Abstract

The grating lateral shearing interferometer may achieve ultra-high accuracy absolute testing after eliminating the systemic errors from the interferometer itself and the orthogonality problem between two shearing directions. Aiming at the interferometer, we proposed a two-step algorithm for removing the rotationally asymmetric systemic errors from our shearing setup. This rotation method provides a new approach for acquiring the wavefront aberration by choosing the rotation angles with the minimum decentration and to satisfy the immune of systemic errors at the same time. Simulation and experiment verified that it is more propitious to eliminate the systemic errors when it is applied to our shearing setup.

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

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References

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2017 (1)

2016 (1)

2015 (1)

2014 (1)

2013 (1)

2012 (2)

2010 (2)

2006 (2)

2005 (1)

S. Kato, C. Ouchi, M. Hasegawa, A. Suzuki, T. Hasegawa, K. Sugisaki, M. Okada, Z. Yucong, K. Murakami, J. Saito, M. Niibe, and M. Takeda, “Comparison of EUV interferometry methods in EUVA project,” Proc. SPIE 5751, 110–117 (2005).
[Crossref]

1997 (1)

1996 (1)

1992 (1)

1984 (1)

B. S. Fritz, “Absolute calibration of an optical flat,” Opt. Eng. 23(4), 379–383 (1984).
[Crossref]

1978 (1)

R. E. Parks, “Removal of test optics errors,” Proc. SPIE 153, 56–63 (1978).
[Crossref]

1973 (2)

A. E. Jensen, “Absolute calibration method for Twyman–Green wavefront testing interferometers,” J. Opt. Soc. Am. 63, 1313A (1973).

J. C. Wyant, “Double frequency Grating Lateral Shear Interferometer,” Appl. Opt. 12(9), 2057–2060 (1973).
[Crossref] [PubMed]

Acosta, E.

Artal, P.

Bloemhof, E. E.

Bueno, J. M.

Chen, L.

Creath, K.

Dou, J.

Du, J.

Evans, C. J.

Fan, Z.

Fritz, B. S.

B. S. Fritz, “Absolute calibration of an optical flat,” Opt. Eng. 23(4), 379–383 (1984).
[Crossref]

Gao, Z.

Ghim, Y. S.

Han, Z. G.

Hasegawa, M.

C. Ouchi, S. Katoa, and M. Hasegawa, “EUV wavefront metrology at EUVA,” Proc. SPIE 6152, 61522 (2006).

S. Kato, C. Ouchi, M. Hasegawa, A. Suzuki, T. Hasegawa, K. Sugisaki, M. Okada, Z. Yucong, K. Murakami, J. Saito, M. Niibe, and M. Takeda, “Comparison of EUV interferometry methods in EUVA project,” Proc. SPIE 5751, 110–117 (2005).
[Crossref]

Hasegawa, T.

S. Kato, C. Ouchi, M. Hasegawa, A. Suzuki, T. Hasegawa, K. Sugisaki, M. Okada, Z. Yucong, K. Murakami, J. Saito, M. Niibe, and M. Takeda, “Comparison of EUV interferometry methods in EUVA project,” Proc. SPIE 5751, 110–117 (2005).
[Crossref]

Hou, X.

Jensen, A. E.

A. E. Jensen, “Absolute calibration method for Twyman–Green wavefront testing interferometers,” J. Opt. Soc. Am. 63, 1313A (1973).

Kato, S.

S. Kato, C. Ouchi, M. Hasegawa, A. Suzuki, T. Hasegawa, K. Sugisaki, M. Okada, Z. Yucong, K. Murakami, J. Saito, M. Niibe, and M. Takeda, “Comparison of EUV interferometry methods in EUVA project,” Proc. SPIE 5751, 110–117 (2005).
[Crossref]

Katoa, S.

C. Ouchi, S. Katoa, and M. Hasegawa, “EUV wavefront metrology at EUVA,” Proc. SPIE 6152, 61522 (2006).

Kestner, R. N.

Kim, S. W.

Lee, J.

Lee, Y. W.

Lee, Y.-W.

Li, L.

Miao, E.

Murakami, K.

S. Kato, C. Ouchi, M. Hasegawa, A. Suzuki, T. Hasegawa, K. Sugisaki, M. Okada, Z. Yucong, K. Murakami, J. Saito, M. Niibe, and M. Takeda, “Comparison of EUV interferometry methods in EUVA project,” Proc. SPIE 5751, 110–117 (2005).
[Crossref]

Niibe, M.

S. Kato, C. Ouchi, M. Hasegawa, A. Suzuki, T. Hasegawa, K. Sugisaki, M. Okada, Z. Yucong, K. Murakami, J. Saito, M. Niibe, and M. Takeda, “Comparison of EUV interferometry methods in EUVA project,” Proc. SPIE 5751, 110–117 (2005).
[Crossref]

Okada, M.

