Abstract

Real-time methods for differentiation of in-plane displacement fields produced by the moire interferometry technique are introduced. Two approaches are developed: (1) optical shearing of displacement patterns and (2) superposition of two lateral shear interferograms of wavefronts from 2 diffraction orders of the specimen grating. Coherence problems are circumvented by polarization effects. In both cases additive-type moire fringes give the map of displacement derivatives of the object under load. The issue of carrier patterns and extraneous fractional fringe order is clarified. Experimental verification of the principle is presented.

© 1987 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. Post, “Developments in Moire Interferometry,” Opt. Eng. 21, 458 (May1982).
  2. D. Post, “Moire Interferometry,” in SEM Handbook on Experimental Mechanics, A. S. Kobayashi, Ed. (Prentice-Hall, Englewood Cliffs, NJ, 1986).
  3. A. McDonach, J. McKelvie, P. Mackenzie, C. A. Walker, “Improved Moire Interferometry and Applications in Fracture Mechanics, Residual Stress and Damaged Composites,” Exp. Tech. 23, No. 2, 20 (June1983).
    [CrossRef]
  4. E. M. Weissman, D. Post, “Full-Field Displacement and Strain Rosettes by Moire Interferometry,” Exp. Mech. 22, No. 9, 324 (1982).
    [CrossRef]
  5. E. M. Weissman, D. Post, A. Asundi, “Whole-Field Strain Determination by Moire Shearing Interferometry,” J. Strain Anal. 19, No. 2, 77 (1984).
    [CrossRef]
  6. L. Pirroda, “Strain Analysis by Grating Interferometry,” Opt. Laser Eng. 5, No. 1, 7 (1984).
    [CrossRef]

1984 (2)

E. M. Weissman, D. Post, A. Asundi, “Whole-Field Strain Determination by Moire Shearing Interferometry,” J. Strain Anal. 19, No. 2, 77 (1984).
[CrossRef]

L. Pirroda, “Strain Analysis by Grating Interferometry,” Opt. Laser Eng. 5, No. 1, 7 (1984).
[CrossRef]

1983 (1)

A. McDonach, J. McKelvie, P. Mackenzie, C. A. Walker, “Improved Moire Interferometry and Applications in Fracture Mechanics, Residual Stress and Damaged Composites,” Exp. Tech. 23, No. 2, 20 (June1983).
[CrossRef]

1982 (2)

E. M. Weissman, D. Post, “Full-Field Displacement and Strain Rosettes by Moire Interferometry,” Exp. Mech. 22, No. 9, 324 (1982).
[CrossRef]

D. Post, “Developments in Moire Interferometry,” Opt. Eng. 21, 458 (May1982).

Asundi, A.

E. M. Weissman, D. Post, A. Asundi, “Whole-Field Strain Determination by Moire Shearing Interferometry,” J. Strain Anal. 19, No. 2, 77 (1984).
[CrossRef]

Mackenzie, P.

A. McDonach, J. McKelvie, P. Mackenzie, C. A. Walker, “Improved Moire Interferometry and Applications in Fracture Mechanics, Residual Stress and Damaged Composites,” Exp. Tech. 23, No. 2, 20 (June1983).
[CrossRef]

McDonach, A.

A. McDonach, J. McKelvie, P. Mackenzie, C. A. Walker, “Improved Moire Interferometry and Applications in Fracture Mechanics, Residual Stress and Damaged Composites,” Exp. Tech. 23, No. 2, 20 (June1983).
[CrossRef]

McKelvie, J.

A. McDonach, J. McKelvie, P. Mackenzie, C. A. Walker, “Improved Moire Interferometry and Applications in Fracture Mechanics, Residual Stress and Damaged Composites,” Exp. Tech. 23, No. 2, 20 (June1983).
[CrossRef]

Pirroda, L.

L. Pirroda, “Strain Analysis by Grating Interferometry,” Opt. Laser Eng. 5, No. 1, 7 (1984).
[CrossRef]

Post, D.

