Abstract

As an alternative to correlation-based techniques widely used in conventional speckle metrology, we propose a new technique that makes use of phase singularities in the complex analytic signal of a speckle pattern as indicators of local speckle displacements. The complex analytic signal is generated by vortex filtering the speckle pattern. Experimental results are presented that demonstrate the validity and the performance of the proposed optical vortex metrology with nano-scale resolution.

© 2006 Optical Society of America

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References

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  1. D. J. Chen, F. P. Chiang, Y.S. Tan, and H. S. Don, “Digital speckle displacement measurement using a complex spectrum method,” Appl. Opt. 32, 1839–1849 (1993).
    [Crossref] [PubMed]
  2. M. Sjödahl and L. R. Benckert, “Electronic speckle photography: analysis of an algorithm giving the displacement with subpixel accuracy,” Appl. Opt. 32, 22789–2284 (1993).
    [Crossref]
  3. M. Sjüdahl, “Electronic speckle photography: increased accuracy by nonintegral pixel shifting,” Appl. Opt. 33, 6667–6673 (1994).
    [Crossref]
  4. T. Fricke-Begemann and K. D. Hinsch, “Measurment of random processes at rough surfaces with digital speckle correlation,” J. Opt. Soc. Am.A 21, 252–262 (2004).
    [Crossref]
  5. D. D. Duncan and S. J. Kirkpatrick, “Performance analysis of a maximum-likehood speckle motion estimator,” Opt. Express 10, 927–941 (2002),u http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-18-927.
    [PubMed]
  6. W. Wang, N. Ishii, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Pseudophase information from the complex analytic signal of speckle fields and its applications. Part I: Microdisplacement observation based on phase-only correlation in the signal domain,” Appl. Opt. 44, 4909–4915 (2005).
    [Crossref] [PubMed]
  7. W. Wang, N. Ishii, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Phase singularities in analytic signal of white-light speckle pattern with application to micro-displacement measurement,” Opt. Commun. 248, 59–68 (2005).
    [Crossref]
  8. P. K. Rastogi, “Techniques of displacement and deformation measurements in speckle metrology,” in Speckle metrology, R. S. Sirohi, ed. (Marcel Dekker, New York, 1993).
  9. D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms and Software (John Wiley & Sons, New York, 1998), Chap. 1.
  10. D. Gabor, “Theory of communications,” J. IEE,  93, 429–457(1946).
  11. K. G. Larkin, D. J. Bone, and 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]
  12. J. F. Nye and M. V. Berry, “Dislocation in wave trains,” Proc. Roy. Soc. Lond. A 336, 165–190 (1974).
    [Crossref]
  13. W. Wang, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental investigation of local properties and statistics of optical vortices in random wave fields,” Phys. Rev. Lett. 94, 103902–103904 (2005).
    [Crossref] [PubMed]
  14. A. Asundi and H. North, “White-light speckle method- Current trends,” Opt. Laser Eng 29, 159–169 (1998).
    [Crossref]

2005 (3)

W. Wang, N. Ishii, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Pseudophase information from the complex analytic signal of speckle fields and its applications. Part I: Microdisplacement observation based on phase-only correlation in the signal domain,” Appl. Opt. 44, 4909–4915 (2005).
[Crossref] [PubMed]

W. Wang, N. Ishii, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Phase singularities in analytic signal of white-light speckle pattern with application to micro-displacement measurement,” Opt. Commun. 248, 59–68 (2005).
[Crossref]

W. Wang, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental investigation of local properties and statistics of optical vortices in random wave fields,” Phys. Rev. Lett. 94, 103902–103904 (2005).
[Crossref] [PubMed]

2004 (1)

T. Fricke-Begemann and K. D. Hinsch, “Measurment of random processes at rough surfaces with digital speckle correlation,” J. Opt. Soc. Am.A 21, 252–262 (2004).
[Crossref]

2002 (1)

2001 (1)

1998 (1)

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

1994 (1)

1993 (2)

D. J. Chen, F. P. Chiang, Y.S. Tan, and H. S. Don, “Digital speckle displacement measurement using a complex spectrum method,” Appl. Opt. 32, 1839–1849 (1993).
[Crossref] [PubMed]

M. Sjödahl and L. R. Benckert, “Electronic speckle photography: analysis of an algorithm giving the displacement with subpixel accuracy,” Appl. Opt. 32, 22789–2284 (1993).
[Crossref]

1974 (1)

J. F. Nye and M. V. Berry, “Dislocation in wave trains,” Proc. Roy. Soc. Lond. A 336, 165–190 (1974).
[Crossref]

1946 (1)

D. Gabor, “Theory of communications,” J. IEE,  93, 429–457(1946).

Asundi, A.

