Abstract

A novel TV holography method is proposed for parallel evaluation of in-plane and out-of-plane deformation fields. The method permits a trade-off between in-plane and out-of-plane measuring sensitivity. A four-exposure, four-frame phase shifting technique is used in the experiments; the experimental results for an aluminum specimen subjected to both rotation in its own plane and a bending couple load at the center are presented.

© 2000 Optical Society of America

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References

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  1. C. Joenathan, “Speckle photography, shearography, and ESPI,” in Optical Measurement Techniques and Applications, P. K. Rastogi, ed. (Artech House, Boston, Mass., 1997), Chap. 6, pp. 151–182.
  2. N. Krishna Mohan, H. O. Saldner, N.-E. Molin, “Electronic speckle pattern interferometry for simultaneous measurement of out-of-plane displacement and slope,” Opt. Lett. 18, 1861–1863 (1993).
    [CrossRef] [PubMed]
  3. H. O. Saldner, N. Krishna Mohan, N.-E. Molin, “Comparative TV holography for vibration analysis,” Opt. Eng. 34, 486–492 (1995).
    [CrossRef]
  4. N. Krishna Mohan, H. O. Saldner, N.-E. Molin, “Recent applications of TV holography and shearography,” in Laser Interferometry VIII: Applications, R. J. Pryputniewicz, G. M. Brown, W. O. Jüptner, eds., Proc. SPIE2861, 248–256 (1996).
    [CrossRef]
  5. G. Pedrini, Y.-L. Zou, H. J. Tiziani, “Simultaneous quantitative evaluation of in-plane and out-of-plane deformations by use of a multidirectional spatial carrier,” Appl. Opt. 36, 786–792 (1997).
    [CrossRef] [PubMed]
  6. M. Sjödahl, H. O. Saldner, “Three-dimensional deformation field measurements with simultaneous TV holography and electronic speckle photography,” Appl. Opt. 36, 3645–3648 (1997).
    [CrossRef] [PubMed]
  7. K. A. Stetson, W. R. Brohinsky, J. Wahid, T. Bushman, “An electro-optic holography system with real-time arithmetic processing,” J. Nondestruct. Eval. 8, 69–76 (1989).
    [CrossRef]
  8. A. Sohmer, C. Joenathan, “Twofold increase in sensitivity with a dual-beam illumination arrangement for electronic speckle pattern interferometry,” Opt. Eng. 35, 1943–1948 (1996).
    [CrossRef]
  9. N. Krishna Mohan, “Measurement of in-plane displacement with twofold sensitivity using phase reversal technique,” Opt. Eng. (to be published).
  10. R. J. Pryputniewicz, “Electro-optic holography,” in Holographic Interferometry—Principles and Methods, P. K. Rastogi, ed. (Springer-Verlag, Berlin, 1994), Chap. 3, pp. 59–74.

1997 (2)

1996 (1)

A. Sohmer, C. Joenathan, “Twofold increase in sensitivity with a dual-beam illumination arrangement for electronic speckle pattern interferometry,” Opt. Eng. 35, 1943–1948 (1996).
[CrossRef]

1995 (1)

H. O. Saldner, N. Krishna Mohan, N.-E. Molin, “Comparative TV holography for vibration analysis,” Opt. Eng. 34, 486–492 (1995).
[CrossRef]

1993 (1)

1989 (1)

K. A. Stetson, W. R. Brohinsky, J. Wahid, T. Bushman, “An electro-optic holography system with real-time arithmetic processing,” J. Nondestruct. Eval. 8, 69–76 (1989).
[CrossRef]

Brohinsky, W. R.

K. A. Stetson, W. R. Brohinsky, J. Wahid, T. Bushman, “An electro-optic holography system with real-time arithmetic processing,” J. Nondestruct. Eval. 8, 69–76 (1989).
[CrossRef]

Bushman, T.

