Abstract

This paper describes a new image-shearing camera which focuses two laterally sheared images at the film plane. With coherent illumination, this camera becomes a shearing interferometer, which directly measures the derivatives of the surface displacements. This strain measuring tool enjoys several advantages over the conventional, holographic, and speckle interferometry, namely, (1) better fringe quality (than speckle interferometry); (2) does not require special vibration isolation; (3) very simple optical setup; (4) direct determination of strains; and (5) extended controllable range of sensitivity.

© 1979 Optical Society of America

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References

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  1. R. K. Erf, Ed., Holographic Nondestructive Testing (Academic, New York, 1974).
  2. R. K. Erf, Ed., Speckle Metrology (Academic, New York, 1978).
  3. Y. Y. Hung, C. E. Taylor, Proc. Soc. Photo-Opt. Instrum. Eng. 41, 169 (1973).
  4. J. A. Leendertz, J. N. Butters, J. Phys. E. 6, 1107 (1973).
    [CrossRef]
  5. Y. Y. Hung, Opt. Commun. 11, 732 (1974).
    [CrossRef]
  6. Y. Y. Hung, I. M. Daniel, R. E. Rowlands, Appl. Opt. 14, 618 (1975).
    [CrossRef] [PubMed]
  7. F. P. Chiang, R. M. Jung, Appl. Opt. 15, 2199 (1976).
    [CrossRef] [PubMed]
  8. Y. Y. Hung, I. M. Daniel, R. E. Rowlands, Exp. Mech. 18 (2), 56 (1978).
    [CrossRef]
  9. F. K. Ligtenberg, Proc. Soc. Exp. Stress Anal. 12 (2), 83 (1954).

1978 (1)

Y. Y. Hung, I. M. Daniel, R. E. Rowlands, Exp. Mech. 18 (2), 56 (1978).
[CrossRef]

1976 (1)

1975 (1)

1974 (1)

Y. Y. Hung, Opt. Commun. 11, 732 (1974).
[CrossRef]

1973 (2)

Y. Y. Hung, C. E. Taylor, Proc. Soc. Photo-Opt. Instrum. Eng. 41, 169 (1973).

J. A. Leendertz, J. N. Butters, J. Phys. E. 6, 1107 (1973).
[CrossRef]

1954 (1)

F. K. Ligtenberg, Proc. Soc. Exp. Stress Anal. 12 (2), 83 (1954).

Butters, J. N.

J. A. Leendertz, J. N. Butters, J. Phys. E. 6, 1107 (1973).
[CrossRef]

Chiang, F. P.

Daniel, I. M.

Y. Y. Hung, I. M. Daniel, R. E. Rowlands, Exp. Mech. 18 (2), 56 (1978).
[CrossRef]

Y. Y. Hung, I. M. Daniel, R. E. Rowlands, Appl. Opt. 14, 618 (1975).
[CrossRef] [PubMed]

Hung, Y. Y.

Y. Y. Hung, I. M. Daniel, R. E. Rowlands, Exp. Mech. 18 (2), 56 (1978).
[CrossRef]

Y. Y. Hung, I. M. Daniel, R. E. Rowlands, Appl. Opt. 14, 618 (1975).
[CrossRef] [PubMed]

Y. Y. Hung, Opt. Commun. 11, 732 (1974).
[CrossRef]

Y. Y. Hung, C. E. Taylor, Proc. Soc. Photo-Opt. Instrum. Eng. 41, 169 (1973).

Jung, R. M.

Leendertz, J. A.

J. A. Leendertz, J. N. Butters, J. Phys. E. 6, 1107 (1973).
[CrossRef]

Ligtenberg, F. K.

F. K. Ligtenberg, Proc. Soc. Exp. Stress Anal. 12 (2), 83 (1954).

Rowlands, R. E.

Y. Y. Hung, I. M. Daniel, R. E. Rowlands, Exp. Mech. 18 (2), 56 (1978).
[CrossRef]

Y. Y. Hung, I. M. Daniel, R. E. Rowlands, Appl. Opt. 14, 618 (1975).
[CrossRef] [PubMed]

Taylor, C. E.

Y. Y. Hung, C. E. Taylor, Proc. Soc. Photo-Opt. Instrum. Eng. 41, 169 (1973).

Appl. Opt. (2)

Exp. Mech. (1)

Y. Y. Hung, I. M. Daniel, R. E. Rowlands, Exp. Mech. 18 (2), 56 (1978).
[CrossRef]

J. Phys. E. (1)

J. A. Leendertz, J. N. Butters, J. Phys. E. 6, 1107 (1973).
[CrossRef]

Opt. Commun. (1)

Y. Y. Hung, Opt. Commun. 11, 732 (1974).
[CrossRef]

Proc. Soc. Exp. Stress Anal. (1)

F. K. Ligtenberg, Proc. Soc. Exp. Stress Anal. 12 (2), 83 (1954).

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

Y. Y. Hung, C. E. Taylor, Proc. Soc. Photo-Opt. Instrum. Eng. 41, 169 (1973).

Other (2)

R. K. Erf, Ed., Holographic Nondestructive Testing (Academic, New York, 1974).

R. K. Erf, Ed., Speckle Metrology (Academic, New York, 1978).

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram of optical setup.

