Abstract

A method for the isolation of two-dimensional (2D) displacement components by using one phase map obtained by phase-shifting electronic speckle pattern interferometry (ESPI) is presented. When the typical ESPI is used for displacement measurement, a mixed phase distribution of deformation is measured. If the deformation of the object is symmetrical, two components of deformation can be separated from each other by using the mixed phase distribution. We turn over the mixed phase map first to obtain the second phase map, and then overlap them. Two displacement components can be separated from each other by boundary alignment and algebraic calculation between the two phase maps. This method has been proved feasible by a typical three-point bending experiment. Some experimental results are offered and compared with the results obtained by a dual-beam symmetrical illuminations experiment. This technique presented provides an alternative approach to 2D deformation measurement.

© 2007 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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2006

P. Sun, "Three-dimensional displacement measurement by using reversed phase-shifting ESPI," Opt. Eng. 45, 936021 (2006).
[CrossRef]

2004

2000

1999

1998

J. N. Petzing and J. R. Tyrer, "Recent development and applications in electronic speckle pattern interferometry," J. Strain Anal. 33, 153-169 (1998).
[CrossRef]

1997

1985

Andersson, A.

Bowe, B.

Creath, K.

Farrant, D. I.

Langhoff, A.

Martin, S.

Martinez, A.

Mohan, N. K.

Molin, N.-E.

Oreb, B. F.

Pedrini, G.

Petzing, J. N.

J. N. Petzing and J. R. Tyrer, "Recent development and applications in electronic speckle pattern interferometry," J. Strain Anal. 33, 153-169 (1998).
[CrossRef]

Puga, H. J.

Rastogi, P. K.

P. K. Rastogi, Digital Speckle Pattern Interferometry and Related Techniques (Wiley, 2001).

Rayas, J. A.

Rodriguez-Vera, R.

Santoyo, F. M.

Schedin, S.

Sjödahl, M.

Sun, P.

P. Sun, "Three-dimensional displacement measurement by using reversed phase-shifting ESPI," Opt. Eng. 45, 936021 (2006).
[CrossRef]

Takatsuji, T.

Tiziani, H. J.

Toal, V.

Tyrer, J. R.

Whelan, M.

Zou, Y.-L.

Appl. Opt.

J. Strain Anal.

J. N. Petzing and J. R. Tyrer, "Recent development and applications in electronic speckle pattern interferometry," J. Strain Anal. 33, 153-169 (1998).
[CrossRef]

Opt. Eng.

P. Sun, "Three-dimensional displacement measurement by using reversed phase-shifting ESPI," Opt. Eng. 45, 936021 (2006).
[CrossRef]

Other

P. K. Rastogi, Digital Speckle Pattern Interferometry and Related Techniques (Wiley, 2001).

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Figures (9)

Fig. 1
Fig. 1

Typical phase-shifting ESPI system.

Fig. 2
Fig. 2

Schematic of the dual-beam symmetrical illuminations (beam A and beam B) sharing one reference (beam C) in the xz plane.

Fig. 3
Fig. 3

Wrapped phase map illuminated by beam A.

Fig. 4
Fig. 4

Wrapped phase map illuminated by beam B.

Fig. 5
Fig. 5

Wrapped phase map after Fig. 4 is rotated π radian around the y axis and reversed.

Fig. 6
Fig. 6

Reconstructed fringe pattern of the in-plane displacement component in the x-axis direction obtained by using Fig. 4 and Fig. 5.

Fig. 7
Fig. 7

Reconstructed fringe pattern of out-of-plane displacement component in the z-axis direction obtained by using Fig. 4 and Fig. 5.

Fig. 8
Fig. 8

Reconstructed fringe pattern of in-plane displacement component in the x-axis direction obtained by using Fig. 3 and Fig. 4.

Fig. 9
Fig. 9

Reconstructed fringe pattern of out-of-plane displacement component in the z-axis direction obtained by using Fig. 3 and Fig. 4.

Equations (5)

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Δ ϕ 1 ( x , y ) = 2 π λ [ d 1 ( x , y ) s 1 ] ,
Δ ϕ 2 ( x , y ) = 2 π λ [ d 2 ( x , y ) s 2 ] .
Δ ϕ 1 ( x , y ) + Δ ϕ 2 ( x , y ) = 4 π λ w ( 1 + cos θ ) ,
Δ ϕ 1 ( x , y ) Δ ϕ 2 ( x , y ) = 4 π λ u sin θ ,
d 2 ( x , y ) = u 2 ( x , y ) i + v 2 ( x , y ) j + w 2 ( x , y ) k .

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