Abstract

We present a common-path phase-shifting interferometer in which photonic crystal polarizers (PCPs) are utilized as a reference mirror and a phase shifter, allowing ultracompact and highly sensitive optics. When a laser beam polarized at 45° relative to the optical axis of the PCP-based reference mirror is incident, the polarization component parallel to the optical axis (s-polarized beam) is reflected and used as a reference beam. The perpendicular component (p-polarized beam) passes through the PCP coupled with a quarter-wave plate (QWP) and serves as a probe beam. This beam, with its polarization transformed in the sequence p, right-circular, s, left-circular, and p, irradiates the sample surface twice, doubling the phase change due to displacement of the sample. The probe beam is then retransmitted through the PCP, where it recombines with the reference beam. Four interferogram channels in phase quadrature are generated using a newly developed phase shifter, composed of a QWP and a monolithically integrated array of four PCPs. Preliminary experiments demonstrate that the PCPs perform successfully as a reference mirror and a phase shifter, and that the interferometer has a remarkable displacement sensitivity, as low as 40pm.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. Malacara, Optical Shop Testing, 2nd ed. (Wiley, 1992).
  2. C. Chou, J.-C. Shyu, Y.-C. Huang, and C.-K. Yuan, “Common-path optical heterodyne profilometer: a configuration,” Appl. Opt. 37, 4137-4142 (1998).
    [CrossRef]
  3. T. Nakata and T. Ninomiya, “A charge-coupled-device-based heterodyne technique for parallel photodisplacement imaging,” J. Appl. Phys. 96, 6970-6980 (2004).
    [CrossRef]
  4. P. Carré, “Installation et utilisation du comparateur photoélectrique et interférential du Bureau International des Poids et Mesures,” Metrologia 2, 13-23 (1966).
    [CrossRef]
  5. R. Crane, “Interference phase measurement,” Appl. Opt. 8, 538-542 (1969).
  6. J. H. Bruning, D. R. Heriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Appl. Opt. 13, 2693-2703 (1974).
    [CrossRef] [PubMed]
  7. J. C. Wyant, “Use of an ac heterodyne lateral shear interferometer with real-time wavefront correction systems,” Appl. Opt. 14, 2622-2626 (1975).
    [CrossRef] [PubMed]
  8. H. Kadono, N. Takai, and T. Asakura, “New common-path phase shifting interferometer using a polarization technique,” Appl. Opt. 26, 898-904 (1987).
    [CrossRef] [PubMed]
  9. O. K. Kwon, “Multichannel phase-shifted interferometer,” Opt. Lett. 9, 59-61 (1984).
    [CrossRef] [PubMed]
  10. C. R. Mercer, K. Creath, and N. Rashidnia, “A phase-stepped point diffraction interferometer using liquid crystals,” Proc. SPIE 2544, 87-93 (1995).
  11. H. Medecki, E. Tejnil, K. A. Goldberg, and J. Bokor, “Phase-shifting point diffraction interferometer,” Opt. Lett. 21, 1526-1528 (1996).
    [CrossRef] [PubMed]
  12. J. Huang, T. Honda, N. Ohyama, and J. Tsujiuchi, “Fringe scanning scatter plate interferometer using a polarized light,” Opt. Commun. 68, 235-238 (1988).