K. A. Stetson, W. R. Brohinsky, J. Wahid, T. Bushman, “An electro-optic holography system with real-time arithmetic processing,” J. Nondestruct. Eval. 8, 69–76 (1989).
[CrossRef]

Joenathan, C.

A. Sohmer, C. Joenathan, “Twofold increase in sensitivity with a dual-beam illumination arrangement for electronic speckle pattern interferometry,” Opt. Eng. 35, 1943–1948 (1996).
[CrossRef]

C. Joenathan, “Speckle photography, shearography, and ESPI,” in Optical Measurement Techniques and Applications, P. K. Rastogi, ed. (Artech House, Boston, Mass., 1997), Chap. 6, pp. 151–182.

Krishna Mohan, N.

H. O. Saldner, N. Krishna Mohan, N.-E. Molin, “Comparative TV holography for vibration analysis,” Opt. Eng. 34, 486–492 (1995).
[CrossRef]

N. Krishna Mohan, H. O. Saldner, N.-E. Molin, “Electronic speckle pattern interferometry for simultaneous measurement of out-of-plane displacement and slope,” Opt. Lett. 18, 1861–1863 (1993).
[CrossRef] [PubMed]

N. Krishna Mohan, “Measurement of in-plane displacement with twofold sensitivity using phase reversal technique,” Opt. Eng. (to be published).

N. Krishna Mohan, H. O. Saldner, N.-E. Molin, “Recent applications of TV holography and shearography,” in Laser Interferometry VIII: Applications, R. J. Pryputniewicz, G. M. Brown, W. O. Jüptner, eds., Proc. SPIE2861, 248–256 (1996).
[CrossRef]

Molin, N.-E.

H. O. Saldner, N. Krishna Mohan, N.-E. Molin, “Comparative TV holography for vibration analysis,” Opt. Eng. 34, 486–492 (1995).
[CrossRef]

N. Krishna Mohan, H. O. Saldner, N.-E. Molin, “Electronic speckle pattern interferometry for simultaneous measurement of out-of-plane displacement and slope,” Opt. Lett. 18, 1861–1863 (1993).
[CrossRef] [PubMed]

N. Krishna Mohan, H. O. Saldner, N.-E. Molin, “Recent applications of TV holography and shearography,” in Laser Interferometry VIII: Applications, R. J. Pryputniewicz, G. M. Brown, W. O. Jüptner, eds., Proc. SPIE2861, 248–256 (1996).
[CrossRef]

Pedrini, G.

Pryputniewicz, R. J.

R. J. Pryputniewicz, “Electro-optic holography,” in Holographic Interferometry—Principles and Methods, P. K. Rastogi, ed. (Springer-Verlag, Berlin, 1994), Chap. 3, pp. 59–74.

Saldner, H. O.

M. Sjödahl, H. O. Saldner, “Three-dimensional deformation field measurements with simultaneous TV holography and electronic speckle photography,” Appl. Opt. 36, 3645–3648 (1997).
[CrossRef] [PubMed]

H. O. Saldner, N. Krishna Mohan, N.-E. Molin, “Comparative TV holography for vibration analysis,” Opt. Eng. 34, 486–492 (1995).
[CrossRef]

N. Krishna Mohan, H. O. Saldner, N.-E. Molin, “Electronic speckle pattern interferometry for simultaneous measurement of out-of-plane displacement and slope,” Opt. Lett. 18, 1861–1863 (1993).
[CrossRef] [PubMed]

N. Krishna Mohan, H. O. Saldner, N.-E. Molin, “Recent applications of TV holography and shearography,” in Laser Interferometry VIII: Applications, R. J. Pryputniewicz, G. M. Brown, W. O. Jüptner, eds., Proc. SPIE2861, 248–256 (1996).
[CrossRef]

Sjödahl, M.

Sohmer, A.

A. Sohmer, C. Joenathan, “Twofold increase in sensitivity with a dual-beam illumination arrangement for electronic speckle pattern interferometry,” Opt. Eng. 35, 1943–1948 (1996).
[CrossRef]

Stetson, K. A.

