Abstract

This research proposes a feedback method to adjust the dual-beam exposure system with spherical collimation lenses to achieve gratings with low spacing error. Through theoretical analysis and numerical calculation, it is proved that the interference aberration can be analyzed with the Zernike polynomials and the adjustment errors can be estimated according to the linear relationship between the errors and the polynomial coefficients. Moreover moving the substrate along its normal is proposed to decrease the spacing error but keep the grating’s period unchanged. In the experiments, the wavefront measurement results of the ± 1st orders are used to deduce the spacing error. Based on the feedback adjustment method, the grating with a spacing error of 0.03 λ within 70 mm × 70 mm is fabricated with the collimation lenses of 0.6 λ spherical aberration.

© 2015 Optical Society of America

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References

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    [Crossref]
  27. C. J. Chen, S. P. Pan, L. C. Chang, and G. S. Peng, “Pitch calibration by reflective laser diffraction,” Proc. SPIE 5190, 156–164 (2003).
    [Crossref]

2013 (2)

C. C. Wu, Y. Z. Chen, and C. H. Liao, “Common-path laser planar encoder,” Opt. Express 21(16), 18872–18883 (2013).
[Crossref] [PubMed]

X. Li, W. Gao, H. Muto, Y. Shimizu, S. Ito, and S. Dian, “A six-degree-of-freedom surface encoder for precision positioning of a planar motion stage,” Precis. Eng. 37(3), 771–781 (2013).
[Crossref]

2012 (1)

R. H. M. Schmidt, “Ultra-precision engineering in lithographic exposure equipment for the semiconductor industry,” Philos. Trans. A Math Phys. Eng. Sci. 370(1973), 3950–3972 (2012).
[Crossref] [PubMed]

2011 (1)

2010 (1)

T. Castenmiller, F. van de Mast, T. de Kort, C. van de Vin, M. de Wit, R. Stegen, and S. van Cleef, “Towards ultimate optical lithography with NXT: 1950i dual stage immersion platform,” Proc. SPIE 7640, 76401N (2010).
[Crossref]

2009 (2)

L. Shi, L. Zeng, and L. Li, “Fabrication of optical mosaic gratings with phase and attitude adjustments employing latent fringes and a red-wavelength dual-beam interferometer,” Opt. Express 17(24), 21530–21543 (2009).
[Crossref] [PubMed]

V. Korpelainen, A. Iho, J. Seppä, and A. Lassila, “High accuracy laser diffractometer: angle-scale traceability by the error separation method with a grating,” Meas. Sci. Technol. 20(8), 084020 (2009).
[Crossref]

2008 (1)

T. Jitsuno, S. Motokoshi, T. Okamoto, T. Mikami, D. Smith, M. L. Schattenburg, H. Kitamura, H. Matsuo, T. Kawasaki, K. Kondo, H. Shiraga, Y. Nakata, H. Habara, K. Tsubakimoto, R. Kodama, K. A. Tanaka, N. Miyanaga, and K. Mima, “Development of 91 cm size gratings and mirrors for LEFX laser system,” Journal of Physics: Conference Series. IOP Publishing 112(3), 032002 (2008).

2007 (1)

S. Wang, J. Wu, C. Li, and G. Chen, “Wavefront aberration analysis of large-aperture grating fabricated by plano-convex lens,” Laser Journal 28, 48–50 (2007) (in Chinese).

2006 (2)

W. Zhang, J. Wu, J. Zhu, and C. Li, “New method for the fabrication of pulse compression grating,” Proc. SPIE 6149, 614921 (2006).
[Crossref]

J. D. Zuegel, S. Borneis, C. Barty, B. Legarrec, C. Danson, N. Miyanaga, P. K. Rambo, C. Leblanc, T. J. Kessler, A. W. Schmid, L. J. Waxer, J. H. Kelly, B. Kruschwitz, R. Jungquist, E. Moses, J. Britten, I. Jovanovic, J. Dawson, and N. Blanchot, “Laser challenges for fast ignition,” Fusion Sci. Technol. 49, 453–482 (2006).

2004 (1)

R. K. Heilmann, C. G. Chen, P. T. Konkola, and M. L. Schattenburg, “Dimensional metrology for nanometre-scale science and engineering: towards sub-nanometre accurate encoders,” Nanotechnology 15(10), S504–S511 (2004).
[Crossref]

2003 (1)

C. J. Chen, S. P. Pan, L. C. Chang, and G. S. Peng, “Pitch calibration by reflective laser diffraction,” Proc. SPIE 5190, 156–164 (2003).
[Crossref]

2002 (1)

H. Schwenke, U. Neuschaefer-Rube, T. Pfeifer, and H. Kunzmann, “Optical methods for dimensional metrology in production engineering,” CIRP Annals Manufacturing Technology. 51(2), 685–699 (2002).
[Crossref]

2001 (1)

M. E. Walsh and H. I. Smith, “Method for reducing hyperbolic phase in interference lithography,” J. Vac. Sci. Technol. B 19(6), 2347–2352 (2001).
[Crossref]

1996 (1)

J. Ferrera, M. L. Schattenburg, and H. I. Smith, “Analysis of distortion in interferometric lithography,” J. Vac. Sci. Technol. B 14(6), 4009–4013 (1996).
[Crossref]

1994 (1)

1993 (1)

J. J. Armstrong and T. J. Kessler, “Large-aperture, high-efficiency holographic gratings for high-power laser systems,” Proc. SPIE 1870, 47–52 (1993).
[Crossref]

1990 (1)

D. Malacara, J. M. Carpio-Valadez, and J. J. Sanchez-Mondragon, “Wavefront fitting with discrete orthogonal polynomials in a unit radius circle,” Opt. Eng. 29(6), 672–675 (1990).
[Crossref]

1986 (1)

Z. Jaroszewicz, “Interferometric testing of the spacing error of a plane diffraction grating,” Opt. Commun. 60(6), 345–349 (1986).
[Crossref]

1980 (1)

1976 (1)

E. G. Loewen, “Diffraction gratings,” Opt. Eng. 15(5), 446–450 (1976).
[Crossref]

Armstrong, J. J.

J. J. Armstrong and T. J. Kessler, “Large-aperture, high-efficiency holographic gratings for high-power laser systems,” Proc. SPIE 1870, 47–52 (1993).
[Crossref]

Barty, C.

