Abstract

As an alternative to the intensity correlation used in conventional speckle metrology, we propose a new technique for displacement observation that is based on spatial-signal-domain phase-only correlation and that makes use of the pseudophase of the complex analytic signal generated from a Hilbert-filtered speckle pattern. Experimental results are presented that demonstrate the validity and the advantage of the proposed signal-domain phase-only correlation technique over both the conventional intensity correlation technique and the spatial-frequency-domain phase-only correlation technique.

© 2005 Optical Society of America

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References

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  1. See, for example, I. Yamaguchi, “Fundamentals and applications of speckle,” in Speckle Metrology 2003, K. Gastinger, O. J. Lokberg, S. Winther, eds., Proc. SPIE4933, 1–8 (2003).
    [CrossRef]
  2. D. J. Chen, F. P. Chiang, Y. S. Tan, H. S. Don, “Digital speckle-displacement measurement using a complex spectrum method,” Appl. Opt. 32, 1839–1849 (1993).
    [CrossRef] [PubMed]
  3. M. Sjödahl, L. R. Benckert, “Electronic speckle photography: analysis of an algorithm giving the displacement with subpixel accuracy,” Appl. Opt. 32, 2278–2284 (1993).
    [CrossRef] [PubMed]
  4. M. Sjödahl, “Electronic speckle photography: increased accuracy by nonintegral pixel shifting,” Appl. Opt. 33, 6667–6673 (1994).
    [CrossRef] [PubMed]
  5. M. Sjödahl, “Accuracy in electronic speckle photography,” Appl. Opt. 36, 2875–2885 (1997).
    [CrossRef] [PubMed]
  6. T. Fricke-Begemann, K. D. Hinsch, “Measurement of random processes at rough surfaces with digital speckle correlation,” J. Opt. Soc. Am. A 21, 252–262 (2004).
    [CrossRef]
  7. A. D. McAulay, “Hilbert transform and mirror-image optical correlators,” Appl. Opt. 39, 2300–2309 (2000).
    [CrossRef]
  8. A. D. McAulay, “Joint transform optical correlator designed and analyzed by use of two- and one-dimensional Hilbert transforms,” Appl. Opt. 40, 662–671 (2001).
    [CrossRef]
  9. J. L. Horner, P. D. Gianino, “Phase-only matched filtering,” Appl. Opt. 23, 812–816 (1984).
    [CrossRef] [PubMed]
  10. K. Takita, T. Aoki, Y. Sasaki, T. Higuchi, K. Kobayashi, “High-accuracy subpixel image registration based on phase-only correlation,” IEICE Trans. Fundam. Electron. Commun. Comp. Sci. E86-A, 1925–1934 (2003).
  11. B. V. K. Vijaya Kumar, L. Hassebrook, “Performance measures for correlation filters,” Appl. Opt. 29, 2997–3006 (1990).
    [CrossRef]
  12. W. Wang, N. Ishii, Y. Miyamoto, M. Takeda, “Phase singularities in dynamic speckle fields and their applications to optical metrology,” in Speckle Metrology 2003,K. Gastinger, O. J. Lokberg, S. Winther, eds., Proc. SPIE4933, 175–180 (2003).
    [CrossRef]
  13. S. L. Hahn, Hilbert Transforms in Signal Processing (Artech House, 1997).
  14. M. Takeda, H. Ina, S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982).
    [CrossRef]
  15. K. G. Larkin, D. J. Bone, M. A. Oldfield, “Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform,” J. Opt. Soc. Am. A 18, 1862–1870 (2001).
    [CrossRef]
  16. A. Asundi, H. North, “White-light speckle method—Current trends,” Opt. Lasers Eng. 29, 159–169 (1998).
    [CrossRef]
  17. R. D. Juday, R. S. Barton, S. E. Monroe, “Experimental optical results with minimum Euclidean distance optimal filters, coupled modulators and quadratic metrics,” Opt. Eng. 38, 302–312 (1999).
    [CrossRef]

2004 (1)

2003 (1)

K. Takita, T. Aoki, Y. Sasaki, T. Higuchi, K. Kobayashi, “High-accuracy subpixel image registration based on phase-only correlation,” IEICE Trans. Fundam. Electron. Commun. Comp. Sci. E86-A, 1925–1934 (2003).

