Abstract

Digital speckle pattern interferometry (DSPI) and digital shearography (DS) are well known optical tools for qualitative as well as quantitative measurements of displacement components and its derivatives of engineering structures subjected either static or dynamic load. Spatial phase shifting (SPS) technique is useful for extracting quantitative displacement data from the system with only two frames. Optical configurations for DSPI and DS with a double aperture mask in front of the imaging lens for spatial phase shifting are proposed in this paper for the measurement of out-of-plane displacement and its first order derivative (slope) respectively. An error compensating four-phase step algorithm is used for quantitative fringe analysis.

© 2006 Optical Society of America

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References

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  1. J. N. Butter, R. C. Jones and C. Wykes, "Electronic speckle pattern interferometry," in R. K. Erf, ed. Speckle Metrology (Academic Press, New York 1978).
  2. P. Meinlschmidt, K. D. Hinsch and R. S. Sirohi eds. Selected papers on electronic speckle pattern interferometry: Principles and Practice, MS132 (Optical Engineering Press, SPIE, Washington, DC., 1996).
  3. P. K. Rastogi, "Techniques of displacement and deformation measurements in speckle metrology," in Speckle Metrology, R. S. Sirohi, ed. (Marcel Dekker, New York, 1993), Chap.2.
  4. P. K. Rastogi, ed. Digital speckle pattern interferometry and related techniques (John Wiley, England, 2001).
  5. W. Steinchen, and L. Yang, Digital shearography: Theory and Application of digital speckle pattern shearing interferometry, PM100 (Optical Engineering Press, SPIE, Washington, DC., 2003).
    [PubMed]
  6. K. Creath, "Phase measurement interferometry techniques," in Progress in optics, vol. xxvi, E. Wolf, ed. (Amsterdam, North-Holland, 1998).
  7. K. Creath, "Phase-shifting speckle interferometry," Appl. Opt. 243053-3058 (1985).
    [CrossRef] [PubMed]
  8. M. Kujawinska, "Spatial phase measurement methods," in Interferogram Analysis -Digital Fringe Pattern Measurement Techniques, D. W. Robinson and G. T. Reid, eds. (Institute of Physics, Bristol, U.K, 1993) Chap.5.
  9. A. J. P. van Haasteren and H.J. Frankena, "Real-time displacement measurement using a multicamera phase-stepping speckle interferometer," Appl. Opt. 33, 4137-4142 (1994).
    [CrossRef]
  10. M. Servin and F. J. Cuevas, "A novel technique for spatial phase-shifting interferometry," J. Mod. Opt. 42, 1853-1862 (1995).
    [CrossRef]
  11. G. Pedrini, Y. L. Zou, and H. Tiziani, "Quantitative evaluation of digital shearing interferogram using the spatial carrier method," Pure Appl. Opt. 5, 313-321 (1996).
    [CrossRef]
  12. R. S. Sirohi, J. Burke, H. Helmers and K. D. Hinsch, "Spatial phase shifting for pure in-plane displacement and displacement-derivative measurements in electronic speckle pattern interferometry (ESPI)," Appl. Opt. 36, 5787- 5791 (1997).
    [CrossRef] [PubMed]
  13. J. Burke, "Application and optimization of the spatial phase shifting technique in digital speckle interferometry," PhD dissertation, Carl von Ossietzky University, Oldenburg, Germany (2000), http://www.physik.uni-oldenburg.de/holo/443.html.
  14. J. A. Leendertz, "Interferometric displacement measurement on scattering surfaces utilizing speckle effect," J. Phys. E: Sci. Instrum. 3, 214-218 (1970).
    [CrossRef]
  15. R. K. Mohanty, C. Joenathan and R. S. Sirohi, "Speckle interferometric methods of measuring small out-of-plane displacements," Opt. Lett. 9, 475-477 (1984).
    [CrossRef] [PubMed]
  16. R. S. Sirohi and N. Krishna Mohan, "An in-plane insensitive multiaperture speckle shear interferometer for slope measurement," Opt. Laser Technol. 29, 415-417 (1997).
    [CrossRef]
  17. J. Schwider, O. Falkenstörfer, H. Schreiber, A. Zöller and N. Streibl, "New compensating four-phase algorithm for phase-shift interferometry," Opt. Eng. 32, 1883-1885 (1993).
    [CrossRef]
  18. J. Huntley, "Random phase measurement errors in digital speckle interferometry," Opt. Lasers Eng. 26, 131-150 (1997).
    [CrossRef]
  19. D. C. Ghiglia, and L. A. Romero, "Robust two-dimensional weighted and un-weighted phase unwrapping that uses fast transforms and iterative methods," J. Opt. Soc. Am. A 11, 107-117 (1994).
    [CrossRef]

1997 (3)

R. S. Sirohi, J. Burke, H. Helmers and K. D. Hinsch, "Spatial phase shifting for pure in-plane displacement and displacement-derivative measurements in electronic speckle pattern interferometry (ESPI)," Appl. Opt. 36, 5787- 5791 (1997).
[CrossRef] [PubMed]