S. Kato, C. Ouchi, M. Hasegawa, A. Suzuki, T. Hasegawa, K. Sugisaki, M. Okada, Z. Yucong, K. Murakami, J. Saito, M. Niibe, and M. Takeda, “Comparison of EUV interferometry methods in EUVA project,” Proc. SPIE 5751, 110–117 (2005).
[Crossref]

Ouchi, C.

C. Ouchi, S. Katoa, and M. Hasegawa, “EUV wavefront metrology at EUVA,” Proc. SPIE 6152, 61522 (2006).

S. Kato, C. Ouchi, M. Hasegawa, A. Suzuki, T. Hasegawa, K. Sugisaki, M. Okada, Z. Yucong, K. Murakami, J. Saito, M. Niibe, and M. Takeda, “Comparison of EUV interferometry methods in EUVA project,” Proc. SPIE 5751, 110–117 (2005).
[Crossref]

Parks, R. E.

R. E. Parks, “Removal of test optics errors,” Proc. SPIE 153, 56–63 (1978).
[Crossref]

Rhee, H. G.

Rhee, H.-G.

Saito, J.

S. Kato, C. Ouchi, M. Hasegawa, A. Suzuki, T. Hasegawa, K. Sugisaki, M. Okada, Z. Yucong, K. Murakami, J. Saito, M. Niibe, and M. Takeda, “Comparison of EUV interferometry methods in EUVA project,” Proc. SPIE 5751, 110–117 (2005).
[Crossref]

Schreiber, H.

Schwarz, C.

Schwider, J.

Song, W.

Su, D.

Sugisaki, K.

S. Kato, C. Ouchi, M. Hasegawa, A. Suzuki, T. Hasegawa, K. Sugisaki, M. Okada, Z. Yucong, K. Murakami, J. Saito, M. Niibe, and M. Takeda, “Comparison of EUV interferometry methods in EUVA project,” Proc. SPIE 5751, 110–117 (2005).
[Crossref]

Sui, Y.

Suzuki, A.

S. Kato, C. Ouchi, M. Hasegawa, A. Suzuki, T. Hasegawa, K. Sugisaki, M. Okada, Z. Yucong, K. Murakami, J. Saito, M. Niibe, and M. Takeda, “Comparison of EUV interferometry methods in EUVA project,” Proc. SPIE 5751, 110–117 (2005).
[Crossref]

Takeda, M.

S. Kato, C. Ouchi, M. Hasegawa, A. Suzuki, T. Hasegawa, K. Sugisaki, M. Okada, Z. Yucong, K. Murakami, J. Saito, M. Niibe, and M. Takeda, “Comparison of EUV interferometry methods in EUVA project,” Proc. SPIE 5751, 110–117 (2005).
[Crossref]

Tan, J.

Tian, C.

Wang, W.

Wu, F.

Wyant, J. C.

Yan, S.

Yang, H.

Yang, H. S.

Yang, Z.

Yin, L.

Yuan, Q.

Yucong, Z.

S. Kato, C. Ouchi, M. Hasegawa, A. Suzuki, T. Hasegawa, K. Sugisaki, M. Okada, Z. Yucong, K. Murakami, J. Saito, M. Niibe, and M. Takeda, “Comparison of EUV interferometry methods in EUVA project,” Proc. SPIE 5751, 110–117 (2005).
[Crossref]

Zhang, M.

Zhang, Y.

Zhu, R. H.

Appl. Opt. (8)

J. Opt. Soc. Am. (1)

A. E. Jensen, “Absolute calibration method for Twyman–Green wavefront testing interferometers,” J. Opt. Soc. Am. 63, 1313A (1973).

J. Opt. Soc. Korea (1)

Opt. Eng. (1)

B. S. Fritz, “Absolute calibration of an optical flat,” Opt. Eng. 23(4), 379–383 (1984).
[Crossref]

Opt. Express (3)

Opt. Lett. (2)

Proc. SPIE (3)

R. E. Parks, “Removal of test optics errors,” Proc. SPIE 153, 56–63 (1978).
[Crossref]

S. Kato, C. Ouchi, M. Hasegawa, A. Suzuki, T. Hasegawa, K. Sugisaki, M. Okada, Z. Yucong, K. Murakami, J. Saito, M. Niibe, and M. Takeda, “Comparison of EUV interferometry methods in EUVA project,” Proc. SPIE 5751, 110–117 (2005).
[Crossref]

C. Ouchi, S. Katoa, and M. Hasegawa, “EUV wavefront metrology at EUVA,” Proc. SPIE 6152, 61522 (2006).

Other (1)

D. Malacara, “Phase shifting interferometry,” in Optical Shop Testing, 2nd ed. (Wiley, 1992), Chap.14.

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Figures (10)

