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References

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  1. D. Post, “Moire Interferometry,” in SEM Handbook on Experimental Mechanics, A. S. Kobayashi, Ed. (Prentice-Hall, Englewood Cliffs, NJ, 1986).
  2. C. A. Walker, J. McKelvie, “A Practical Multiplied Moire System,” Exp. Mec. 18, 316 (1978).
    [CrossRef]
  3. M. L. Basehore, D. Post, “Displacement Fields (U,W) Obtained Simultaneously by Moire Interferometry,” Appl. Opt. 21, 2558 (1982).
    [CrossRef] [PubMed]
  4. K. Patorski, “A Method for Obtaining Out-of-Plane Displacements by Moire Interferometry,” Opt. Commun. 60, 128 (1986).
    [CrossRef]
  5. L. Pirodda, “Strain Analysis by Grating Interferometry,” Opt. Lasers Eng. 5, 7 (1984).
    [CrossRef]
  6. K. Patorski, “Generation of the Derivative of Out-of-Plane Displacements Using Conjugate Shear and Moire Interferometry,” Appl. Opt. 25, 3146 (1986).
    [CrossRef] [PubMed]
  7. K. Matsumoto, M. Takashima, “Improvement on Moire Technique of In-Plane Deformation Measurements,” Appl. Opt. 12, 858 (1973).
    [CrossRef] [PubMed]
  8. M. L. Basehore, D. Post, “Moire Method for In-Plane and Out-of-Plane Displacement Measurements,” Exp. Mech. 21, 331 (1981).
    [CrossRef]
  9. K. Patorski, M. Kujawinska, “Optical Differentiation of Displacement Patterns Using Moire Interferometry,” Appl. Opt. 24, 3041 (1985).
    [CrossRef] [PubMed]

1986 (2)

K. Patorski, “A Method for Obtaining Out-of-Plane Displacements by Moire Interferometry,” Opt. Commun. 60, 128 (1986).
[CrossRef]

K. Patorski, “Generation of the Derivative of Out-of-Plane Displacements Using Conjugate Shear and Moire Interferometry,” Appl. Opt. 25, 3146 (1986).
[CrossRef] [PubMed]

1985 (1)

1984 (1)

L. Pirodda, “Strain Analysis by Grating Interferometry,” Opt. Lasers Eng. 5, 7 (1984).
[CrossRef]

1982 (1)

1981 (1)

M. L. Basehore, D. Post, “Moire Method for In-Plane and Out-of-Plane Displacement Measurements,” Exp. Mech. 21, 331 (1981).
[CrossRef]

1978 (1)

C. A. Walker, J. McKelvie, “A Practical Multiplied Moire System,” Exp. Mec. 18, 316 (1978).
[CrossRef]

1973 (1)

Basehore, M. L.

M. L. Basehore, D. Post, “Displacement Fields (U,W) Obtained Simultaneously by Moire Interferometry,” Appl. Opt. 21, 2558 (1982).
[CrossRef] [PubMed]

M. L. Basehore, D. Post, “Moire Method for In-Plane and Out-of-Plane Displacement Measurements,” Exp. Mech. 21, 331 (1981).
[CrossRef]

Kujawinska, M.

Matsumoto, K.

McKelvie, J.

C. A. Walker, J. McKelvie, “A Practical Multiplied Moire System,” Exp. Mec. 18, 316 (1978).
[CrossRef]

Patorski, K.

Pirodda, L.

L. Pirodda, “Strain Analysis by Grating Interferometry,” Opt. Lasers Eng. 5, 7 (1984).
[CrossRef]

Post, D.

M. L. Basehore, D. Post, “Displacement Fields (U,W) Obtained Simultaneously by Moire Interferometry,” Appl. Opt. 21, 2558 (1982).
[CrossRef] [PubMed]

M. L. Basehore, D. Post, “Moire Method for In-Plane and Out-of-Plane Displacement Measurements,” Exp. Mech. 21, 331 (1981).
[CrossRef]

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

Takashima, M.

Walker, C. A.

