Abstract

We report a novel experimental method to measure nanometer displacements using wavelength shifts of spectral peaks around spectral switch or singular phase points in the interference spectra due to temporal correlation in a Michelson interferometer illuminated by a broadband white-light source. Dramatic changes in the spectral characteristics are recorded as a function of path difference between the interfering beams around the spectral switch position. These are then compared with measurements far from it in order to demonstrate the higher sensitivities involved in the proposed method.

© 2008 Optical Society of America

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  3. M. A. Choma, A. K. Ellerbee, C. Yang, T. L. Creazzo, and J. A. Izatt, “Spectral-domain phase microscopy,” Opt. Lett. 30, 1162-1164 (2005).
    [CrossRef]
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    [CrossRef]
  5. P. Hariharan, Optical Interferometry, 2nd ed. (Academic, 2003).
  6. K. Nakayama, M. Tanaka, F. Shiota, and K. Kuroda, “Precision physical measurements and nanometrology,” Metrologia 28, 483-502 (1991).
    [CrossRef]
  7. H. J. Tiziani, “Optical methods for precision measurements,” Opt. Quantum Electron. 21, 253-282 (1989).
    [CrossRef]
  8. L. M. Smith and C. C. Dobson, “Absolute displacement measurements using modulation of the spectrum of the white light in a Michelson interferometer,” Appl. Opt. 28, 3339-3342(1989).
  9. U. Schnell, E. Zimmermann, and R. Dändliker, “Absolute distance measurement with synchronously sampled white light channelled spectrum interferometry,” Pure Appl. Opt. 4, 643-651 (1995).
    [CrossRef]
  10. P. Sandoz, G. Tribillon, and H. Perrin, “High-resolution profilometry by using phase calculation algorithms for spectroscopic analysis of white-light interferogram,” J. Mod. Opt. 43, 701-708 (1996).
  11. I. Verrier, G. Brun, and J. P. Goure, “SISAM interferometer for distance measurements,” Appl. Opt. 36, 6225-6230(1997).
    [CrossRef]
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    [CrossRef]
  13. S. Costantino, O. E. Martinez, and J. R. Torga, “Wide band interferometry for thickness measurement,” Opt. Express. 11, 952-957 (2003).
  14. H. Chen, T. Liu, and Z. Meng, “Nanometrology based on white-light spectral interferometry in thickness measurement,” Proc. SPIE 6831, 683108 (2007).
  15. V. N. Kumar and D. N. Rao, “Using interference in the frequency domain for precise determination of thickness and refractive index of normal dispersive materials,” J. Opt. Soc. Am. B 12, 1559-1563 (1995).
    [CrossRef]
  16. M. M. Brundavanam, N. K. Viswanathan, and D. N. Rao, “Spectral anomalies due to temporal correlation in a white light interferometer,” Opt. Lett. 32, 2279-2281 (2007).
    [CrossRef]
  17. P. Hlubina, “Experimental demonstration of the spectral interference between two beams of a low-coherence source at the output of a Michelson interferometer,” J. Mod. Opt. 44, 1049-1059 (1997).
    [CrossRef]
  18. V. N. Kumar, “Spectral interferometry: a study of the degree of coherence in the space-frequency domain and the applications,” Ph.D. thesis (University of Hyderabad, 1997).

2007 (3)

H. Stoyanov, “Nanoscale linear measurements based on the attenuated total internal reflection: an interferometric approach,” Proc. SPIE 6604, 66040R (2007).
[CrossRef]

H. Chen, T. Liu, and Z. Meng, “Nanometrology based on white-light spectral interferometry in thickness measurement,” Proc. SPIE 6831, 683108 (2007).