R. S. Sirohi and N. Krishna Mohan, "An in-plane insensitive multiaperture speckle shear interferometer for slope measurement," Opt. Laser Technol. 29, 415-417 (1997).
[CrossRef]

J. Huntley, "Random phase measurement errors in digital speckle interferometry," Opt. Lasers Eng. 26, 131-150 (1997).
[CrossRef]

1996 (1)

G. Pedrini, Y. L. Zou, and H. Tiziani, "Quantitative evaluation of digital shearing interferogram using the spatial carrier method," Pure Appl. Opt. 5, 313-321 (1996).
[CrossRef]

1995 (1)

M. Servin and F. J. Cuevas, "A novel technique for spatial phase-shifting interferometry," J. Mod. Opt. 42, 1853-1862 (1995).
[CrossRef]

1994 (2)

1993 (1)

J. Schwider, O. Falkenstörfer, H. Schreiber, A. Zöller and N. Streibl, "New compensating four-phase algorithm for phase-shift interferometry," Opt. Eng. 32, 1883-1885 (1993).
[CrossRef]

1985 (1)

1984 (1)

1970 (1)

J. A. Leendertz, "Interferometric displacement measurement on scattering surfaces utilizing speckle effect," J. Phys. E: Sci. Instrum. 3, 214-218 (1970).
[CrossRef]

Burke, J.

Creath, K.

Cuevas, F. J.

M. Servin and F. J. Cuevas, "A novel technique for spatial phase-shifting interferometry," J. Mod. Opt. 42, 1853-1862 (1995).
[CrossRef]

Falkenstörfer, O.

J. Schwider, O. Falkenstörfer, H. Schreiber, A. Zöller and N. Streibl, "New compensating four-phase algorithm for phase-shift interferometry," Opt. Eng. 32, 1883-1885 (1993).
[CrossRef]

Frankena, H.J.

Ghiglia, D. C.

Helmers, H.

Hinsch, K. D.

Huntley, J.

J. Huntley, "Random phase measurement errors in digital speckle interferometry," Opt. Lasers Eng. 26, 131-150 (1997).
[CrossRef]

Joenathan, C.

Krishna Mohan, N.

R. S. Sirohi and N. Krishna Mohan, "An in-plane insensitive multiaperture speckle shear interferometer for slope measurement," Opt. Laser Technol. 29, 415-417 (1997).
[CrossRef]

Leendertz, J. A.

J. A. Leendertz, "Interferometric displacement measurement on scattering surfaces utilizing speckle effect," J. Phys. E: Sci. Instrum. 3, 214-218 (1970).
[CrossRef]

Mohanty, R. K.

Pedrini, G.

G. Pedrini, Y. L. Zou, and H. Tiziani, "Quantitative evaluation of digital shearing interferogram using the spatial carrier method," Pure Appl. Opt. 5, 313-321 (1996).
[CrossRef]

Romero, L. A.

Schreiber, H.

J. Schwider, O. Falkenstörfer, H. Schreiber, A. Zöller and N. Streibl, "New compensating four-phase algorithm for phase-shift interferometry," Opt. Eng. 32, 1883-1885 (1993).
[CrossRef]

Schwider, J.

J. Schwider, O. Falkenstörfer, H. Schreiber, A. Zöller and N. Streibl, "New compensating four-phase algorithm for phase-shift interferometry," Opt. Eng. 32, 1883-1885 (1993).
[CrossRef]

Servin, M.

M. Servin and F. J. Cuevas, "A novel technique for spatial phase-shifting interferometry," J. Mod. Opt. 42, 1853-1862 (1995).
[CrossRef]

Sirohi, R. S.

Streibl, N.

J. Schwider, O. Falkenstörfer, H. Schreiber, A. Zöller and N. Streibl, "New compensating four-phase algorithm for phase-shift interferometry," Opt. Eng. 32, 1883-1885 (1993).
[CrossRef]

Tiziani, H.

G. Pedrini, Y. L. Zou, and H. Tiziani, "Quantitative evaluation of digital shearing interferogram using the spatial carrier method," Pure Appl. Opt. 5, 313-321 (1996).
[CrossRef]

van Haasteren, A. J. P.

Zöller, A.

J. Schwider, O. Falkenstörfer, H. Schreiber, A. Zöller and N. Streibl, "New compensating four-phase algorithm for phase-shift interferometry," Opt. Eng. 32, 1883-1885 (1993).
[CrossRef]

Zou, Y. L.

