Abstract

We propose a novel highly sensitive wave front detection method for a quick check of a flat wave front by taking advantage of a non-zero-order π phase plate that yields a non-zero-order diffraction pattern. When a light beam with a flat wave front illuminates a phase plate, the zero-order intensity is zero. When there is a slight distortion of the wave front, the zero-order intensity increases. The ratio of first-order intensity to that of zero-order intensity is used as the criterion with which to judge whether the wave front under test is flat, eliminating the influence of background light. Experimental results demonstrate that this method is efficient, robust, and cost-effective and should be highly interesting for a quick check of a flat wave front of a large-aperture laser beam and adaptive optical systems.

© 2005 Optical Society of America

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References

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  1. J. M. Geary, Introduction to Wavefront Sensors, Vol. TT18 of Tutorial Texts (SPIE Press, 1995).
    [CrossRef]
  2. B. C. Platt, R. Shack, “History and principles of Shack–Hartmann wavefront sensing,” J. Refract. Surg. 17, S573–S577 (2001).
    [PubMed]
  3. G. W. R. Leibbrandt, G. Harbers, P. J. Kunst, “Wave-front analysis with high accuracy by use of a double-grating lateral shearing interferometer,” Appl. Opt. 35, 6151–6161 (1996).
    [CrossRef] [PubMed]
  4. Y. Zhu, K. Sugisaki, K. Murakami, K. Ota, H. Kondo, M. Ishii, J. Kawakami, T. Oshino, J. Saito, A. Suzuki, M. Hasegawa, Y. Sekine, S. Takeuchi, C. Ouchi, O. Kakuchi, Y. Watanabe, T. Hasegawa, S. Hara, “Shearing interferometry for at wavelength wavefront measurement of extreme-ultraviolet lithography projection optics,” Jpn. J. Appl. Phys. 42, 5844–5847 (2003).
    [CrossRef]
  5. Y. Bitou, “Digital phase-shifting interferometer with an electrically addressed liquid-crystal spatial light modulator,” Opt. Lett. 28, 1576–1578 (2003).
    [CrossRef] [PubMed]
  6. Y. Yasuno, T. F. Wiesendanger, A. K. Ruprecht, S. Makita, T. Yatagai, H. J. Tiziani, “Wavefront-flatness evaluation by wavefront-correlation-information-entropy method and its application for adaptive confocal microscope,” Opt. Commun. 232, 91–97 (2004).
    [CrossRef]
  7. C. Zhou, L. Liu, “Numerical study of Dammann array illuminators,” Appl. Opt. 34, 5961–5969 (1995).
    [CrossRef] [PubMed]
  8. B. J. Thompson, “Diffraction by semitransparent and phase annuli,” J. Opt. Soc. Am. 55, 145–149 (1965).
    [CrossRef]
  9. C. Zhou, J. Jia, L. Liu, “Circular Dammann grating,” Opt. Lett. 28, 2174–2176 (2003).
    [CrossRef] [PubMed]
  10. J. Jia, C. Zhou, X. Sun, L. Liu, “Superresolution laser beam shaping,” Appl. Opt. 43, 2112–2117 (2004).
    [CrossRef] [PubMed]
  11. H. Luo, C. Zhou, “Comparison of superresolution effects with annular phase and amplitude filters,” Appl. Opt. 43, 6242–6247 (2004).
    [CrossRef] [PubMed]
  12. T. R. M. Sales, G. M. Morris, “Diffractive superresolution elements,” J. Opt. Soc. Am. A 14, 1637–1646 (1997).
    [CrossRef]

2004 (3)

Y. Yasuno, T. F. Wiesendanger, A. K. Ruprecht, S. Makita, T. Yatagai, H. J. Tiziani, “Wavefront-flatness evaluation by wavefront-correlation-information-entropy method and its application for adaptive confocal microscope,” Opt. Commun. 232, 91–97 (2004).
[CrossRef]