    [CrossRef]
  13. D.-C. Su and L.-H. Shyu, “Phase-shifting scatter plate interferometer using a polarization technique,” J. Mod. Opt. 38, 951-959 (1991).
    [CrossRef]
  14. M. B. North-Morris, J. VanDelden, and J. C. Wyant, “Phase-shifting birefringent scatterplate interferometer,” Appl. Opt. 41, 668-677 (2002).
    [CrossRef] [PubMed]
  15. C. Zhao, D. Kang, and J. H. Burge, “Effects of birefringence on Fizeau interferometry that uses a polarization phase-shifting technique,” Appl. Opt. 44, 7548-7553 (2005).
    [CrossRef] [PubMed]
  16. R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 23, 361-364 (1984).
  17. T. Keem, S. Gonda, I. Misumi, Q. Huang, and T. Kurosawa, “Simple, real-time method for removing the cyclic error of a homodyne interferometer with a quadrature detector system,” Appl. Opt. 44, 3492-3498 (2005).
    [CrossRef] [PubMed]
  18. J. Millerd, N. Brock, J. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304-314 (2004).
    [CrossRef]
  19. M. Novak, J. Millerd, N. Brock, M. B. North-Morris, J. Hayes, and J. C. Wyant, “Analysis of a micropolarizer array-based simultaneous phase-shifting interferometer,” Appl. Opt. 44, 6861-6868 (2005).
    [CrossRef] [PubMed]
  20. T. Nakata and M. Watanabe, “Common-path double-pass optical interferometry using a wire-grid polarizer as a reference mirror,” Opt. Rev. 15, 276-279 (2008).
    [CrossRef]
  21. B. Schnabel, E. Kley, and F. Wyrowski, “Study on polarizing visible light by subwavelength-period metal-stripe gratings,” Opt. Eng. 38, 220-226 (1999).
    [CrossRef]
  22. X. J. Yu and H. S. Kwok, “Optical wire-grid polarizers at oblique angles of incidence,” J. Appl. Phys. 93, 4407-4412(2003).
    [CrossRef]
  23. M. Xu, H. P. Urbach, D. K. G. de Bore, and H. J. Cornelissen, “Wire-grid diffraction gratings used as polarizing beam splitter for visible light and applied in liquid crystal on silicon,” Opt. Express 13, 2303-2320 (2005).
    [CrossRef] [PubMed]
  24. S. Kawakami, “Fabrication of submicrometer 3D periodic structures composed of Si/SiO2,” Electron. Lett. 33, 1260-1261 (1997).
    [CrossRef]
  25. S. Kawakami, T. Kawashima, and T. Sato, “Mechanism of shape formation of three-dimensional periodic nanostructures by bias sputtering,” Appl. Phys. Lett. 74, 463-465(1999).
    [CrossRef]
  26. Y. Ohtera, T. Sato, T. Kawashima, T. Tamamura, and S. Kawakami, “Photonic crystal polarization splitters,” Electron. Lett. 35, 1271-1272 (1999).
    [CrossRef]
  27. T. Sato, K. Miura, N. Ishino, Y. Ohtera, T. Tamamura, and S. Kawakami, “Photonic crystals for the visible range fabricated by autocloning technique and their application,” Opt. Quantum Electron. 34, 63-70 (2002).
    [CrossRef]
  28. T. Sato, T. Araki, Y. Sasaki, T. Tsuru, T. Tadokoro, and S. Kawakami, “Compact ellipsometer employing a static polarimeter module with arrayed polarizer and wave-plate elements,” Appl. Opt. 46, 4963-4967 (2007).
    [CrossRef] [PubMed]