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

Benckert, L. R.

M. Sjödahl and L. R. Benckert, “Electronic speckle photography: analysis of an algorithm giving the displacement with subpixel accuracy,” Appl. Opt. 32, 22789–2284 (1993).
[Crossref]

Berry, M. V.

J. F. Nye and M. V. Berry, “Dislocation in wave trains,” Proc. Roy. Soc. Lond. A 336, 165–190 (1974).
[Crossref]

Bone, D. J.

Chen, D. J.

Chiang, F. P.

Don, H. S.

Duncan, D. D.

Fricke-Begemann, T.

T. Fricke-Begemann and K. D. Hinsch, “Measurment of random processes at rough surfaces with digital speckle correlation,” J. Opt. Soc. Am.A 21, 252–262 (2004).
[Crossref]

Gabor, D.

D. Gabor, “Theory of communications,” J. IEE,  93, 429–457(1946).

Ghiglia, D. C.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms and Software (John Wiley & Sons, New York, 1998), Chap. 1.

Hanson, S. G.

W. Wang, N. Ishii, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Phase singularities in analytic signal of white-light speckle pattern with application to micro-displacement measurement,” Opt. Commun. 248, 59–68 (2005).
[Crossref]

W. Wang, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental investigation of local properties and statistics of optical vortices in random wave fields,” Phys. Rev. Lett. 94, 103902–103904 (2005).
[Crossref] [PubMed]

W. Wang, N. Ishii, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Pseudophase information from the complex analytic signal of speckle fields and its applications. Part I: Microdisplacement observation based on phase-only correlation in the signal domain,” Appl. Opt. 44, 4909–4915 (2005).
[Crossref] [PubMed]

Hinsch, K. D.

T. Fricke-Begemann and K. D. Hinsch, “Measurment of random processes at rough surfaces with digital speckle correlation,” J. Opt. Soc. Am.A 21, 252–262 (2004).
[Crossref]

Ishii, N.

W. Wang, N. Ishii, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Phase singularities in analytic signal of white-light speckle pattern with application to micro-displacement measurement,” Opt. Commun. 248, 59–68 (2005).
[Crossref]

W. Wang, N. Ishii, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Pseudophase information from the complex analytic signal of speckle fields and its applications. Part I: Microdisplacement observation based on phase-only correlation in the signal domain,” Appl. Opt. 44, 4909–4915 (2005).
[Crossref] [PubMed]

Kirkpatrick, S. J.

Larkin, K. G.

Miyamoto, Y.

W. Wang, N. Ishii, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Pseudophase information from the complex analytic signal of speckle fields and its applications. Part I: Microdisplacement observation based on phase-only correlation in the signal domain,” Appl. Opt. 44, 4909–4915 (2005).
[Crossref] [PubMed]

W. Wang, N. Ishii, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Phase singularities in analytic signal of white-light speckle pattern with application to micro-displacement measurement,” Opt. Commun. 248, 59–68 (2005).
[Crossref]

W. Wang, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental investigation of local properties and statistics of optical vortices in random wave fields,” Phys. Rev. Lett. 94, 103902–103904 (2005).
[Crossref] [PubMed]

North, H.

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

Nye, J. F.

J. F. Nye and M. V. Berry, “Dislocation in wave trains,” Proc. Roy. Soc. Lond. A 336, 165–190 (1974).
[Crossref]

Oldfield, M. A.

Pritt, M. D.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms and Software (John Wiley & Sons, New York, 1998), Chap. 1.

Rastogi, P. K.

P. K. Rastogi, “Techniques of displacement and deformation measurements in speckle metrology,” in Speckle metrology, R. S. Sirohi, ed. (Marcel Dekker, New York, 1993).

Sjödahl, M.

M. Sjödahl and L. R. Benckert, “Electronic speckle photography: analysis of an algorithm giving the displacement with subpixel accuracy,” Appl. Opt. 32, 22789–2284 (1993).
[Crossref]

Sjüdahl, M.

Takeda, M.

