Abstract

The introduction of a pulsed laser into an electronic speckle-shearing pattern interferometer allows high-speed transient deformations to be measured. We report on a computerized system that permits automatic data reduction by introducing carrier fringes through the translation of a diverging lens. The quantitative determination of the phase map that is due to deformation is carried out by the spatial synchronous detection method. Experimental results obtained for a metal plate transiently deformed by an electromagnetic hammer illustrate the advantages of the proposed system.

© 1998 Optical Society of America

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References

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  1. P. Boone, R. Verbiest, “Application of hologram interferometry to plate deformation and translation measurements,” Opt. Acta 16, 555–567 (1969).
    [CrossRef]
  2. J. A. Leendertz, J. N. Butters, “An image-shearing speckle-pattern interferometer for measuring bending moments,” J. Phys. E 6, 1107–1110 (1973).
    [CrossRef]
  3. R. Spooren, A. A. Dyrseth, M. Vaz, “Electronic shear interferometry: application of a (double-) pulsed laser,” Appl. Opt. 32, 4719–4727 (1993).
    [CrossRef] [PubMed]
  4. D. Kerr, G. H. Kaufmann, N. A. Halliwell, “Contrast enhancement of ESPI pulsed addition fringes,” Opt. Laser Eng. 20, 25–34 (1994).
    [CrossRef]
  5. A. Dávila, D. Kerr, G. H. Kaufmann, “Fast electro-optical system for pulsed ESPI carrier fringe generation,” Opt. Commun. 123, 457–464 (1996).
    [CrossRef]
  6. D. W. Templeton, Y. Y. Hung, “Shearographic fringe carrier method for data reduction computerization,” Opt. Eng. 28, 30–34 (1989).
    [CrossRef]
  7. J. Takezaki, Y. Y. Hung, “Direct measurement of flexural strains: plates by shearography,” J. Appl. Mech. 53, 125–129 (1986).
    [CrossRef]
  8. R. S. Sirohi, “Speckle methods in experimental mechanics,” in Speckle Metrology, R. S. Sirohi, ed. (Dekker, New York, 1993), pp. 99–155.
  9. C. W. Lindsey, M. K. Simon, eds., Phase-Locked Loops and Their Applications (IEEE Press, Piscataway, N.J., 1978).
  10. V. I. Vlad, D. Malacara, “Direct spatial reconstruction of optical phase from phase-modulated images,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1994), Vol. 23, pp. 261–317.
    [CrossRef]
  11. D. Kerr, G. H. Kaufmann, G. E. Galizzi, “Unwrapping of interferometric phase-fringe maps by the discrete cosine transform,” Appl. Opt. 35, 810–816 (1996).
    [CrossRef] [PubMed]
  12. J. D. Valera, J. D. C. Jones, “Phase stepping in fiber-based speckle shearing interferometry,” Opt. Lett. 19, 1161–1163 (1994).
    [CrossRef] [PubMed]

1996 (2)

A. Dávila, D. Kerr, G. H. Kaufmann, “Fast electro-optical system for pulsed ESPI carrier fringe generation,” Opt. Commun. 123, 457–464 (1996).
[CrossRef]

D. Kerr, G. H. Kaufmann, G. E. Galizzi, “Unwrapping of interferometric phase-fringe maps by the discrete cosine transform,” Appl. Opt. 35, 810–816 (1996).
[CrossRef] [PubMed]

1994 (2)

J. D. Valera, J. D. C. Jones, “Phase stepping in fiber-based speckle shearing interferometry,” Opt. Lett. 19, 1161–1163 (1994).
[CrossRef] [PubMed]

D. Kerr, G. H. Kaufmann, N. A. Halliwell, “Contrast enhancement of ESPI pulsed addition fringes,” Opt. Laser Eng. 20, 25–34 (1994).
[CrossRef]

1993 (1)

1989 (1)

D. W. Templeton, Y. Y. Hung, “Shearographic fringe carrier method for data reduction computerization,” Opt. Eng. 28, 30–34 (1989).
[CrossRef]

1986 (1)

J. Takezaki, Y. Y. Hung, “Direct measurement of flexural strains: plates by shearography,” J. Appl. Mech. 53, 125–129 (1986).
[CrossRef]

1973 (1)

J. A. Leendertz, J. N. Butters, “An image-shearing speckle-pattern interferometer for measuring bending moments,” J. Phys. E 6, 1107–1110 (1973).
[CrossRef]

1969 (1)

P. Boone, R. Verbiest, “Application of hologram interferometry to plate deformation and translation measurements,” Opt. Acta 16, 555–567 (1969).
[CrossRef]

Boone, P.