2008 (1)

T. Nakata and M. Watanabe, “Common-path double-pass optical interferometry using a wire-grid polarizer as a reference mirror,” Opt. Rev. 15, 276-279 (2008).
[CrossRef]

2007 (1)

2005 (4)

2004 (2)

T. Nakata and T. Ninomiya, “A charge-coupled-device-based heterodyne technique for parallel photodisplacement imaging,” J. Appl. Phys. 96, 6970-6980 (2004).
[CrossRef]

J. Millerd, N. Brock, J. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304-314 (2004).
[CrossRef]

2003 (1)

X. J. Yu and H. S. Kwok, “Optical wire-grid polarizers at oblique angles of incidence,” J. Appl. Phys. 93, 4407-4412(2003).
[CrossRef]

2002 (2)

T. Sato, K. Miura, N. Ishino, Y. Ohtera, T. Tamamura, and S. Kawakami, “Photonic crystals for the visible range fabricated by autocloning technique and their application,” Opt. Quantum Electron. 34, 63-70 (2002).
[CrossRef]

M. B. North-Morris, J. VanDelden, and J. C. Wyant, “Phase-shifting birefringent scatterplate interferometer,” Appl. Opt. 41, 668-677 (2002).
[CrossRef] [PubMed]

1999 (3)

S. Kawakami, T. Kawashima, and T. Sato, “Mechanism of shape formation of three-dimensional periodic nanostructures by bias sputtering,” Appl. Phys. Lett. 74, 463-465(1999).
[CrossRef]

Y. Ohtera, T. Sato, T. Kawashima, T. Tamamura, and S. Kawakami, “Photonic crystal polarization splitters,” Electron. Lett. 35, 1271-1272 (1999).
[CrossRef]

B. Schnabel, E. Kley, and F. Wyrowski, “Study on polarizing visible light by subwavelength-period metal-stripe gratings,” Opt. Eng. 38, 220-226 (1999).
[CrossRef]

1998 (1)

1997 (1)

S. Kawakami, “Fabrication of submicrometer 3D periodic structures composed of Si/SiO2,” Electron. Lett. 33, 1260-1261 (1997).
[CrossRef]

1996 (1)

1995 (1)

C. R. Mercer, K. Creath, and N. Rashidnia, “A phase-stepped point diffraction interferometer using liquid crystals,” Proc. SPIE 2544, 87-93 (1995).

1991 (1)

D.-C. Su and L.-H. Shyu, “Phase-shifting scatter plate interferometer using a polarization technique,” J. Mod. Opt. 38, 951-959 (1991).
[CrossRef]

1988 (1)

J. Huang, T. Honda, N. Ohyama, and J. Tsujiuchi, “Fringe scanning scatter plate interferometer using a polarized light,” Opt. Commun. 68, 235-238 (1988).
[CrossRef]

1987 (1)

1984 (2)

R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 23, 361-364 (1984).

O. K. Kwon, “Multichannel phase-shifted interferometer,” Opt. Lett. 9, 59-61 (1984).
[CrossRef] [PubMed]

1975 (1)

1974 (1)

1969 (1)

R. Crane, “Interference phase measurement,” Appl. Opt. 8, 538-542 (1969).

1966 (1)

P. Carré, “Installation et utilisation du comparateur photoélectrique et interférential du Bureau International des Poids et Mesures,” Metrologia 2, 13-23 (1966).
[CrossRef]

Araki, T.

Asakura, T.

Bokor, J.

Brangaccio, D. J.

Brock, N.

M. Novak, J. Millerd, N. Brock, M. B. North-Morris, J. Hayes, and J. C. Wyant, “Analysis of a micropolarizer array-based simultaneous phase-shifting interferometer,” Appl. Opt. 44, 6861-6868 (2005).
[CrossRef] [PubMed]

J. Millerd, N. Brock, J. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304-314 (2004).
[CrossRef]

Bruning, J. H.

Burge, J. H.

Carré, P.

P. Carré, “Installation et utilisation du comparateur photoélectrique et interférential du Bureau International des Poids et Mesures,” Metrologia 2, 13-23 (1966).
[CrossRef]

Chou, C.

Cornelissen, H. J.

Crane, R.

R. Crane, “Interference phase measurement,” Appl. Opt. 8, 538-542 (1969).

Creath, K.

C. R. Mercer, K. Creath, and N. Rashidnia, “A phase-stepped point diffraction interferometer using liquid crystals,” Proc. SPIE 2544, 87-93 (1995).

de Bore, D. K. G.

Gallagher, J. E.

Goldberg, K. A.

Gonda, S.

Hayes, J.

M. Novak, J. Millerd, N. Brock, M. B. North-Morris, J. Hayes, and J. C. Wyant, “Analysis of a micropolarizer array-based simultaneous phase-shifting interferometer,” Appl. Opt. 44, 6861-6868 (2005).
[CrossRef] [PubMed]

J. Millerd, N. Brock, J. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304-314 (2004).
[CrossRef]

Heriott, D. R.

Honda, T.

J. Huang, T. Honda, N. Ohyama, and J. Tsujiuchi, “Fringe scanning scatter plate interferometer using a polarized light,” Opt. Commun. 68, 235-238 (1988).
[CrossRef]

Huang, J.

