K. Lawson, “The use of Power Spectral Density (PSD) functions in specifying optics for the National Ignition Facility,” Proc. SPIE 2576, 281–292 (1995).
[Crossref]

Aikens, D. M.

J. K. Lawson, C. R. Wolfe, K. R. Manes, J. B. Trenholme, D. M. Aikens, and R. E. English, “Specification of optical components using the power spectral density function,” Proc. SPIE 2536, 38–50 (1995).
[Crossref]

D. M. Aikens, C. R. Wolfe, and J. K. Lawson, “The use of Power Spectral Density (PSD) functions in specifying optics for the National Ignition Facility,” Proc. SPIE 2576, 281–292 (1995).
[Crossref]

and, Q. L

X. Wei, Y. He, K. Xu, B. Gao, Q. L and, and L. Chai, “Computer-generated holograms for precision optical testing,” Proc. SPIE 9684, 96842C (2016).
[Crossref]

Atherton, L. J.

P. A. Baisden, L. J. Atherton, R. A. Hawley, T. A. Land, J. A. Menapace, P. E. Miller, M. J. Runkel, M. L. Spaeth, C. J. Stolz, T. I. Suratwala, P. J. Wegner, and L. L. Wong, “Large Optics for the National Ignition Facility,” Fusion Sci. Technol. 69(1), 295–351 (2016).
[Crossref]

Baisden, P. A.

P. A. Baisden, L. J. Atherton, R. A. Hawley, T. A. Land, J. A. Menapace, P. E. Miller, M. J. Runkel, M. L. Spaeth, C. J. Stolz, T. I. Suratwala, P. J. Wegner, and L. L. Wong, “Large Optics for the National Ignition Facility,” Fusion Sci. Technol. 69(1), 295–351 (2016).
[Crossref]

Bennett, J. M.

Burge, J. H.

Chai, L.

X. Wei, Y. He, K. Xu, B. Gao, Q. L and, and L. Chai, “Computer-generated holograms for precision optical testing,” Proc. SPIE 9684, 96842C (2016).
[Crossref]

Chang, Y. C.

Cui, J.-P.

DeBoo, B.

Elson, J. M.

English, R. E.

J. K. Lawson, C. R. Wolfe, K. R. Manes, J. B. Trenholme, D. M. Aikens, and R. E. English, “Specification of optical components using the power spectral density function,” Proc. SPIE 2536, 38–50 (1995).
[Crossref]

Gao, B.

X. Wei, Y. He, K. Xu, B. Gao, Q. L and, and L. Chai, “Computer-generated holograms for precision optical testing,” Proc. SPIE 9684, 96842C (2016).
[Crossref]

Hawley, R. A.

P. A. Baisden, L. J. Atherton, R. A. Hawley, T. A. Land, J. A. Menapace, P. E. Miller, M. J. Runkel, M. L. Spaeth, C. J. Stolz, T. I. Suratwala, P. J. Wegner, and L. L. Wong, “Large Optics for the National Ignition Facility,” Fusion Sci. Technol. 69(1), 295–351 (2016).
[Crossref]

He, Y.

Y. He, X. Hou, F. Wu, X. Ma, and R. Liang, “Analysis of spurious diffraction orders of computer-generated hologram in symmetric aspheric metrology,” Opt. Express 25(17), 20556–20572 (2017).
[Crossref]

X. Wei, Y. He, K. Xu, B. Gao, Q. L and, and L. Chai, “Computer-generated holograms for precision optical testing,” Proc. SPIE 9684, 96842C (2016).
[Crossref]

Hou, X.

Jiao, J.

Jin, C.

C. Jin, S. Liu, Y. Zhou, X. Xu, C. Wei, and J. Shao, “Study on measurement of medium and low spatial wavefront errors of long focal length lens,” Chin. Opt. Lett. 12(A02), S21203 (2014).
[Crossref]

Johnson, M. A.

T. G. Parham, T. J. McCarville, and M. A. Johnson, “Focal length measurements for the National Ignition Facility large lenses,” Optical Fabrication and Testing (OFT 2002) paper: OWD8 http://www.opticsinfobase.org/abstract.cfm?URI=OFT-2002-OWD8.

Land, T. A.

P. A. Baisden, L. J. Atherton, R. A. Hawley, T. A. Land, J. A. Menapace, P. E. Miller, M. J. Runkel, M. L. Spaeth, C. J. Stolz, T. I. Suratwala, P. J. Wegner, and L. L. Wong, “Large Optics for the National Ignition Facility,” Fusion Sci. Technol. 69(1), 295–351 (2016).
[Crossref]

Lawson, J. K.

