Abstract

The deflectometry provides a powerful metrological technique enabling the high-precision testing of reflective surfaces with high dynamic range, such as aspheric and freeform surfaces. In the fringe-illumination deflectometry based on reverse-Hartmann-test configuration, the calibration of system geometry is required to achieve “null” testing. However, the system miscalibration can introduce a significant systematic error in the testing results. A general double-step calibration method, which is based on the low-order Zernike aberration optimization and high-order aberration separation, is proposed to separate and eliminate the geometrical error due to system miscalibration. Both the numerical simulation and experiments have been performed to validate the feasibility of the proposed calibration method. The proposed method provides a general way for the accurate calibration of system geometrical error, avoids the over-correction and is feasible for the testing of various complex freeform surfaces.

© 2018 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]

2017 (3)

2016 (3)

2015 (2)

G. P. Butel, G. A. Smith, and J. H. Burge, “Deflectometry using portable devices,” Opt. Eng. 54(2), 025111 (2015).
[Crossref]

X. Wu, J. Zhu, T. Yang, and G. Jin, “Transverse image translation using an optical freeform single lens,” Appl. Opt. 54(28), E55–E62 (2015).
[Crossref] [PubMed]

2014 (1)

R. Huang, P. Su, T. Horne, G. Brusa, and J. Burge, “Optical metrology of a large deformable aspherical mirror using software configurable optical test system,” Opt. Eng. 53(8), 085106 (2014).
[Crossref]

2013 (1)

C. Andraka, S. Sadlon, B. Myer, K. Trapeznikov, and C. Liebner, “Rapid reflective facet characterization using fringe reflection techniques,” J. Sol. Ener. 136(1), 011002 (2013).
[Crossref]

2012 (1)

2011 (2)

D. Wang, Y. Yang, C. Chen, and Y. Zhuo, “Point diffraction interferometer with adjustable fringe contrast for testing spherical surfaces,” Appl. Opt. 50(16), 2342–2348 (2011).
[Crossref] [PubMed]

D. Wang, Y. Yang, C. Chen, and Y. Zhuo, “Calibration of geometrical systematic error in high-precision spherical surface measurement,” Opt. Commun. 284(16–17), 3878–3885 (2011).
[Crossref]

2010 (1)

2004 (1)

M. Knauer, J. Kaminski, and G. Hausler, “Phase measuring deflectometry: a new approach to measure specular free-form surfaces,” Proc. SPIE 5457, 366–376 (2004).
[Crossref]

2002 (1)

K. Otaki, K. Ota, K. Nishiyama, T. Yamamoto, Y. Fukuda, and S. Okazaki, “Development of the point diffraction interferometer for extreme ultraviolet lithography: Design, fabrication, and evaluation,” J. Vac. Sci. Technol. B 20(6), 2449–2458 (2002).
[Crossref]

1990 (1)

N. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. 29(10), 1174–1180 (1990).
[Crossref]

1980 (1)

1972 (1)

1964 (1)

J. L. Rayces, “Exact relation between wave aberration and ray aberration and ray aberration,” J. Mod. Opt. 11(2), 85–88 (1964).

Andraka, C.

C. Andraka, S. Sadlon, B. Myer, K. Trapeznikov, and C. Liebner, “Rapid reflective facet characterization using fringe reflection techniques,” J. Sol. Ener. 136(1), 011002 (2013).
[Crossref]

Angel, R. P.

Bauer, A.

Brusa, G.

R. Huang, P. Su, T. Horne, G. Brusa, and J. Burge, “Optical metrology of a large deformable aspherical mirror using software configurable optical test system,” Opt. Eng. 53(8), 085106 (2014).
[Crossref]

Burge, J.

R. Huang, P. Su, T. Horne, G. Brusa, and J. Burge, “Optical metrology of a large deformable aspherical mirror using software configurable optical test system,” Opt. Eng. 53(8), 085106 (2014).
[Crossref]

Burge, J. H.

Butel, G. P.

G. P. Butel, G. A. Smith, and J. H. Burge, “Deflectometry using portable devices,” Opt. Eng. 54(2), 025111 (2015).
[Crossref]

Chen, C.