J. Huang, T. Honda, N. Ohyama, and J. Tsujiuchi, “Fringe scanning scatter plate interferometer using a polarized light,” Opt. Commun. 68, 235-238 (1988).
[CrossRef]

Huang, Q.

Huang, Y.-C.

Ishino, N.

T. Sato, K. Miura, N. Ishino, Y. Ohtera, T. Tamamura, and S. Kawakami, “Photonic crystals for the visible range fabricated by autocloning technique and their application,” Opt. Quantum Electron. 34, 63-70 (2002).
[CrossRef]

Kadono, H.

Kang, D.

Kawakami, S.

T. Sato, T. Araki, Y. Sasaki, T. Tsuru, T. Tadokoro, and S. Kawakami, “Compact ellipsometer employing a static polarimeter module with arrayed polarizer and wave-plate elements,” Appl. Opt. 46, 4963-4967 (2007).
[CrossRef] [PubMed]

T. Sato, K. Miura, N. Ishino, Y. Ohtera, T. Tamamura, and S. Kawakami, “Photonic crystals for the visible range fabricated by autocloning technique and their application,” Opt. Quantum Electron. 34, 63-70 (2002).
[CrossRef]

S. Kawakami, T. Kawashima, and T. Sato, “Mechanism of shape formation of three-dimensional periodic nanostructures by bias sputtering,” Appl. Phys. Lett. 74, 463-465(1999).
[CrossRef]

Y. Ohtera, T. Sato, T. Kawashima, T. Tamamura, and S. Kawakami, “Photonic crystal polarization splitters,” Electron. Lett. 35, 1271-1272 (1999).
[CrossRef]

S. Kawakami, “Fabrication of submicrometer 3D periodic structures composed of Si/SiO2,” Electron. Lett. 33, 1260-1261 (1997).
[CrossRef]

Kawashima, T.

Y. Ohtera, T. Sato, T. Kawashima, T. Tamamura, and S. Kawakami, “Photonic crystal polarization splitters,” Electron. Lett. 35, 1271-1272 (1999).
[CrossRef]

S. Kawakami, T. Kawashima, and T. Sato, “Mechanism of shape formation of three-dimensional periodic nanostructures by bias sputtering,” Appl. Phys. Lett. 74, 463-465(1999).
[CrossRef]

Keem, T.

Kley, E.

B. Schnabel, E. Kley, and F. Wyrowski, “Study on polarizing visible light by subwavelength-period metal-stripe gratings,” Opt. Eng. 38, 220-226 (1999).
[CrossRef]

Kurosawa, T.

Kwok, H. S.

X. J. Yu and H. S. Kwok, “Optical wire-grid polarizers at oblique angles of incidence,” J. Appl. Phys. 93, 4407-4412(2003).
[CrossRef]

Kwon, O. K.

Malacara, D.

D. Malacara, Optical Shop Testing, 2nd ed. (Wiley, 1992).

Medecki, H.

Mercer, C. R.

C. R. Mercer, K. Creath, and N. Rashidnia, “A phase-stepped point diffraction interferometer using liquid crystals,” Proc. SPIE 2544, 87-93 (1995).

Millerd, J.

M. Novak, J. Millerd, N. Brock, M. B. North-Morris, J. Hayes, and J. C. Wyant, “Analysis of a micropolarizer array-based simultaneous phase-shifting interferometer,” Appl. Opt. 44, 6861-6868 (2005).
[CrossRef] [PubMed]

J. Millerd, N. Brock, J. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304-314 (2004).
[CrossRef]

Misumi, I.

Miura, K.

T. Sato, K. Miura, N. Ishino, Y. Ohtera, T. Tamamura, and S. Kawakami, “Photonic crystals for the visible range fabricated by autocloning technique and their application,” Opt. Quantum Electron. 34, 63-70 (2002).
[CrossRef]

Moore, R.

R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 23, 361-364 (1984).

Nakata, T.

