Abstract

Periodic nonlinear errors caused by frequency mixing are serious obstacles for increasing the resolution of heterodyne grating interferometers. To eliminate the periodic nonlinear errors, a spatially separated heterodyne grating interferometer is proposed in this study. Two modulated beams with different frequencies are transferred respectively by two fibers, which form a spatially separated construction. A couple of comparison experiments in both time domain and frequency domain are designed and conducted. The results of the frequency-spectrum analysis experiment showed that the periodic nonlinear errors were no larger than 0.086 nm, which proved that the proposed system was effectual in eliminating periodic nonlinear errors.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2017 (1)

2016 (3)

S. Zhao, H. Wei, M. Zhu, and Y. Li, “Green laser interferometric metrology system with sub-nanometer periodic nonlinearity,” Appl. Opt. 55(11), 3006–3011 (2016).
[PubMed]

H. L. Hsieh and W. Chen, “Heterodyne Wollaston laser encoder for measurement of in-plane displacement,” Opt. Express 24(8), 8693–8707 (2016).
[PubMed]

A. Pirati, R. Peeters, D. Smith, S. Lok, M. van Noordenburg, R. van Es, E. Verhoeven, H. Meijer, A. Minnaert, J. van der Horst, H. Meiling, J. Mallmann, C. Wagner, J. Stoeldraijer, G. Fisser, J. Finders, C. Zoldesi, U. Stamm, H. Boom, D. Brandt, D. Brown, I. Fomenkov, and M. Purvis, “EUV lithography performance for manufacturing: status and outlook,” Proc. SPIE 9776, 97760A (2016).

2015 (2)

2013 (1)

2012 (2)

P. Kim, K. Kim, and K. You, “Adaptive compensation for the nonlinearity error in a heterodyne interferometer,” J. Korean Phys. Soc. 61(11), 1759–1765 (2012).

C. Weichert, P. Köchert, R. Köning, J. Flügge, B. Andreas, U. Kuetgens, and A. Yacoot, “A heterodyne interferometer with periodic nonlinearities smaller than ±10 pm,” Meas. Sci. Technol. 23(9), 094005 (2012).

2010 (1)

H. L. Hsieh, J. Y. Lee, W. T. Wu, J. C. Chen, R. Deturche, and G. Lerondel, “Quasi-common-optical-path heterodyne grating interferometer for displacement measurement,” Meas. Sci. Technol. 21(11), 115304 (2010).

2009 (1)

W. Hou, Y. Zhang, and H. Hu, “A simple technique for elimination the nonlinearity of a heterodyne interferometer,” Meas. Sci. Technol. 20(10), 105303 (2009).

2008 (2)

T. B. Eom, J. A. Kim, C. S. Kang, B. C. Park, and J. W. Kim, “A simple phase-encoding electronics for reducing the nonlinearity error of a heterodyne interferometer,” Meas. Sci. Technol. 19(7), 075302 (2008).

R. F. Pease and S. Y. Chou, “Lithography and other patterning techniques for future electronics,” Proc. IEEE 96(2), 248–270 (2008).

2007 (1)

J. Y. Lee, H. Y. Chen, C. C. Hsu, and C. C. Wu, “Optical heterodyne grating interferometry for displacement measurement with subnanometric resolution,” Sens. Actuators A Phys. 137(1), 185–191 (2007).

2005 (1)

C. F. Kao, S. H. Lu, and M. H. Lu, “High resolution planar encoder by retro-reflection,” Rev. Sci. Instrum. 76(8), 085110 (2005).

2002 (3)

T. Schmitz and J. Beckwith, “Acousto-optic displacement-measuring interferometer: a new heterodyne interferometer with Angstrom-level periodic error,” J. Mod. Opt. 49(13), 2105–2114 (2002).

G. E. Sommargren, D. W. Phillion, M. A. Johnson, N. Q. Nguyen, A. Barty, F. J. Snell, D. R. Dillon, and L. S. Bradsher, “100-picometer interferometry for EUVL,” Proc. SPIE 4688, 316–328 (2002).

H. Schwenke, U. Neuschaefer-Rube, T. Pfeifer, and H. Kunzmann, “Optical methods for dimensional metrology in production engineering,” CIRP Ann. - Manuf. Techn. 51(2), 685–699 (2002).

2000 (1)

V. G. Badami and S. R. Patterson, “A frequency domain method for the measurement of nonlinearity in heterodyne interferometry,” Precis. Eng. 24(1), 41–49 (2000).

1999 (1)

1994 (1)

T. T. Saito, R. J. Wasley, I. F. Stowers, R. R. Donaldson, and D. C. Thompson, “Precision and manufacturing at the Lawrence Livermore National Laboratory,” Nasa 1(2), 81–89 (1994).

Andreas, B.