M. M. Brundavanam, N. K. Viswanathan, and D. N. Rao, “Spectral anomalies due to temporal correlation in a white light interferometer,” Opt. Lett. 32, 2279-2281 (2007).
[CrossRef]

2006 (1)

2005 (1)

2004 (1)

J. Lawall, “Interferometry for accurate displacement metrology,” Opt. Photon. News 15(10), 40-46 (2004).
[CrossRef]

2003 (1)

S. Costantino, O. E. Martinez, and J. R. Torga, “Wide band interferometry for thickness measurement,” Opt. Express. 11, 952-957 (2003).

2002 (1)

P. Hlubina, “Dispersive white-light spectral interferometry to measure distances and displacements,” Opt. Commun. 212, 65-70 (2002).
[CrossRef]

1997 (2)

P. Hlubina, “Experimental demonstration of the spectral interference between two beams of a low-coherence source at the output of a Michelson interferometer,” J. Mod. Opt. 44, 1049-1059 (1997).
[CrossRef]

I. Verrier, G. Brun, and J. P. Goure, “SISAM interferometer for distance measurements,” Appl. Opt. 36, 6225-6230(1997).
[CrossRef]

1996 (1)

P. Sandoz, G. Tribillon, and H. Perrin, “High-resolution profilometry by using phase calculation algorithms for spectroscopic analysis of white-light interferogram,” J. Mod. Opt. 43, 701-708 (1996).

1995 (2)

U. Schnell, E. Zimmermann, and R. Dändliker, “Absolute distance measurement with synchronously sampled white light channelled spectrum interferometry,” Pure Appl. Opt. 4, 643-651 (1995).
[CrossRef]

V. N. Kumar and D. N. Rao, “Using interference in the frequency domain for precise determination of thickness and refractive index of normal dispersive materials,” J. Opt. Soc. Am. B 12, 1559-1563 (1995).
[CrossRef]

1991 (1)

K. Nakayama, M. Tanaka, F. Shiota, and K. Kuroda, “Precision physical measurements and nanometrology,” Metrologia 28, 483-502 (1991).
[CrossRef]

1989 (2)

Brun, G.

Brundavanam, M. M.

Chen, H.

H. Chen, T. Liu, and Z. Meng, “Nanometrology based on white-light spectral interferometry in thickness measurement,” Proc. SPIE 6831, 683108 (2007).

Choma, M. A.

Costantino, S.

S. Costantino, O. E. Martinez, and J. R. Torga, “Wide band interferometry for thickness measurement,” Opt. Express. 11, 952-957 (2003).

Creazzo, T. L.

Dändliker, R.

U. Schnell, E. Zimmermann, and R. Dändliker, “Absolute distance measurement with synchronously sampled white light channelled spectrum interferometry,” Pure Appl. Opt. 4, 643-651 (1995).
[CrossRef]

Dobson, C. C.

Ellerbee, A. K.

Goure, J. P.

Hanson, S. G.

Hariharan, P.

P. Hariharan, Optical Interferometry, 2nd ed. (Academic, 2003).

Hlubina, P.

P. Hlubina, “Dispersive white-light spectral interferometry to measure distances and displacements,” Opt. Commun. 212, 65-70 (2002).
[CrossRef]

P. Hlubina, “Experimental demonstration of the spectral interference between two beams of a low-coherence source at the output of a Michelson interferometer,” J. Mod. Opt. 44, 1049-1059 (1997).
[CrossRef]

Ishijima, R.

Izatt, J. A.

Kumar, V. N.

V. N. Kumar and D. N. Rao, “Using interference in the frequency domain for precise determination of thickness and refractive index of normal dispersive materials,” J. Opt. Soc. Am. B 12, 1559-1563 (1995).
[CrossRef]

V. N. Kumar, “Spectral interferometry: a study of the degree of coherence in the space-frequency domain and the applications,” Ph.D. thesis (University of Hyderabad, 1997).

Kuroda, K.

K. Nakayama, M. Tanaka, F. Shiota, and K. Kuroda, “Precision physical measurements and nanometrology,” Metrologia 28, 483-502 (1991).
[CrossRef]

Lawall, J.