J. D. Zuegel, S. Borneis, C. Barty, B. Legarrec, C. Danson, N. Miyanaga, P. K. Rambo, C. Leblanc, T. J. Kessler, A. W. Schmid, L. J. Waxer, J. H. Kelly, B. Kruschwitz, R. Jungquist, E. Moses, J. Britten, I. Jovanovic, J. Dawson, and N. Blanchot, “Laser challenges for fast ignition,” Fusion Sci. Technol. 49, 453–482 (2006).

Blanchot, N.

J. D. Zuegel, S. Borneis, C. Barty, B. Legarrec, C. Danson, N. Miyanaga, P. K. Rambo, C. Leblanc, T. J. Kessler, A. W. Schmid, L. J. Waxer, J. H. Kelly, B. Kruschwitz, R. Jungquist, E. Moses, J. Britten, I. Jovanovic, J. Dawson, and N. Blanchot, “Laser challenges for fast ignition,” Fusion Sci. Technol. 49, 453–482 (2006).

Borneis, S.

J. D. Zuegel, S. Borneis, C. Barty, B. Legarrec, C. Danson, N. Miyanaga, P. K. Rambo, C. Leblanc, T. J. Kessler, A. W. Schmid, L. J. Waxer, J. H. Kelly, B. Kruschwitz, R. Jungquist, E. Moses, J. Britten, I. Jovanovic, J. Dawson, and N. Blanchot, “Laser challenges for fast ignition,” Fusion Sci. Technol. 49, 453–482 (2006).

Britten, J.

J. D. Zuegel, S. Borneis, C. Barty, B. Legarrec, C. Danson, N. Miyanaga, P. K. Rambo, C. Leblanc, T. J. Kessler, A. W. Schmid, L. J. Waxer, J. H. Kelly, B. Kruschwitz, R. Jungquist, E. Moses, J. Britten, I. Jovanovic, J. Dawson, and N. Blanchot, “Laser challenges for fast ignition,” Fusion Sci. Technol. 49, 453–482 (2006).

Carpio-Valadez, J. M.

D. Malacara, J. M. Carpio-Valadez, and J. J. Sanchez-Mondragon, “Wavefront fitting with discrete orthogonal polynomials in a unit radius circle,” Opt. Eng. 29(6), 672–675 (1990).
[Crossref]

Castenmiller, T.

T. Castenmiller, F. van de Mast, T. de Kort, C. van de Vin, M. de Wit, R. Stegen, and S. van Cleef, “Towards ultimate optical lithography with NXT: 1950i dual stage immersion platform,” Proc. SPIE 7640, 76401N (2010).
[Crossref]

Chang, L. C.

C. J. Chen, S. P. Pan, L. C. Chang, and G. S. Peng, “Pitch calibration by reflective laser diffraction,” Proc. SPIE 5190, 156–164 (2003).
[Crossref]

Chen, C. G.

R. K. Heilmann, C. G. Chen, P. T. Konkola, and M. L. Schattenburg, “Dimensional metrology for nanometre-scale science and engineering: towards sub-nanometre accurate encoders,” Nanotechnology 15(10), S504–S511 (2004).
[Crossref]

Chen, C. J.

C. J. Chen, S. P. Pan, L. C. Chang, and G. S. Peng, “Pitch calibration by reflective laser diffraction,” Proc. SPIE 5190, 156–164 (2003).
[Crossref]

Chen, G.

S. Wang, J. Wu, C. Li, and G. Chen, “Wavefront aberration analysis of large-aperture grating fabricated by plano-convex lens,” Laser Journal 28, 48–50 (2007) (in Chinese).

Chen, Y. Z.

Danson, C.

J. D. Zuegel, S. Borneis, C. Barty, B. Legarrec, C. Danson, N. Miyanaga, P. K. Rambo, C. Leblanc, T. J. Kessler, A. W. Schmid, L. J. Waxer, J. H. Kelly, B. Kruschwitz, R. Jungquist, E. Moses, J. Britten, I. Jovanovic, J. Dawson, and N. Blanchot, “Laser challenges for fast ignition,” Fusion Sci. Technol. 49, 453–482 (2006).

Dawson, J.

J. D. Zuegel, S. Borneis, C. Barty, B. Legarrec, C. Danson, N. Miyanaga, P. K. Rambo, C. Leblanc, T. J. Kessler, A. W. Schmid, L. J. Waxer, J. H. Kelly, B. Kruschwitz, R. Jungquist, E. Moses, J. Britten, I. Jovanovic, J. Dawson, and N. Blanchot, “Laser challenges for fast ignition,” Fusion Sci. Technol. 49, 453–482 (2006).

de Kort, T.

T. Castenmiller, F. van de Mast, T. de Kort, C. van de Vin, M. de Wit, R. Stegen, and S. van Cleef, “Towards ultimate optical lithography with NXT: 1950i dual stage immersion platform,” Proc. SPIE 7640, 76401N (2010).
[Crossref]

de Wit, M.

T. Castenmiller, F. van de Mast, T. de Kort, C. van de Vin, M. de Wit, R. Stegen, and S. van Cleef, “Towards ultimate optical lithography with NXT: 1950i dual stage immersion platform,” Proc. SPIE 7640, 76401N (2010).
[Crossref]

Dian, S.

X. Li, W. Gao, H. Muto, Y. Shimizu, S. Ito, and S. Dian, “A six-degree-of-freedom surface encoder for precision positioning of a planar motion stage,” Precis. Eng. 37(3), 771–781 (2013).
[Crossref]

Ferrera, J.

J. Ferrera, M. L. Schattenburg, and H. I. Smith, “Analysis of distortion in interferometric lithography,” J. Vac. Sci. Technol. B 14(6), 4009–4013 (1996).
[Crossref]

Gao, W.

X. Li, W. Gao, H. Muto, Y. Shimizu, S. Ito, and S. Dian, “A six-degree-of-freedom surface encoder for precision positioning of a planar motion stage,” Precis. Eng. 37(3), 771–781 (2013).
[Crossref]

Habara, H.