C. Weichert, P. Köchert, R. Köning, J. Flügge, B. Andreas, U. Kuetgens, and A. Yacoot, “A heterodyne interferometer with periodic nonlinearities smaller than ±10 pm,” Meas. Sci. Technol. 23(9), 094005 (2012).

Badami, V. G.

V. G. Badami and S. R. Patterson, “A frequency domain method for the measurement of nonlinearity in heterodyne interferometry,” Precis. Eng. 24(1), 41–49 (2000).

Bai, Y.

Barty, A.

G. E. Sommargren, D. W. Phillion, M. A. Johnson, N. Q. Nguyen, A. Barty, F. J. Snell, D. R. Dillon, and L. S. Bradsher, “100-picometer interferometry for EUVL,” Proc. SPIE 4688, 316–328 (2002).

Beckwith, J.

T. Schmitz and J. Beckwith, “Acousto-optic displacement-measuring interferometer: a new heterodyne interferometer with Angstrom-level periodic error,” J. Mod. Opt. 49(13), 2105–2114 (2002).

Boom, H.

A. Pirati, R. Peeters, D. Smith, S. Lok, M. van Noordenburg, R. van Es, E. Verhoeven, H. Meijer, A. Minnaert, J. van der Horst, H. Meiling, J. Mallmann, C. Wagner, J. Stoeldraijer, G. Fisser, J. Finders, C. Zoldesi, U. Stamm, H. Boom, D. Brandt, D. Brown, I. Fomenkov, and M. Purvis, “EUV lithography performance for manufacturing: status and outlook,” Proc. SPIE 9776, 97760A (2016).

Bradsher, L. S.

G. E. Sommargren, D. W. Phillion, M. A. Johnson, N. Q. Nguyen, A. Barty, F. J. Snell, D. R. Dillon, and L. S. Bradsher, “100-picometer interferometry for EUVL,” Proc. SPIE 4688, 316–328 (2002).

Brandt, D.

A. Pirati, R. Peeters, D. Smith, S. Lok, M. van Noordenburg, R. van Es, E. Verhoeven, H. Meijer, A. Minnaert, J. van der Horst, H. Meiling, J. Mallmann, C. Wagner, J. Stoeldraijer, G. Fisser, J. Finders, C. Zoldesi, U. Stamm, H. Boom, D. Brandt, D. Brown, I. Fomenkov, and M. Purvis, “EUV lithography performance for manufacturing: status and outlook,” Proc. SPIE 9776, 97760A (2016).

Brown, D.

A. Pirati, R. Peeters, D. Smith, S. Lok, M. van Noordenburg, R. van Es, E. Verhoeven, H. Meijer, A. Minnaert, J. van der Horst, H. Meiling, J. Mallmann, C. Wagner, J. Stoeldraijer, G. Fisser, J. Finders, C. Zoldesi, U. Stamm, H. Boom, D. Brandt, D. Brown, I. Fomenkov, and M. Purvis, “EUV lithography performance for manufacturing: status and outlook,” Proc. SPIE 9776, 97760A (2016).

Chen, B.

Chen, H. Y.

J. Y. Lee, H. Y. Chen, C. C. Hsu, and C. C. Wu, “Optical heterodyne grating interferometry for displacement measurement with subnanometric resolution,” Sens. Actuators A Phys. 137(1), 185–191 (2007).

Chen, J. C.

H. L. Hsieh, J. Y. Lee, W. T. Wu, J. C. Chen, R. Deturche, and G. Lerondel, “Quasi-common-optical-path heterodyne grating interferometer for displacement measurement,” Meas. Sci. Technol. 21(11), 115304 (2010).

Chen, W.

Chou, S. Y.

R. F. Pease and S. Y. Chou, “Lithography and other patterning techniques for future electronics,” Proc. IEEE 96(2), 248–270 (2008).

Deslattes, R. D.

Deturche, R.

H. L. Hsieh, J. Y. Lee, W. T. Wu, J. C. Chen, R. Deturche, and G. Lerondel, “Quasi-common-optical-path heterodyne grating interferometer for displacement measurement,” Meas. Sci. Technol. 21(11), 115304 (2010).

Dillon, D. R.

G. E. Sommargren, D. W. Phillion, M. A. Johnson, N. Q. Nguyen, A. Barty, F. J. Snell, D. R. Dillon, and L. S. Bradsher, “100-picometer interferometry for EUVL,” Proc. SPIE 4688, 316–328 (2002).

Donaldson, R. R.

T. T. Saito, R. J. Wasley, I. F. Stowers, R. R. Donaldson, and D. C. Thompson, “Precision and manufacturing at the Lawrence Livermore National Laboratory,” Nasa 1(2), 81–89 (1994).

Eom, T. B.

T. B. Eom, J. A. Kim, C. S. Kang, B. C. Park, and J. W. Kim, “A simple phase-encoding electronics for reducing the nonlinearity error of a heterodyne interferometer,” Meas. Sci. Technol. 19(7), 075302 (2008).