J. K. Lawson, C. R. Wolfe, K. R. Manes, J. B. Trenholme, D. M. Aikens, and R. E. English, “Specification of optical components using the power spectral density function,” Proc. SPIE 2536, 38–50 (1995).
[Crossref]

D. M. Aikens, C. R. Wolfe, and J. K. Lawson, “The use of Power Spectral Density (PSD) functions in specifying optics for the National Ignition Facility,” Proc. SPIE 2576, 281–292 (1995).
[Crossref]

Li, M.

Liang, R.

Lindlein, N.

Liu, J.

Liu, S.

C. Jin, S. Liu, Y. Zhou, X. Xu, C. Wei, and J. Shao, “Study on measurement of medium and low spatial wavefront errors of long focal length lens,” Chin. Opt. Lett. 12(A02), S21203 (2014).
[Crossref]

Ma, D.

Ma, P.

Ma, X.

Manes, K. R.

J. K. Lawson, C. R. Wolfe, K. R. Manes, J. B. Trenholme, D. M. Aikens, and R. E. English, “Specification of optical components using the power spectral density function,” Proc. SPIE 2536, 38–50 (1995).
[Crossref]

McCarville, T. J.

T. G. Parham, T. J. McCarville, and M. A. Johnson, “Focal length measurements for the National Ignition Facility large lenses,” Optical Fabrication and Testing (OFT 2002) paper: OWD8 http://www.opticsinfobase.org/abstract.cfm?URI=OFT-2002-OWD8.

Menapace, J. A.

P. A. Baisden, L. J. Atherton, R. A. Hawley, T. A. Land, J. A. Menapace, P. E. Miller, M. J. Runkel, M. L. Spaeth, C. J. Stolz, T. I. Suratwala, P. J. Wegner, and L. L. Wong, “Large Optics for the National Ignition Facility,” Fusion Sci. Technol. 69(1), 295–351 (2016).
[Crossref]

Miller, P. E.

P. A. Baisden, L. J. Atherton, R. A. Hawley, T. A. Land, J. A. Menapace, P. E. Miller, M. J. Runkel, M. L. Spaeth, C. J. Stolz, T. I. Suratwala, P. J. Wegner, and L. L. Wong, “Large Optics for the National Ignition Facility,” Fusion Sci. Technol. 69(1), 295–351 (2016).
[Crossref]

Parham, T. G.

T. G. Parham, T. J. McCarville, and M. A. Johnson, “Focal length measurements for the National Ignition Facility large lenses,” Optical Fabrication and Testing (OFT 2002) paper: OWD8 http://www.opticsinfobase.org/abstract.cfm?URI=OFT-2002-OWD8.

Runkel, M. J.

P. A. Baisden, L. J. Atherton, R. A. Hawley, T. A. Land, J. A. Menapace, P. E. Miller, M. J. Runkel, M. L. Spaeth, C. J. Stolz, T. I. Suratwala, P. J. Wegner, and L. L. Wong, “Large Optics for the National Ignition Facility,” Fusion Sci. Technol. 69(1), 295–351 (2016).
[Crossref]

Sasian, J.

Shao, J.

C. Jin, S. Liu, Y. Zhou, X. Xu, C. Wei, and J. Shao, “Study on measurement of medium and low spatial wavefront errors of long focal length lens,” Chin. Opt. Lett. 12(A02), S21203 (2014).
[Crossref]

Spaeth, M. L.

P. A. Baisden, L. J. Atherton, R. A. Hawley, T. A. Land, J. A. Menapace, P. E. Miller, M. J. Runkel, M. L. Spaeth, C. J. Stolz, T. I. Suratwala, P. J. Wegner, and L. L. Wong, “Large Optics for the National Ignition Facility,” Fusion Sci. Technol. 69(1), 295–351 (2016).
[Crossref]

Stolz, C. J.

P. A. Baisden, L. J. Atherton, R. A. Hawley, T. A. Land, J. A. Menapace, P. E. Miller, M. J. Runkel, M. L. Spaeth, C. J. Stolz, T. I. Suratwala, P. J. Wegner, and L. L. Wong, “Large Optics for the National Ignition Facility,” Fusion Sci. Technol. 69(1), 295–351 (2016).
[Crossref]

Suratwala, T. I.

P. A. Baisden, L. J. Atherton, R. A. Hawley, T. A. Land, J. A. Menapace, P. E. Miller, M. J. Runkel, M. L. Spaeth, C. J. Stolz, T. I. Suratwala, P. J. Wegner, and L. L. Wong, “Large Optics for the National Ignition Facility,” Fusion Sci. Technol. 69(1), 295–351 (2016).
[Crossref]

Trenholme, J. B.