C. A. Walker, J. McKelvie, “A Practical Multiplied Moire System,” Exp. Mec. 18, 316 (1978).
[CrossRef]

Appl. Opt. (4)

Exp. Mec. (1)

C. A. Walker, J. McKelvie, “A Practical Multiplied Moire System,” Exp. Mec. 18, 316 (1978).
[CrossRef]

Exp. Mech. (1)

M. L. Basehore, D. Post, “Moire Method for In-Plane and Out-of-Plane Displacement Measurements,” Exp. Mech. 21, 331 (1981).
[CrossRef]

Opt. Commun. (1)

K. Patorski, “A Method for Obtaining Out-of-Plane Displacements by Moire Interferometry,” Opt. Commun. 60, 128 (1986).
[CrossRef]

Opt. Lasers Eng. (1)

L. Pirodda, “Strain Analysis by Grating Interferometry,” Opt. Lasers Eng. 5, 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).

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Figures (2)

Fig. 1
Fig. 1

Directions of the illuminating L and R and diffracted beams L−1 and R+1 in the moire interferometry configuration. Specimen grating SG is rotated by Δα about the axis parallel to grating lines. 00 and |α| represent the grating normal and its symmetrical illumination angle before rotation, respectively.

Fig. 2
Fig. 2

Optical path change w′(x,y) introduced into the diffracted beam L−1 by the out-of-plane displacement w(x,y) of the point 0 of the specimen. w′(x,y) = w(x,y) (1 + cosα). SG and SG′ depict specimen grating surfaces before and after loading, respectively.

Equations (22)

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E - 1 L ( x , y ) = exp { - i [ 2 π d { u ( x , y ) + u 1 ( x , y ) } - k w ( x , y ) ] } ,
E + 1 R ( x , y ) = exp { i [ 2 π d { u ( x , y ) - u 2 ( x , y ) } + k w ( x , y ) ] } ,
w ( x , y ) = w ( x , y ) ( 1 + cos α ) ;
I ( x , y ) = 2 ( 1 + cos { 4 π d u ( x , y ) + 2 π d [ u 1 ( x , y ) - u 2 ( x , y ) ] } ) .
I W ( x , y ) 4 + 2 cos { 2 π d [ u 1 ( x , y ) + u 2 ( x , y ) ] + 2 k ( 1 + cos α ) w ( x , y ) } .
I D W ( x , y ) 4 + 2 cos Δ { 2 π d [ u 1 ( x , y ) + u 2 ( x , y ) ] x + 2 k ( 1 + cos α ) w ( x , y ) x } ,
sin ( θ + Δ θ ) = sin ( α + Δ α ) ± λ d .
sin θ cos Δ θ + cos θ sin Δ θ = sin α cos Δ α + cos α sin Δ α + λ d .
( 1 - Δ θ 2 2 ) sin θ + Δ θ cos θ = ( 1 - Δ α 2 2 ) sin α + Δ α cos α + λ d ,
- Δ θ 2 2 sin θ + Δ θ cos θ = - Δ α 2 2 sin α + Δ α cos α .
Δ θ cos θ = - Δ α 2 2 sin α + Δ α cos α .
Δ θ L = - Δ α 2 2 sin α cos θ + Δ α cos α cos θ .
Δ θ R = Δ α 2 2 sin α cos θ + Δ α cos α cos θ .
2 π d u ( x ) = 2 π λ 0 x Δ θ d x ,
u 1 ( x , y ) = d λ 0 x Δ θ L d x = d λ 0 x ( - Δ α 2 sin α 2 cos θ + Δ α cos α cos θ ) d x ,
u 2 ( x , y ) = d λ 0 x Δ θ R d x = d λ 0 x ( Δ α 2 sin α 2 cos θ + Δ α cos α cos θ ) d x .
u 1 ( x , y ) - u 2 ( x , y ) = 2 d λ 0 x - Δ α 2 sin α 2 cos θ d x ,
u 1 ( x , y ) + u 2 ( x , y ) = 2 d λ 0 x Δ α cos α cos θ d x .
1 2 [ u 1 ( x , y ) - u 2 ( x , y ) ] x = - d λ Δ α 2 2 sin α = - Δ α 2 2 .
λ d [ u 1 ( x , y ) + u 2 ( x , y ) ] = 2 0 x Δ α cos α cos θ d x ,
[ u 1 ( x , y ) + u 2 ( x , y ) ] x = 2 d λ Δ α cos α cos θ .
I D W ( x , y ) 4 + 2 cos 2 k Δ w ( x , y ) w ( 1 + cos α + cos α cos θ ) .

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