T. Jitsuno, S. Motokoshi, T. Okamoto, T. Mikami, D. Smith, M. L. Schattenburg, H. Kitamura, H. Matsuo, T. Kawasaki, K. Kondo, H. Shiraga, Y. Nakata, H. Habara, K. Tsubakimoto, R. Kodama, K. A. Tanaka, N. Miyanaga, and K. Mima, “Development of 91 cm size gratings and mirrors for LEFX laser system,” Journal of Physics: Conference Series. IOP Publishing 112(3), 032002 (2008).

Hegedus, Z. S.

Heilmann, R. K.

R. K. Heilmann, C. G. Chen, P. T. Konkola, and M. L. Schattenburg, “Dimensional metrology for nanometre-scale science and engineering: towards sub-nanometre accurate encoders,” Nanotechnology 15(10), S504–S511 (2004).
[Crossref]

Hibino, K.

Iho, A.

V. Korpelainen, A. Iho, J. Seppä, and A. Lassila, “High accuracy laser diffractometer: angle-scale traceability by the error separation method with a grating,” Meas. Sci. Technol. 20(8), 084020 (2009).
[Crossref]

Ito, S.

X. Li, W. Gao, H. Muto, Y. Shimizu, S. Ito, and S. Dian, “A six-degree-of-freedom surface encoder for precision positioning of a planar motion stage,” Precis. Eng. 37(3), 771–781 (2013).
[Crossref]

Jaroszewicz, Z.

Z. Jaroszewicz, “Interferometric testing of the spacing error of a plane diffraction grating,” Opt. Commun. 60(6), 345–349 (1986).
[Crossref]

Jitsuno, T.

T. Jitsuno, S. Motokoshi, T. Okamoto, T. Mikami, D. Smith, M. L. Schattenburg, H. Kitamura, H. Matsuo, T. Kawasaki, K. Kondo, H. Shiraga, Y. Nakata, H. Habara, K. Tsubakimoto, R. Kodama, K. A. Tanaka, N. Miyanaga, and K. Mima, “Development of 91 cm size gratings and mirrors for LEFX laser system,” Journal of Physics: Conference Series. IOP Publishing 112(3), 032002 (2008).

Jovanovic, I.

J. D. Zuegel, S. Borneis, C. Barty, B. Legarrec, C. Danson, N. Miyanaga, P. K. Rambo, C. Leblanc, T. J. Kessler, A. W. Schmid, L. J. Waxer, J. H. Kelly, B. Kruschwitz, R. Jungquist, E. Moses, J. Britten, I. Jovanovic, J. Dawson, and N. Blanchot, “Laser challenges for fast ignition,” Fusion Sci. Technol. 49, 453–482 (2006).

Jungquist, R.

J. D. Zuegel, S. Borneis, C. Barty, B. Legarrec, C. Danson, N. Miyanaga, P. K. Rambo, C. Leblanc, T. J. Kessler, A. W. Schmid, L. J. Waxer, J. H. Kelly, B. Kruschwitz, R. Jungquist, E. Moses, J. Britten, I. Jovanovic, J. Dawson, and N. Blanchot, “Laser challenges for fast ignition,” Fusion Sci. Technol. 49, 453–482 (2006).

Kawasaki, T.

T. Jitsuno, S. Motokoshi, T. Okamoto, T. Mikami, D. Smith, M. L. Schattenburg, H. Kitamura, H. Matsuo, T. Kawasaki, K. Kondo, H. Shiraga, Y. Nakata, H. Habara, K. Tsubakimoto, R. Kodama, K. A. Tanaka, N. Miyanaga, and K. Mima, “Development of 91 cm size gratings and mirrors for LEFX laser system,” Journal of Physics: Conference Series. IOP Publishing 112(3), 032002 (2008).

Kelly, J. H.

J. D. Zuegel, S. Borneis, C. Barty, B. Legarrec, C. Danson, N. Miyanaga, P. K. Rambo, C. Leblanc, T. J. Kessler, A. W. Schmid, L. J. Waxer, J. H. Kelly, B. Kruschwitz, R. Jungquist, E. Moses, J. Britten, I. Jovanovic, J. Dawson, and N. Blanchot, “Laser challenges for fast ignition,” Fusion Sci. Technol. 49, 453–482 (2006).

Kessler, T. J.

J. D. Zuegel, S. Borneis, C. Barty, B. Legarrec, C. Danson, N. Miyanaga, P. K. Rambo, C. Leblanc, T. J. Kessler, A. W. Schmid, L. J. Waxer, J. H. Kelly, B. Kruschwitz, R. Jungquist, E. Moses, J. Britten, I. Jovanovic, J. Dawson, and N. Blanchot, “Laser challenges for fast ignition,” Fusion Sci. Technol. 49, 453–482 (2006).

J. J. Armstrong and T. J. Kessler, “Large-aperture, high-efficiency holographic gratings for high-power laser systems,” Proc. SPIE 1870, 47–52 (1993).
[Crossref]

Kitamura, H.

T. Jitsuno, S. Motokoshi, T. Okamoto, T. Mikami, D. Smith, M. L. Schattenburg, H. Kitamura, H. Matsuo, T. Kawasaki, K. Kondo, H. Shiraga, Y. Nakata, H. Habara, K. Tsubakimoto, R. Kodama, K. A. Tanaka, N. Miyanaga, and K. Mima, “Development of 91 cm size gratings and mirrors for LEFX laser system,” Journal of Physics: Conference Series. IOP Publishing 112(3), 032002 (2008).

Kodama, R.

T. Jitsuno, S. Motokoshi, T. Okamoto, T. Mikami, D. Smith, M. L. Schattenburg, H. Kitamura, H. Matsuo, T. Kawasaki, K. Kondo, H. Shiraga, Y. Nakata, H. Habara, K. Tsubakimoto, R. Kodama, K. A. Tanaka, N. Miyanaga, and K. Mima, “Development of 91 cm size gratings and mirrors for LEFX laser system,” Journal of Physics: Conference Series. IOP Publishing 112(3), 032002 (2008).

Kondo, K.

T. Jitsuno, S. Motokoshi, T. Okamoto, T. Mikami, D. Smith, M. L. Schattenburg, H. Kitamura, H. Matsuo, T. Kawasaki, K. Kondo, H. Shiraga, Y. Nakata, H. Habara, K. Tsubakimoto, R. Kodama, K. A. Tanaka, N. Miyanaga, and K. Mima, “Development of 91 cm size gratings and mirrors for LEFX laser system,” Journal of Physics: Conference Series. IOP Publishing 112(3), 032002 (2008).