J. Lawall, “Interferometry for accurate displacement metrology,” Opt. Photon. News 15(10), 40-46 (2004).
[CrossRef]

Liu, T.

H. Chen, T. Liu, and Z. Meng, “Nanometrology based on white-light spectral interferometry in thickness measurement,” Proc. SPIE 6831, 683108 (2007).

Martinez, O. E.

S. Costantino, O. E. Martinez, and J. R. Torga, “Wide band interferometry for thickness measurement,” Opt. Express. 11, 952-957 (2003).

Meng, Z.

H. Chen, T. Liu, and Z. Meng, “Nanometrology based on white-light spectral interferometry in thickness measurement,” Proc. SPIE 6831, 683108 (2007).

Miyamoto, Y.

Nakayama, K.

K. Nakayama, M. Tanaka, F. Shiota, and K. Kuroda, “Precision physical measurements and nanometrology,” Metrologia 28, 483-502 (1991).
[CrossRef]

Perrin, H.

P. Sandoz, G. Tribillon, and H. Perrin, “High-resolution profilometry by using phase calculation algorithms for spectroscopic analysis of white-light interferogram,” J. Mod. Opt. 43, 701-708 (1996).

Rao, D. N.

Sandoz, P.

P. Sandoz, G. Tribillon, and H. Perrin, “High-resolution profilometry by using phase calculation algorithms for spectroscopic analysis of white-light interferogram,” J. Mod. Opt. 43, 701-708 (1996).

Schnell, U.

U. Schnell, E. Zimmermann, and R. Dändliker, “Absolute distance measurement with synchronously sampled white light channelled spectrum interferometry,” Pure Appl. Opt. 4, 643-651 (1995).
[CrossRef]

Shiota, F.

K. Nakayama, M. Tanaka, F. Shiota, and K. Kuroda, “Precision physical measurements and nanometrology,” Metrologia 28, 483-502 (1991).
[CrossRef]

Smith, L. M.

Stoyanov, H.

H. Stoyanov, “Nanoscale linear measurements based on the attenuated total internal reflection: an interferometric approach,” Proc. SPIE 6604, 66040R (2007).
[CrossRef]

Takeda, M.

Tanaka, M.

K. Nakayama, M. Tanaka, F. Shiota, and K. Kuroda, “Precision physical measurements and nanometrology,” Metrologia 28, 483-502 (1991).
[CrossRef]

Tiziani, H. J.

H. J. Tiziani, “Optical methods for precision measurements,” Opt. Quantum Electron. 21, 253-282 (1989).
[CrossRef]

Torga, J. R.

S. Costantino, O. E. Martinez, and J. R. Torga, “Wide band interferometry for thickness measurement,” Opt. Express. 11, 952-957 (2003).

Tribillon, G.

P. Sandoz, G. Tribillon, and H. Perrin, “High-resolution profilometry by using phase calculation algorithms for spectroscopic analysis of white-light interferogram,” J. Mod. Opt. 43, 701-708 (1996).

Verrier, I.

Viswanathan, N. K.

Wada, A.

Wang, W.

Yang, C.

Yokozeki, T.

Zimmermann, E.

U. Schnell, E. Zimmermann, and R. Dändliker, “Absolute distance measurement with synchronously sampled white light channelled spectrum interferometry,” Pure Appl. Opt. 4, 643-651 (1995).
[CrossRef]

Appl. Opt. (2)

J. Mod. Opt. (2)

P. Hlubina, “Experimental demonstration of the spectral interference between two beams of a low-coherence source at the output of a Michelson interferometer,” J. Mod. Opt. 44, 1049-1059 (1997).
[CrossRef]

P. Sandoz, G. Tribillon, and H. Perrin, “High-resolution profilometry by using phase calculation algorithms for spectroscopic analysis of white-light interferogram,” J. Mod. Opt. 43, 701-708 (1996).