T. Nakata and M. Watanabe, “Common-path double-pass optical interferometry using a wire-grid polarizer as a reference mirror,” Opt. Rev. 15, 276-279 (2008).
[CrossRef]

T. Nakata and T. Ninomiya, “A charge-coupled-device-based heterodyne technique for parallel photodisplacement imaging,” J. Appl. Phys. 96, 6970-6980 (2004).
[CrossRef]

Ninomiya, T.

T. Nakata and T. Ninomiya, “A charge-coupled-device-based heterodyne technique for parallel photodisplacement imaging,” J. Appl. Phys. 96, 6970-6980 (2004).
[CrossRef]

North-Morris, M. B.

Novak, M.

M. Novak, J. Millerd, N. Brock, M. B. North-Morris, J. Hayes, and J. C. Wyant, “Analysis of a micropolarizer array-based simultaneous phase-shifting interferometer,” Appl. Opt. 44, 6861-6868 (2005).
[CrossRef] [PubMed]

J. Millerd, N. Brock, J. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304-314 (2004).
[CrossRef]

Ohtera, Y.

T. Sato, K. Miura, N. Ishino, Y. Ohtera, T. Tamamura, and S. Kawakami, “Photonic crystals for the visible range fabricated by autocloning technique and their application,” Opt. Quantum Electron. 34, 63-70 (2002).
[CrossRef]

Y. Ohtera, T. Sato, T. Kawashima, T. Tamamura, and S. Kawakami, “Photonic crystal polarization splitters,” Electron. Lett. 35, 1271-1272 (1999).
[CrossRef]

Ohyama, N.

J. Huang, T. Honda, N. Ohyama, and J. Tsujiuchi, “Fringe scanning scatter plate interferometer using a polarized light,” Opt. Commun. 68, 235-238 (1988).
[CrossRef]

Rashidnia, N.

C. R. Mercer, K. Creath, and N. Rashidnia, “A phase-stepped point diffraction interferometer using liquid crystals,” Proc. SPIE 2544, 87-93 (1995).

Rosenfeld, D. P.

Sasaki, Y.

Sato, T.

T. Sato, T. Araki, Y. Sasaki, T. Tsuru, T. Tadokoro, and S. Kawakami, “Compact ellipsometer employing a static polarimeter module with arrayed polarizer and wave-plate elements,” Appl. Opt. 46, 4963-4967 (2007).
[CrossRef] [PubMed]

T. Sato, K. Miura, N. Ishino, Y. Ohtera, T. Tamamura, and S. Kawakami, “Photonic crystals for the visible range fabricated by autocloning technique and their application,” Opt. Quantum Electron. 34, 63-70 (2002).
[CrossRef]

S. Kawakami, T. Kawashima, and T. Sato, “Mechanism of shape formation of three-dimensional periodic nanostructures by bias sputtering,” Appl. Phys. Lett. 74, 463-465(1999).
[CrossRef]

Y. Ohtera, T. Sato, T. Kawashima, T. Tamamura, and S. Kawakami, “Photonic crystal polarization splitters,” Electron. Lett. 35, 1271-1272 (1999).
[CrossRef]

Schnabel, B.

B. Schnabel, E. Kley, and F. Wyrowski, “Study on polarizing visible light by subwavelength-period metal-stripe gratings,” Opt. Eng. 38, 220-226 (1999).
[CrossRef]

Shyu, J.-C.

Shyu, L.-H.

D.-C. Su and L.-H. Shyu, “Phase-shifting scatter plate interferometer using a polarization technique,” J. Mod. Opt. 38, 951-959 (1991).
[CrossRef]

Smythe, R.

R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 23, 361-364 (1984).

Su, D.-C.

D.-C. Su and L.-H. Shyu, “Phase-shifting scatter plate interferometer using a polarization technique,” J. Mod. Opt. 38, 951-959 (1991).
[CrossRef]

Tadokoro, T.

Takai, N.

Tamamura, T.