Finders, J.

A. Pirati, R. Peeters, D. Smith, S. Lok, M. van Noordenburg, R. van Es, E. Verhoeven, H. Meijer, A. Minnaert, J. van der Horst, H. Meiling, J. Mallmann, C. Wagner, J. Stoeldraijer, G. Fisser, J. Finders, C. Zoldesi, U. Stamm, H. Boom, D. Brandt, D. Brown, I. Fomenkov, and M. Purvis, “EUV lithography performance for manufacturing: status and outlook,” Proc. SPIE 9776, 97760A (2016).

Fisser, G.

A. Pirati, R. Peeters, D. Smith, S. Lok, M. van Noordenburg, R. van Es, E. Verhoeven, H. Meijer, A. Minnaert, J. van der Horst, H. Meiling, J. Mallmann, C. Wagner, J. Stoeldraijer, G. Fisser, J. Finders, C. Zoldesi, U. Stamm, H. Boom, D. Brandt, D. Brown, I. Fomenkov, and M. Purvis, “EUV lithography performance for manufacturing: status and outlook,” Proc. SPIE 9776, 97760A (2016).

Flügge, J.

C. Weichert, P. Köchert, R. Köning, J. Flügge, B. Andreas, U. Kuetgens, and A. Yacoot, “A heterodyne interferometer with periodic nonlinearities smaller than ±10 pm,” Meas. Sci. Technol. 23(9), 094005 (2012).

Fomenkov, I.

A. Pirati, R. Peeters, D. Smith, S. Lok, M. van Noordenburg, R. van Es, E. Verhoeven, H. Meijer, A. Minnaert, J. van der Horst, H. Meiling, J. Mallmann, C. Wagner, J. Stoeldraijer, G. Fisser, J. Finders, C. Zoldesi, U. Stamm, H. Boom, D. Brandt, D. Brown, I. Fomenkov, and M. Purvis, “EUV lithography performance for manufacturing: status and outlook,” Proc. SPIE 9776, 97760A (2016).

Hou, W.

W. Hou, Y. Zhang, and H. Hu, “A simple technique for elimination the nonlinearity of a heterodyne interferometer,” Meas. Sci. Technol. 20(10), 105303 (2009).

Hsieh, H. L.

Hsu, C. C.

J. Y. Lee, H. Y. Chen, C. C. Hsu, and C. C. Wu, “Optical heterodyne grating interferometry for displacement measurement with subnanometric resolution,” Sens. Actuators A Phys. 137(1), 185–191 (2007).

Hu, H.

W. Hou, Y. Zhang, and H. Hu, “A simple technique for elimination the nonlinearity of a heterodyne interferometer,” Meas. Sci. Technol. 20(10), 105303 (2009).

Hu, P.

Jiang, G. A.

Johnson, M. A.

G. E. Sommargren, D. W. Phillion, M. A. Johnson, N. Q. Nguyen, A. Barty, F. J. Snell, D. R. Dillon, and L. S. Bradsher, “100-picometer interferometry for EUVL,” Proc. SPIE 4688, 316–328 (2002).

Kang, C. S.

T. B. Eom, J. A. Kim, C. S. Kang, B. C. Park, and J. W. Kim, “A simple phase-encoding electronics for reducing the nonlinearity error of a heterodyne interferometer,” Meas. Sci. Technol. 19(7), 075302 (2008).

Kao, C. F.

C. F. Kao, S. H. Lu, and M. H. Lu, “High resolution planar encoder by retro-reflection,” Rev. Sci. Instrum. 76(8), 085110 (2005).

Kim, J. A.

T. B. Eom, J. A. Kim, C. S. Kang, B. C. Park, and J. W. Kim, “A simple phase-encoding electronics for reducing the nonlinearity error of a heterodyne interferometer,” Meas. Sci. Technol. 19(7), 075302 (2008).

Kim, J. W.

T. B. Eom, J. A. Kim, C. S. Kang, B. C. Park, and J. W. Kim, “A simple phase-encoding electronics for reducing the nonlinearity error of a heterodyne interferometer,” Meas. Sci. Technol. 19(7), 075302 (2008).

Kim, K.

P. Kim, K. Kim, and K. You, “Adaptive compensation for the nonlinearity error in a heterodyne interferometer,” J. Korean Phys. Soc. 61(11), 1759–1765 (2012).

Kim, P.

P. Kim, K. Kim, and K. You, “Adaptive compensation for the nonlinearity error in a heterodyne interferometer,” J. Korean Phys. Soc. 61(11), 1759–1765 (2012).

Köchert, P.

C. Weichert, P. Köchert, R. Köning, J. Flügge, B. Andreas, U. Kuetgens, and A. Yacoot, “A heterodyne interferometer with periodic nonlinearities smaller than ±10 pm,” Meas. Sci. Technol. 23(9), 094005 (2012).

