Abstract

Phase stepping by wavelength modulation of the optical source is demonstrated in a path-length unbalanced shearing interferometer. A magnification difference, which accompanies the path-length imbalance in the interferometer, introduces an unwanted radial shear, which is shown to be compensated by inclusion of a block of high-refractive-index material in the longer interferometer arm. The block also increases the phase shift obtained for a given wavelength change. The phase-stepping technique is demonstrated with a three-step algorithm to measure out-of-plane strain on a flat metal plate.

© 1996 Optical Society of America

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References

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  1. R. P. Tatam, J. C. Davies, C. H. Buckberry, J. D. C. Jones, Opt. Laser Technol. 22, 317 (1990).
    [CrossRef]
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    [PubMed]
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    [CrossRef]
  6. A. Dandridge, L. Goldberg, Electron. Lett. 18, 302 (1982).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]

1995 (1)

R. Onodera, Y. Ishii, N. Ohde, Y. Takahashi, T. Yoshino, J. Lightwave Technol. 13, 675 (1995).
[CrossRef]

1994 (2)

J. D. Valera, J. D. C. Jones, Opt. Lett. 19, 1161 (1994).
[PubMed]

N. K. Mohan, H. O. Saldner, N. E. Molin, Opt. Commun. 108, 197 (1994).
[CrossRef]

1993 (1)

H. D. Ford, H. Atcha, R. P. Tatam, Meas. Sci. Technol. 4, 601 (1993).
[CrossRef]

1991 (2)

H. Kadono, S. Toyooka, Y. Iwasaki, J. Opt. Soc. Am. A 8, 2001 (1991).
[CrossRef]

D. P. Towers, T. R. Judge, P. J. Bryanston-Cross, Opt. Lasers Eng. 14, 239 (1991).
[CrossRef]

1990 (1)

R. P. Tatam, J. C. Davies, C. H. Buckberry, J. D. C. Jones, Opt. Laser Technol. 22, 317 (1990).
[CrossRef]

1989 (1)

P. Hariharan, Proc. SPIE 1162, 86 (1989).

1987 (2)

1985 (1)

1982 (1)

A. Dandridge, L. Goldberg, Electron. Lett. 18, 302 (1982).
[CrossRef]

1979 (1)

1973 (1)

J. A. Leendertz, J. N. Butters, J. Phys. E 6, 1107 (1973).
[CrossRef]

Atcha, H.

H. D. Ford, H. Atcha, R. P. Tatam, Meas. Sci. Technol. 4, 601 (1993).
[CrossRef]

Bryanston-Cross, P. J.

D. P. Towers, T. R. Judge, P. J. Bryanston-Cross, Opt. Lasers Eng. 14, 239 (1991).
[CrossRef]

Buckberry, C. H.

R. P. Tatam, J. C. Davies, C. H. Buckberry, J. D. C. Jones, Opt. Laser Technol. 22, 317 (1990).
[CrossRef]

Butters, J. N.

J. A. Leendertz, J. N. Butters, J. Phys. E 6, 1107 (1973).
[CrossRef]

Chen, J.

Creath, K.

K. Creath, in Interferogram Analysis—Digital Fringe Pattern Measurement Techniques, D. W. Robinson, G. T. Reid, eds. (Institute of Physics, Bristol, UK, 1993), pp. 94–140.

Dandridge, A.

A. Dandridge, L. Goldberg, Electron. Lett. 18, 302 (1982).
[CrossRef]

Davies, J. C.

R. P. Tatam, J. C. Davies, C. H. Buckberry, J. D. C. Jones, Opt. Laser Technol. 22, 317 (1990).
[CrossRef]

Delisle, C.

Ford, H. D.

H. D. Ford, H. Atcha, R. P. Tatam, Meas. Sci. Technol. 4, 601 (1993).
[CrossRef]

Goldberg, L.

A. Dandridge, L. Goldberg, Electron. Lett. 18, 302 (1982).
[CrossRef]

Hariharan, P.

P. Hariharan, Proc. SPIE 1162, 86 (1989).

Hung, Y. Y.

Ishii, Y.

R. Onodera, Y. Ishii, N. Ohde, Y. Takahashi, T. Yoshino, J. Lightwave Technol. 13, 675 (1995).
[CrossRef]

Y. Ishii, J. Chen, K. Murata, Opt. Lett. 12, 233 (1987).
[CrossRef] [PubMed]

Iwasaki, Y.

Jones, J. D. C.

J. D. Valera, J. D. C. Jones, Opt. Lett. 19, 1161 (1994).
[PubMed]

R. P. Tatam, J. C. Davies, C. H. Buckberry, J. D. C. Jones, Opt. Laser Technol. 22, 317 (1990).
[CrossRef]

Judge, T. R.

D. P. Towers, T. R. Judge, P. J. Bryanston-Cross, Opt. Lasers Eng. 14, 239 (1991).
[CrossRef]

Kadono, H.

Kothiyal, M. P.

Leendertz, J. A.

J. A. Leendertz, J. N. Butters, J. Phys. E 6, 1107 (1973).
[CrossRef]

Liang, C. Y.

Mohan, N. K.

N. K. Mohan, H. O. Saldner, N. E. Molin, Opt. Commun. 108, 197 (1994).
[CrossRef]

Molin, N. E.