T. Sato, K. Miura, N. Ishino, Y. Ohtera, T. Tamamura, and S. Kawakami, “Photonic crystals for the visible range fabricated by autocloning technique and their application,” Opt. Quantum Electron. 34, 63-70 (2002).
[CrossRef]

Y. Ohtera, T. Sato, T. Kawashima, T. Tamamura, and S. Kawakami, “Photonic crystal polarization splitters,” Electron. Lett. 35, 1271-1272 (1999).
[CrossRef]

Tejnil, E.

Tsujiuchi, J.

J. Huang, T. Honda, N. Ohyama, and J. Tsujiuchi, “Fringe scanning scatter plate interferometer using a polarized light,” Opt. Commun. 68, 235-238 (1988).
[CrossRef]

Tsuru, T.

Urbach, H. P.

VanDelden, J.

Watanabe, M.

T. Nakata and M. Watanabe, “Common-path double-pass optical interferometry using a wire-grid polarizer as a reference mirror,” Opt. Rev. 15, 276-279 (2008).
[CrossRef]

White, A. D.

Wyant, J. C.

Wyrowski, F.

B. Schnabel, E. Kley, and F. Wyrowski, “Study on polarizing visible light by subwavelength-period metal-stripe gratings,” Opt. Eng. 38, 220-226 (1999).
[CrossRef]

Xu, M.

Yu, X. J.

X. J. Yu and H. S. Kwok, “Optical wire-grid polarizers at oblique angles of incidence,” J. Appl. Phys. 93, 4407-4412(2003).
[CrossRef]

Yuan, C.-K.

Zhao, C.

Appl. Opt. (10)

R. Crane, “Interference phase measurement,” Appl. Opt. 8, 538-542 (1969).

J. H. Bruning, D. R. Heriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Appl. Opt. 13, 2693-2703 (1974).
[CrossRef] [PubMed]

J. C. Wyant, “Use of an ac heterodyne lateral shear interferometer with real-time wavefront correction systems,” Appl. Opt. 14, 2622-2626 (1975).
[CrossRef] [PubMed]

H. Kadono, N. Takai, and T. Asakura, “New common-path phase shifting interferometer using a polarization technique,” Appl. Opt. 26, 898-904 (1987).
[CrossRef] [PubMed]

C. Chou, J.-C. Shyu, Y.-C. Huang, and C.-K. Yuan, “Common-path optical heterodyne profilometer: a configuration,” Appl. Opt. 37, 4137-4142 (1998).
[CrossRef]

M. B. North-Morris, J. VanDelden, and J. C. Wyant, “Phase-shifting birefringent scatterplate interferometer,” Appl. Opt. 41, 668-677 (2002).
[CrossRef] [PubMed]

T. Keem, S. Gonda, I. Misumi, Q. Huang, and T. Kurosawa, “Simple, real-time method for removing the cyclic error of a homodyne interferometer with a quadrature detector system,” Appl. Opt. 44, 3492-3498 (2005).
[CrossRef] [PubMed]

M. Novak, J. Millerd, N. Brock, M. B. North-Morris, J. Hayes, and J. C. Wyant, “Analysis of a micropolarizer array-based simultaneous phase-shifting interferometer,” Appl. Opt. 44, 6861-6868 (2005).
[CrossRef] [PubMed]

C. Zhao, D. Kang, and J. H. Burge, “Effects of birefringence on Fizeau interferometry that uses a polarization phase-shifting technique,” Appl. Opt. 44, 7548-7553 (2005).
[CrossRef] [PubMed]

T. Sato, T. Araki, Y. Sasaki, T. Tsuru, T. Tadokoro, and S. Kawakami, “Compact ellipsometer employing a static polarimeter module with arrayed polarizer and wave-plate elements,” Appl. Opt. 46, 4963-4967 (2007).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

S. Kawakami, T. Kawashima, and T. Sato, “Mechanism of shape formation of three-dimensional periodic nanostructures by bias sputtering,” Appl. Phys. Lett. 74, 463-465(1999).
[CrossRef]

Electron. Lett. (2)

Y. Ohtera, T. Sato, T. Kawashima, T. Tamamura, and S. Kawakami, “Photonic crystal polarization splitters,” Electron. Lett. 35, 1271-1272 (1999).
[CrossRef]