J. Jia, C. Zhou, X. Sun, L. Liu, “Superresolution laser beam shaping,” Appl. Opt. 43, 2112–2117 (2004).
[CrossRef] [PubMed]

H. Luo, C. Zhou, “Comparison of superresolution effects with annular phase and amplitude filters,” Appl. Opt. 43, 6242–6247 (2004).
[CrossRef] [PubMed]

2003 (3)

Y. Zhu, K. Sugisaki, K. Murakami, K. Ota, H. Kondo, M. Ishii, J. Kawakami, T. Oshino, J. Saito, A. Suzuki, M. Hasegawa, Y. Sekine, S. Takeuchi, C. Ouchi, O. Kakuchi, Y. Watanabe, T. Hasegawa, S. Hara, “Shearing interferometry for at wavelength wavefront measurement of extreme-ultraviolet lithography projection optics,” Jpn. J. Appl. Phys. 42, 5844–5847 (2003).
[CrossRef]

Y. Bitou, “Digital phase-shifting interferometer with an electrically addressed liquid-crystal spatial light modulator,” Opt. Lett. 28, 1576–1578 (2003).
[CrossRef] [PubMed]

C. Zhou, J. Jia, L. Liu, “Circular Dammann grating,” Opt. Lett. 28, 2174–2176 (2003).
[CrossRef] [PubMed]

2001 (1)

B. C. Platt, R. Shack, “History and principles of Shack–Hartmann wavefront sensing,” J. Refract. Surg. 17, S573–S577 (2001).
[PubMed]

1997 (1)

1996 (1)

1995 (1)

1965 (1)

Bitou, Y.

Geary, J. M.

J. M. Geary, Introduction to Wavefront Sensors, Vol. TT18 of Tutorial Texts (SPIE Press, 1995).
[CrossRef]

Hara, S.

Y. Zhu, K. Sugisaki, K. Murakami, K. Ota, H. Kondo, M. Ishii, J. Kawakami, T. Oshino, J. Saito, A. Suzuki, M. Hasegawa, Y. Sekine, S. Takeuchi, C. Ouchi, O. Kakuchi, Y. Watanabe, T. Hasegawa, S. Hara, “Shearing interferometry for at wavelength wavefront measurement of extreme-ultraviolet lithography projection optics,” Jpn. J. Appl. Phys. 42, 5844–5847 (2003).
[CrossRef]

Harbers, G.

Hasegawa, M.

Y. Zhu, K. Sugisaki, K. Murakami, K. Ota, H. Kondo, M. Ishii, J. Kawakami, T. Oshino, J. Saito, A. Suzuki, M. Hasegawa, Y. Sekine, S. Takeuchi, C. Ouchi, O. Kakuchi, Y. Watanabe, T. Hasegawa, S. Hara, “Shearing interferometry for at wavelength wavefront measurement of extreme-ultraviolet lithography projection optics,” Jpn. J. Appl. Phys. 42, 5844–5847 (2003).
[CrossRef]

Hasegawa, T.

Y. Zhu, K. Sugisaki, K. Murakami, K. Ota, H. Kondo, M. Ishii, J. Kawakami, T. Oshino, J. Saito, A. Suzuki, M. Hasegawa, Y. Sekine, S. Takeuchi, C. Ouchi, O. Kakuchi, Y. Watanabe, T. Hasegawa, S. Hara, “Shearing interferometry for at wavelength wavefront measurement of extreme-ultraviolet lithography projection optics,” Jpn. J. Appl. Phys. 42, 5844–5847 (2003).
[CrossRef]

Ishii, M.