Köning, R.

C. Weichert, P. Köchert, R. Köning, J. Flügge, B. Andreas, U. Kuetgens, and A. Yacoot, “A heterodyne interferometer with periodic nonlinearities smaller than ±10 pm,” Meas. Sci. Technol. 23(9), 094005 (2012).

Kuetgens, U.

C. Weichert, P. Köchert, R. Köning, J. Flügge, B. Andreas, U. Kuetgens, and A. Yacoot, “A heterodyne interferometer with periodic nonlinearities smaller than ±10 pm,” Meas. Sci. Technol. 23(9), 094005 (2012).

Kunzmann, H.

H. Schwenke, U. Neuschaefer-Rube, T. Pfeifer, and H. Kunzmann, “Optical methods for dimensional metrology in production engineering,” CIRP Ann. - Manuf. Techn. 51(2), 685–699 (2002).

Lawall, J.

Lee, J. Y.

J. Y. Lee and G. A. Jiang, “Displacement measurement using a wavelength-phase-shifting grating interferometer,” Opt. Express 21(21), 25553–25564 (2013).
[PubMed]

H. L. Hsieh, J. Y. Lee, W. T. Wu, J. C. Chen, R. Deturche, and G. Lerondel, “Quasi-common-optical-path heterodyne grating interferometer for displacement measurement,” Meas. Sci. Technol. 21(11), 115304 (2010).

J. Y. Lee, H. Y. Chen, C. C. Hsu, and C. C. Wu, “Optical heterodyne grating interferometry for displacement measurement with subnanometric resolution,” Sens. Actuators A Phys. 137(1), 185–191 (2007).

Lerondel, G.

H. L. Hsieh, J. Y. Lee, W. T. Wu, J. C. Chen, R. Deturche, and G. Lerondel, “Quasi-common-optical-path heterodyne grating interferometer for displacement measurement,” Meas. Sci. Technol. 21(11), 115304 (2010).

Li, Y.

Lok, S.

A. Pirati, R. Peeters, D. Smith, S. Lok, M. van Noordenburg, R. van Es, E. Verhoeven, H. Meijer, A. Minnaert, J. van der Horst, H. Meiling, J. Mallmann, C. Wagner, J. Stoeldraijer, G. Fisser, J. Finders, C. Zoldesi, U. Stamm, H. Boom, D. Brandt, D. Brown, I. Fomenkov, and M. Purvis, “EUV lithography performance for manufacturing: status and outlook,” Proc. SPIE 9776, 97760A (2016).

Lu, M. H.

C. F. Kao, S. H. Lu, and M. H. Lu, “High resolution planar encoder by retro-reflection,” Rev. Sci. Instrum. 76(8), 085110 (2005).

Lu, S. H.

C. F. Kao, S. H. Lu, and M. H. Lu, “High resolution planar encoder by retro-reflection,” Rev. Sci. Instrum. 76(8), 085110 (2005).

Mallmann, J.

A. Pirati, R. Peeters, D. Smith, S. Lok, M. van Noordenburg, R. van Es, E. Verhoeven, H. Meijer, A. Minnaert, J. van der Horst, H. Meiling, J. Mallmann, C. Wagner, J. Stoeldraijer, G. Fisser, J. Finders, C. Zoldesi, U. Stamm, H. Boom, D. Brandt, D. Brown, I. Fomenkov, and M. Purvis, “EUV lithography performance for manufacturing: status and outlook,” Proc. SPIE 9776, 97760A (2016).

Meijer, H.

A. Pirati, R. Peeters, D. Smith, S. Lok, M. van Noordenburg, R. van Es, E. Verhoeven, H. Meijer, A. Minnaert, J. van der Horst, H. Meiling, J. Mallmann, C. Wagner, J. Stoeldraijer, G. Fisser, J. Finders, C. Zoldesi, U. Stamm, H. Boom, D. Brandt, D. Brown, I. Fomenkov, and M. Purvis, “EUV lithography performance for manufacturing: status and outlook,” Proc. SPIE 9776, 97760A (2016).

Meiling, H.

A. Pirati, R. Peeters, D. Smith, S. Lok, M. van Noordenburg, R. van Es, E. Verhoeven, H. Meijer, A. Minnaert, J. van der Horst, H. Meiling, J. Mallmann, C. Wagner, J. Stoeldraijer, G. Fisser, J. Finders, C. Zoldesi, U. Stamm, H. Boom, D. Brandt, D. Brown, I. Fomenkov, and M. Purvis, “EUV lithography performance for manufacturing: status and outlook,” Proc. SPIE 9776, 97760A (2016).

Minnaert, A.