2001 (2)

2000 (1)

1999 (1)

R. D. Juday, R. S. Barton, S. E. Monroe, “Experimental optical results with minimum Euclidean distance optimal filters, coupled modulators and quadratic metrics,” Opt. Eng. 38, 302–312 (1999).
[CrossRef]

1998 (1)

A. Asundi, H. North, “White-light speckle method—Current trends,” Opt. Lasers Eng. 29, 159–169 (1998).
[CrossRef]

1997 (1)

1994 (1)

1993 (2)

1990 (1)

1984 (1)

1982 (1)

Aoki, T.

K. Takita, T. Aoki, Y. Sasaki, T. Higuchi, K. Kobayashi, “High-accuracy subpixel image registration based on phase-only correlation,” IEICE Trans. Fundam. Electron. Commun. Comp. Sci. E86-A, 1925–1934 (2003).

Asundi, A.

A. Asundi, H. North, “White-light speckle method—Current trends,” Opt. Lasers Eng. 29, 159–169 (1998).
[CrossRef]

Barton, R. S.

R. D. Juday, R. S. Barton, S. E. Monroe, “Experimental optical results with minimum Euclidean distance optimal filters, coupled modulators and quadratic metrics,” Opt. Eng. 38, 302–312 (1999).
[CrossRef]

Benckert, L. R.

Bone, D. J.

Chen, D. J.

Chiang, F. P.

Don, H. S.

Fricke-Begemann, T.

Gianino, P. D.

Hahn, S. L.

S. L. Hahn, Hilbert Transforms in Signal Processing (Artech House, 1997).

Hassebrook, L.

Higuchi, T.

K. Takita, T. Aoki, Y. Sasaki, T. Higuchi, K. Kobayashi, “High-accuracy subpixel image registration based on phase-only correlation,” IEICE Trans. Fundam. Electron. Commun. Comp. Sci. E86-A, 1925–1934 (2003).

Hinsch, K. D.

Horner, J. L.

Ina, H.

Ishii, N.

W. Wang, N. Ishii, Y. Miyamoto, M. Takeda, “Phase singularities in dynamic speckle fields and their applications to optical metrology,” in Speckle Metrology 2003,K. Gastinger, O. J. Lokberg, S. Winther, eds., Proc. SPIE4933, 175–180 (2003).
[CrossRef]

Juday, R. D.

R. D. Juday, R. S. Barton, S. E. Monroe, “Experimental optical results with minimum Euclidean distance optimal filters, coupled modulators and quadratic metrics,” Opt. Eng. 38, 302–312 (1999).
[CrossRef]

Kobayashi, K.

K. Takita, T. Aoki, Y. Sasaki, T. Higuchi, K. Kobayashi, “High-accuracy subpixel image registration based on phase-only correlation,” IEICE Trans. Fundam. Electron. Commun. Comp. Sci. E86-A, 1925–1934 (2003).

Kobayashi, S.

Larkin, K. G.

McAulay, A. D.

Miyamoto, Y.

W. Wang, N. Ishii, Y. Miyamoto, M. Takeda, “Phase singularities in dynamic speckle fields and their applications to optical metrology,” in Speckle Metrology 2003,K. Gastinger, O. J. Lokberg, S. Winther, eds., Proc. SPIE4933, 175–180 (2003).
[CrossRef]

Monroe, S. E.

R. D. Juday, R. S. Barton, S. E. Monroe, “Experimental optical results with minimum Euclidean distance optimal filters, coupled modulators and quadratic metrics,” Opt. Eng. 38, 302–312 (1999).
[CrossRef]

North, H.

A. Asundi, H. North, “White-light speckle method—Current trends,” Opt. Lasers Eng. 29, 159–169 (1998).
[CrossRef]

Oldfield, M. A.

Sasaki, Y.

K. Takita, T. Aoki, Y. Sasaki, T. Higuchi, K. Kobayashi, “High-accuracy subpixel image registration based on phase-only correlation,” IEICE Trans. Fundam. Electron. Commun. Comp. Sci. E86-A, 1925–1934 (2003).

Sjödahl, M.

Takeda, M.

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

W. Wang, N. Ishii, Y. Miyamoto, M. Takeda, “Phase singularities in dynamic speckle fields and their applications to optical metrology,” in Speckle Metrology 2003,K. Gastinger, O. J. Lokberg, S. Winther, eds., Proc. SPIE4933, 175–180 (2003).
[CrossRef]

Takita, K.