Y. Zhu, K. Sugisaki, K. Murakami, K. Ota, H. Kondo, M. Ishii, J. Kawakami, T. Oshino, J. Saito, A. Suzuki, M. Hasegawa, Y. Sekine, S. Takeuchi, C. Ouchi, O. Kakuchi, Y. Watanabe, T. Hasegawa, S. Hara, “Shearing interferometry for at wavelength wavefront measurement of extreme-ultraviolet lithography projection optics,” Jpn. J. Appl. Phys. 42, 5844–5847 (2003).
[CrossRef]

Jia, J.

Kakuchi, O.

Y. Zhu, K. Sugisaki, K. Murakami, K. Ota, H. Kondo, M. Ishii, J. Kawakami, T. Oshino, J. Saito, A. Suzuki, M. Hasegawa, Y. Sekine, S. Takeuchi, C. Ouchi, O. Kakuchi, Y. Watanabe, T. Hasegawa, S. Hara, “Shearing interferometry for at wavelength wavefront measurement of extreme-ultraviolet lithography projection optics,” Jpn. J. Appl. Phys. 42, 5844–5847 (2003).
[CrossRef]

Kawakami, J.

Y. Zhu, K. Sugisaki, K. Murakami, K. Ota, H. Kondo, M. Ishii, J. Kawakami, T. Oshino, J. Saito, A. Suzuki, M. Hasegawa, Y. Sekine, S. Takeuchi, C. Ouchi, O. Kakuchi, Y. Watanabe, T. Hasegawa, S. Hara, “Shearing interferometry for at wavelength wavefront measurement of extreme-ultraviolet lithography projection optics,” Jpn. J. Appl. Phys. 42, 5844–5847 (2003).
[CrossRef]

Kondo, H.

Y. Zhu, K. Sugisaki, K. Murakami, K. Ota, H. Kondo, M. Ishii, J. Kawakami, T. Oshino, J. Saito, A. Suzuki, M. Hasegawa, Y. Sekine, S. Takeuchi, C. Ouchi, O. Kakuchi, Y. Watanabe, T. Hasegawa, S. Hara, “Shearing interferometry for at wavelength wavefront measurement of extreme-ultraviolet lithography projection optics,” Jpn. J. Appl. Phys. 42, 5844–5847 (2003).
[CrossRef]

Kunst, P. J.

Leibbrandt, G. W. R.

Liu, L.

Luo, H.

Makita, S.

Y. Yasuno, T. F. Wiesendanger, A. K. Ruprecht, S. Makita, T. Yatagai, H. J. Tiziani, “Wavefront-flatness evaluation by wavefront-correlation-information-entropy method and its application for adaptive confocal microscope,” Opt. Commun. 232, 91–97 (2004).
[CrossRef]

Morris, G. M.

Murakami, K.

Y. Zhu, K. Sugisaki, K. Murakami, K. Ota, H. Kondo, M. Ishii, J. Kawakami, T. Oshino, J. Saito, A. Suzuki, M. Hasegawa, Y. Sekine, S. Takeuchi, C. Ouchi, O. Kakuchi, Y. Watanabe, T. Hasegawa, S. Hara, “Shearing interferometry for at wavelength wavefront measurement of extreme-ultraviolet lithography projection optics,” Jpn. J. Appl. Phys. 42, 5844–5847 (2003).
[CrossRef]

Oshino, T.

Y. Zhu, K. Sugisaki, K. Murakami, K. Ota, H. Kondo, M. Ishii, J. Kawakami, T. Oshino, J. Saito, A. Suzuki, M. Hasegawa, Y. Sekine, S. Takeuchi, C. Ouchi, O. Kakuchi, Y. Watanabe, T. Hasegawa, S. Hara, “Shearing interferometry for at wavelength wavefront measurement of extreme-ultraviolet lithography projection optics,” Jpn. J. Appl. Phys. 42, 5844–5847 (2003).
[CrossRef]

Ota, K.