A. Pirati, R. Peeters, D. Smith, S. Lok, M. van Noordenburg, R. van Es, E. Verhoeven, H. Meijer, A. Minnaert, J. van der Horst, H. Meiling, J. Mallmann, C. Wagner, J. Stoeldraijer, G. Fisser, J. Finders, C. Zoldesi, U. Stamm, H. Boom, D. Brandt, D. Brown, I. Fomenkov, and M. Purvis, “EUV lithography performance for manufacturing: status and outlook,” Proc. SPIE 9776, 97760A (2016).

Neuschaefer-Rube, U.

H. Schwenke, U. Neuschaefer-Rube, T. Pfeifer, and H. Kunzmann, “Optical methods for dimensional metrology in production engineering,” CIRP Ann. - Manuf. Techn. 51(2), 685–699 (2002).

Nguyen, N. Q.

G. E. Sommargren, D. W. Phillion, M. A. Johnson, N. Q. Nguyen, A. Barty, F. J. Snell, D. R. Dillon, and L. S. Bradsher, “100-picometer interferometry for EUVL,” Proc. SPIE 4688, 316–328 (2002).

Pan, S. W.

Park, B. C.

T. B. Eom, J. A. Kim, C. S. Kang, B. C. Park, and J. W. Kim, “A simple phase-encoding electronics for reducing the nonlinearity error of a heterodyne interferometer,” Meas. Sci. Technol. 19(7), 075302 (2008).

Patterson, S. R.

V. G. Badami and S. R. Patterson, “A frequency domain method for the measurement of nonlinearity in heterodyne interferometry,” Precis. Eng. 24(1), 41–49 (2000).

Pease, R. F.

R. F. Pease and S. Y. Chou, “Lithography and other patterning techniques for future electronics,” Proc. IEEE 96(2), 248–270 (2008).

Peeters, R.

A. Pirati, R. Peeters, D. Smith, S. Lok, M. van Noordenburg, R. van Es, E. Verhoeven, H. Meijer, A. Minnaert, J. van der Horst, H. Meiling, J. Mallmann, C. Wagner, J. Stoeldraijer, G. Fisser, J. Finders, C. Zoldesi, U. Stamm, H. Boom, D. Brandt, D. Brown, I. Fomenkov, and M. Purvis, “EUV lithography performance for manufacturing: status and outlook,” Proc. SPIE 9776, 97760A (2016).

Pfeifer, T.

H. Schwenke, U. Neuschaefer-Rube, T. Pfeifer, and H. Kunzmann, “Optical methods for dimensional metrology in production engineering,” CIRP Ann. - Manuf. Techn. 51(2), 685–699 (2002).

Phillion, D. W.

G. E. Sommargren, D. W. Phillion, M. A. Johnson, N. Q. Nguyen, A. Barty, F. J. Snell, D. R. Dillon, and L. S. Bradsher, “100-picometer interferometry for EUVL,” Proc. SPIE 4688, 316–328 (2002).

Pirati, A.

A. Pirati, R. Peeters, D. Smith, S. Lok, M. van Noordenburg, R. van Es, E. Verhoeven, H. Meijer, A. Minnaert, J. van der Horst, H. Meiling, J. Mallmann, C. Wagner, J. Stoeldraijer, G. Fisser, J. Finders, C. Zoldesi, U. Stamm, H. Boom, D. Brandt, D. Brown, I. Fomenkov, and M. Purvis, “EUV lithography performance for manufacturing: status and outlook,” Proc. SPIE 9776, 97760A (2016).

Purvis, M.

A. Pirati, R. Peeters, D. Smith, S. Lok, M. van Noordenburg, R. van Es, E. Verhoeven, H. Meijer, A. Minnaert, J. van der Horst, H. Meiling, J. Mallmann, C. Wagner, J. Stoeldraijer, G. Fisser, J. Finders, C. Zoldesi, U. Stamm, H. Boom, D. Brandt, D. Brown, I. Fomenkov, and M. Purvis, “EUV lithography performance for manufacturing: status and outlook,” Proc. SPIE 9776, 97760A (2016).

Saito, T. T.

T. T. Saito, R. J. Wasley, I. F. Stowers, R. R. Donaldson, and D. C. Thompson, “Precision and manufacturing at the Lawrence Livermore National Laboratory,” Nasa 1(2), 81–89 (1994).

Schmitz, T.

T. Schmitz and J. Beckwith, “Acousto-optic displacement-measuring interferometer: a new heterodyne interferometer with Angstrom-level periodic error,” J. Mod. Opt. 49(13), 2105–2114 (2002).

Schwenke, H.

H. Schwenke, U. Neuschaefer-Rube, T. Pfeifer, and H. Kunzmann, “Optical methods for dimensional metrology in production engineering,” CIRP Ann. - Manuf. Techn. 51(2), 685–699 (2002).

Smith, D.