K. Takita, T. Aoki, Y. Sasaki, T. Higuchi, K. Kobayashi, “High-accuracy subpixel image registration based on phase-only correlation,” IEICE Trans. Fundam. Electron. Commun. Comp. Sci. E86-A, 1925–1934 (2003).

Tan, Y. S.

Vijaya Kumar, B. V. K.

Wang, W.

W. Wang, N. Ishii, Y. Miyamoto, M. Takeda, “Phase singularities in dynamic speckle fields and their applications to optical metrology,” in Speckle Metrology 2003,K. Gastinger, O. J. Lokberg, S. Winther, eds., Proc. SPIE4933, 175–180 (2003).
[CrossRef]

Yamaguchi, I.

See, for example, I. Yamaguchi, “Fundamentals and applications of speckle,” in Speckle Metrology 2003, K. Gastinger, O. J. Lokberg, S. Winther, eds., Proc. SPIE4933, 1–8 (2003).
[CrossRef]

Appl. Opt. (8)

IEICE Trans. Fundam. Electron. Commun. Comp. Sci. (1)

K. Takita, T. Aoki, Y. Sasaki, T. Higuchi, K. Kobayashi, “High-accuracy subpixel image registration based on phase-only correlation,” IEICE Trans. Fundam. Electron. Commun. Comp. Sci. E86-A, 1925–1934 (2003).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Opt. Eng. (1)

R. D. Juday, R. S. Barton, S. E. Monroe, “Experimental optical results with minimum Euclidean distance optimal filters, coupled modulators and quadratic metrics,” Opt. Eng. 38, 302–312 (1999).
[CrossRef]

Opt. Lasers Eng. (1)

A. Asundi, H. North, “White-light speckle method—Current trends,” Opt. Lasers Eng. 29, 159–169 (1998).
[CrossRef]

Other (3)

W. Wang, N. Ishii, Y. Miyamoto, M. Takeda, “Phase singularities in dynamic speckle fields and their applications to optical metrology,” in Speckle Metrology 2003,K. Gastinger, O. J. Lokberg, S. Winther, eds., Proc. SPIE4933, 175–180 (2003).
[CrossRef]

S. L. Hahn, Hilbert Transforms in Signal Processing (Artech House, 1997).

See, for example, I. Yamaguchi, “Fundamentals and applications of speckle,” in Speckle Metrology 2003, K. Gastinger, O. J. Lokberg, S. Winther, eds., Proc. SPIE4933, 1–8 (2003).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Modulus of correlation functions: (a) intensity correlation and (b) SDPOC.

Fig. 2
Fig. 2

Optical flow of the in-plane displacement obtained by (a) the conventional intensity correlation method and by (b) the proposed SDPOC technique.

Fig. 3
Fig. 3

Three-dimensional view of the optical flow for a rotation angle of 2°: (a) intensity correlation and (b) SDPOC.

Fig. 4
Fig. 4

Three-dimensional view of the optical flow for a rotation angle of 1°: (a) intensity correlation and (b) SDPOC.

Fig. 5
Fig. 5

Modulus of (a) the autocorrelation function and (b) the cross-correlation function given by the intensity correlation.

Fig. 6
Fig. 6

Modulus of (a) the autocorrelation function and (b) the cross-correlation function given by the FDPOC technique.

Fig. 7
Fig. 7

Modulus of (a) the autocorrelation function and (b) the cross-correlation function given by the SDPOC technique.

Equations (6)

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I ˜ ( x , y ) = 2 - + - + step ( f x ) F ( f x , f y ) × exp [ j 2 π ( f x x + f y y ) ] d f x d f y ,
step ( f ) = { 1 for f > 0 0.5 for f = 0 0 for f < 0 .
I ˜ ( x , y ) = I ˜ ( x , y ) exp [ j ϕ ( x , y ) ] = I ( x , y ) + j π P - + I ( ξ , y ) x - ξ d ξ ,
C I ( Δ x , Δ y ) = I 1 ( x + Δ x , y + Δ y ) I 2 ( x , y ) ,
C P SDPOC ( Δ x , Δ y ) = exp [ j ϕ 1 ( x + Δ x , y + Δ y ) ] × exp [ - j ϕ 2 ( x , y ) ] ,
C P FDPOC ( Δ x , Δ y ) = - + - + exp [ j φ 1 ( f x , f y ) ] × exp [ - j φ 2 ( f x , f y ) ] × exp [ j 2 π ( f x Δ x + f y Δ y ) ] d f x d f y ,

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