Abstract

As an alternative to the conventional optical frequency scanning technique, an angular spectrum scanning technique is proposed for absolute interferometry. Instead of sweeping the optical frequency over a wide range of spectrum, we sweep the angular spectrum by changing the incident angle of a monochromatic plane wave with a spatial light modulator (SLM). The use of monochromatic light combined with the SLM enables dispersion-free absolute interferometry that is free from mechanical moving components.

© 2006 Optical Society of America

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References

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  1. P. A. Flournoy, R. W. McClure, and G. Wyntjes, "White-light interferometric thickness gauge," Appl. Opt. 11, 1907-1915 (1972,9).
    [CrossRef] [PubMed]
  2. N. Tanaka, M. Takeda, and K. Matsumoto, "Interferometrically measuring the physical properties of test object," United States Patent 4,072,422 (filed October 20 1976, issued Februay 7, 1978).
  3. M. Davidson, K. Kaufman, I. Mazor, and F. Cohen, "An application of interference microscopy to integrated circuit inspection and metrology," in Integrated Circuit Metrology, Inspection, and Process Control, K. M. Monahan, ed., Proc. SPIE 775, 233-247 (1987).
  4. B. S. Lee and T. C. Strand, "Profilometry with a coherence scanning microscope," Appl. Opt. 29, 3784-3788 (1990).
    [CrossRef] [PubMed]
  5. T. Dresel, G. Hausler, and H. Venzke, "Three-dimensional sensing of rough surfaces by coherence radar," Appl. Opt. 31, 919-925 (1992).
    [CrossRef] [PubMed]
  6. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
    [CrossRef] [PubMed]
  7. J. Ch. Vienot, R. Ferriere, and J. P. Goedgebur, "Conjugation of space and time variables in optics," in No. 65 of AIP Conference Proceedings of Optics in Four Dimensions, M. A. Machado and L. M. Narducci, eds. (American Institute of Physics, New York, 1981), pp.49-62.
  8. J. Schwider and L. Zhou, "Dispersive interferometric profilometer," Opt. Lett. 19, 995-997 (1994).
    [CrossRef] [PubMed]
  9. M. Takeda and H. Yamamoto, "Fourier-transform speckle profilometry: Three-dimensional shape measurements of diffuse objects with large height steps and /or spatially isolated surfaces," Appl. Opt. 33, 7829-7837 (1994).
    [CrossRef] [PubMed]
  10. S. Kuwamura and I. Yamaguchi, "Wavelength scanning profilometry for real-time surface shape measurement," Appl. Opt. 36, 4473-4482 (1997).
    [CrossRef] [PubMed]
  11. H. J. Tiziani, B. Franze, and P. Haible, "Wavelength-shift speckle interferometry for absolute profilometry using mode-hope free external cavity diode laser," J. Mod. Opt. 44, 1485-1496 (1997).
    [CrossRef]
  12. M. Kinoshita, M. Takeda, H. Yago, Y. Watanabe, and T. Kurokawa, "Optical frequency-domain microprofilometry with a frequency-tunable liquid-crystal Fabry-Perot etalon device," Appl. Opt. 38, 7063- 7068 (1999).
    [CrossRef]
  13. D. S. Mehta, M. Sugai, H. Hinosugi, S. Saito, M. Takeda, T. Kurokawa, H. Takahashi, M. Ando, M. Shishido, and T. Yoshizawa, "Simultaneous three-dimensional step-height measurement and high-resolution tomographic imaging with a spectral interferometric microscope," Appl. Opt. 41, 3874-3885 (2002).
    [CrossRef] [PubMed]
  14. D. S. Mehta, H. Hinosugi, S. Saito, M. Takeda, T. Kurokawa, H. Takahashi, M. Ando, M. Shishido, T. Yoshizawa, "Spectral interferometric microscope with tandem liquid-crystal Fabry-Perot interferometers for extension of the dynamic range in three-dimensional step-height measurement," Appl. Opt. 42, 682-690 (2003).
    [CrossRef] [PubMed]
  15. M. Kuechel, "Apparatus and method(s) for reducing the effects of coherent artifacts in an interferometry," US Patent 6804011 B2, (2004) or US Patent Application 2003/0030819 A1, (2003).
  16. M. Kuechel, "Spatial coherence in interferometry," presented at the June 2004 Optatec conference, Germany, 2004.
  17. M. Takeda, H. Ina, and S. Kobyashi, "Fourier transform method of fringe-pattern analysis for computer-based topography and interferometry," J. Opt. Soc. Am. 72, 156-160 (1982).
    [CrossRef]

AIP Conf. Proc. Optics in Four Dimensio

J. Ch. Vienot, R. Ferriere, and J. P. Goedgebur, "Conjugation of space and time variables in optics," in No. 65 of AIP Conference Proceedings of Optics in Four Dimensions, M. A. Machado and L. M. Narducci, eds. (American Institute of Physics, New York, 1981), pp.49-62.

Appl. Opt.