Y. Zhu, K. Sugisaki, K. Murakami, K. Ota, H. Kondo, M. Ishii, J. Kawakami, T. Oshino, J. Saito, A. Suzuki, M. Hasegawa, Y. Sekine, S. Takeuchi, C. Ouchi, O. Kakuchi, Y. Watanabe, T. Hasegawa, S. Hara, “Shearing interferometry for at wavelength wavefront measurement of extreme-ultraviolet lithography projection optics,” Jpn. J. Appl. Phys. 42, 5844–5847 (2003).
[CrossRef]

Ouchi, C.

Y. Zhu, K. Sugisaki, K. Murakami, K. Ota, H. Kondo, M. Ishii, J. Kawakami, T. Oshino, J. Saito, A. Suzuki, M. Hasegawa, Y. Sekine, S. Takeuchi, C. Ouchi, O. Kakuchi, Y. Watanabe, T. Hasegawa, S. Hara, “Shearing interferometry for at wavelength wavefront measurement of extreme-ultraviolet lithography projection optics,” Jpn. J. Appl. Phys. 42, 5844–5847 (2003).
[CrossRef]

Platt, B. C.

B. C. Platt, R. Shack, “History and principles of Shack–Hartmann wavefront sensing,” J. Refract. Surg. 17, S573–S577 (2001).
[PubMed]

Ruprecht, A. K.

Y. Yasuno, T. F. Wiesendanger, A. K. Ruprecht, S. Makita, T. Yatagai, H. J. Tiziani, “Wavefront-flatness evaluation by wavefront-correlation-information-entropy method and its application for adaptive confocal microscope,” Opt. Commun. 232, 91–97 (2004).
[CrossRef]

Saito, J.

Y. Zhu, K. Sugisaki, K. Murakami, K. Ota, H. Kondo, M. Ishii, J. Kawakami, T. Oshino, J. Saito, A. Suzuki, M. Hasegawa, Y. Sekine, S. Takeuchi, C. Ouchi, O. Kakuchi, Y. Watanabe, T. Hasegawa, S. Hara, “Shearing interferometry for at wavelength wavefront measurement of extreme-ultraviolet lithography projection optics,” Jpn. J. Appl. Phys. 42, 5844–5847 (2003).
[CrossRef]

Sales, T. R. M.

Sekine, Y.

Y. Zhu, K. Sugisaki, K. Murakami, K. Ota, H. Kondo, M. Ishii, J. Kawakami, T. Oshino, J. Saito, A. Suzuki, M. Hasegawa, Y. Sekine, S. Takeuchi, C. Ouchi, O. Kakuchi, Y. Watanabe, T. Hasegawa, S. Hara, “Shearing interferometry for at wavelength wavefront measurement of extreme-ultraviolet lithography projection optics,” Jpn. J. Appl. Phys. 42, 5844–5847 (2003).
[CrossRef]

Shack, R.

B. C. Platt, R. Shack, “History and principles of Shack–Hartmann wavefront sensing,” J. Refract. Surg. 17, S573–S577 (2001).
[PubMed]

Sugisaki, K.

Y. Zhu, K. Sugisaki, K. Murakami, K. Ota, H. Kondo, M. Ishii, J. Kawakami, T. Oshino, J. Saito, A. Suzuki, M. Hasegawa, Y. Sekine, S. Takeuchi, C. Ouchi, O. Kakuchi, Y. Watanabe, T. Hasegawa, S. Hara, “Shearing interferometry for at wavelength wavefront measurement of extreme-ultraviolet lithography projection optics,” Jpn. J. Appl. Phys. 42, 5844–5847 (2003).
[CrossRef]

Sun, X.

Suzuki, A.

Y. Zhu, K. Sugisaki, K. Murakami, K. Ota, H. Kondo, M. Ishii, J. Kawakami, T. Oshino, J. Saito, A. Suzuki, M. Hasegawa, Y. Sekine, S. Takeuchi, C. Ouchi, O. Kakuchi, Y. Watanabe, T. Hasegawa, S. Hara, “Shearing interferometry for at wavelength wavefront measurement of extreme-ultraviolet lithography projection optics,” Jpn. J. Appl. Phys. 42, 5844–5847 (2003).
[CrossRef]

Takeuchi, S.

