Abstract

In this paper, we suggest and demonstrate a technique for summation of moire fringes. We show that summation of fringes requires the formation of a conjugate grating, analogous to a conjugate wave in interferometry. A detailed example of fringe summation in moire deflectometry is presented.

© 1983 Optical Society of America

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References

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  1. A. J. Durelli, V. J. Parks, Moire Analysis of Strain (Prentice-Hall, Englewood Cliffs, N.J., 1970).
  2. O. Kafri, Opt. Lett. 5, 555 (1980);Phys. Bull. 33, 197 (1982).
    [CrossRef] [PubMed]
  3. For example, J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  4. A. Yariv, Opt. Commun. 25, 23 (1978).
    [CrossRef]
  5. A. Livnat, O. Kafri, Appl. Opt. 22, 3232 (1983).
    [CrossRef] [PubMed]
  6. O. Kafri, A. Livnat, Appl. Opt. 20, 3098 (1981).
    [CrossRef] [PubMed]
  7. O. Kafri, A. Livnat, Appl. Opt. 22, 2115 (1983).
    [CrossRef] [PubMed]
  8. O. Kafri, A. Livnat, E. Keren, Appl. Opt. 21, 3884 (1982).
    [CrossRef] [PubMed]
  9. O. Kafri, A. Livnat, E. Keren, Appl. Opt. 22, 650 (1983).
    [CrossRef]

1983

1982

1981

1980

1978

A. Yariv, Opt. Commun. 25, 23 (1978).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Distorted grating.

Fig. 2
Fig. 2

By shifting the observers position from A to B a distorted grating and its conjugate are obtained.

Fig. 3
Fig. 3

Schematic setup of the moire deflectometer for obtaining the distorted grating.

Fig. 4
Fig. 4

(a) Deflectogram of a 1000-mm focal length lens. (b) Conjugate deflectogram of (a).

Fig. 5
Fig. 5

(a) Four gratings moire at infinite fringe mode of the sum of two 1000-mm focal length lenses. (b) An infinite fringe moire deflectogram of a 500-mm focal length lens.

Equations (11)

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y = np + f ( y , z ) ,
f ( y , z ) = lp ,
y = mp + g ( y , z ) ,
f ( y , z ) g ( y , z ) = lp .
y = np f ( y , z ) ,
y = n p cos α + f ( y , z ) tan α .
y = np + Δ ϕ ( y , z ) ,
[ y + Δ ϕ ( y , z ) ] cos ( θ / 2 ) = np + z sin ( θ / 2 ) .
y cos ( θ / 2 ) = mp z sin ( θ / 2 ) .
z = l p θ + Δ θ ϕ ( y , z ) .
ϕ ( y , z ) + ξ ( y , z ) = kp Δ .

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