M. Takeda and H. Yamamoto, "Fourier-transform speckle profilometry: Three-dimensional shape measurements of diffuse objects with large height steps and /or spatially isolated surfaces," Appl. Opt. 33, 7829-7837 (1994).
[CrossRef] [PubMed]

S. Kuwamura and I. Yamaguchi, "Wavelength scanning profilometry for real-time surface shape measurement," Appl. Opt. 36, 4473-4482 (1997).
[CrossRef] [PubMed]

P. A. Flournoy, R. W. McClure, and G. Wyntjes, "White-light interferometric thickness gauge," Appl. Opt. 11, 1907-1915 (1972,9).
[CrossRef] [PubMed]

B. S. Lee and T. C. Strand, "Profilometry with a coherence scanning microscope," Appl. Opt. 29, 3784-3788 (1990).
[CrossRef] [PubMed]

T. Dresel, G. Hausler, and H. Venzke, "Three-dimensional sensing of rough surfaces by coherence radar," Appl. Opt. 31, 919-925 (1992).
[CrossRef] [PubMed]

M. Kinoshita, M. Takeda, H. Yago, Y. Watanabe, and T. Kurokawa, "Optical frequency-domain microprofilometry with a frequency-tunable liquid-crystal Fabry-Perot etalon device," Appl. Opt. 38, 7063- 7068 (1999).
[CrossRef]

D. S. Mehta, M. Sugai, H. Hinosugi, S. Saito, M. Takeda, T. Kurokawa, H. Takahashi, M. Ando, M. Shishido, and T. Yoshizawa, "Simultaneous three-dimensional step-height measurement and high-resolution tomographic imaging with a spectral interferometric microscope," Appl. Opt. 41, 3874-3885 (2002).
[CrossRef] [PubMed]

D. S. Mehta, H. Hinosugi, S. Saito, M. Takeda, T. Kurokawa, H. Takahashi, M. Ando, M. Shishido, T. Yoshizawa, "Spectral interferometric microscope with tandem liquid-crystal Fabry-Perot interferometers for extension of the dynamic range in three-dimensional step-height measurement," Appl. Opt. 42, 682-690 (2003).
[CrossRef] [PubMed]

J. Mod. Opt.

H. J. Tiziani, B. Franze, and P. Haible, "Wavelength-shift speckle interferometry for absolute profilometry using mode-hope free external cavity diode laser," J. Mod. Opt. 44, 1485-1496 (1997).
[CrossRef]

J. Opt. Soc. Am.

M. Takeda, H. Ina, and S. Kobyashi, "Fourier transform method of fringe-pattern analysis for computer-based topography and interferometry," J. Opt. Soc. Am. 72, 156-160 (1982).
[CrossRef]

Opt. Lett.

J. Schwider and L. Zhou, "Dispersive interferometric profilometer," Opt. Lett. 19, 995-997 (1994).
[CrossRef] [PubMed]

Proc. SPIE

M. Davidson, K. Kaufman, I. Mazor, and F. Cohen, "An application of interference microscopy to integrated circuit inspection and metrology," in Integrated Circuit Metrology, Inspection, and Process Control, K. M. Monahan, ed., Proc. SPIE 775, 233-247 (1987).

Science

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Other

N. Tanaka, M. Takeda, and K. Matsumoto, "Interferometrically measuring the physical properties of test object," United States Patent 4,072,422 (filed October 20 1976, issued Februay 7, 1978).

M. Kuechel, "Apparatus and method(s) for reducing the effects of coherent artifacts in an interferometry," US Patent 6804011 B2, (2004) or US Patent Application 2003/0030819 A1, (2003).

M. Kuechel, "Spatial coherence in interferometry," presented at the June 2004 Optatec conference, Germany, 2004.

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Figures (8)

Fig. 1.
Fig. 1.

Simplified optical geometry for two-beam interferometry.

Fig. 2.
Fig. 2.

Angular-spectrum scanning in k-vector space.

Fig. 3.
Fig. 3.

Experimental setup.

Fig. 4.
Fig. 4.

Angular spectrum scanning by varying the radius of ring source.

Fig. 5.
Fig. 5.

Fringe intensity variation with the angular spectrum scan.

Fig. 6.
Fig. 6.

(a) Fourier spectra of the fringe signals. (b) Determination of the phase slope by least squares fit to the unwrapped phase.

Fig. 7.
Fig. 7.

Calibration for the conversion of the phase slope value to the height values.

Fig. 8.
Fig. 8.

Experimental result. (a) Three-dimensional height distribution. (b) Height profile along the 122nd pixel row.

Equations (6)

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Δ φ = k 2 h = 2 k h h = 2 hk cos θ ,
k h = k cos θ = k f ( r 2 + f 2 ) 1 1 k ( 1 r 2 2 f 2 ) ,
r n = r 1 n 1 2 ,
g ( x , y ; n ) = a ( x , y ; n ) + b ( x , y ; n ) cos [ 2 h x y k ( 1 r 1 2 n 2 f 2 ) ] ,
Δ φ ( x , y ; n ) = 2 h x y k ( 1 r 1 2 n 2 f 2 )
h ( x , y ) = f 2 k r 1 2 × [ Δ φ ( x , y ; n ) ] n ,

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