Abstract

In this paper, we propose and demonstrate a finite fringe shadow moire technique. This technique enables the mapping of the slope of diffusive objects as well as absolute mapping of out-of-plane distortions.

© 1983 Optical Society of America

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References

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  1. O. Kafri, Opt. Lett. 5, 555 (1980);Phys. Bull. 33, 197 (1982).
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  2. O. Kafri, A. Livnat, Appl. Opt. 20, 3098 (1981).
    [CrossRef] [PubMed]
  3. C. A. Sciammarella, B. E. Ross, D. Sturgeon, Exp. Mech. 5, 154 (1965).
    [CrossRef]
  4. D. M. Meadows, W. O. Johnson, J. B. Allen, Appl. Opt. 9, 942 (1970).
    [CrossRef] [PubMed]
  5. O. Kafri, E. Keren, Appl. Opt. 20, 2885 (1981).
    [CrossRef] [PubMed]
  6. J. Der Hovanesian, Y. Y. Hung, Appl. Opt. 10, 2734 (1971).
    [CrossRef]
  7. O. Kafri, A. Livnat, E. Keren, Appl. Opt. 21, 3884 (1982).
    [CrossRef] [PubMed]
  8. O. Kafri, A. Livnat, E. Keren, Appl. Opt. 22, 650 (1983).
    [CrossRef]
  9. O. Kafri, E. Margalit, Appl. Opt. 20, 2344 (1981).
    [CrossRef] [PubMed]
  10. Y. Yoshino, M. Tsukiji, H. Takasaki, Appl. Opt. 15, 2414 (1976);also R. P. Khetan, F. P. Chiang, in Proceedings, Fifteenth Mid-Western Mechanical Conference, Chicago (Mar. 1977).
    [CrossRef] [PubMed]
  11. A. J. Durelli, V. J. Parks, Moire Analysis of Strain (Prentice-Hall, Englewood Cliffs, N.J., 1970).

1983 (1)

1982 (1)

1981 (3)

1980 (1)

1976 (1)

1971 (1)

1970 (1)

1965 (1)

C. A. Sciammarella, B. E. Ross, D. Sturgeon, Exp. Mech. 5, 154 (1965).
[CrossRef]

Allen, J. B.

Der Hovanesian, J.

Durelli, A. J.

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

Hung, Y. Y.

Johnson, W. O.

Kafri, O.

Keren, E.

Livnat, A.

Margalit, E.

Meadows, D. M.

Parks, V. J.

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

Ross, B. E.

C. A. Sciammarella, B. E. Ross, D. Sturgeon, Exp. Mech. 5, 154 (1965).
[CrossRef]

Sciammarella, C. A.

C. A. Sciammarella, B. E. Ross, D. Sturgeon, Exp. Mech. 5, 154 (1965).
[CrossRef]

Sturgeon, D.

C. A. Sciammarella, B. E. Ross, D. Sturgeon, Exp. Mech. 5, 154 (1965).
[CrossRef]

Takasaki, H.

Tsukiji, M.

Yoshino, Y.

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Figures (5)

Fig. 1
Fig. 1

Experimental setup. The shadow of the grating is projected on the object. The camera is located at an angle α to the light propagation axis.

Fig. 2
Fig. 2

(a) Contour map of a diffusive dome (r = 104.7 mm, hmax = 21 mm) obtained by the setup of Fig. 1. (b) Finite fringe mapping of the same dome. The fringe distortion is proportional to the height at the location of the fringe.

Fig. 3
Fig. 3

When the object is doubly exposed, with the grating rotated by an angle θ between the two exposures, the moire fringes are straight.

Fig. 4
Fig. 4

(a) Double-exposure map of a can. The can was squeezed slightly between the two exposures, and the contour map of the deformation is obtained. (b) Finite fringe map of the same object.

Fig. 5
Fig. 5

Finite fringe slope mapping of the diffusive dome.

Equations (15)

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y cos ( θ / 2 ) = z sin ( θ / 2 ) + kp k = 0 , ± 1 , ± 2 ,
y cos α cos ( θ / 2 ) = z sin ( θ / 2 ) + kp .
y cos α cos ( θ / 2 ) = z sin ( θ / 2 ) + m p m = 0 , ± 1 , ± 2 .
z = ( k m ) p 2 sin ( θ / 2 ) lp θ ,
Δ y = h / tan α .
[ y + h ( z , y ) / sin α ] cos α cos ( θ / 2 ) = z sin ( θ / 2 ) + kp .
h / tan α = z θ + kp .
z = h / θ tan α .
[ y + h ( z , y ) / sin α ] cos α cos ( θ / 2 ) = z sin ( θ / 2 ) + kp ;
[ y + δ y + h ( z , y + δ y ) / sin α ] cos α cos ( θ / 2 ) = z sin ( θ / 2 ) + mp .
h ( z , y ) h ( z , y + δ y ) δ y = z θ tan α δ y h y .
z = G ( y , z ) + k p ,
G y G ( y , z ) G ( y δ y , z ) dy = l p dy .
z y = l p dy = δ y θ tan α 2 h y 2 .
( 2 h y 2 ) inc = p tan α dy δ y .

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