Konkola, P. T.

R. K. Heilmann, C. G. Chen, P. T. Konkola, and M. L. Schattenburg, “Dimensional metrology for nanometre-scale science and engineering: towards sub-nanometre accurate encoders,” Nanotechnology 15(10), S504–S511 (2004).
[Crossref]

Korpelainen, V.

V. Korpelainen, A. Iho, J. Seppä, and A. Lassila, “High accuracy laser diffractometer: angle-scale traceability by the error separation method with a grating,” Meas. Sci. Technol. 20(8), 084020 (2009).
[Crossref]

Kruschwitz, B.

J. D. Zuegel, S. Borneis, C. Barty, B. Legarrec, C. Danson, N. Miyanaga, P. K. Rambo, C. Leblanc, T. J. Kessler, A. W. Schmid, L. J. Waxer, J. H. Kelly, B. Kruschwitz, R. Jungquist, E. Moses, J. Britten, I. Jovanovic, J. Dawson, and N. Blanchot, “Laser challenges for fast ignition,” Fusion Sci. Technol. 49, 453–482 (2006).

Kunzmann, H.

H. Schwenke, U. Neuschaefer-Rube, T. Pfeifer, and H. Kunzmann, “Optical methods for dimensional metrology in production engineering,” CIRP Annals Manufacturing Technology. 51(2), 685–699 (2002).
[Crossref]

Lassila, A.

V. Korpelainen, A. Iho, J. Seppä, and A. Lassila, “High accuracy laser diffractometer: angle-scale traceability by the error separation method with a grating,” Meas. Sci. Technol. 20(8), 084020 (2009).
[Crossref]

Leblanc, C.

J. D. Zuegel, S. Borneis, C. Barty, B. Legarrec, C. Danson, N. Miyanaga, P. K. Rambo, C. Leblanc, T. J. Kessler, A. W. Schmid, L. J. Waxer, J. H. Kelly, B. Kruschwitz, R. Jungquist, E. Moses, J. Britten, I. Jovanovic, J. Dawson, and N. Blanchot, “Laser challenges for fast ignition,” Fusion Sci. Technol. 49, 453–482 (2006).

Legarrec, B.

J. D. Zuegel, S. Borneis, C. Barty, B. Legarrec, C. Danson, N. Miyanaga, P. K. Rambo, C. Leblanc, T. J. Kessler, A. W. Schmid, L. J. Waxer, J. H. Kelly, B. Kruschwitz, R. Jungquist, E. Moses, J. Britten, I. Jovanovic, J. Dawson, and N. Blanchot, “Laser challenges for fast ignition,” Fusion Sci. Technol. 49, 453–482 (2006).

Li, C.

S. Wang, J. Wu, C. Li, and G. Chen, “Wavefront aberration analysis of large-aperture grating fabricated by plano-convex lens,” Laser Journal 28, 48–50 (2007) (in Chinese).

W. Zhang, J. Wu, J. Zhu, and C. Li, “New method for the fabrication of pulse compression grating,” Proc. SPIE 6149, 614921 (2006).
[Crossref]

Li, L.

Li, X.

X. Li, W. Gao, H. Muto, Y. Shimizu, S. Ito, and S. Dian, “A six-degree-of-freedom surface encoder for precision positioning of a planar motion stage,” Precis. Eng. 37(3), 771–781 (2013).
[Crossref]

Liao, C. H.

Loewen, E. G.

E. G. Loewen, “Diffraction gratings,” Opt. Eng. 15(5), 446–450 (1976).
[Crossref]

Malacara, D.

D. Malacara, J. M. Carpio-Valadez, and J. J. Sanchez-Mondragon, “Wavefront fitting with discrete orthogonal polynomials in a unit radius circle,” Opt. Eng. 29(6), 672–675 (1990).
[Crossref]

Matsuo, H.

T. Jitsuno, S. Motokoshi, T. Okamoto, T. Mikami, D. Smith, M. L. Schattenburg, H. Kitamura, H. Matsuo, T. Kawasaki, K. Kondo, H. Shiraga, Y. Nakata, H. Habara, K. Tsubakimoto, R. Kodama, K. A. Tanaka, N. Miyanaga, and K. Mima, “Development of 91 cm size gratings and mirrors for LEFX laser system,” Journal of Physics: Conference Series. IOP Publishing 112(3), 032002 (2008).

Mikami, T.

T. Jitsuno, S. Motokoshi, T. Okamoto, T. Mikami, D. Smith, M. L. Schattenburg, H. Kitamura, H. Matsuo, T. Kawasaki, K. Kondo, H. Shiraga, Y. Nakata, H. Habara, K. Tsubakimoto, R. Kodama, K. A. Tanaka, N. Miyanaga, and K. Mima, “Development of 91 cm size gratings and mirrors for LEFX laser system,” Journal of Physics: Conference Series. IOP Publishing 112(3), 032002 (2008).

Mima, K.

T. Jitsuno, S. Motokoshi, T. Okamoto, T. Mikami, D. Smith, M. L. Schattenburg, H. Kitamura, H. Matsuo, T. Kawasaki, K. Kondo, H. Shiraga, Y. Nakata, H. Habara, K. Tsubakimoto, R. Kodama, K. A. Tanaka, N. Miyanaga, and K. Mima, “Development of 91 cm size gratings and mirrors for LEFX laser system,” Journal of Physics: Conference Series. IOP Publishing 112(3), 032002 (2008).

Miyanaga, N.

T. Jitsuno, S. Motokoshi, T. Okamoto, T. Mikami, D. Smith, M. L. Schattenburg, H. Kitamura, H. Matsuo, T. Kawasaki, K. Kondo, H. Shiraga, Y. Nakata, H. Habara, K. Tsubakimoto, R. Kodama, K. A. Tanaka, N. Miyanaga, and K. Mima, “Development of 91 cm size gratings and mirrors for LEFX laser system,” Journal of Physics: Conference Series. IOP Publishing 112(3), 032002 (2008).

