Abstract

The use of complex amplitude correlation to compensate for large in-plane motion in digital speckle pattern interferometry is investigated. The result is compared with experiments where digital speckle photography (DSP) is used for compensation. An advantage of using complex amplitude correlation instead of intensity correlation (as in DSP) is that the phase change describing the deformation is retrieved directly from the correlation peak, and there is no need to compensate for the large movement and then use the interferometric algorithms. A discovered drawback of this method is that the correlation values drop quickly if a phase gradient larger than π is present in the subimages used for cross correlation. This means that, for the complex amplitude correlation to be used, the size of the subimages must be well chosen or a third parämeter in the cross-correlation algorithm that compensates for the phase variation is needed. Correlation values and wrapped phase maps from the two techniques (intensity and complex amplitude correlation) are presented.

© 2006 Optical Society of America

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References

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2004 (1)

1999 (1)

1998 (1)

C. Joenathan, B. Franze, P. Haible, and H. J. Tiziani, "Large in-plane displacement in dual-beam speckle interferometry using temporal phase measurement," J. Mod. Opt. 45, 1975-1984 (1998).
[CrossRef]

1997 (2)

1994 (1)

1993 (2)

1992 (1)

1983 (1)

M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, and S. R. McNeill, "Determination of displacement using an improved digital correlation method," Image Vision Comput. 1, 133-139 (1983).
[CrossRef]

Benckert, L. R.

Coupland, J. M.

Franze, B.

C. Joenathan, B. Franze, P. Haible, and H. J. Tiziani, "Large in-plane displacement in dual-beam speckle interferometry using temporal phase measurement," J. Mod. Opt. 45, 1975-1984 (1998).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley Interscience, 1985).

Haible, P.

C. Joenathan, B. Franze, P. Haible, and H. J. Tiziani, "Large in-plane displacement in dual-beam speckle interferometry using temporal phase measurement," J. Mod. Opt. 45, 1975-1984 (1998).
[CrossRef]

Halliwell, N. A.

Huntley, J. M.

Joenathan, C.

C. Joenathan, B. Franze, P. Haible, and H. J. Tiziani, "Large in-plane displacement in dual-beam speckle interferometry using temporal phase measurement," J. Mod. Opt. 45, 1975-1984 (1998).
[CrossRef]

McNeill, S. R.

M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, and S. R. McNeill, "Determination of displacement using an improved digital correlation method," Image Vision Comput. 1, 133-139 (1983).
[CrossRef]

Peters, W. H.

M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, and S. R. McNeill, "Determination of displacement using an improved digital correlation method," Image Vision Comput. 1, 133-139 (1983).
[CrossRef]

Ranson, W. F.

M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, and S. R. McNeill, "Determination of displacement using an improved digital correlation method," Image Vision Comput. 1, 133-139 (1983).
[CrossRef]

Runnemalm, A.

Saldner, H.

Saldner, H. O

Sirohi, R. S.

R. S. Sirohi, Speckle Metrology (Marcel Dekker, 1993), pp. 69-71.

Sjödahl, M.

Sutton, M. A.

M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, and S. R. McNeill, "Determination of displacement using an improved digital correlation method," Image Vision Comput. 1, 133-139 (1983).
[CrossRef]

Svanbro, A.

Tiziani, H. J.

C. Joenathan, B. Franze, P. Haible, and H. J. Tiziani, "Large in-plane displacement in dual-beam speckle interferometry using temporal phase measurement," J. Mod. Opt. 45, 1975-1984 (1998).
[CrossRef]

Wolters, W. J.

M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, and S. R. McNeill, "Determination of displacement using an improved digital correlation method," Image Vision Comput. 1, 133-139 (1983).
[CrossRef]

Appl. Opt. (8)

Image Vision Comput. (1)

M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, and S. R. McNeill, "Determination of displacement using an improved digital correlation method," Image Vision Comput. 1, 133-139 (1983).
[CrossRef]

J. Mod. Opt. (1)

C. Joenathan, B. Franze, P. Haible, and H. J. Tiziani, "Large in-plane displacement in dual-beam speckle interferometry using temporal phase measurement," J. Mod. Opt. 45, 1975-1984 (1998).
[CrossRef]

Other (3)

M. Sjödahl, "Digital speckle photography" in Digital Speckle Pattern Interferometry and Related Techniques, P K. Rastogi, ed. (Wiley, 2001), pp. 289-336.