D. Wang, Y. Yang, C. Chen, and Y. Zhuo, “Calibration of geometrical systematic error in high-precision spherical surface measurement,” Opt. Commun. 284(16–17), 3878–3885 (2011).
[Crossref]

D. Wang, Y. Yang, C. Chen, and Y. Zhuo, “Point diffraction interferometer with adjustable fringe contrast for testing spherical surfaces,” Appl. Opt. 50(16), 2342–2348 (2011).
[Crossref] [PubMed]

Cheng, H. N.

Fox, D. G.

Fukuda, Y.

K. Otaki, K. Ota, K. Nishiyama, T. Yamamoto, Y. Fukuda, and S. Okazaki, “Development of the point diffraction interferometer for extreme ultraviolet lithography: Design, fabrication, and evaluation,” J. Vac. Sci. Technol. B 20(6), 2449–2458 (2002).
[Crossref]

Gannon, C.

Hausler, G.

M. Knauer, J. Kaminski, and G. Hausler, “Phase measuring deflectometry: a new approach to measure specular free-form surfaces,” Proc. SPIE 5457, 366–376 (2004).
[Crossref]

Horne, T.

R. Huang, P. Su, T. Horne, G. Brusa, and J. Burge, “Optical metrology of a large deformable aspherical mirror using software configurable optical test system,” Opt. Eng. 53(8), 085106 (2014).
[Crossref]

Huang, C. Y.

Huang, R.

R. Huang, P. Su, T. Horne, G. Brusa, and J. Burge, “Optical metrology of a large deformable aspherical mirror using software configurable optical test system,” Opt. Eng. 53(8), 085106 (2014).
[Crossref]

Huang, Z.

Idir, M.

Jin, G.

Kaminski, J.

M. Knauer, J. Kaminski, and G. Hausler, “Phase measuring deflectometry: a new approach to measure specular free-form surfaces,” Proc. SPIE 5457, 366–376 (2004).
[Crossref]

Kaznatcheev, K.

King, C. M.

Knauer, M.

M. Knauer, J. Kaminski, and G. Hausler, “Phase measuring deflectometry: a new approach to measure specular free-form surfaces,” Proc. SPIE 5457, 366–376 (2004).
[Crossref]

Liang, R.

Liebner, C.

C. Andraka, S. Sadlon, B. Myer, K. Trapeznikov, and C. Liebner, “Rapid reflective facet characterization using fringe reflection techniques,” J. Sol. Ener. 136(1), 011002 (2013).
[Crossref]

Liu, Z.

Myer, B.

C. Andraka, S. Sadlon, B. Myer, K. Trapeznikov, and C. Liebner, “Rapid reflective facet characterization using fringe reflection techniques,” J. Sol. Ener. 136(1), 011002 (2013).
[Crossref]

Nishiyama, K.

K. Otaki, K. Ota, K. Nishiyama, T. Yamamoto, Y. Fukuda, and S. Okazaki, “Development of the point diffraction interferometer for extreme ultraviolet lithography: Design, fabrication, and evaluation,” J. Vac. Sci. Technol. B 20(6), 2449–2458 (2002).
[Crossref]

Okazaki, S.

K. Otaki, K. Ota, K. Nishiyama, T. Yamamoto, Y. Fukuda, and S. Okazaki, “Development of the point diffraction interferometer for extreme ultraviolet lithography: Design, fabrication, and evaluation,” J. Vac. Sci. Technol. B 20(6), 2449–2458 (2002).
[Crossref]

Ota, K.

K. Otaki, K. Ota, K. Nishiyama, T. Yamamoto, Y. Fukuda, and S. Okazaki, “Development of the point diffraction interferometer for extreme ultraviolet lithography: Design, fabrication, and evaluation,” J. Vac. Sci. Technol. B 20(6), 2449–2458 (2002).
[Crossref]

Otaki, K.

K. Otaki, K. Ota, K. Nishiyama, T. Yamamoto, Y. Fukuda, and S. Okazaki, “Development of the point diffraction interferometer for extreme ultraviolet lithography: Design, fabrication, and evaluation,” J. Vac. Sci. Technol. B 20(6), 2449–2458 (2002).
[Crossref]

Pan, C.

Pang, Y.

Parks, R. E.

Rayces, J. L.