J. D. Zuegel, S. Borneis, C. Barty, B. Legarrec, C. Danson, N. Miyanaga, P. K. Rambo, C. Leblanc, T. J. Kessler, A. W. Schmid, L. J. Waxer, J. H. Kelly, B. Kruschwitz, R. Jungquist, E. Moses, J. Britten, I. Jovanovic, J. Dawson, and N. Blanchot, “Laser challenges for fast ignition,” Fusion Sci. Technol. 49, 453–482 (2006).

Moses, E.

J. D. Zuegel, S. Borneis, C. Barty, B. Legarrec, C. Danson, N. Miyanaga, P. K. Rambo, C. Leblanc, T. J. Kessler, A. W. Schmid, L. J. Waxer, J. H. Kelly, B. Kruschwitz, R. Jungquist, E. Moses, J. Britten, I. Jovanovic, J. Dawson, and N. Blanchot, “Laser challenges for fast ignition,” Fusion Sci. Technol. 49, 453–482 (2006).

Motokoshi, S.

T. Jitsuno, S. Motokoshi, T. Okamoto, T. Mikami, D. Smith, M. L. Schattenburg, H. Kitamura, H. Matsuo, T. Kawasaki, K. Kondo, H. Shiraga, Y. Nakata, H. Habara, K. Tsubakimoto, R. Kodama, K. A. Tanaka, N. Miyanaga, and K. Mima, “Development of 91 cm size gratings and mirrors for LEFX laser system,” Journal of Physics: Conference Series. IOP Publishing 112(3), 032002 (2008).

Muto, H.

X. Li, W. Gao, H. Muto, Y. Shimizu, S. Ito, and S. Dian, “A six-degree-of-freedom surface encoder for precision positioning of a planar motion stage,” Precis. Eng. 37(3), 771–781 (2013).
[Crossref]

Nakata, Y.

T. Jitsuno, S. Motokoshi, T. Okamoto, T. Mikami, D. Smith, M. L. Schattenburg, H. Kitamura, H. Matsuo, T. Kawasaki, K. Kondo, H. Shiraga, Y. Nakata, H. Habara, K. Tsubakimoto, R. Kodama, K. A. Tanaka, N. Miyanaga, and K. Mima, “Development of 91 cm size gratings and mirrors for LEFX laser system,” Journal of Physics: Conference Series. IOP Publishing 112(3), 032002 (2008).

Neuschaefer-Rube, U.

H. Schwenke, U. Neuschaefer-Rube, T. Pfeifer, and H. Kunzmann, “Optical methods for dimensional metrology in production engineering,” CIRP Annals Manufacturing Technology. 51(2), 685–699 (2002).
[Crossref]

Okamoto, T.

T. Jitsuno, S. Motokoshi, T. Okamoto, T. Mikami, D. Smith, M. L. Schattenburg, H. Kitamura, H. Matsuo, T. Kawasaki, K. Kondo, H. Shiraga, Y. Nakata, H. Habara, K. Tsubakimoto, R. Kodama, K. A. Tanaka, N. Miyanaga, and K. Mima, “Development of 91 cm size gratings and mirrors for LEFX laser system,” Journal of Physics: Conference Series. IOP Publishing 112(3), 032002 (2008).

Pan, S. P.

C. J. Chen, S. P. Pan, L. C. Chang, and G. S. Peng, “Pitch calibration by reflective laser diffraction,” Proc. SPIE 5190, 156–164 (2003).
[Crossref]

Peng, G. S.

C. J. Chen, S. P. Pan, L. C. Chang, and G. S. Peng, “Pitch calibration by reflective laser diffraction,” Proc. SPIE 5190, 156–164 (2003).
[Crossref]

Pfeifer, T.

H. Schwenke, U. Neuschaefer-Rube, T. Pfeifer, and H. Kunzmann, “Optical methods for dimensional metrology in production engineering,” CIRP Annals Manufacturing Technology. 51(2), 685–699 (2002).
[Crossref]

Rambo, P. K.

J. D. Zuegel, S. Borneis, C. Barty, B. Legarrec, C. Danson, N. Miyanaga, P. K. Rambo, C. Leblanc, T. J. Kessler, A. W. Schmid, L. J. Waxer, J. H. Kelly, B. Kruschwitz, R. Jungquist, E. Moses, J. Britten, I. Jovanovic, J. Dawson, and N. Blanchot, “Laser challenges for fast ignition,” Fusion Sci. Technol. 49, 453–482 (2006).

Sanchez-Mondragon, J. J.

D. Malacara, J. M. Carpio-Valadez, and J. J. Sanchez-Mondragon, “Wavefront fitting with discrete orthogonal polynomials in a unit radius circle,” Opt. Eng. 29(6), 672–675 (1990).
[Crossref]

Schattenburg, M. L.

T. Jitsuno, S. Motokoshi, T. Okamoto, T. Mikami, D. Smith, M. L. Schattenburg, H. Kitamura, H. Matsuo, T. Kawasaki, K. Kondo, H. Shiraga, Y. Nakata, H. Habara, K. Tsubakimoto, R. Kodama, K. A. Tanaka, N. Miyanaga, and K. Mima, “Development of 91 cm size gratings and mirrors for LEFX laser system,” Journal of Physics: Conference Series. IOP Publishing 112(3), 032002 (2008).

R. K. Heilmann, C. G. Chen, P. T. Konkola, and M. L. Schattenburg, “Dimensional metrology for nanometre-scale science and engineering: towards sub-nanometre accurate encoders,” Nanotechnology 15(10), S504–S511 (2004).
[Crossref]

J. Ferrera, M. L. Schattenburg, and H. I. Smith, “Analysis of distortion in interferometric lithography,” J. Vac. Sci. Technol. B 14(6), 4009–4013 (1996).
[Crossref]

Schmid, A. W.

J. D. Zuegel, S. Borneis, C. Barty, B. Legarrec, C. Danson, N. Miyanaga, P. K. Rambo, C. Leblanc, T. J. Kessler, A. W. Schmid, L. J. Waxer, J. H. Kelly, B. Kruschwitz, R. Jungquist, E. Moses, J. Britten, I. Jovanovic, J. Dawson, and N. Blanchot, “Laser challenges for fast ignition,” Fusion Sci. Technol. 49, 453–482 (2006).

Schmidt, R. H. M.

