Abstract

A simple, yet powerful, means of computing the phase of fringe patterns depicting dynamic phenomena is presented. It is shown that the basic principle of the phase-shifting methods can be extended to the case of dynamic situations. The crux is to recognize that the phenomenon under examination can itself provide the necessary incremental phase shifts. This new method possesses a very wide range of applications in the field of deformation measurement.

© 1996 Optical Society of America

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References

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  1. A. J. P. van Haasteren, H. J. Frankena, “Real-time displacement measurement using a multicamera phase-stepping speckle interferometer,” Appl. Opt. 33, 4137–4142 (1994).
    [CrossRef]
  2. D. W. Robinson, G. T. Reid, eds., Interferogram Analysis: Digital Fringe Pattern Measurement Techniques (Institute of Physics Publishing, Bristol, UK, 1993).
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    [CrossRef] [PubMed]
  4. I.-B. Kong, S.-W. Kim, “General algorithm of phase-shifting interferometry by iterative least-squares fitting,” Opt. Eng. 34, 183–187 (1995).
    [CrossRef]
  5. P. Carré, “Installation et utilisation du comparateur photoélectrique et interférentiel du Bureau International des Poids et Mesures,” Metrologia 2, 13–23 (1966).
    [CrossRef]
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  10. P. Jacquot, X. Colonna de Lega, P. M. Boone, “Common-path holographic interferometer for flatness testing,” in Optical Measurements and Sensors for the Process Industries, C. Gorecki, R. W. Preater, eds., Proc. SPIE2248, 125–135 (1994).
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    [CrossRef] [PubMed]

1995 (3)

1994 (1)

1993 (1)

1987 (1)

1985 (1)

1983 (1)

1966 (1)

P. Carré, “Installation et utilisation du comparateur photoélectrique et interférentiel du Bureau International des Poids et Mesures,” Metrologia 2, 13–23 (1966).
[CrossRef]

Boone, P. M.

P. Jacquot, X. Colonna de Lega, P. M. Boone, “Common-path holographic interferometer for flatness testing,” in Optical Measurements and Sensors for the Process Industries, C. Gorecki, R. W. Preater, eds., Proc. SPIE2248, 125–135 (1994).

Burow, R.

Carré, P.

P. Carré, “Installation et utilisation du comparateur photoélectrique et interférentiel du Bureau International des Poids et Mesures,” Metrologia 2, 13–23 (1966).
[CrossRef]

Cheng, Y.-Y.

Colonna de Lega, X.

P. Jacquot, X. Colonna de Lega, P. M. Boone, “Common-path holographic interferometer for flatness testing,” in Optical Measurements and Sensors for the Process Industries, C. Gorecki, R. W. Preater, eds., Proc. SPIE2248, 125–135 (1994).

Creath, K.

Eiju, T.

Elssner, K. E.

Frankena, H. J.

Grant, I.

Grzanna, J.

Hariharan, P.

Huntley, J. M.

Jacquot, P.

P. Jacquot, X. Colonna de Lega, P. M. Boone, “Common-path holographic interferometer for flatness testing,” in Optical Measurements and Sensors for the Process Industries, C. Gorecki, R. W. Preater, eds., Proc. SPIE2248, 125–135 (1994).

Kim, S.-W.

I.-B. Kong, S.-W. Kim, “General algorithm of phase-shifting interferometry by iterative least-squares fitting,” Opt. Eng. 34, 183–187 (1995).
[CrossRef]

Kong, I.-B.

I.-B. Kong, S.-W. Kim, “General algorithm of phase-shifting interferometry by iterative least-squares fitting,” Opt. Eng. 34, 183–187 (1995).
[CrossRef]

Merkel, K.

Oreb, B. F.

Saldner, H.

Schmit, J.

Schwider, J.

Spolaszyk, R.

van Haasteren, A. J. P.

Wang, J.

Wyant, J. C.

Appl. Opt. (7)

Metrologia (1)

P. Carré, “Installation et utilisation du comparateur photoélectrique et interférentiel du Bureau International des Poids et Mesures,” Metrologia 2, 13–23 (1966).
[CrossRef]

Opt. Eng. (1)

I.-B. Kong, S.-W. Kim, “General algorithm of phase-shifting interferometry by iterative least-squares fitting,” Opt. Eng. 34, 183–187 (1995).
[CrossRef]

Other (2)

D. W. Robinson, G. T. Reid, eds., Interferogram Analysis: Digital Fringe Pattern Measurement Techniques (Institute of Physics Publishing, Bristol, UK, 1993).

P. Jacquot, X. Colonna de Lega, P. M. Boone, “Common-path holographic interferometer for flatness testing,” in Optical Measurements and Sensors for the Process Industries, C. Gorecki, R. W. Preater, eds., Proc. SPIE2248, 125–135 (1994).

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Figures (4)

Fig. 1
Fig. 1

(a)–(e) Five successive images acquired during deformation; (f) wrapped phase map filtered in the sine and cosine domain (see text).

Fig. 2
Fig. 2

Wrapped phase profile along a horizontal radius of the fringes in Fig. 1(f).

Fig. 3
Fig. 3

(a) Two examples of phase shifts induced by a deformation, α1 and α2; (b) the same after introduction of a reference phase step α r .

Fig. 4
Fig. 4

(a)–(e) Five successive images acquired during deformation with a superimposed π/2 phase step; (f) resulting wrapped phase map (no filtering).

Equations (5)

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{ φ ( x , y , t 0 + i Δ t ) φ ( x , y , t 0 ) + i Δ t φ t ( x , y , t 0 ) , i [ - k , k ] , Δ t φ t ( x , y , t 0 ) < π .
I 1 = I 0 [ 1 + V cos ( φ - 2 α ) ] , I 2 = I 0 [ 1 + V cos ( φ - α ) ] , I 3 = I 0 [ 1 + V cos ( φ ) ] , I 4 = I 0 [ 1 + V cos ( φ + α ) ] , I 5 = I 0 [ 1 + V cos ( φ + 2 α ) ] .
cos α = 1 2 I 5 - I 1 I 4 - I 2 = 1 2 2 sin α cos α sin φ sin α sin φ ,
tan φ = 2 ( I 2 - I 4 ) 2 I 3 - I 1 - I 5 sin α = 4 sin φ sin α 4 cos φ sin 2 α sin α .
{ φ ( x , y , t 0 + i Δ t ) φ ( x , y , t 0 ) + i Δ φ t ( x , y , t 0 ) t + 1 2 ( i Δ t ) 2 2 φ t 2 ( x , y , t 0 ) , i [ - k , k ] ( Δ t ) 2 2 φ t 2 ( x , y , t 0 ) Δ t φ t ( x , y , t 0 ) < π .

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