W. Wang, N. Ishii, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Pseudophase information from the complex analytic signal of speckle fields and its applications. Part I: Microdisplacement observation based on phase-only correlation in the signal domain,” Appl. Opt. 44, 4909–4915 (2005).
[Crossref] [PubMed]

W. Wang, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental investigation of local properties and statistics of optical vortices in random wave fields,” Phys. Rev. Lett. 94, 103902–103904 (2005).
[Crossref] [PubMed]

W. Wang, N. Ishii, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Phase singularities in analytic signal of white-light speckle pattern with application to micro-displacement measurement,” Opt. Commun. 248, 59–68 (2005).
[Crossref]

Tan, Y.S.

Wang, W.

W. Wang, N. Ishii, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Pseudophase information from the complex analytic signal of speckle fields and its applications. Part I: Microdisplacement observation based on phase-only correlation in the signal domain,” Appl. Opt. 44, 4909–4915 (2005).
[Crossref] [PubMed]

W. Wang, N. Ishii, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Phase singularities in analytic signal of white-light speckle pattern with application to micro-displacement measurement,” Opt. Commun. 248, 59–68 (2005).
[Crossref]

W. Wang, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental investigation of local properties and statistics of optical vortices in random wave fields,” Phys. Rev. Lett. 94, 103902–103904 (2005).
[Crossref] [PubMed]

Appl. Opt. (4)

J. IEE (1)

D. Gabor, “Theory of communications,” J. IEE,  93, 429–457(1946).

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

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

T. Fricke-Begemann and K. D. Hinsch, “Measurment of random processes at rough surfaces with digital speckle correlation,” J. Opt. Soc. Am.A 21, 252–262 (2004).
[Crossref]

Opt. Commun. (1)

W. Wang, N. Ishii, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Phase singularities in analytic signal of white-light speckle pattern with application to micro-displacement measurement,” Opt. Commun. 248, 59–68 (2005).
[Crossref]

Opt. Express (1)

Opt. Laser Eng (1)

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

Phys. Rev. Lett. (1)

W. Wang, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Experimental investigation of local properties and statistics of optical vortices in random wave fields,” Phys. Rev. Lett. 94, 103902–103904 (2005).
[Crossref] [PubMed]

Proc. Roy. Soc. Lond. A (1)

J. F. Nye and M. V. Berry, “Dislocation in wave trains,” Proc. Roy. Soc. Lond. A 336, 165–190 (1974).
[Crossref]

Other (2)

P. K. Rastogi, “Techniques of displacement and deformation measurements in speckle metrology,” in Speckle metrology, R. S. Sirohi, ed. (Marcel Dekker, New York, 1993).

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms and Software (John Wiley & Sons, New York, 1998), Chap. 1.

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Figures (5)

Fig. 1.
Fig. 1.

Real and imaginary parts of analytic signal, and the corresponding phase structure around a phase singularity. Left column: before interpolation; right column: after interpolation.

Fig. 2.
Fig. 2.

Experimental set-up for generation and record of white-light speckle pattern

Fig. 3.
Fig. 3.

Histograms of coordinate changes of phase singularities for speckle pattern before and after displacement. (a) x-direction; (b) y-direction. Unit pixel corresponds to 578nm.

Fig. 4.
Fig. 4.

Variation of the peak positions and peak heights of the displacement histograms of phase singularities, with the amount of voltages applied to piezoelectric transducer. (Unit pixel corresponds to 578nm.)

Fig. 5.
Fig. 5.

Relation between the applied voltage to PZT and the displacement detected from the peak position of the displacement histogram of the phase singularities. (Unit pixel corresponds to 578nm.)

Equations (8)

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

I ˜ x y = + + V f x f y . f x f y exp [ j 2 π ( f x x + f y y ) ] d f x d f y ,
V f x f y = f x + j f y f x 2 + f y 2 = exp [ f x f y ] .
I ˜ x y = I ˜ x y exp [ x y ] = I x y v x y ,
v x y = j ( x + jy ) 2 π ( x 2 + y 2 ) 3 2 = j exp ( ) 2 π r 2 .
I ˜ x y = Re [ I ˜ x y ] + j Im [ I ˜ x y ] .
Re [ I ˜ x y ] = 0 , Im [ I ˜ x y ] = 0 .
Re [ I ˜ x y ] = a r x + b r y + c r , Im [ I ˜ x y ] = a i x + b i y + c i .
x = c i b r c r b i a r b i a i b r , y = a i c r a r c i a r b i a i b r .

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