Fig. 1
Fig. 1 The sketch of grating lateral shearing interferometer.
Fig. 2
Fig. 2 The interferograms in X orientation: (a) at the 0° position; (b) at the 180° position.
Fig. 3
Fig. 3 Immunization capabilities of variable systemic errors about two algorithms: (a) The real wavefront aberrations generated for simulation with random Zernike coefficients for m = 1-5 (PV: 6.2757λ; RMS: 0.9758λ); (b) The wavefront aberrations contains the systemic errors (PV: 16.182λ; RMS: 2.6038λ); (c) The wavefront aberrations acquired by error-immune algorithm with the angles being 0°, 90°, 135°, and 180° (PV: 4.0146λ; RMS: 0.73895λ); (d) The wavefront aberrations acquired by new algorithm with the angles being 0°, 90°, and 315° (PV: 3.784λ; RMS: 0.73364λ).
Fig. 4
Fig. 4 Comparison of two algorithms: The residuals between the original wavefront aberrations and (a) the wavefront aberrations acquired by error-immune algorithm (PV: 3.9117λ; RMS: 0.68021λ); (b) the wavefront aberrations acquired by new algorithm (PV: 3.3947λ; RMS: 0.64313λ).
Fig. 5
Fig. 5 The PV and RMS values of the wavefront aberrations at eight angular positions before systemic errors eliminated and after systemic errors eliminated by average-rotation algorithm.
Fig. 6
Fig. 6 The wavefront aberrations acquired by different single-rotation algorithms: (a) 45° (b) 135° (c) 225° (d) 315°.
Fig. 7
Fig. 7 The decentration and the RMS value of residuals of two wavefronts errors acquired by different single-rotation algorithms.
Fig. 8
Fig. 8 The result acquired by error-immune algorithm: (a) The wavefront aberrations of the lens on 0° position. The residuals between 0° position and: (b) 90° position (PV: 0.029128λ; RMS: 0.0031796λ); (c) 135° position (PV: 0.042076λ; RMS: 0.0077323λ); (d) 180° position (PV: 0.056729λ; RMS: 0.01229λ).
Fig. 9
Fig. 9 The result acquired by new algorithm: (a) The systemic errors of the lens on original position. The residuals between 0° position and: (b) 315° position (PV: 0.016595λ; RMS: 0.0023007λ); (c) 90° position (PV: 0.046724λ; RMS: 0.0065709λ); (d) the difference of wavefront aberrations at 0° position between new algorithm and error-immune algorithm (PV: 0.024148λ; RMS: 0.0025226λ).
Fig. 10
Fig. 10 Comparison of the first 36 terms in the Zernike polynomial between error-immune algorithm and new algorithm.

Tables (1)

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Table 1 The PV and RMS residuals of wavefront aberrations at two angular positions in different single-rotation algorithms.

Equations (11)

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W(ρ,θ)= W s (ρ,θ)+T(ρ,θ)+V(ρ,θ)
W(ρ,θ+φ)= W s (ρ,θ)+T(ρ,θ+φ)+V'(ρ,θ)
ΔW(ρ,θ)=T(ρ,θ+φ)T(ρ,θ)+ΔV(ρ,θ)
ΔW(ρ,θ)= m,n R n m (ρ){ a n m cos[m(θ+φ)] a n m cos(mθ) + a n m sin[m(θ+φ)] a n m sin(mθ)}+ΔV(ρ,θ) = m,n R n m (ρ) [ α n m,φ cos(mθ)+ α n m,φ sin(mθ)]+ΔV(ρ,θ)
W(x,y)= W 1 (x+s/2,y) W +1 (xs/2,y)
W'(x,y)= W 1 '(x+s/2+Δx,y+Δy) W +1 '(xs/2+Δx,y+Δy)
j=0 N1 W j (ρ,θ)= j=0 N1 T j (ρ,θ) +8 W s (ρ,θ)+ j=0 N1 V j (ρ,θ)
j=0 N1 W j (ρ,θ)= j=0 N1 T j (ρ,θ) +8 W s (ρ,θ) = j=0 N1 T j 1,3,5 (ρ,θ) + j=0 N1 T j 2 (ρ,θ)+ j=0 N1 T j 4 (ρ,θ)+8 W s (ρ,θ) =0+0+0+8 W s (ρ,θ)
x j (ρ,θ)= T j (ρ,θ)+ V j (ρ,θ)= W j (ρ,θ) 1 8 j=0 N1 W j (ρ,θ)
ϕ 0 = argmax ϕ ρ θ [x(ρ,θ+ϕ)x(ρ,θ+ϕ+180°)] 2 ρ θ [x(ρ,θ+ϕ)x(ρ,θ+ϕ+45°)] 2 + ρ θ [x(ρ,θ+ϕ)x(ρ,θ+ϕ45°)] 2
Δ W odd (ρ,θ)= W odd '(ρ,θ) W odd (ρ,θ) = m,n R n m (ρ) [ α n m,±π/2 odd cos(mθ)+ α n m,±π/2 odd sin(mθ)]+ΔV(ρ,θ)

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