J. L. Rayces, “Exact relation between wave aberration and ray aberration and ray aberration,” J. Mod. Opt. 11(2), 85–88 (1964).

Rimmer, M. P.

Roddier, N.

N. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. 29(10), 1174–1180 (1990).
[Crossref]

Rolland, J. P.

Sadlon, S.

C. Andraka, S. Sadlon, B. Myer, K. Trapeznikov, and C. Liebner, “Rapid reflective facet characterization using fringe reflection techniques,” J. Sol. Ener. 136(1), 011002 (2013).
[Crossref]

Smith, G. A.

G. P. Butel, G. A. Smith, and J. H. Burge, “Deflectometry using portable devices,” Opt. Eng. 54(2), 025111 (2015).
[Crossref]

Southwell, W. H.

Su, P.

Thompson, K. P.

Trapeznikov, K.

C. Andraka, S. Sadlon, B. Myer, K. Trapeznikov, and C. Liebner, “Rapid reflective facet characterization using fringe reflection techniques,” J. Sol. Ener. 136(1), 011002 (2013).
[Crossref]

Wang, D.

Wang, L.

Wang, Y.

Wu, R.

Wu, X.

Yamamoto, T.

K. Otaki, K. Ota, K. Nishiyama, T. Yamamoto, Y. Fukuda, and S. Okazaki, “Development of the point diffraction interferometer for extreme ultraviolet lithography: Design, fabrication, and evaluation,” J. Vac. Sci. Technol. B 20(6), 2449–2458 (2002).
[Crossref]

Yang, T.

Yang, Y.

D. Wang, Y. Yang, C. Chen, and Y. Zhuo, “Calibration of geometrical systematic error in high-precision spherical surface measurement,” Opt. Commun. 284(16–17), 3878–3885 (2011).
[Crossref]

D. Wang, Y. Yang, C. Chen, and Y. Zhuo, “Point diffraction interferometer with adjustable fringe contrast for testing spherical surfaces,” Appl. Opt. 50(16), 2342–2348 (2011).
[Crossref] [PubMed]

Zhang, S.

Zhu, J.

Zhuo, Y.

D. Wang, Y. Yang, C. Chen, and Y. Zhuo, “Calibration of geometrical systematic error in high-precision spherical surface measurement,” Opt. Commun. 284(16–17), 3878–3885 (2011).
[Crossref]

D. Wang, Y. Yang, C. Chen, and Y. Zhuo, “Point diffraction interferometer with adjustable fringe contrast for testing spherical surfaces,” Appl. Opt. 50(16), 2342–2348 (2011).
[Crossref] [PubMed]

Appl. Opt. (4)

Chin. Opt. Lett. (1)

J. Mod. Opt. (1)

J. L. Rayces, “Exact relation between wave aberration and ray aberration and ray aberration,” J. Mod. Opt. 11(2), 85–88 (1964).

J. Opt. Soc. Am. (1)

J. Sol. Ener. (1)

C. Andraka, S. Sadlon, B. Myer, K. Trapeznikov, and C. Liebner, “Rapid reflective facet characterization using fringe reflection techniques,” J. Sol. Ener. 136(1), 011002 (2013).
[Crossref]

J. Vac. Sci. Technol. B (1)

K. Otaki, K. Ota, K. Nishiyama, T. Yamamoto, Y. Fukuda, and S. Okazaki, “Development of the point diffraction interferometer for extreme ultraviolet lithography: Design, fabrication, and evaluation,” J. Vac. Sci. Technol. B 20(6), 2449–2458 (2002).
[Crossref]

Light Sci. Appl. (1)

T. Yang, G. Jin, and J. Zhu, “Automated design of freeform imaging systems,” Light Sci. Appl. 6(10), e17081 (2017).
[Crossref]

Opt. Commun. (1)

D. Wang, Y. Yang, C. Chen, and Y. Zhuo, “Calibration of geometrical systematic error in high-precision spherical surface measurement,” Opt. Commun. 284(16–17), 3878–3885 (2011).
[Crossref]

Opt. Eng. (3)

N. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Opt. Eng. 29(10), 1174–1180 (1990).
[Crossref]

G. P. Butel, G. A. Smith, and J. H. Burge, “Deflectometry using portable devices,” Opt. Eng. 54(2), 025111 (2015).
[Crossref]

