Abstract

A photopolymer holographic grating is used to produce the two sheared images in an electronic speckle pattern shearing interferometer. A ground glass screen following the grating eliminates unwanted diffraction orders and removes the requirement for the CCD camera to resolve the diffraction grating’s pitch. The sheared images on the ground glass are further imaged onto the CCD camera. The fringe pattern contrast was estimated to be above 90%. A validation of the system was done by comparing the theoretical phase difference distribution with the experimental data from the three-point bending test.

© 2004 Optical Society of America

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References

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  1. Y. Iwahashi, K. Iwata, R. Nagata, “Single-aperture speckle shearing interferometry with a single grating,” Appl. Opt. 23, 247–249 (1984).
    [CrossRef] [PubMed]
  2. C. Joenathan, R. S. Sirohi, “Holographic gratings in speckle shearing interferometry,” Appl. Opt. 24, 2750–2751 (1985).
    [CrossRef] [PubMed]
  3. H. Rabal, R. Henao, R. Torroba, “Digital speckle pattern shearing interferometry using diffraction gratings,” Optics Commun. 126, 191–196 (1996).
    [CrossRef]
  4. C. Joenathan, L. Bürkle, “Electronic speckle pattern shearing interferometer using holographic gratings,” Opt. Eng. 36, 2473–2477 (1997).
    [CrossRef]
  5. S. Martin, P. Leclère, V. Toal, Y. Renotte, Y. Lion, “Characterisation of acrylamide-based photopolymer holographic recording material,” Opt. Eng. 32, 3942–3946 (1994).
  6. C. M. Vest, Holographic Interferometry (Wiley, New York, 1979).
  7. Y. Y. Hung, C. Y. Liang, “Image shearing camera for direct measurement of surface-strains,” Appl. Opt. 10, 1046–1050 (1979).
    [CrossRef]
  8. T. J. Lardner, R. R. Archer, Mechanics of Solids (McGraw-Hill, New York, 1994).

1997

C. Joenathan, L. Bürkle, “Electronic speckle pattern shearing interferometer using holographic gratings,” Opt. Eng. 36, 2473–2477 (1997).
[CrossRef]

1996

H. Rabal, R. Henao, R. Torroba, “Digital speckle pattern shearing interferometry using diffraction gratings,” Optics Commun. 126, 191–196 (1996).
[CrossRef]

1994

S. Martin, P. Leclère, V. Toal, Y. Renotte, Y. Lion, “Characterisation of acrylamide-based photopolymer holographic recording material,” Opt. Eng. 32, 3942–3946 (1994).

1985

1984

1979

Y. Y. Hung, C. Y. Liang, “Image shearing camera for direct measurement of surface-strains,” Appl. Opt. 10, 1046–1050 (1979).
[CrossRef]

Archer, R. R.

T. J. Lardner, R. R. Archer, Mechanics of Solids (McGraw-Hill, New York, 1994).

Bürkle, L.

C. Joenathan, L. Bürkle, “Electronic speckle pattern shearing interferometer using holographic gratings,” Opt. Eng. 36, 2473–2477 (1997).
[CrossRef]

Henao, R.

H. Rabal, R. Henao, R. Torroba, “Digital speckle pattern shearing interferometry using diffraction gratings,” Optics Commun. 126, 191–196 (1996).
[CrossRef]

Hung, Y. Y.

Y. Y. Hung, C. Y. Liang, “Image shearing camera for direct measurement of surface-strains,” Appl. Opt. 10, 1046–1050 (1979).
[CrossRef]

Iwahashi, Y.

Iwata, K.

Joenathan, C.

C. Joenathan, L. Bürkle, “Electronic speckle pattern shearing interferometer using holographic gratings,” Opt. Eng. 36, 2473–2477 (1997).
[CrossRef]

C. Joenathan, R. S. Sirohi, “Holographic gratings in speckle shearing interferometry,” Appl. Opt. 24, 2750–2751 (1985).
[CrossRef] [PubMed]

Lardner, T. J.

T. J. Lardner, R. R. Archer, Mechanics of Solids (McGraw-Hill, New York, 1994).

Leclère, P.

S. Martin, P. Leclère, V. Toal, Y. Renotte, Y. Lion, “Characterisation of acrylamide-based photopolymer holographic recording material,” Opt. Eng. 32, 3942–3946 (1994).