J. W. Goodman, Statistical Optics (Wiley Interscience, 1985).

R. S. Sirohi, Speckle Metrology (Marcel Dekker, 1993), pp. 69-71.

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Figures (8)

Fig. 1
Fig. 1

(Color online) Schematic sketch of the optical in-plane measuring setup. Nd:YAG, a laser ( 532   nm ) ; BS, 50:50 beam splitter; PZ, piezo-mounted mirror used to phase step the light; OF, optical single-mode fibers; CCD, camera used to capture the frames.

Fig. 2
Fig. 2

(Color online) Correlation values for various translations of the object. The complex amplitude correlation, intensity correlation, and the theoretical value are shown.

Fig. 3
Fig. 3

(Color online) Correlation values for a rotation round the z axis (see Fig. 1) of the object plus translation in the x direction. Both complex amplitude correlation and intensity correlation results are shown. The size of the subimage for intensity correlation is 32 × 32 pixels, while the amplitude correlation is performed for (a) 32 × 32 pixels and (b) 16 × 16 pixels.

Fig. 4
Fig. 4

Wrapped phase map describing a rotation of 1 arc min round the z axis with an overlaid movement of 100 μ m in the x direction. The result shown is achieved by traditional DSPI algorithms.

Fig. 5
Fig. 5

Wrapped phase map describing the same rotation and movement as in Fig 4. The translation is compensated for by intensity correlation, and the phase map is obtained with the algorithms of DSPI. Subimages of 32 × 32 pixels are used.

Fig. 6
Fig. 6

Wrapped phase maps describing the same rotation and movement as in Fig. 4. The amplitude correlation obtains the phase value from the correlation peak; (a) the result for a subimage of 32 × 32 pixels; (b) If the subimages are reduced to 16 × 16 pixels to ensure that the phase gradient across the subimage is less than π, the wrapped phase map is much less distorted, and the correlation values increase.

Fig. 7
Fig. 7

(Color online) Correlation value versus number of fringes per subimage for the amplitude correlation and intensity correlation. Both experimental and simulated results are shown.

Fig. 8
Fig. 8

(Color online) Correlation values for two different cameras (NEC and pixel synchronous) compared with the theoretical values.

Equations (20)

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I ( n ) = I 0 + I M   cos ( ϕ + n π / 2 ) ,
I ( n ) = I 0 + I M   cos ( ϕ + n π / 2 + Δ ϕ ) ,
n = 0 , 1 , 2 , 3 ,
C = I ( 0 ) I ( 2 ) = 2 I M   cos   ϕ ,
S = I ( 3 ) I ( 1 ) = 2 I M   sin   ϕ ,
C = I ( 0 ) I ( 2 ) = 2 I M   cos ( ϕ + Δ ϕ ) ,
S = I ( 3 ) I ( 1 ) = 2 I M   sin ( ϕ + Δ ϕ ) ,
Δ ϕ w = arctan ( S C SC C C + S S ) ,
Ref int = ( C 2 + S 2 ) 1 / 2 ,
Def int = ( C 2 + S 2 ) 1 / 2 .
Ref amp = sign ( C ) | C | + i   sign ( S ) | S | ,
Def amp = sign ( C ) | C | + i   sign ( S ) | S | .
phase amp = arctan [ Im ( c amp ) Re ( c amp ) ] max ,
μ = 2 π [ arccos ( | A p | D * ) ( | A p | D * ) 1 ( | A p | D * ) 2 ] = Θ sin   Θ π ,
Θ = 2   arccos ( | A p | D * ) ,
γ 0 , int = ( Θ sin   Θ π ) 2 .
γ 0 , amp = | Θ sin   Θ π | .
A x = a x [ 1 + L L s ( 1 l sx 2 ) ] ,
A y = a y + L l s x Ω z
σ = 1.22 λ ( 1 + M ) f # ,

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