R. H. M. Schmidt, “Ultra-precision engineering in lithographic exposure equipment for the semiconductor industry,” Philos. Trans. A Math Phys. Eng. Sci. 370(1973), 3950–3972 (2012).
[Crossref] [PubMed]

Schwenke, H.

H. Schwenke, U. Neuschaefer-Rube, T. Pfeifer, and H. Kunzmann, “Optical methods for dimensional metrology in production engineering,” CIRP Annals Manufacturing Technology. 51(2), 685–699 (2002).
[Crossref]

Seppä, J.

V. Korpelainen, A. Iho, J. Seppä, and A. Lassila, “High accuracy laser diffractometer: angle-scale traceability by the error separation method with a grating,” Meas. Sci. Technol. 20(8), 084020 (2009).
[Crossref]

Shi, L.

Shimizu, Y.

X. Li, W. Gao, H. Muto, Y. Shimizu, S. Ito, and S. Dian, “A six-degree-of-freedom surface encoder for precision positioning of a planar motion stage,” Precis. Eng. 37(3), 771–781 (2013).
[Crossref]

Shiraga, H.

T. Jitsuno, S. Motokoshi, T. Okamoto, T. Mikami, D. Smith, M. L. Schattenburg, H. Kitamura, H. Matsuo, T. Kawasaki, K. Kondo, H. Shiraga, Y. Nakata, H. Habara, K. Tsubakimoto, R. Kodama, K. A. Tanaka, N. Miyanaga, and K. Mima, “Development of 91 cm size gratings and mirrors for LEFX laser system,” Journal of Physics: Conference Series. IOP Publishing 112(3), 032002 (2008).

Silva, D. E.

Smith, D.

T. Jitsuno, S. Motokoshi, T. Okamoto, T. Mikami, D. Smith, M. L. Schattenburg, H. Kitamura, H. Matsuo, T. Kawasaki, K. Kondo, H. Shiraga, Y. Nakata, H. Habara, K. Tsubakimoto, R. Kodama, K. A. Tanaka, N. Miyanaga, and K. Mima, “Development of 91 cm size gratings and mirrors for LEFX laser system,” Journal of Physics: Conference Series. IOP Publishing 112(3), 032002 (2008).

Smith, H. I.

M. E. Walsh and H. I. Smith, “Method for reducing hyperbolic phase in interference lithography,” J. Vac. Sci. Technol. B 19(6), 2347–2352 (2001).
[Crossref]

J. Ferrera, M. L. Schattenburg, and H. I. Smith, “Analysis of distortion in interferometric lithography,” J. Vac. Sci. Technol. B 14(6), 4009–4013 (1996).
[Crossref]

Stegen, R.

T. Castenmiller, F. van de Mast, T. de Kort, C. van de Vin, M. de Wit, R. Stegen, and S. van Cleef, “Towards ultimate optical lithography with NXT: 1950i dual stage immersion platform,” Proc. SPIE 7640, 76401N (2010).
[Crossref]

Tanaka, K. A.

T. Jitsuno, S. Motokoshi, T. Okamoto, T. Mikami, D. Smith, M. L. Schattenburg, H. Kitamura, H. Matsuo, T. Kawasaki, K. Kondo, H. Shiraga, Y. Nakata, H. Habara, K. Tsubakimoto, R. Kodama, K. A. Tanaka, N. Miyanaga, and K. Mima, “Development of 91 cm size gratings and mirrors for LEFX laser system,” Journal of Physics: Conference Series. IOP Publishing 112(3), 032002 (2008).

Tsubakimoto, K.

T. Jitsuno, S. Motokoshi, T. Okamoto, T. Mikami, D. Smith, M. L. Schattenburg, H. Kitamura, H. Matsuo, T. Kawasaki, K. Kondo, H. Shiraga, Y. Nakata, H. Habara, K. Tsubakimoto, R. Kodama, K. A. Tanaka, N. Miyanaga, and K. Mima, “Development of 91 cm size gratings and mirrors for LEFX laser system,” Journal of Physics: Conference Series. IOP Publishing 112(3), 032002 (2008).

van Cleef, S.

T. Castenmiller, F. van de Mast, T. de Kort, C. van de Vin, M. de Wit, R. Stegen, and S. van Cleef, “Towards ultimate optical lithography with NXT: 1950i dual stage immersion platform,” Proc. SPIE 7640, 76401N (2010).
[Crossref]

van de Mast, F.

T. Castenmiller, F. van de Mast, T. de Kort, C. van de Vin, M. de Wit, R. Stegen, and S. van Cleef, “Towards ultimate optical lithography with NXT: 1950i dual stage immersion platform,” Proc. SPIE 7640, 76401N (2010).
[Crossref]

van de Vin, C.

T. Castenmiller, F. van de Mast, T. de Kort, C. van de Vin, M. de Wit, R. Stegen, and S. van Cleef, “Towards ultimate optical lithography with NXT: 1950i dual stage immersion platform,” Proc. SPIE 7640, 76401N (2010).
[Crossref]

Walsh, M. E.

M. E. Walsh and H. I. Smith, “Method for reducing hyperbolic phase in interference lithography,” J. Vac. Sci. Technol. B 19(6), 2347–2352 (2001).
[Crossref]

Wang, J. Y.

Wang, S.

S. Wang, J. Wu, C. Li, and G. Chen, “Wavefront aberration analysis of large-aperture grating fabricated by plano-convex lens,” Laser Journal 28, 48–50 (2007) (in Chinese).

Waxer, L. J.

J. D. Zuegel, S. Borneis, C. Barty, B. Legarrec, C. Danson, N. Miyanaga, P. K. Rambo, C. Leblanc, T. J. Kessler, A. W. Schmid, L. J. Waxer, J. H. Kelly, B. Kruschwitz, R. Jungquist, E. Moses, J. Britten, I. Jovanovic, J. Dawson, and N. Blanchot, “Laser challenges for fast ignition,” Fusion Sci. Technol. 49, 453–482 (2006).

Wu, C. C.

Wu, J.

S. Wang, J. Wu, C. Li, and G. Chen, “Wavefront aberration analysis of large-aperture grating fabricated by plano-convex lens,” Laser Journal 28, 48–50 (2007) (in Chinese).

