Abstract

In-plane strain is traditionally mapped by fixing a grating onto a test object and monitoring its displacements under stress by either a moiré method or interferometry. The strain (or displacement derivative) is obtained by an additional mathematical or moiré shearing technique. We suggest an application of moiré deflectometry that will yield the strain directly. The setup is much simpler than existing methods and has the additional advantages of tunable sensitivity and immunity to mechanical shock and vibration.

© 1989 Optical Society of America

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References

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  1. P. S. Theocaris, Moiré Fringes in Strain Analysis (Pergamon, London, 1969).
  2. A. J. Durelli, V. J. Parks, Moiré Analysis of Strain (Prentice-Hall, Englewood Cliffs, N.J., 1970).
  3. D. Post, Opt. Eng. 21, 458 (1982).
  4. E. M. Weisman, D. Post, Appl. Opt. 21, 1621 (1982).
    [CrossRef]
  5. O. Kafri, Opt. Lett. 5, 555 (1980).
    [CrossRef] [PubMed]
  6. O. Kafri, I. Glatt, Opt. Eng. 24, 944 (1986).
  7. K. Patorski, D. Post, R. Czarmek, Y. Guo, Appl. Opt. 26, 1977 (1987).
    [CrossRef] [PubMed]
  8. O. Kafri, J. Krasinski, Appl. Opt. 24, 2746 (1985).
    [CrossRef]
  9. O. Kafri, I. Glatt, Appl. Opt. 27, 351 (1988).
    [CrossRef] [PubMed]

1988 (1)

1987 (1)

1986 (1)

O. Kafri, I. Glatt, Opt. Eng. 24, 944 (1986).

1985 (1)

1982 (2)

1980 (1)

Czarmek, R.

Durelli, A. J.

A. J. Durelli, V. J. Parks, Moiré Analysis of Strain (Prentice-Hall, Englewood Cliffs, N.J., 1970).

Glatt, I.

O. Kafri, I. Glatt, Appl. Opt. 27, 351 (1988).
[CrossRef] [PubMed]

O. Kafri, I. Glatt, Opt. Eng. 24, 944 (1986).

Guo, Y.

Kafri, O.

Krasinski, J.

Parks, V. J.

A. J. Durelli, V. J. Parks, Moiré Analysis of Strain (Prentice-Hall, Englewood Cliffs, N.J., 1970).

Patorski, K.

Post, D.

Theocaris, P. S.

P. S. Theocaris, Moiré Fringes in Strain Analysis (Pergamon, London, 1969).

Weisman, E. M.

Appl. Opt. (4)

Opt. Eng. (2)

D. Post, Opt. Eng. 21, 458 (1982).

O. Kafri, I. Glatt, Opt. Eng. 24, 944 (1986).

Opt. Lett. (1)

Other (2)

P. S. Theocaris, Moiré Fringes in Strain Analysis (Pergamon, London, 1969).

A. J. Durelli, V. J. Parks, Moiré Analysis of Strain (Prentice-Hall, Englewood Cliffs, N.J., 1970).

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Figures (3)

Fig. 1
Fig. 1

Moiré interferometry setup. Two mutually coherent beams are projected onto a fixed grating at opposite diffraction-order angles of the grating. The reflected beam normal to the grating reveals a contour map of the surface displacement.

Fig. 2
Fig. 2

Moiré deflectometry setup. A collimated beam is projected onto a fixed grating at a diffraction-order angle of the grating. The first-order beam normal to the grating projects the shadow of grating G1 onto grating G2 separated by a distance d. The moiré pattern is a contour map of the surface strain. The zeroth-order beam follows the law of reflection and contains the out-of-plane information.

Fig. 3
Fig. 3

Collimated beam transmitted through a diffraction grating. The moiré pattern obtained by the deflectometer of the zeroth order is not sensitive to the test-grating rotation (density). In the first-order beam the moiré fringes move proportional to the sine of the grating.

Equations (9)

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sin ϕ = m λ p ,
δ ϕ sin δ ϕ = m λ ( 1 p + δ p 1 p ) m λ δ p p 2 ,
q p d = m λ p 2 δ p .
x x = u ( x , y ) x ,
u = δ p and x x = δ p / p .
x x = q p p m λ d .
δ x = λ 2 δ ϕ .
x x = p 2 m δ x .
x x ( min ) = p 2 a per fringe .

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