Y. Zhu, K. Sugisaki, K. Murakami, K. Ota, H. Kondo, M. Ishii, J. Kawakami, T. Oshino, J. Saito, A. Suzuki, M. Hasegawa, Y. Sekine, S. Takeuchi, C. Ouchi, O. Kakuchi, Y. Watanabe, T. Hasegawa, S. Hara, “Shearing interferometry for at wavelength wavefront measurement of extreme-ultraviolet lithography projection optics,” Jpn. J. Appl. Phys. 42, 5844–5847 (2003).
[CrossRef]

Thompson, B. J.

Tiziani, H. J.

Y. Yasuno, T. F. Wiesendanger, A. K. Ruprecht, S. Makita, T. Yatagai, H. J. Tiziani, “Wavefront-flatness evaluation by wavefront-correlation-information-entropy method and its application for adaptive confocal microscope,” Opt. Commun. 232, 91–97 (2004).
[CrossRef]

Watanabe, Y.

Y. Zhu, K. Sugisaki, K. Murakami, K. Ota, H. Kondo, M. Ishii, J. Kawakami, T. Oshino, J. Saito, A. Suzuki, M. Hasegawa, Y. Sekine, S. Takeuchi, C. Ouchi, O. Kakuchi, Y. Watanabe, T. Hasegawa, S. Hara, “Shearing interferometry for at wavelength wavefront measurement of extreme-ultraviolet lithography projection optics,” Jpn. J. Appl. Phys. 42, 5844–5847 (2003).
[CrossRef]

Wiesendanger, T. F.

Y. Yasuno, T. F. Wiesendanger, A. K. Ruprecht, S. Makita, T. Yatagai, H. J. Tiziani, “Wavefront-flatness evaluation by wavefront-correlation-information-entropy method and its application for adaptive confocal microscope,” Opt. Commun. 232, 91–97 (2004).
[CrossRef]

Yasuno, Y.

Y. Yasuno, T. F. Wiesendanger, A. K. Ruprecht, S. Makita, T. Yatagai, H. J. Tiziani, “Wavefront-flatness evaluation by wavefront-correlation-information-entropy method and its application for adaptive confocal microscope,” Opt. Commun. 232, 91–97 (2004).
[CrossRef]

Yatagai, T.

Y. Yasuno, T. F. Wiesendanger, A. K. Ruprecht, S. Makita, T. Yatagai, H. J. Tiziani, “Wavefront-flatness evaluation by wavefront-correlation-information-entropy method and its application for adaptive confocal microscope,” Opt. Commun. 232, 91–97 (2004).
[CrossRef]

Zhou, C.

Zhu, Y.

Y. Zhu, K. Sugisaki, K. Murakami, K. Ota, H. Kondo, M. Ishii, J. Kawakami, T. Oshino, J. Saito, A. Suzuki, M. Hasegawa, Y. Sekine, S. Takeuchi, C. Ouchi, O. Kakuchi, Y. Watanabe, T. Hasegawa, S. Hara, “Shearing interferometry for at wavelength wavefront measurement of extreme-ultraviolet lithography projection optics,” Jpn. J. Appl. Phys. 42, 5844–5847 (2003).
[CrossRef]

Appl. Opt. (4)

J. Opt. Soc. Am. (1)

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

J. Refract. Surg. (1)

B. C. Platt, R. Shack, “History and principles of Shack–Hartmann wavefront sensing,” J. Refract. Surg. 17, S573–S577 (2001).
[PubMed]

Jpn. J. Appl. Phys. (1)