W. Zhang, J. Wu, J. Zhu, and C. Li, “New method for the fabrication of pulse compression grating,” Proc. SPIE 6149, 614921 (2006).
[Crossref]

Zeng, L.

Zhang, W.

W. Zhang, J. Wu, J. Zhu, and C. Li, “New method for the fabrication of pulse compression grating,” Proc. SPIE 6149, 614921 (2006).
[Crossref]

Zhu, J.

W. Zhang, J. Wu, J. Zhu, and C. Li, “New method for the fabrication of pulse compression grating,” Proc. SPIE 6149, 614921 (2006).
[Crossref]

Zuegel, J. D.

J. D. Zuegel, S. Borneis, C. Barty, B. Legarrec, C. Danson, N. Miyanaga, P. K. Rambo, C. Leblanc, T. J. Kessler, A. W. Schmid, L. J. Waxer, J. H. Kelly, B. Kruschwitz, R. Jungquist, E. Moses, J. Britten, I. Jovanovic, J. Dawson, and N. Blanchot, “Laser challenges for fast ignition,” Fusion Sci. Technol. 49, 453–482 (2006).

Appl. Opt. (2)

CIRP Annals Manufacturing Technology. (1)

H. Schwenke, U. Neuschaefer-Rube, T. Pfeifer, and H. Kunzmann, “Optical methods for dimensional metrology in production engineering,” CIRP Annals Manufacturing Technology. 51(2), 685–699 (2002).
[Crossref]

Fusion Sci. Technol. (1)

J. D. Zuegel, S. Borneis, C. Barty, B. Legarrec, C. Danson, N. Miyanaga, P. K. Rambo, C. Leblanc, T. J. Kessler, A. W. Schmid, L. J. Waxer, J. H. Kelly, B. Kruschwitz, R. Jungquist, E. Moses, J. Britten, I. Jovanovic, J. Dawson, and N. Blanchot, “Laser challenges for fast ignition,” Fusion Sci. Technol. 49, 453–482 (2006).

J. Vac. Sci. Technol. B (2)

J. Ferrera, M. L. Schattenburg, and H. I. Smith, “Analysis of distortion in interferometric lithography,” J. Vac. Sci. Technol. B 14(6), 4009–4013 (1996).
[Crossref]

M. E. Walsh and H. I. Smith, “Method for reducing hyperbolic phase in interference lithography,” J. Vac. Sci. Technol. B 19(6), 2347–2352 (2001).
[Crossref]

Journal of Physics: Conference Series. IOP Publishing (1)

T. Jitsuno, S. Motokoshi, T. Okamoto, T. Mikami, D. Smith, M. L. Schattenburg, H. Kitamura, H. Matsuo, T. Kawasaki, K. Kondo, H. Shiraga, Y. Nakata, H. Habara, K. Tsubakimoto, R. Kodama, K. A. Tanaka, N. Miyanaga, and K. Mima, “Development of 91 cm size gratings and mirrors for LEFX laser system,” Journal of Physics: Conference Series. IOP Publishing 112(3), 032002 (2008).

Laser Journal (1)

S. Wang, J. Wu, C. Li, and G. Chen, “Wavefront aberration analysis of large-aperture grating fabricated by plano-convex lens,” Laser Journal 28, 48–50 (2007) (in Chinese).

Meas. Sci. Technol. (1)

V. Korpelainen, A. Iho, J. Seppä, and A. Lassila, “High accuracy laser diffractometer: angle-scale traceability by the error separation method with a grating,” Meas. Sci. Technol. 20(8), 084020 (2009).
[Crossref]

Nanotechnology (1)

R. K. Heilmann, C. G. Chen, P. T. Konkola, and M. L. Schattenburg, “Dimensional metrology for nanometre-scale science and engineering: towards sub-nanometre accurate encoders,” Nanotechnology 15(10), S504–S511 (2004).
[Crossref]

Opt. Commun. (1)

Z. Jaroszewicz, “Interferometric testing of the spacing error of a plane diffraction grating,” Opt. Commun. 60(6), 345–349 (1986).
[Crossref]

Opt. Eng. (2)

E. G. Loewen, “Diffraction gratings,” Opt. Eng. 15(5), 446–450 (1976).
[Crossref]

D. Malacara, J. M. Carpio-Valadez, and J. J. Sanchez-Mondragon, “Wavefront fitting with discrete orthogonal polynomials in a unit radius circle,” Opt. Eng. 29(6), 672–675 (1990).
[Crossref]

Opt. Express (3)

Philos. Trans. A Math Phys. Eng. Sci. (1)

R. H. M. Schmidt, “Ultra-precision engineering in lithographic exposure equipment for the semiconductor industry,” Philos. Trans. A Math Phys. Eng. Sci. 370(1973), 3950–3972 (2012).
[Crossref] [PubMed]

Precis. Eng. (1)

X. Li, W. Gao, H. Muto, Y. Shimizu, S. Ito, and S. Dian, “A six-degree-of-freedom surface encoder for precision positioning of a planar motion stage,” Precis. Eng. 37(3), 771–781 (2013).
[Crossref]

Proc. SPIE (4)

T. Castenmiller, F. van de Mast, T. de Kort, C. van de Vin, M. de Wit, R. Stegen, and S. van Cleef, “Towards ultimate optical lithography with NXT: 1950i dual stage immersion platform,” Proc. SPIE 7640, 76401N (2010).
[Crossref]

J. J. Armstrong and T. J. Kessler, “Large-aperture, high-efficiency holographic gratings for high-power laser systems,” Proc. SPIE 1870, 47–52 (1993).
[Crossref]

C. J. Chen, S. P. Pan, L. C. Chang, and G. S. Peng, “Pitch calibration by reflective laser diffraction,” Proc. SPIE 5190, 156–164 (2003).
[Crossref]

W. Zhang, J. Wu, J. Zhu, and C. Li, “New method for the fabrication of pulse compression grating,” Proc. SPIE 6149, 614921 (2006).
[Crossref]

Other (5)

M. E. Walsh, “On the Design of Lithographic Interferometers and TheirAapplication,” Ph.D. dissertation, (Massachusetts Institute of Technology, Boston, MA, 2004).