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

Metrologia (1)

K. Nakayama, M. Tanaka, F. Shiota, and K. Kuroda, “Precision physical measurements and nanometrology,” Metrologia 28, 483-502 (1991).
[CrossRef]

Opt. Commun. (1)

P. Hlubina, “Dispersive white-light spectral interferometry to measure distances and displacements,” Opt. Commun. 212, 65-70 (2002).
[CrossRef]

Opt. Express (1)

Opt. Express. (1)

S. Costantino, O. E. Martinez, and J. R. Torga, “Wide band interferometry for thickness measurement,” Opt. Express. 11, 952-957 (2003).

Opt. Lett. (2)

Opt. Photon. News (1)

J. Lawall, “Interferometry for accurate displacement metrology,” Opt. Photon. News 15(10), 40-46 (2004).
[CrossRef]

Opt. Quantum Electron. (1)

H. J. Tiziani, “Optical methods for precision measurements,” Opt. Quantum Electron. 21, 253-282 (1989).
[CrossRef]

Proc. SPIE (2)

H. Stoyanov, “Nanoscale linear measurements based on the attenuated total internal reflection: an interferometric approach,” Proc. SPIE 6604, 66040R (2007).
[CrossRef]

H. Chen, T. Liu, and Z. Meng, “Nanometrology based on white-light spectral interferometry in thickness measurement,” Proc. SPIE 6831, 683108 (2007).

Pure Appl. Opt. (1)

U. Schnell, E. Zimmermann, and R. Dändliker, “Absolute distance measurement with synchronously sampled white light channelled spectrum interferometry,” Pure Appl. Opt. 4, 643-651 (1995).
[CrossRef]

Other (2)

P. Hariharan, Optical Interferometry, 2nd ed. (Academic, 2003).

V. N. Kumar, “Spectral interferometry: a study of the degree of coherence in the space-frequency domain and the applications,” Ph.D. thesis (University of Hyderabad, 1997).

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Figures (5)

Fig. 1
Fig. 1

Schematic of the experimental setup. WLS: white-light source; BS: 50/50 beam splitter; M 1 and M 2 : mirrors; n-PZ: nanopositioner; Sp: spectrometer; and PC: personal computer.

Fig. 2
Fig. 2

Spectral modulations around the spectral switch position with two spectral fringes (Method 1). (a) and (c) The spectra around the spectral switch position for path differences of 260 and 300 nm , respectively. (b) The spectrum at the spectral switch position for the path difference 280 nm . Open circles: experimental data. Continuous curves: the spectra calculated using Eq. (2).

Fig. 3
Fig. 3

Plot of [ ( λ 0 λ peak ) / λ 0 ] as a function of normalized path difference around the spectral switch position. Open circles: experimental data of Method 1; continuous curve: curve calculated using Eq. (2) for two-fringe spectrum; open triangles: experimental data of Method 2; and dashed curve: curve calculated using Eq. (2) for nine fringe spectrum.

Fig. 4
Fig. 4

Experimental spectra with nine spectral fringes (Method 2). Continuous curve: initial position of the spectrum (red shifted). Dotted curve: blue shifted spectrum for 10 nm displacement of the mirror M 2 crossing through the spectral switch position.

Fig. 5
Fig. 5

Plot of SSA versus displacement d measured in Methods 1 and 2. Open circles and continuous curve: experimental data and corresponding linear fit (Method 1). Open triangles and dotted curve: experimental data and corresponding linear fit (Method 2).

Equations (3)

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S ( λ ) = 1 2 S 0 ( λ ) { 1 + Re [ μ 12 ( λ ) ] cos [ κ Δ l ] } ,
S ( λ ) = 1 2 S 0 ( λ ) { 1 + cos [ κ Δ l ] } .
SSA = { [ ( λ 0 λ blue peak ) / λ 0 ] [ ( λ 0 λ red peak ) / λ 0 ] } = ( λ red peak λ blue peak ) / λ 0 ,

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