P. Boone, R. Verbiest, “Application of hologram interferometry to plate deformation and translation measurements,” Opt. Acta 16, 555–567 (1969).
[CrossRef]

Butters, J. N.

J. A. Leendertz, J. N. Butters, “An image-shearing speckle-pattern interferometer for measuring bending moments,” J. Phys. E 6, 1107–1110 (1973).
[CrossRef]

Dávila, A.

A. Dávila, D. Kerr, G. H. Kaufmann, “Fast electro-optical system for pulsed ESPI carrier fringe generation,” Opt. Commun. 123, 457–464 (1996).
[CrossRef]

Dyrseth, A. A.

Galizzi, G. E.

Halliwell, N. A.

D. Kerr, G. H. Kaufmann, N. A. Halliwell, “Contrast enhancement of ESPI pulsed addition fringes,” Opt. Laser Eng. 20, 25–34 (1994).
[CrossRef]

Hung, Y. Y.

D. W. Templeton, Y. Y. Hung, “Shearographic fringe carrier method for data reduction computerization,” Opt. Eng. 28, 30–34 (1989).
[CrossRef]

J. Takezaki, Y. Y. Hung, “Direct measurement of flexural strains: plates by shearography,” J. Appl. Mech. 53, 125–129 (1986).
[CrossRef]

Jones, J. D. C.

Kaufmann, G. H.

D. Kerr, G. H. Kaufmann, G. E. Galizzi, “Unwrapping of interferometric phase-fringe maps by the discrete cosine transform,” Appl. Opt. 35, 810–816 (1996).
[CrossRef] [PubMed]

A. Dávila, D. Kerr, G. H. Kaufmann, “Fast electro-optical system for pulsed ESPI carrier fringe generation,” Opt. Commun. 123, 457–464 (1996).
[CrossRef]

D. Kerr, G. H. Kaufmann, N. A. Halliwell, “Contrast enhancement of ESPI pulsed addition fringes,” Opt. Laser Eng. 20, 25–34 (1994).
[CrossRef]

Kerr, D.

A. Dávila, D. Kerr, G. H. Kaufmann, “Fast electro-optical system for pulsed ESPI carrier fringe generation,” Opt. Commun. 123, 457–464 (1996).
[CrossRef]

D. Kerr, G. H. Kaufmann, G. E. Galizzi, “Unwrapping of interferometric phase-fringe maps by the discrete cosine transform,” Appl. Opt. 35, 810–816 (1996).
[CrossRef] [PubMed]

D. Kerr, G. H. Kaufmann, N. A. Halliwell, “Contrast enhancement of ESPI pulsed addition fringes,” Opt. Laser Eng. 20, 25–34 (1994).
[CrossRef]

Leendertz, J. A.

J. A. Leendertz, J. N. Butters, “An image-shearing speckle-pattern interferometer for measuring bending moments,” J. Phys. E 6, 1107–1110 (1973).
[CrossRef]

Malacara, D.

V. I. Vlad, D. Malacara, “Direct spatial reconstruction of optical phase from phase-modulated images,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1994), Vol. 23, pp. 261–317.
[CrossRef]

Sirohi, R. S.

R. S. Sirohi, “Speckle methods in experimental mechanics,” in Speckle Metrology, R. S. Sirohi, ed. (Dekker, New York, 1993), pp. 99–155.

Spooren, R.

Takezaki, J.

J. Takezaki, Y. Y. Hung, “Direct measurement of flexural strains: plates by shearography,” J. Appl. Mech. 53, 125–129 (1986).
[CrossRef]

Templeton, D. W.

D. W. Templeton, Y. Y. Hung, “Shearographic fringe carrier method for data reduction computerization,” Opt. Eng. 28, 30–34 (1989).
[CrossRef]

Valera, J. D.

Vaz, M.

Verbiest, R.

P. Boone, R. Verbiest, “Application of hologram interferometry to plate deformation and translation measurements,” Opt. Acta 16, 555–567 (1969).
[CrossRef]

Vlad, V. I.