N. K. Mohan, H. O. Saldner, N. E. Molin, Opt. Commun. 108, 197 (1994).
[CrossRef]

Murata, K.

Ohde, N.

R. Onodera, Y. Ishii, N. Ohde, Y. Takahashi, T. Yoshino, J. Lightwave Technol. 13, 675 (1995).
[CrossRef]

Onodera, R.

R. Onodera, Y. Ishii, N. Ohde, Y. Takahashi, T. Yoshino, J. Lightwave Technol. 13, 675 (1995).
[CrossRef]

Saldner, H. O.

N. K. Mohan, H. O. Saldner, N. E. Molin, Opt. Commun. 108, 197 (1994).
[CrossRef]

Seiler, F.

F. Seiler, J. Srulijes, in Proceedings of 3rd International Symposium on Applications of Laser Anemometry to Fluid Mechanics (Springer-Verlag, Berlin, 1986), paper 191.

Srulijes, J.

F. Seiler, J. Srulijes, in Proceedings of 3rd International Symposium on Applications of Laser Anemometry to Fluid Mechanics (Springer-Verlag, Berlin, 1986), paper 191.

Takahashi, Y.

R. Onodera, Y. Ishii, N. Ohde, Y. Takahashi, T. Yoshino, J. Lightwave Technol. 13, 675 (1995).
[CrossRef]

Tatam, R. P.

H. D. Ford, H. Atcha, R. P. Tatam, Meas. Sci. Technol. 4, 601 (1993).
[CrossRef]

R. P. Tatam, J. C. Davies, C. H. Buckberry, J. D. C. Jones, Opt. Laser Technol. 22, 317 (1990).
[CrossRef]

Tatsuno, K.

Towers, D. P.

D. P. Towers, T. R. Judge, P. J. Bryanston-Cross, Opt. Lasers Eng. 14, 239 (1991).
[CrossRef]

Toyooka, S.

Tsunoda, Y.

Valera, J. D.

Yoshino, T.

R. Onodera, Y. Ishii, N. Ohde, Y. Takahashi, T. Yoshino, J. Lightwave Technol. 13, 675 (1995).
[CrossRef]

Appl. Opt. (3)

Electron. Lett. (1)

A. Dandridge, L. Goldberg, Electron. Lett. 18, 302 (1982).
[CrossRef]

J. Lightwave Technol. (1)

R. Onodera, Y. Ishii, N. Ohde, Y. Takahashi, T. Yoshino, J. Lightwave Technol. 13, 675 (1995).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Phys. E (1)

J. A. Leendertz, J. N. Butters, J. Phys. E 6, 1107 (1973).
[CrossRef]

Meas. Sci. Technol. (1)

H. D. Ford, H. Atcha, R. P. Tatam, Meas. Sci. Technol. 4, 601 (1993).
[CrossRef]

Opt. Commun. (1)

N. K. Mohan, H. O. Saldner, N. E. Molin, Opt. Commun. 108, 197 (1994).
[CrossRef]

Opt. Laser Technol. (1)

R. P. Tatam, J. C. Davies, C. H. Buckberry, J. D. C. Jones, Opt. Laser Technol. 22, 317 (1990).
[CrossRef]

Opt. Lasers Eng. (1)

D. P. Towers, T. R. Judge, P. J. Bryanston-Cross, Opt. Lasers Eng. 14, 239 (1991).
[CrossRef]

Opt. Lett. (2)

Proc. SPIE (1)

P. Hariharan, Proc. SPIE 1162, 86 (1989).

Other (2)

F. Seiler, J. Srulijes, in Proceedings of 3rd International Symposium on Applications of Laser Anemometry to Fluid Mechanics (Springer-Verlag, Berlin, 1986), paper 191.

K. Creath, in Interferogram Analysis—Digital Fringe Pattern Measurement Techniques, D. W. Robinson, G. T. Reid, eds. (Institute of Physics, Bristol, UK, 1993), pp. 94–140.

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Figures (4)

Fig. 1
Fig. 1

Optical configuration of the shearography system. BS, beam splitter; M1, mirror 1; M2, mirror 2 (with piezoelectric translator).

Fig. 2
Fig. 2

Unbalanced shearing head including the Perspex block.

Fig. 3
Fig. 3

Interferograms of the flat plate under deformation, for phase steps of (a) 0° and (b) 120°.

Fig. 4
Fig. 4

(a) Unwrapped phase map for the flat plate, representing the gradient of deformation. (b) Curves showing expected patterns of deformation and deformation gradient for the flat plate.

Equations (8)

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Δ ϕ = ( 2 π Δ l Δ ν ) / c ,
d = l ( n b n b 1 ) .
L = 2 l ( 1 + n b ) .
E tot = a ( x , y ) exp [ i θ ( x , y ) ] + a ( x + δ x , y ) exp [ i θ ( x + δ x , y ) ] ,
I = 4 a 2 sin [ ϕ + ( Δ / 2 ) ] sin ( Δ / 2 ) ,
Δ x = 2 π λ ( A u x + B v x + C w x ) δ x ,
Δ x 2 π λ ( 2 w x ) δ x ,
ϕ = tan 1 ( 3 I 1 I 3 2 I 2 I 1 I 3 ) .

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