E. M. Weissman, D. Post, A. Asundi, “Whole-Field Strain Determination by Moire Shearing Interferometry,” J. Strain Anal. 19, No. 2, 77 (1984).
[CrossRef]

D. Post, “Developments in Moire Interferometry,” Opt. Eng. 21, 458 (May1982).

E. M. Weissman, D. Post, “Full-Field Displacement and Strain Rosettes by Moire Interferometry,” Exp. Mech. 22, No. 9, 324 (1982).
[CrossRef]

D. Post, “Moire Interferometry,” in SEM Handbook on Experimental Mechanics, A. S. Kobayashi, Ed. (Prentice-Hall, Englewood Cliffs, NJ, 1986).

Walker, C. A.

A. McDonach, J. McKelvie, P. Mackenzie, C. A. Walker, “Improved Moire Interferometry and Applications in Fracture Mechanics, Residual Stress and Damaged Composites,” Exp. Tech. 23, No. 2, 20 (June1983).
[CrossRef]

Weissman, E. M.

E. M. Weissman, D. Post, A. Asundi, “Whole-Field Strain Determination by Moire Shearing Interferometry,” J. Strain Anal. 19, No. 2, 77 (1984).
[CrossRef]

E. M. Weissman, D. Post, “Full-Field Displacement and Strain Rosettes by Moire Interferometry,” Exp. Mech. 22, No. 9, 324 (1982).
[CrossRef]

Exp. Mech. (1)

E. M. Weissman, D. Post, “Full-Field Displacement and Strain Rosettes by Moire Interferometry,” Exp. Mech. 22, No. 9, 324 (1982).
[CrossRef]

Exp. Tech. (1)

A. McDonach, J. McKelvie, P. Mackenzie, C. A. Walker, “Improved Moire Interferometry and Applications in Fracture Mechanics, Residual Stress and Damaged Composites,” Exp. Tech. 23, No. 2, 20 (June1983).
[CrossRef]

J. Strain Anal. (1)

E. M. Weissman, D. Post, A. Asundi, “Whole-Field Strain Determination by Moire Shearing Interferometry,” J. Strain Anal. 19, No. 2, 77 (1984).
[CrossRef]

Opt. Eng. (1)

D. Post, “Developments in Moire Interferometry,” Opt. Eng. 21, 458 (May1982).

Opt. Laser Eng. (1)

L. Pirroda, “Strain Analysis by Grating Interferometry,” Opt. Laser Eng. 5, No. 1, 7 (1984).
[CrossRef]

Other (1)

D. Post, “Moire Interferometry,” in SEM Handbook on Experimental Mechanics, A. S. Kobayashi, Ed. (Prentice-Hall, Englewood Cliffs, NJ, 1986).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Schematic representation of a moire interferometry arrangement with an added beam splitting and shearing unit Q. SG, specimen grating; L, imaging lens; OP, observation plane; WA and WB, wavefronts of diffraction orders from SG; W A * and W B *, replicas of WA and WB, respectively, shifted by the shear amount Δ.

Fig. 2
Fig. 2

Real-time arrangement for differentiation of in-plane displacement patterns using the Wallaston prism W. Superscript 45 denotes the polarization azimuth.

Fig. 3
Fig. 3

(a) Real-time systems using a polarizing beam splitter. Mirror M provides the symmetrical illumination beam. Rotation of one of the mirrors M1 and M2 introduces a lateral shift Δ. (b) Real-time systems using a polarizing beam splitter. Mirror M provides the symmetrical illumination beam. Rotation of one of the mirrors M1 or M2 introduces a lateral shift Δ.

Fig. 4
Fig. 4

Optical arrangement using an afocal imaging system L1–L2 and a polarizing beam splitter.

Fig. 5
Fig. 5

Analogous optical system that does not require the polarizing beam splitter. P1, P2, linear polarizers with axes mutually orthogonal.

Fig. 6
Fig. 6

Real-time patterns of (a) ΔUx and (b) ΔUy for a cantilever beam. x and y are horizontal and vertical coordinates, respectively. U is the x component of specimen displacements. x = 1.2 mm; y = 0.9 mm.

Fig. 7
Fig. 7

Equivalent patterns for increased load level, requiring nonlinear recording. x = 0.5 mm; y = 0.3 mm.

Fig. 8
Fig. 8

Real-time arrangement for overlapping the lateral shear interferograms of the specimen grating diffraction orders. P1 and P2 denote linear polarizers with the axes set parallel and perpendicular to the SG lines, respectively.

Metrics