J. K. Lawson, C. R. Wolfe, K. R. Manes, J. B. Trenholme, D. M. Aikens, and R. E. English, “Specification of optical components using the power spectral density function,” Proc. SPIE 2536, 38–50 (1995).
[Crossref]

Wang, X.

Wegner, P. J.

P. A. Baisden, L. J. Atherton, R. A. Hawley, T. A. Land, J. A. Menapace, P. E. Miller, M. J. Runkel, M. L. Spaeth, C. J. Stolz, T. I. Suratwala, P. J. Wegner, and L. L. Wong, “Large Optics for the National Ignition Facility,” Fusion Sci. Technol. 69(1), 295–351 (2016).
[Crossref]

Wei, C.

C. Jin, S. Liu, Y. Zhou, X. Xu, C. Wei, and J. Shao, “Study on measurement of medium and low spatial wavefront errors of long focal length lens,” Chin. Opt. Lett. 12(A02), S21203 (2014).
[Crossref]

Wei, X.

X. Wei, Y. He, K. Xu, B. Gao, Q. L and, and L. Chai, “Computer-generated holograms for precision optical testing,” Proc. SPIE 9684, 96842C (2016).
[Crossref]

Wolfe, C. R.

J. K. Lawson, C. R. Wolfe, K. R. Manes, J. B. Trenholme, D. M. Aikens, and R. E. English, “Specification of optical components using the power spectral density function,” Proc. SPIE 2536, 38–50 (1995).
[Crossref]

D. M. Aikens, C. R. Wolfe, and J. K. Lawson, “The use of Power Spectral Density (PSD) functions in specifying optics for the National Ignition Facility,” Proc. SPIE 2576, 281–292 (1995).
[Crossref]

Wong, L. L.

P. A. Baisden, L. J. Atherton, R. A. Hawley, T. A. Land, J. A. Menapace, P. E. Miller, M. J. Runkel, M. L. Spaeth, C. J. Stolz, T. I. Suratwala, P. J. Wegner, and L. L. Wong, “Large Optics for the National Ignition Facility,” Fusion Sci. Technol. 69(1), 295–351 (2016).
[Crossref]

Wu, D.-L.

Wu, F.

Xu, H.

Xu, K.

X. Wei, Y. He, K. Xu, B. Gao, Q. L and, and L. Chai, “Computer-generated holograms for precision optical testing,” Proc. SPIE 9684, 96842C (2016).
[Crossref]

Xu, X.

C. Jin, S. Liu, Y. Zhou, X. Xu, C. Wei, and J. Shao, “Study on measurement of medium and low spatial wavefront errors of long focal length lens,” Chin. Opt. Lett. 12(A02), S21203 (2014).
[Crossref]

Xue, D.

Yan, D.-Y.

Yan, L.

Zeng, X.

Zhang, N.

Zhang, X.

Zhang, Z.

Zhao, C.

C. Zhao and J. H. Burge, “Optical testing with computer generated holograms: comprehensive error analysis,” Proc. SPIE 8838, 88380H (2013).
[Crossref]

Zhou, P.

Zhou, Y.

C. Jin, S. Liu, Y. Zhou, X. Xu, C. Wei, and J. Shao, “Study on measurement of medium and low spatial wavefront errors of long focal length lens,” Chin. Opt. Lett. 12(A02), S21203 (2014).
[Crossref]

Zhu, D.

Appl. Opt. (5)

Chin. Opt. Lett. (1)

C. Jin, S. Liu, Y. Zhou, X. Xu, C. Wei, and J. Shao, “Study on measurement of medium and low spatial wavefront errors of long focal length lens,” Chin. Opt. Lett. 12(A02), S21203 (2014).
[Crossref]

Fusion Sci. Technol. (1)

P. A. Baisden, L. J. Atherton, R. A. Hawley, T. A. Land, J. A. Menapace, P. E. Miller, M. J. Runkel, M. L. Spaeth, C. J. Stolz, T. I. Suratwala, P. J. Wegner, and L. L. Wong, “Large Optics for the National Ignition Facility,” Fusion Sci. Technol. 69(1), 295–351 (2016).
[Crossref]

Opt. Express (4)

Proc. SPIE (4)

C. Zhao and J. H. Burge, “Optical testing with computer generated holograms: comprehensive error analysis,” Proc. SPIE 8838, 88380H (2013).
[Crossref]

J. K. Lawson, C. R. Wolfe, K. R. Manes, J. B. Trenholme, D. M. Aikens, and R. E. English, “Specification of optical components using the power spectral density function,” Proc. SPIE 2536, 38–50 (1995).
[Crossref]