V. I. Vlad, D. Malacara, “Direct spatial reconstruction of optical phase from phase-modulated images,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1994), Vol. 23, pp. 261–317.
[CrossRef]

Appl. Opt. (2)

J. Appl. Mech. (1)

J. Takezaki, Y. Y. Hung, “Direct measurement of flexural strains: plates by shearography,” J. Appl. Mech. 53, 125–129 (1986).
[CrossRef]

J. Phys. E (1)

J. A. Leendertz, J. N. Butters, “An image-shearing speckle-pattern interferometer for measuring bending moments,” J. Phys. E 6, 1107–1110 (1973).
[CrossRef]

Opt. Acta (1)

P. Boone, R. Verbiest, “Application of hologram interferometry to plate deformation and translation measurements,” Opt. Acta 16, 555–567 (1969).
[CrossRef]

Opt. Commun. (1)

A. Dávila, D. Kerr, G. H. Kaufmann, “Fast electro-optical system for pulsed ESPI carrier fringe generation,” Opt. Commun. 123, 457–464 (1996).
[CrossRef]

Opt. Eng. (1)

D. W. Templeton, Y. Y. Hung, “Shearographic fringe carrier method for data reduction computerization,” Opt. Eng. 28, 30–34 (1989).
[CrossRef]

Opt. Laser Eng. (1)

D. Kerr, G. H. Kaufmann, N. A. Halliwell, “Contrast enhancement of ESPI pulsed addition fringes,” Opt. Laser Eng. 20, 25–34 (1994).
[CrossRef]

Opt. Lett. (1)

Other (3)

R. S. Sirohi, “Speckle methods in experimental mechanics,” in Speckle Metrology, R. S. Sirohi, ed. (Dekker, New York, 1993), pp. 99–155.

C. W. Lindsey, M. K. Simon, eds., Phase-Locked Loops and Their Applications (IEEE Press, Piscataway, N.J., 1978).

V. I. Vlad, D. Malacara, “Direct spatial reconstruction of optical phase from phase-modulated images,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1994), Vol. 23, pp. 261–317.
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Shearographic setup for carrier fringe generation: LB, laser beam; BS, beam splitter; M’s, mirrors; DL, diverging lens; CCD, video camera; O, object.

Fig. 2
Fig. 2

Experimental setup: LASER, Nd:YAG laser; BS, beam splitter; M’s, mirrors; DL, diverging lens; CCD, video camera; O, object; LS, loudspeaker; PG’s, pulse generators; PC, digital image processing system; VSYNC, vertical synchronization.

Fig. 3
Fig. 3

Timing diagram of the synchronization scheme: (a) video signal, (b) laser pulses, (c) start of impact.

Fig. 4
Fig. 4

Correlation fringes obtained by single-pulse subtraction speckle-shearing interferometry after the start of the impact: (a) 50 μs, (b) 100 μs.

Fig. 5
Fig. 5

Shear interferogram of reference carrier fringes with no load.

Fig. 6
Fig. 6

Shear interferogram of the impacted plate 50 μs after the start of the impact.

Fig. 7
Fig. 7

Wrapped phase distribution of the shear interferogram shown in Fig. 6.

Fig. 8
Fig. 8

Central part of Fig. 7: continuous phase distribution of the shear interferogram shown in Fig. 6 with the tilt that is due to the carrier fringes removed.

Fig. 9
Fig. 9

Lines of constant slope displacement obtained from Fig. 8 (units, nanometers per millimeter).

Equations (13)

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I 1 = 2 I 0 1 + cos   ψ r ,
I 2 = 2 I 0 1 + cos ψ r + Δ ψ c + Δ ψ d ,
I 12 = I 1 - I 2 2 = 4 I 0 sin ψ r + Δ ψ c + Δ ψ d 2 sin Δ ψ c + Δ ψ d 2 2 .
Δ ψ d = 2 π λ u x sin   θ + w x 1 + cos   θ Δ x ,
Δ W = x 2 + y 2 2 1 R 2 - 1 R 1 2 π λ ,
Δ ψ c = Δ W x   Δ x = Mx Δ x   R 1 - R 2 R 1 R 2 2 π λ .
Δ ψ c / 2 = m π .
d R 2 λ Mx 0 Δ x .
I 12 = 8 I 0 2 sin 2 ψ r + Δ ψ c + Δ ψ d 2 × 1 - exp - i Δ ψ c + Δ ψ d + exp i Δ ψ c + Δ ψ d 2 ,
I ˆ 12 = 4 I 0 2 sin 2 ψ r + Δ ψ c + Δ ψ d 2 2   exp - i Δ ψ c - exp - i 2 Δ ψ c + Δ ψ d - exp i Δ ψ d ,
S n x = I ¯ 12 sin 2 π xf c ,
C n x = I ¯ 12 cos 2 π xf c
ϕ n x = arctan S n x C n x .

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