R. Huang, P. Su, T. Horne, G. Brusa, and J. Burge, “Optical metrology of a large deformable aspherical mirror using software configurable optical test system,” Opt. Eng. 53(8), 085106 (2014).
[Crossref]

Opt. Express (5)

Proc. SPIE (1)

M. Knauer, J. Kaminski, and G. Hausler, “Phase measuring deflectometry: a new approach to measure specular free-form surfaces,” Proc. SPIE 5457, 366–376 (2004).
[Crossref]

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Figures (7)

Fig. 1
Fig. 1 System layout of the reverse Hartmann test for freeform surface testing. (a) Traditional Hartmann test, (b) reverse Hartmann test for freeform surface testing.
Fig. 2
Fig. 2 Zernike coefficient deviations introduced by geometrical error of test convex surface with the 15 mm semi-diameter and 200 mm curvature radius. (a) Lateral displacement error in x axis and (b) tilt error about x axis.
Fig. 3
Fig. 3 Procedure for reverse Hartmann test. (a) The whole test procedure, and (b) procedure for double-step calibration of systematic error.
Fig. 4
Fig. 4 Surface testing results in the simulation. (a) Actual surface error, (b) testing surface error and (c) residual error with existence of system geometrical error, (d) testing surface error and (e) residual error after first-step calibration, (f) testing surface error and (g) residual error after second-step calibration.
Fig. 5
Fig. 5 Linearity about Zernike coefficients of system geometrical error. Zernike coefficient deviations due to (a) lateral displacement error of test surface about x axis and (b) tilt error of test surface about x axis.
Fig. 6
Fig. 6 Change about Zernike coefficients (Z5-Z16) of residual geometric aberration in calibration process.
Fig. 7
Fig. 7 Testing surface error in the experiment. Surface errors measured with reverse Hartmann test system (a) based on CMM-measured parameter, (b) after first-step calibration and (c) after second-step calibration, and the corresponding changes (e) after first-step calibration and (f) after second-step; (d) measured surface error after double-steps calibration with additional geometrical error; (g) surface error measured with ZYGO interferometer.

Tables (3)

Tables Icon

Table 1 PV and RMS values of testing surface error in the simulation

Tables Icon

Table 2 Change about the geometrical error in the calibration process

Tables Icon

Table 3 PV and RMS values of testing surface error in the experiment

Equations (13)

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{ Δ w x = W( x,y ) x = x test x model 2 d s2s = Δ x spot 2 d s2s Δ w y = W( x,y ) y = y test y model 2 d s2s = Δ y spot 2 d s2s ,
W= i=1 N ( C i Z i ) ,
W meas (0) = W surf + W geo (0) (GE)= i=1 N [ C meas, i (0) Z i ] ,
W geo (0) (GE)= k=1 M W geo (0) ( ε k ) = i=1 N { [ k=1 M C geo, i (k) ] Z i } ,
C geo, i (k) = Γ i (k) ( ε k ) ρ i (k) ε k ,
O 1 ( G E (H) )=min[ ( W geo, 4 ) 2 +c ],
W meas (1) = i=1 N [ C meas, i (1) Z i ] i=1 N { { C meas, i (0) k=1 M [ ρ i (k) ( ε k ε ˜ k ) ] } Z i } ,
W geo (1) (G E 1 )= k=1 M W geo (1) ( ε ˜ k ) = i=1 N { { k=1 M [ ρ i (k) ε ˜ k ] } Z i } .
r k, i = C geo, i (k) C geo, i (τ) ρ i (k) ε ˜ k ρ i (τ) ε ˜ τ ,
W geo ( H ) = i=1 N { [ k=1 s ( r k, i ρ i (τ) e τ ) ] Z i } ,
O 2 ( G E (L) )=min[ ( W geo (L) ) 2 +c ]=min[ ( W meas (2) W meas (1) W geo ( H ) ) 2 +c ],
O 2 ( G E (L) )=min { { i=1 N [ C meas, i (2) C meas, i (1) k=1 s ( r k, i ρ i (τ) ε ˜ τ ) ] } 2 +c } ε ˜ τ 0 ,
W surf W meas (0) W geo (0) ( G E (H) ,G E (L) ).

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