Liang, C. Y.

Y. Y. Hung, C. Y. Liang, “Image shearing camera for direct measurement of surface-strains,” Appl. Opt. 10, 1046–1050 (1979).
[CrossRef]

Lion, Y.

S. Martin, P. Leclère, V. Toal, Y. Renotte, Y. Lion, “Characterisation of acrylamide-based photopolymer holographic recording material,” Opt. Eng. 32, 3942–3946 (1994).

Martin, S.

S. Martin, P. Leclère, V. Toal, Y. Renotte, Y. Lion, “Characterisation of acrylamide-based photopolymer holographic recording material,” Opt. Eng. 32, 3942–3946 (1994).

Nagata, R.

Rabal, H.

H. Rabal, R. Henao, R. Torroba, “Digital speckle pattern shearing interferometry using diffraction gratings,” Optics Commun. 126, 191–196 (1996).
[CrossRef]

Renotte, Y.

S. Martin, P. Leclère, V. Toal, Y. Renotte, Y. Lion, “Characterisation of acrylamide-based photopolymer holographic recording material,” Opt. Eng. 32, 3942–3946 (1994).

Sirohi, R. S.

Toal, V.

S. Martin, P. Leclère, V. Toal, Y. Renotte, Y. Lion, “Characterisation of acrylamide-based photopolymer holographic recording material,” Opt. Eng. 32, 3942–3946 (1994).

Torroba, R.

H. Rabal, R. Henao, R. Torroba, “Digital speckle pattern shearing interferometry using diffraction gratings,” Optics Commun. 126, 191–196 (1996).
[CrossRef]

Vest, C. M.

C. M. Vest, Holographic Interferometry (Wiley, New York, 1979).

Appl. Opt.

Opt. Eng.

C. Joenathan, L. Bürkle, “Electronic speckle pattern shearing interferometer using holographic gratings,” Opt. Eng. 36, 2473–2477 (1997).
[CrossRef]

S. Martin, P. Leclère, V. Toal, Y. Renotte, Y. Lion, “Characterisation of acrylamide-based photopolymer holographic recording material,” Opt. Eng. 32, 3942–3946 (1994).

Optics Commun.

H. Rabal, R. Henao, R. Torroba, “Digital speckle pattern shearing interferometry using diffraction gratings,” Optics Commun. 126, 191–196 (1996).
[CrossRef]

Other

C. M. Vest, Holographic Interferometry (Wiley, New York, 1979).

T. J. Lardner, R. R. Archer, Mechanics of Solids (McGraw-Hill, New York, 1994).

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Figures (5)

Fig. 1
Fig. 1

An optical setup of the ESPSI system with a photopolymer grating.

Fig. 2
Fig. 2

Deformation of a symmetric beam subjected to pure bending in its plane of symmetry.

Fig. 3
Fig. 3

ESPSI fringes in aluminium tin filled with hot water recorded during cooling a) at the beginning, b) after 3 s, c) after 6 s, d) after 9 s. The field of view is 20 mm × 26 mm.

Fig. 4
Fig. 4

ESPSI fringes on PVC during pure bending under deflection of a) 5 μm, b) 20 μm. The field of view is 19 mm × 22 mm. The shear is Δx = 6 mm.

Fig. 5
Fig. 5

Distribution of the phase difference versus the distance on the x axis: ––––, 30-μm deflection (theory); ao-43-12-2439-i001, 30-μm deflection (experiment); ┅┅┅, 35-μm deflection (theory); ao-43-12-2439-i002, 35-μm deflection (experiment); ———, 40-μm deflection (theory); ao-43-12-2439-i003, 40-μm deflection (experiment). The error bars in the y direction are within the size of the symbols.

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

Φ=2πλ nL-β,
Δ=Φλ δλ+Φn δn+ΦL δL=-2πLnλ2 δλ+2πLλ δn+2πnλ δL,
Δ=2πλAδu+Bδν+Cδw,
Δ=2πλA ux+B νx+C wx.
Δ=2πλA ux+C wx.
Δ=2πλuxsin θ+wx1+cos θΔx.
uxsin θ+wx1+cos θ=λnΔx.
ε=ux=zR,
s=R-R2-D221/2,
ε=ux=4dsD2+4s2,
wxx=-PL2-4x216EI 0xL2,
wxx=-P3L-2x2x-L16EIL2xL,

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