A. Pirati, R. Peeters, D. Smith, S. Lok, M. van Noordenburg, R. van Es, E. Verhoeven, H. Meijer, A. Minnaert, J. van der Horst, H. Meiling, J. Mallmann, C. Wagner, J. Stoeldraijer, G. Fisser, J. Finders, C. Zoldesi, U. Stamm, H. Boom, D. Brandt, D. Brown, I. Fomenkov, and M. Purvis, “EUV lithography performance for manufacturing: status and outlook,” Proc. SPIE 9776, 97760A (2016).

Snell, F. J.

G. E. Sommargren, D. W. Phillion, M. A. Johnson, N. Q. Nguyen, A. Barty, F. J. Snell, D. R. Dillon, and L. S. Bradsher, “100-picometer interferometry for EUVL,” Proc. SPIE 4688, 316–328 (2002).

Sommargren, G. E.

G. E. Sommargren, D. W. Phillion, M. A. Johnson, N. Q. Nguyen, A. Barty, F. J. Snell, D. R. Dillon, and L. S. Bradsher, “100-picometer interferometry for EUVL,” Proc. SPIE 4688, 316–328 (2002).

Stamm, U.

A. Pirati, R. Peeters, D. Smith, S. Lok, M. van Noordenburg, R. van Es, E. Verhoeven, H. Meijer, A. Minnaert, J. van der Horst, H. Meiling, J. Mallmann, C. Wagner, J. Stoeldraijer, G. Fisser, J. Finders, C. Zoldesi, U. Stamm, H. Boom, D. Brandt, D. Brown, I. Fomenkov, and M. Purvis, “EUV lithography performance for manufacturing: status and outlook,” Proc. SPIE 9776, 97760A (2016).

Stoeldraijer, J.

A. Pirati, R. Peeters, D. Smith, S. Lok, M. van Noordenburg, R. van Es, E. Verhoeven, H. Meijer, A. Minnaert, J. van der Horst, H. Meiling, J. Mallmann, C. Wagner, J. Stoeldraijer, G. Fisser, J. Finders, C. Zoldesi, U. Stamm, H. Boom, D. Brandt, D. Brown, I. Fomenkov, and M. Purvis, “EUV lithography performance for manufacturing: status and outlook,” Proc. SPIE 9776, 97760A (2016).

Stowers, I. F.

T. T. Saito, R. J. Wasley, I. F. Stowers, R. R. Donaldson, and D. C. Thompson, “Precision and manufacturing at the Lawrence Livermore National Laboratory,” Nasa 1(2), 81–89 (1994).

Tan, J.

Thompson, D. C.

T. T. Saito, R. J. Wasley, I. F. Stowers, R. R. Donaldson, and D. C. Thompson, “Precision and manufacturing at the Lawrence Livermore National Laboratory,” Nasa 1(2), 81–89 (1994).

van der Horst, J.

A. Pirati, R. Peeters, D. Smith, S. Lok, M. van Noordenburg, R. van Es, E. Verhoeven, H. Meijer, A. Minnaert, J. van der Horst, H. Meiling, J. Mallmann, C. Wagner, J. Stoeldraijer, G. Fisser, J. Finders, C. Zoldesi, U. Stamm, H. Boom, D. Brandt, D. Brown, I. Fomenkov, and M. Purvis, “EUV lithography performance for manufacturing: status and outlook,” Proc. SPIE 9776, 97760A (2016).

van Es, R.

A. Pirati, R. Peeters, D. Smith, S. Lok, M. van Noordenburg, R. van Es, E. Verhoeven, H. Meijer, A. Minnaert, J. van der Horst, H. Meiling, J. Mallmann, C. Wagner, J. Stoeldraijer, G. Fisser, J. Finders, C. Zoldesi, U. Stamm, H. Boom, D. Brandt, D. Brown, I. Fomenkov, and M. Purvis, “EUV lithography performance for manufacturing: status and outlook,” Proc. SPIE 9776, 97760A (2016).

van Noordenburg, M.

A. Pirati, R. Peeters, D. Smith, S. Lok, M. van Noordenburg, R. van Es, E. Verhoeven, H. Meijer, A. Minnaert, J. van der Horst, H. Meiling, J. Mallmann, C. Wagner, J. Stoeldraijer, G. Fisser, J. Finders, C. Zoldesi, U. Stamm, H. Boom, D. Brandt, D. Brown, I. Fomenkov, and M. Purvis, “EUV lithography performance for manufacturing: status and outlook,” Proc. SPIE 9776, 97760A (2016).

Verhoeven, E.

A. Pirati, R. Peeters, D. Smith, S. Lok, M. van Noordenburg, R. van Es, E. Verhoeven, H. Meijer, A. Minnaert, J. van der Horst, H. Meiling, J. Mallmann, C. Wagner, J. Stoeldraijer, G. Fisser, J. Finders, C. Zoldesi, U. Stamm, H. Boom, D. Brandt, D. Brown, I. Fomenkov, and M. Purvis, “EUV lithography performance for manufacturing: status and outlook,” Proc. SPIE 9776, 97760A (2016).