G. Pedrini, Y. L. Zou, and H. Tiziani, "Quantitative evaluation of digital shearing interferogram using the spatial carrier method," Pure Appl. Opt. 5, 313-321 (1996).
[CrossRef]

Appl. Opt. (3)

J. Mod. Opt. (1)

M. Servin and F. J. Cuevas, "A novel technique for spatial phase-shifting interferometry," J. Mod. Opt. 42, 1853-1862 (1995).
[CrossRef]

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

J. Phys. E: Sci. Instrum. (1)

J. A. Leendertz, "Interferometric displacement measurement on scattering surfaces utilizing speckle effect," J. Phys. E: Sci. Instrum. 3, 214-218 (1970).
[CrossRef]

Opt. Eng. (1)

J. Schwider, O. Falkenstörfer, H. Schreiber, A. Zöller and N. Streibl, "New compensating four-phase algorithm for phase-shift interferometry," Opt. Eng. 32, 1883-1885 (1993).
[CrossRef]

Opt. Laser Technol. (1)

R. S. Sirohi and N. Krishna Mohan, "An in-plane insensitive multiaperture speckle shear interferometer for slope measurement," Opt. Laser Technol. 29, 415-417 (1997).
[CrossRef]

Opt. Lasers Eng. (1)

J. Huntley, "Random phase measurement errors in digital speckle interferometry," Opt. Lasers Eng. 26, 131-150 (1997).
[CrossRef]

Opt. Lett. (1)

Pure Appl. Opt. (1)

G. Pedrini, Y. L. Zou, and H. Tiziani, "Quantitative evaluation of digital shearing interferogram using the spatial carrier method," Pure Appl. Opt. 5, 313-321 (1996).
[CrossRef]

Other (8)

M. Kujawinska, "Spatial phase measurement methods," in Interferogram Analysis -Digital Fringe Pattern Measurement Techniques, D. W. Robinson and G. T. Reid, eds. (Institute of Physics, Bristol, U.K, 1993) Chap.5.

J. N. Butter, R. C. Jones and C. Wykes, "Electronic speckle pattern interferometry," in R. K. Erf, ed. Speckle Metrology (Academic Press, New York 1978).

P. Meinlschmidt, K. D. Hinsch and R. S. Sirohi eds. Selected papers on electronic speckle pattern interferometry: Principles and Practice, MS132 (Optical Engineering Press, SPIE, Washington, DC., 1996).

P. K. Rastogi, "Techniques of displacement and deformation measurements in speckle metrology," in Speckle Metrology, R. S. Sirohi, ed. (Marcel Dekker, New York, 1993), Chap.2.

P. K. Rastogi, ed. Digital speckle pattern interferometry and related techniques (John Wiley, England, 2001).

W. Steinchen, and L. Yang, Digital shearography: Theory and Application of digital speckle pattern shearing interferometry, PM100 (Optical Engineering Press, SPIE, Washington, DC., 2003).
[PubMed]

K. Creath, "Phase measurement interferometry techniques," in Progress in optics, vol. xxvi, E. Wolf, ed. (Amsterdam, North-Holland, 1998).

J. Burke, "Application and optimization of the spatial phase shifting technique in digital speckle interferometry," PhD dissertation, Carl von Ossietzky University, Oldenburg, Germany (2000), http://www.physik.uni-oldenburg.de/holo/443.html.

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Figures (6)

Fig. 1.
Fig. 1.

Schematic of an out-of-plane sensitive digital speckle pattern interferometry arrangement: O, Object; RM, Reference mirror; BS, Beam splitter; M, Mirrors; P, Front surfaces coated right angle prism; A, double-aperture mask; GG, Ground glass; L, Imaging Lens.

Fig. 2.
Fig. 2.

Schematic of an in-plane insensitive digital shearography arrangement: O, Diffusely reflecting surface; BS1, Beam splitter; BS2, Cube beam splitter; M1-M5, Mirrors; P, Front surfaces coated right angle prism; A, Two-aperture mask; L, Lens.

Fig. 3.
Fig. 3.

Magnified portion of the speckle pattern with double aperture arrangement revealing the spatial carrier fringe

Fig. 4.
Fig. 4.

Speckle correlation fringes with spatial phase shift: (a) -90° and (b) 0°

Fig. 5.
Fig. 5.

Out-of-plane displacement measurement: (a) raw and (b) filtered phase maps, (c) unwrapped 2D and (d) 3D plots

Fig. 6.
Fig. 6.

Slope measurement: (a) raw and (b) filtered phase maps, (c) unwrapped 2D and (d) 3D plots

Equations (8)

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Δ ϕ ( x , y ) = 4 π λ w ( x , y )
Δ ϕ = 4 π λ w x Δ x
Δ φ = 2 π λ D V x
d a D i . e . d s 1.22 = λ V d a λ V D = 2 π ω 0
I n ( x k + n , y ) = I b ( x k + n , y ) + γ ( x k + n , y ) cos [ ϕ ( x k + n , y ) + ω 0 ( k + n ) ) ]
ϕ ( x k , y ) + ω 0 k = tan 1 ( ( I 1 + I 2 + I 4 ) 3 I 3 3 I 2 ( I 1 + I 3 + I 4 ) ) = tan 1 ( N s D s )
I n , c ( x , y ) = I f ( x k + n , y l ) I i ( x k , y l )
Δ ϕ ( x , y ) = tan 1 ( N f D i N i D f N f N i + D f D i ) = tan 1 ( N D )

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