S. Kawakami, “Fabrication of submicrometer 3D periodic structures composed of Si/SiO2,” Electron. Lett. 33, 1260-1261 (1997).
[CrossRef]

J. Appl. Phys. (2)

X. J. Yu and H. S. Kwok, “Optical wire-grid polarizers at oblique angles of incidence,” J. Appl. Phys. 93, 4407-4412(2003).
[CrossRef]

T. Nakata and T. Ninomiya, “A charge-coupled-device-based heterodyne technique for parallel photodisplacement imaging,” J. Appl. Phys. 96, 6970-6980 (2004).
[CrossRef]

J. Mod. Opt. (1)

D.-C. Su and L.-H. Shyu, “Phase-shifting scatter plate interferometer using a polarization technique,” J. Mod. Opt. 38, 951-959 (1991).
[CrossRef]

Metrologia (1)

P. Carré, “Installation et utilisation du comparateur photoélectrique et interférential du Bureau International des Poids et Mesures,” Metrologia 2, 13-23 (1966).
[CrossRef]

Opt. Commun. (1)

J. Huang, T. Honda, N. Ohyama, and J. Tsujiuchi, “Fringe scanning scatter plate interferometer using a polarized light,” Opt. Commun. 68, 235-238 (1988).
[CrossRef]

Opt. Eng. (2)

R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 23, 361-364 (1984).

B. Schnabel, E. Kley, and F. Wyrowski, “Study on polarizing visible light by subwavelength-period metal-stripe gratings,” Opt. Eng. 38, 220-226 (1999).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Opt. Quantum Electron. (1)

T. Sato, K. Miura, N. Ishino, Y. Ohtera, T. Tamamura, and S. Kawakami, “Photonic crystals for the visible range fabricated by autocloning technique and their application,” Opt. Quantum Electron. 34, 63-70 (2002).
[CrossRef]

Opt. Rev. (1)

T. Nakata and M. Watanabe, “Common-path double-pass optical interferometry using a wire-grid polarizer as a reference mirror,” Opt. Rev. 15, 276-279 (2008).
[CrossRef]

Proc. SPIE (2)

J. Millerd, N. Brock, J. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304-314 (2004).
[CrossRef]

C. R. Mercer, K. Creath, and N. Rashidnia, “A phase-stepped point diffraction interferometer using liquid crystals,” Proc. SPIE 2544, 87-93 (1995).

Other (1)

D. Malacara, Optical Shop Testing, 2nd ed. (Wiley, 1992).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Photonic crystal polarizer composed of two-dimensional submicrometer-order periodic structures.

Fig. 2
Fig. 2

PCP-based common-path optical interferometer for the measurement of sample displacement. PCP, photonic crystal polarizer; QWP, quarter-wave plate.

Fig. 3
Fig. 3

Common-path optical interferometer coupled with PCP-based phase-shifting technique. PD, photodiode.

Fig. 4
Fig. 4

Structure of PCP-based phase shifter.

Fig. 5
Fig. 5

Ultracompact common-path phase-shifting interfero meter module including monolithically integrated PCP array used for the phase shifter. (a) With insulation cover. (b) With cover removed. NPBS, nonpolarizing beam splitter.

Fig. 6
Fig. 6

Experimental setup for PCP-based interferometry. PZT stage, piezoelectric scanning stage; PMF, polarization maintaining fiber; ADC, analog-to-digital converter; PC, personal computer.

Fig. 7
Fig. 7

Transmittance and extinction ratio of PCP used for the reference mirror and the phase shifter.

Fig. 8
Fig. 8

Experimental results. (a) Four channels of interference signal in phase quadrature and measured displacement signal derived from the interference signals. (b) Displacement signal magnified in area A of (a) ( 1 nm range).

Equations (2)

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

I q = I m + I r + 2 I m I r cos ( 8 π n D λ + π 2 q ) ,
D = λ 8 π n tan 1 ( I 3 I 1 I 0 I 2 ) .

Metrics