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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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, M. V. Berry, "Dislocation in wave trains," Proc. Roy. Soc. Lond. A 336, 165-190 (1974).
[CrossRef]

Speckle metrology (1)

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

Other (1)

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)

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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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