D. Malacara, Optical Shop Testing (John Wiley & Sons, 2007), Chap. 13.

F. Meli, “WGDM-7: Preliminary comparison on Nanometrology: Nano4: 1D gratings,” Final report, OFMET, Wabern, 30 (2000).

M. Hercher, “High Speed, high accuracy stage for advanced lithography,” DARPA Phase II final report, Optra Inc. (2001).

J. A. Britten, S. J. Bryan, L. J. Summers, H. T. Nguyen, and B. W. Shore, “Large aperture, high-efficiency multilayer dielectric reflection gratings,” in Conference on Lasers and Electro-Optics, OSA, paper CPDB7 (2002).
[Crossref]

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Figures (8)

Fig. 1
Fig. 1 Schematic of a dual-beam exposure system. (a) Two expanding-collimation systems constitute the whole system. (b) Here the impact of a deviation of PH2 along O2X2 is shown: the optical axes of the two ECSs are e1 and e2, the incident angles are θ1 and θ1, the incident point of the e2 axis on the substrate is moved by δx2 from the ideal position. Moving e2 to e2' (or e1 to e1') will correct the Xi direction error, but the grating period will be changed at the same time. If the substrate is moved from G to G', the Condition of Aberration Symmetry can also be satisfied.
Fig. 2
Fig. 2 Simulated interference aberration under ideal condition. (a) Two point sources are both located at the foci of the collimating lenses. (b) When there are same position errors (1, 1, 0.1) for the two point sources in the ECSs, which means the incident angles are different but the optical axes keep across the same point on the substrate surface approximately, the interference aberration can also be compensated well.
Fig. 3
Fig. 3 Interference aberration with different adjustment errors of the point source. (a) Relative position error of (0, 0, 0.1), this aberration corresponds to the defocus term of the Zernike polynomial. (b) and (c) Relative position error of (1, 0, 0) and (0, 1, 0). They correspond to coma terms of Zernike polynomials. (d) Relative position error of (1, 1, 0.1). Usually the existence of all kinds of position errors will introduce this distribution of aberration.
Fig. 4
Fig. 4 Linear relationship between the adjustment errors and the fitted Zernike coefficients. The data markers are given by theoretical calculation and the lines are linearly fitted with the data samples. X, Y and Z errors are the relative position errors of the point source and s is the position error of the substrate in its normal direction.
Fig. 5
Fig. 5 Adjust the substrate to compensation the Xi direction position error. (a) 0.5mm X2 direction error of point source is added. (b) The substrate is moved along its normal by −0.86mm to compensate the X2 direction error.
Fig. 6
Fig. 6 Example of spacing error minimization process. (a) Spacing error before fine adjustments. (b) Spacing error after adjusting the focus of point source and normal position of the substrate according to theoretical prediction. (c) After the second feedback adjustment, the spacing error is decreased to about 0.03λ. (d) Only adjust the position of the point source to minimize the spacing error.
Fig. 7
Fig. 7 Linear relationship between the Zernike coefficients and the adjustment parameters in experiment. (a) The 3rd Zernike term and the Z direction position of the point source. (b) The 6th Zernike term and Xi direction position of the point source (the circle points and the red line), the normal position of the substrate (the cross points and the black line).
Fig. 8
Fig. 8 Measurement results of the spherical collimating lenses. (a) Aberration of L1. (b) Aberration of L2. (c) The difference between L1 and L2.

Tables (3)

Tables Icon

Table 1 The Fitted Zernike Polynomial Coefficients of Fig. 3

Tables Icon

Table 2 The Fitted Zernike Polynomial Coefficients of Fig. 6

Tables Icon

Table 3 Grating Samples’ Periods

Equations (9)

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

d= λ 0 2sinθ ,
ϕ i = 2π λ 0 z i + A i ( x i 2 + y i 2 )+ B i ( x i 2 + y i 2 ) 2 ,
ϕ= ϕ 1 ϕ 2 .
x 1 = x 0 cos θ 1 x 2 =( x 0 δ x 2 )cos θ 2 y i = y 0 z i = l i ( 1 ) i x 0 sin θ i .
ϕ= ϕ G + ϕ F + ϕ I + ϕ C + ϕ R ,
ϕ G = 2π λ 0 ( x 0 sin θ 1 + x 0 sin θ 2 + l 1 l 2 ) ϕ F =( A 1 A 2 )( x 0 2 cos θ 1 + y 0 2 )+( B 1 B 2 )( x 0 2 cos θ 1 + y 0 2 ) ϕ I =[ A 2 x 0 2 + B 2 x 0 4 ( cos 2 θ 1 + cos 2 θ 2 )+2 B 2 x 0 2 y 0 2 ]( cos θ 1 +cos θ 2 )( cos θ 1 cos θ 2 ) ϕ C =4 B 2 x 0 δ x 2 cos 2 θ 2 ( x 0 2 cos 2 θ 2 + y 0 2 ) ϕ R =2 B 2 δ x 2 2 cos 2 θ 2 ( x 0 2 cos 2 θ 2 + y 0 2 )4 B 2 x 0 2 δ x 2 2 cos 4 θ 2 ( B 2 δ x 2 4 cos 4 θ 2 + A 2 δ x 2 2 cos 2 θ 2 )+( 4 B 2 x 0 δ x 2 3 cos 4 θ 2 +2 A 2 x 0 δ x 2 cos 2 θ 2 ).
cos θ 1 cos θ 2 =( θ 1 θ 2 )sin θ 1 ,
Δx=( j1 )mm Δy=( 11j )mm Δz=( j1 )0.1mm j=1,2...11.
ϕ 0 ( x 0 , y 0 )= 2π λ Δ Z 0 ( x 0 , y 0 )cos κ 0 + φ 0 ( x 0 , y 0 ) ϕ +1 ( x 0 , y 0 )= 2π λ Δ Z 0 ( x 0 , y 0 )cosκ+Δ X 0 ( x 0 , y 0 ) π d + φ 1 ( x 0 , y 0 ) ϕ 1 ( x 0 , y 0 )= 2π λ Δ Z 0 ( x 0 , y 0 )cosκΔ X 0 ( x 0 , y 0 ) π d + φ 1 ( x 0 , y 0 ) Φ +1,1 = 1 2 [ ϕ +1 ( x 0 , y 0 ) ϕ 1 ( x 0 , y 0 ) ]=Δ X 0 ( x 0 , y 0 ) π d ,

Metrics