Fig. 2
Fig. 2

Imaging detail of the image shearing camera.

Fig. 3
Fig. 3

Schematic diagram of the Fourier filtering technique.

Fig. 4
Fig. 4

Optical path diagram.

Fig. 5
Fig. 5

Fringe pattern depicting ∂w/∂x of a rectangular plate loaded at the center.

Fig. 6
Fig. 6

Moiré fringe pattern formed by shifting two fringe patterns of Fig. 5, measuring ∂2w/∂x2 of the plate deformation.

Equations (31)

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δ x = D i ( μ - 1 ) α ,
δ x = ( δ x ) / M ,
δ x = δ x [ ( D o ) / ( D i ) ] = D o ( μ - 1 ) α
U ( x , y ) = a exp [ θ ( x , y ) ] ,
U ( x + δ x , y ) = a exp [ θ ( x + δ x , y ) ] ,
U T = U ( x , y ) + U ( x + δ x , y ) = a { exp [ θ ( x , y ) ] + exp [ θ ( x + δ x , y ) ] } ,
I = U T U T * = 2 a 2 ( 1 + cos ϕ ) ,
I = 2 a 2 [ 1 + cos ( ϕ + Δ ) ] .
I T = I + I = 2 a 2 [ 2 + cos ϕ + cos ( ϕ + Δ ) ] .
I ave = 1 2 π 0 2 π I T d ϕ = 4 a 2 .
I T = 4 a 2 [ 1 + cos ( ϕ + Δ 2 ) · cos ( Δ 2 ) ] .
cos ( Δ / 2 ) = 0
Δ = ( 2 N + 1 ) π ,
δ l ( x , y , z ) = ( S P + P O ) = ( S P + P O ) ,
S P = [ ( x - x s + u ) 2 + ( y - y s + v ) 2 + ( z - z s + w ) 2 ] 1 / 2 , S P = [ ( x - x s ) 2 + ( y - y s ) 2 + ( z - z s ) 2 ] 1 / 2 , P O = [ ( x - x o + u ) 2 + ( y - y o + v ) 2 + ( z - z o + w ) 2 ] 1 / 2 , P O = [ ( x - x o ) 2 + ( y - y o ) 2 + ( z - z o ) 2 ] 1 / 2 .
δ l = ( x - x o R o + x - x s R s ) u + ( y - y o R o + x - x s R s ) v + ( z - z o R o + z - z s R s ) w ,
δ l = ( x - x o R o + x - x s R s ) ( u + δ u ) + ( y - y o R o + x - x s R s ) ( v + δ v ) + ( z - z o R o + z - z s R s ) ( w + δ w ) .
δ l - δ l = ( x - x o R o + x - x s R s ) δ u + ( y - y o R o + y - y s R s ) δ v + ( z - z o R o + z - z s R s ) δ w .
Δ = [ ( 2 π ) / λ ] [ δ l - δ l ] = [ ( 2 π ) / λ ] ( A δ u + B δ v + C δ w ) ,
A = ( x - x o R o + x - x s R s ) B = ( y - y o R o + y - y s R s ) C = ( z - z o R o + z - z s R s ) } .
Δ = 2 π λ ( A δ u δ x + B δ v δ x + C δ w δ x ) δ x .
Δ = 2 π λ ( A u x + B v x + C w x ) δ x .
Δ = 2 π λ ( A u y + B v y + C w y ) δ y .
A = x Z o + x - x s R s B = y Z o + y R s C = z - z o z o + z - z s R s } .
A = - x s R s = - sin θ B 0 C = - ( 1 + Z s R s ) = - ( 1 + cos θ ) } ,
Δ = - 2 π λ [ ( 1 + cos θ ) w x + ( sin θ ) u x ] δ x ,
Δ = - 2 π λ [ ( 1 - cos θ ) w y + ( sin θ ) u y ] δ y .
Δ = - 2 π λ [ ( 1 + cos θ ) w x + ( sin θ ) v x ] δ x ,
Δ = - 2 π λ [ ( 1 + cos θ ) w y + ( sin θ ) v y ] δ y .
u x = ( λ 2 π ) ( 1 + cos θ s ) Δ 1 - ( 1 + cos θ 1 ) Δ 2 ( 1 + cos θ 1 ) sin θ 2 - ( 1 + cos θ 2 ) sin θ 1 ,
x = u / x y = u / y γ = ( u / y ) + ( v / x ) } .

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