D. M. Aikens, C. R. Wolfe, and J. K. Lawson, “The use of Power Spectral Density (PSD) functions in specifying optics for the National Ignition Facility,” Proc. SPIE 2576, 281–292 (1995).
[Crossref]

X. Wei, Y. He, K. Xu, B. Gao, Q. L and, and L. Chai, “Computer-generated holograms for precision optical testing,” Proc. SPIE 9684, 96842C (2016).
[Crossref]

Other (1)

T. G. Parham, T. J. McCarville, and M. A. Johnson, “Focal length measurements for the National Ignition Facility large lenses,” Optical Fabrication and Testing (OFT 2002) paper: OWD8 http://www.opticsinfobase.org/abstract.cfm?URI=OFT-2002-OWD8.

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Figures (9)

Fig. 1.
Fig. 1. Schematic drawing of test configuration for large aperture long-focal-length lens. (a) Convex mirror method; (b) CGH method.
Fig. 2.
Fig. 2. CGH substrate figure before etching (a) CGH substrate figure map: PV = 0.059λ and RMS = 0.0062λ; (b) PSD1 band-passed figure map: RMS = 0.8018nm.
Fig. 3.
Fig. 3. 0th order measurement. (a) CGH substrate figure map before data patching: PV = 0.161λ and RMS = 0.0145λ; (b) CGH substrate figure map after data patching: PV = 0.118λ and RMS = 0.0145λ; (c) PSD1 band-passed figure map: RMS = 0.6924 nm.
Fig. 4.
Fig. 4. 1st order measurement. (a) Wavefront map before data patching: PV = 0.225λ and RMS = 0.0181λ; (b) Wavefront map after data patching: PV = 0.225λ and RMS = 0.0181λ; (c) PSD1 band-passed wavefront map: RMS = 3.0232 nm.
Fig. 5.
Fig. 5. Data mapping between 0th order and 1st order. (a) Mapping function; (b) CGH substrate figure map after data mapping: PV = 0.113λ and RMS = 0.0134λ; (c) PSD1 band-passed substrate figure map: RMS = 0.6894 nm.
Fig. 6.
Fig. 6. Transmitted wavefront of large aperture long-focal-length lens after CGH substrate calibration. (a) Wavefront map: PV = 0.201λ and RMS = 0.0112λ; (b) PSD1 band-passed wavefront map: RMS = 2.8908 nm.
Fig. 7.
Fig. 7. The PSD1 band-passed RMS in 16 sub-apertures of 100 mm × 100 mm size.
Fig. 8.
Fig. 8. The PSD1 band-passed 1D collapse PSD curves of large aperture long-focal-length lens (a) with and (b) without the CGH substrate calibration.
Fig. 9.
Fig. 9. Schematic drawing of the binary linear grating model.

Tables (2)

Tables Icon

Table 1. Diffraction wavefront and sensitivity functions for error analysis of CGH

Tables Icon

Table 2. Errors analysis for the CGH test in PSD1 frequency band

Equations (11)

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

U ( v x , v y ) = 0 L y 0 L x u ( x , y ) e i 2 π ( v x x + v y y ) d x d y
P S D ( v x , v y ) = | U ( v x , v y ) | 2 L x L y
{ x = m Δ x , 0 m M 1 y = n Δ y , 0 n N 1 ν x = m ν Δ ν x = m ν / ( M Δ x ) , M / 2 m ν M / 2 1 ν y = n ν Δ ν y = n ν / ( N Δ y ) , N / 2 n ν N / 2 1
U ( m ν , n ν ) = Δ x Δ y n = 0 N 1 m = 0 M 1 u ( m , n ) e i 2 π ( m ν m / M + n ν n / N )
P S D ( m ν , n ν ) = | U ( m ν , n ν ) | 2 ( M Δ x ) ( N Δ y ) = Δ x Δ y M N | n = 0 N 1 m = 0 M 1 u ( m , n ) e i 2 π ( m ν m / M + n ν n / N ) | 2
P S D ( n ν ) = m ν = m ν 1 m ν 2 P S D ( m ν , n ν ) Δ ν x
R M S ( m ν , n ν ) = n ν = n ν 1 n ν 2 m ν = m ν 1 m ν 2 P S D ( m ν , n ν ) Δ ν x Δ ν y
Δ W D = 1 2 π Ψ D Δ D
Δ W ϕ = Ψ ϕ Δ ϕ
Δ W P = m o λ ε S
σ P S D 1 2  =  S P S D 1 S N σ Δ W 2 = π ν h 2 π ν l 2 ( 2 ν x c ) ( 2 ν y c ) σ Δ W 2

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