Abstract

The compensation of large in-plane motions in digital speckle-pattern interferometry (DSPI) with the use of digital speckle photography (DSP) is demonstrated. Ordinary recordings of DSPI are recombined and analyzed with DSP. The DSP result is used to compensate for the bulk speckle motion prior to calculation of the phase map. This results in a high fringe contrast even for deformations of several speckle diameters. In addition, for the case of an in-plane deformation, it is shown that the absolute phase change in each pixel may be unwrapped by use of the DSP result as an initial guess. The principles of this method and experiments showing the in-plane rotation of a plate and the encounter of two rounded plates are presented.

© 1999 Optical Society of America

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References

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1998 (2)

1997 (1)

1994 (2)

1993 (1)

Benckert, L. R.

Burka, J.

Franze, B.

Haible, P.

Helmers, H.

Huntley, J. M.

Joenathan, C.

Kreis, T.

T. Kreis, Holographic Interferometry: Principles and Methods (Akademie Verlag, Berlin, 1996), pp. 107, 265–266.

Papoulis, A.

A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1965).

Saldner, H. O.

Sirohi, R. S.

R. S. Sirohi, Speckle Metrology (Marcel Dekker, New York, 1993), pp. 69–71.

Sjödahl, M.

Stetson, K. A.

K. A. Stetson, “Theory and applications of electronic holography,” in Proceedings of the International Conference on Hologram Interferometry and Speckle Metrology, K. A. Stetson, R. J. Pryputniewicz, eds. (Society for Experimental Mechanics, Bethel, Conn., 1990), pp. 294–300.

Tiziani, H. J.

Appl. Opt. (6)

Other (4)

A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1965).

R. S. Sirohi, Speckle Metrology (Marcel Dekker, New York, 1993), pp. 69–71.

T. Kreis, Holographic Interferometry: Principles and Methods (Akademie Verlag, Berlin, 1996), pp. 107, 265–266.

K. A. Stetson, “Theory and applications of electronic holography,” in Proceedings of the International Conference on Hologram Interferometry and Speckle Metrology, K. A. Stetson, R. J. Pryputniewicz, eds. (Society for Experimental Mechanics, Bethel, Conn., 1990), pp. 294–300.

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Figures (3)

Fig. 1
Fig. 1

Optical configuration of the system for measurements of large in-plane deformations. The system is sensitive to deformations in the x direction. M, mirror; BS, beam splitter; PS, phase-stepped mirror; BE, beam expander; CCD, video camera.

Fig. 2
Fig. 2

Rotation of a plate. (a) Wrapped phase map obtained when ordinary DSPI is used. (b) Deformation field obtained with DSP. (c) Wrapped phase map obtained with DSPI when the information from (b) is used. (d) Unwrapped deformation in each pixel in the x direction.

Fig. 3
Fig. 3

Two plates that were moved toward each other. (a) Mesh of the measured displacement in the x direction, by use of DSP. The 6-pixel displacement is approximately 3 speckle diameters. (b) Retrieved phase map.

Equations (13)

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Inx1, y1=I0x1, y1+Imx1, y1cosϕx1, y1+nπ/2,  n=0, 1, 2, 3,
Inx2, y2=I0x2, y2+Imx2, y2cosϕx2, y2+nπ/2+Ωx2, y2,  n=0, 1, 2, 3,
C1=I0x1, y1-I2x1, y1=2Imx1, y1cosϕx1, y1,
S1=I3x1, y1-I1x1, y1=2Imx1, y1sinϕx1, y1,
C2=I0x2, y2-I2x2, y2=2Imx2, y2cosϕx2, y2+Ωx2, y2,
S2=I3x2, y2-I1x2, y2=2Imx2, y2sinϕx2, y2+Ωx2, y2.
2Imx1, y1=C12+S121/2,
2Imx2, y2=C22+S221/2.
Ωx, y=4π/λux, ysin θ,
Ωwx, y=arctanC1S2-C2S1C1C2+S1S2,
Ωˆx, y=4π/λuDSPx, ysin θ,
Ωx, y=2πm+Ωwx, y,
m=INTΩˆx1, y1-Ωwx1, y12π,

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