K. A. Stetson, W. R. Brohinsky, J. Wahid, T. Bushman, “An electro-optic holography system with real-time arithmetic processing,” J. Nondestruct. Eval. 8, 69–76 (1989).
[CrossRef]

Tiziani, H. J.

Wahid, J.

K. A. Stetson, W. R. Brohinsky, J. Wahid, T. Bushman, “An electro-optic holography system with real-time arithmetic processing,” J. Nondestruct. Eval. 8, 69–76 (1989).
[CrossRef]

Zou, Y.-L.

Appl. Opt. (2)

J. Nondestruct. Eval. (1)

K. A. Stetson, W. R. Brohinsky, J. Wahid, T. Bushman, “An electro-optic holography system with real-time arithmetic processing,” J. Nondestruct. Eval. 8, 69–76 (1989).
[CrossRef]

Opt. Eng. (2)

A. Sohmer, C. Joenathan, “Twofold increase in sensitivity with a dual-beam illumination arrangement for electronic speckle pattern interferometry,” Opt. Eng. 35, 1943–1948 (1996).
[CrossRef]

H. O. Saldner, N. Krishna Mohan, N.-E. Molin, “Comparative TV holography for vibration analysis,” Opt. Eng. 34, 486–492 (1995).
[CrossRef]

Opt. Lett. (1)

Other (4)

N. Krishna Mohan, H. O. Saldner, N.-E. Molin, “Recent applications of TV holography and shearography,” in Laser Interferometry VIII: Applications, R. J. Pryputniewicz, G. M. Brown, W. O. Jüptner, eds., Proc. SPIE2861, 248–256 (1996).
[CrossRef]

N. Krishna Mohan, “Measurement of in-plane displacement with twofold sensitivity using phase reversal technique,” Opt. Eng. (to be published).

R. J. Pryputniewicz, “Electro-optic holography,” in Holographic Interferometry—Principles and Methods, P. K. Rastogi, ed. (Springer-Verlag, Berlin, 1994), Chap. 3, pp. 59–74.

C. Joenathan, “Speckle photography, shearography, and ESPI,” in Optical Measurement Techniques and Applications, P. K. Rastogi, ed. (Artech House, Boston, Mass., 1997), Chap. 6, pp. 151–182.

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Figures (4)

Fig. 1
Fig. 1

Schematic arrangement for simultaneous measurement of in-plane and out-of-plane deformations: BS’s, beam splitters; M’s, mirrors; PZM, piezoelectric mirror; S’s, mechanical shutters; k, propagation vectors.

Fig. 2
Fig. 2

(a) In-plane rotation fringes (u component), (b) phase map for in-plane rotation. We obtain the experimental results by combining the set of phase-shifted images from exposure 1 with exposure 3 from image A.

Fig. 3
Fig. 3

(a) Out-of-plane deformation fringes (w component), (b) phase map for out-of-plane deformation. We obtain the experimental results by combining the set of phase shifted images from exposure 2 with exposure 4 from image B.

Fig. 4
Fig. 4

(a) Measured in-plane deformation component, (b) measured out-of-plane deformation.

Equations (10)

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Ininitial 1=I1+I2+2I1I2 cosφ+nπ/2,
Ininitial 2=I1+Ir+2I1Ir cosφ+nπ/2,
Infinal 1=I1+I2+2I1I2 cosφ+Δϕ+nπ/2,
Infinal 2=I1+Ir+2I1Ir cosφ+Δϕ+nπ/2,
Δϕ=-k1-k1L--k2-k1L=k2-k1L,
Δϕ=-k2-k1L=-k2+k1L.
IImage A=|8I1I2 cosΔϕ/2|2, IImage B=|8I1Ir cosΔϕ/2|2.
k1=2πλ-ıˆ sin θ-kˆ cos θ, k2=2πλıˆ sin θ-kˆ cos θ, L=ıˆu+jˆv+kˆw.
Δϕ=4πλ u sin θ,
Δϕ=4πλ w cos θ.

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