Wagner, C.

A. Pirati, R. Peeters, D. Smith, S. Lok, M. van Noordenburg, R. van Es, E. Verhoeven, H. Meijer, A. Minnaert, J. van der Horst, H. Meiling, J. Mallmann, C. Wagner, J. Stoeldraijer, G. Fisser, J. Finders, C. Zoldesi, U. Stamm, H. Boom, D. Brandt, D. Brown, I. Fomenkov, and M. Purvis, “EUV lithography performance for manufacturing: status and outlook,” Proc. SPIE 9776, 97760A (2016).

Wasley, R. J.

T. T. Saito, R. J. Wasley, I. F. Stowers, R. R. Donaldson, and D. C. Thompson, “Precision and manufacturing at the Lawrence Livermore National Laboratory,” Nasa 1(2), 81–89 (1994).

Wei, H.

Weichert, C.

C. Weichert, P. Köchert, R. Köning, J. Flügge, B. Andreas, U. Kuetgens, and A. Yacoot, “A heterodyne interferometer with periodic nonlinearities smaller than ±10 pm,” Meas. Sci. Technol. 23(9), 094005 (2012).

Wu, C. C.

J. Y. Lee, H. Y. Chen, C. C. Hsu, and C. C. Wu, “Optical heterodyne grating interferometry for displacement measurement with subnanometric resolution,” Sens. Actuators A Phys. 137(1), 185–191 (2007).

Wu, C. M.

Wu, G.

Wu, W. T.

H. L. Hsieh, J. Y. Lee, W. T. Wu, J. C. Chen, R. Deturche, and G. Lerondel, “Quasi-common-optical-path heterodyne grating interferometer for displacement measurement,” Meas. Sci. Technol. 21(11), 115304 (2010).

Xie, J.

Yacoot, A.

C. Weichert, P. Köchert, R. Köning, J. Flügge, B. Andreas, U. Kuetgens, and A. Yacoot, “A heterodyne interferometer with periodic nonlinearities smaller than ±10 pm,” Meas. Sci. Technol. 23(9), 094005 (2012).

Yan, L.

You, K.

P. Kim, K. Kim, and K. You, “Adaptive compensation for the nonlinearity error in a heterodyne interferometer,” J. Korean Phys. Soc. 61(11), 1759–1765 (2012).

Zhang, S.

Zhang, Y.

W. Hou, Y. Zhang, and H. Hu, “A simple technique for elimination the nonlinearity of a heterodyne interferometer,” Meas. Sci. Technol. 20(10), 105303 (2009).

Zhao, J.

Zhao, S.

Zhu, M.

Zoldesi, C.

A. Pirati, R. Peeters, D. Smith, S. Lok, M. van Noordenburg, R. van Es, E. Verhoeven, H. Meijer, A. Minnaert, J. van der Horst, H. Meiling, J. Mallmann, C. Wagner, J. Stoeldraijer, G. Fisser, J. Finders, C. Zoldesi, U. Stamm, H. Boom, D. Brandt, D. Brown, I. Fomenkov, and M. Purvis, “EUV lithography performance for manufacturing: status and outlook,” Proc. SPIE 9776, 97760A (2016).

Appl. Opt. (2)

CIRP Ann. - Manuf. Techn. (1)

H. Schwenke, U. Neuschaefer-Rube, T. Pfeifer, and H. Kunzmann, “Optical methods for dimensional metrology in production engineering,” CIRP Ann. - Manuf. Techn. 51(2), 685–699 (2002).

J. Korean Phys. Soc. (1)

P. Kim, K. Kim, and K. You, “Adaptive compensation for the nonlinearity error in a heterodyne interferometer,” J. Korean Phys. Soc. 61(11), 1759–1765 (2012).

J. Mod. Opt. (1)

T. Schmitz and J. Beckwith, “Acousto-optic displacement-measuring interferometer: a new heterodyne interferometer with Angstrom-level periodic error,” J. Mod. Opt. 49(13), 2105–2114 (2002).

Meas. Sci. Technol. (4)

H. L. Hsieh, J. Y. Lee, W. T. Wu, J. C. Chen, R. Deturche, and G. Lerondel, “Quasi-common-optical-path heterodyne grating interferometer for displacement measurement,” Meas. Sci. Technol. 21(11), 115304 (2010).

C. Weichert, P. Köchert, R. Köning, J. Flügge, B. Andreas, U. Kuetgens, and A. Yacoot, “A heterodyne interferometer with periodic nonlinearities smaller than ±10 pm,” Meas. Sci. Technol. 23(9), 094005 (2012).

T. B. Eom, J. A. Kim, C. S. Kang, B. C. Park, and J. W. Kim, “A simple phase-encoding electronics for reducing the nonlinearity error of a heterodyne interferometer,” Meas. Sci. Technol. 19(7), 075302 (2008).