Y. Zhu, K. Sugisaki, K. Murakami, K. Ota, H. Kondo, M. Ishii, J. Kawakami, T. Oshino, J. Saito, A. Suzuki, M. Hasegawa, Y. Sekine, S. Takeuchi, C. Ouchi, O. Kakuchi, Y. Watanabe, T. Hasegawa, S. Hara, “Shearing interferometry for at wavelength wavefront measurement of extreme-ultraviolet lithography projection optics,” Jpn. J. Appl. Phys. 42, 5844–5847 (2003).
[CrossRef]

Opt. Commun. (1)

Y. Yasuno, T. F. Wiesendanger, A. K. Ruprecht, S. Makita, T. Yatagai, H. J. Tiziani, “Wavefront-flatness evaluation by wavefront-correlation-information-entropy method and its application for adaptive confocal microscope,” Opt. Commun. 232, 91–97 (2004).
[CrossRef]

Opt. Lett. (2)

Other (1)

J. M. Geary, Introduction to Wavefront Sensors, Vol. TT18 of Tutorial Texts (SPIE Press, 1995).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Experimental setup for measurement of a wave front with a non-zero-order phase plate.

Fig. 2
Fig. 2

Representation of a non-zero-order phase plate with ϕ = π and α1 = (1/2)1/2.

Fig. 3
Fig. 3

Surface-relief profile of an etched nonzero phase plate measured with a Taylor–Hobson profilometer.

Fig. 4
Fig. 4

Experimental images captured at the focal plane of the lens in Fig. 1 with two phase plates with the etched surface depths of 0.608 μm (a) and 0.592 μm (b). The depth differences of the two phase plates are corresponding to the π-phase departure of 0.2% and 2.5%, respectively.

Fig. 5
Fig. 5

(a) Theoretical and (b) experimental normalized intensity distribution in the focal plane of the lens in Fig. 1 obtained with three phase plates of etched depths of 0.608 μm (curve 1), 0.612 μm (curve 2), and 0.592 μm (curve 3).

Fig. 6
Fig. 6

Measured values of I1/I0 obtained by use of seven phase plates with the different etched depths listed in Table 1.

Tables (1)

Tables Icon

Table 1 Experimental Results for the Values of I1/I0 and Seven Phase Plates with Different Etched Depths

Equations (7)

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ψ ( η ) = 2 J 1 ( η ) η - [ 1 - exp ( i ϕ 0 ) ] ( - 1 ) N + 1 j = 1 N - 1 × ( - 1 ) j α j 2 2 J 1 ( α j η ) α j η ,
ψ ( η = 0 ) = 2 J 1 ( η ) η - [ 1 - exp ( i ϕ 0 ) ] α 1 2 2 J 1 ( α 1 η ) α 1 η = 1 - α 1 2 + α 1 2 cos ϕ 0 + i α 1 2 sin ϕ 0 ,
I ( 0 ) = ψ ( 0 ) ψ ( 0 ) * = 1 - 2 α 1 2 + 2 α 1 4 + 2 ( α 1 2 - α 1 4 ) cos ϕ 0 = cos 2 ϕ 0 2 ,
I 0 ( δ ϕ ) = cos 2 π + δ ϕ 2 = sin 2 δ ϕ 2 .
I ( η 1 ) = 4 η 1 2 { [ J 1 ( η 1 ) ] 2 - 2 ( 1 - cos ϕ 0 ) × [ J 1 ( η 1 ) - α 1 J 1 ( α 1 η 1 ) ] α 1 J 1 ( α 1 η 1 ) } .
I 1 ( δ ϕ ) I 0 ( δ ϕ ) = 4 η 1 2 { [ J 1 ( η 1 ) ] 2 - 4 cos 2 δ ϕ 2 [ J 1 ( η 1 ) - α 1 J 1 ( α 1 η 1 ) ] α 1 J 1 ( α 1 η 1 ) } sin 2 δ ϕ 2 I 1 sin 2 δ ϕ 2 .
Δ ϕ = Δ l ( n - 1 ) λ 2 π ,

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