W. Hou, Y. Zhang, and H. Hu, “A simple technique for elimination the nonlinearity of a heterodyne interferometer,” Meas. Sci. Technol. 20(10), 105303 (2009).

Nasa (1)

T. T. Saito, R. J. Wasley, I. F. Stowers, R. R. Donaldson, and D. C. Thompson, “Precision and manufacturing at the Lawrence Livermore National Laboratory,” Nasa 1(2), 81–89 (1994).

Opt. Express (5)

Precis. Eng. (1)

V. G. Badami and S. R. Patterson, “A frequency domain method for the measurement of nonlinearity in heterodyne interferometry,” Precis. Eng. 24(1), 41–49 (2000).

Proc. IEEE (1)

R. F. Pease and S. Y. Chou, “Lithography and other patterning techniques for future electronics,” Proc. IEEE 96(2), 248–270 (2008).

Proc. SPIE (2)

G. E. Sommargren, D. W. Phillion, M. A. Johnson, N. Q. Nguyen, A. Barty, F. J. Snell, D. R. Dillon, and L. S. Bradsher, “100-picometer interferometry for EUVL,” Proc. SPIE 4688, 316–328 (2002).

A. Pirati, R. Peeters, D. Smith, S. Lok, M. van Noordenburg, R. van Es, E. Verhoeven, H. Meijer, A. Minnaert, J. van der Horst, H. Meiling, J. Mallmann, C. Wagner, J. Stoeldraijer, G. Fisser, J. Finders, C. Zoldesi, U. Stamm, H. Boom, D. Brandt, D. Brown, I. Fomenkov, and M. Purvis, “EUV lithography performance for manufacturing: status and outlook,” Proc. SPIE 9776, 97760A (2016).

Rev. Sci. Instrum. (1)

C. F. Kao, S. H. Lu, and M. H. Lu, “High resolution planar encoder by retro-reflection,” Rev. Sci. Instrum. 76(8), 085110 (2005).

Sens. Actuators A Phys. (1)

J. Y. Lee, H. Y. Chen, C. C. Hsu, and C. C. Wu, “Optical heterodyne grating interferometry for displacement measurement with subnanometric resolution,” Sens. Actuators A Phys. 137(1), 185–191 (2007).

Other (3)

SIOS Meßtechnik GmbH datasheets, “SP-NG Series Laser Interferometer,” (SIOS Meßtechnik GmbH, 2017), http://www.sios-de.com/wp-content/uploads/2017/08/SP-NG_engl.pdf .

J. D. Ellis, Field Guide to Displacement Measuring Interferometry (SPIE Press, 2014).

P. J. de Groot, V. G. Badami, and J. Liesener, “Concepts and geometries for the next generation of precision heterodyne optical encoders,” in Proceedings of American Society for Precision Engineering. (Academic, 2016), pp. 146–149.

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Figures (5)

Fig. 1
Fig. 1 PBS leakage in a heterodyne grating interferometer. (a) Comparison of common-path (COP) grating interferometer with an actual and an ideal PBS. (b) Displacement chart of the actual and measured displacement in simulation.

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Fig. 2
Fig. 2 Optical configuration of proposed grating interferometer.

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Fig. 3
Fig. 3 Diagrams of the experiments for testing system performance. (a) Comparison experiment of the complete proposed grating interferometer and a commercial heterodyne interferometer. (b) Comparison experiment of a spatially separated grating interferometer and a COP configuration.

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Fig. 4
Fig. 4 Measurement result of functional experiment tests. (a) An advance and return movement. (b) Advance movements at different velocities.

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Fig. 5
Fig. 5 Measurement results of the frequency spectrum analysis experiment. (a) Motionless spectrum. (b) Moving spectrum of the COP grating interferometer. (c) Moving spectrum of spatially separated grating interferometer.

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Tables (1)

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Table 1 Nonlinearity Results of Constant Speed Stage

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Equations (8)

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i m ∝cos[ ( ω 1 − ω 2 )t+( ϕ +1 − ϕ −1 ) ],
ϕ k = 2kπ⋅Δx g = 2kπ⋅vt g ,
i m ∝cos[ ( ω 1 − ω 2 )t+ 4πv g ⋅t ].
i m ∝ABcos[ ( ω 1 − ω 2 )t+ 4πv g ⋅t ]+( Ab+aB )cos[ ( ω 1 − ω 2 )t ], +abcos[ ( ω 1 − ω 2 )t− 4πv g ⋅t ]
Δ f k = d ϕ k dt = 2π⋅k⋅v g .
Δ x error = g⋅ 10 −ΔdB/20 2π⋅FF ,
i r ∝cos( ω 1 − ω 2 )t.
i m ∝cos[ ( ω 1 − ω 2 )t+2( ϕ +1 − ϕ −1 ) ].

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