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References

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  1. O. Kafri, A. Livnat, Appl. Opt. 20, 3098 (1981).
    [CrossRef] [PubMed]
  2. O. Kafri, Opt. Lett. 5, 555 (1980).
    [CrossRef] [PubMed]

1981

1980

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Figures (4)

Fig. 1
Fig. 1

Shadow of the grating G2 produced by a collimated beam is reflected from water surface and produces a moiré pattern by interfering with the grating G1 near the screen S. When the surface level changes by H, the image of G2 is laterally translated by an amount δ.

Fig. 2
Fig. 2

Moiré pattern observed when two gratings are rotated an angle θ relative to each other; p is the pitch of each grating, while, for small θ, p/θ is the pitch of the moiré fringes.

Fig. 3
Fig. 3

Moiré pattern as obtained in the setup of Fig. 1. The difference between the water level of the upper half of the picture and the lower half is 64.4 μm.

Fig. 4
Fig. 4

Ray incident at a flat window of n index of refraction and thickness H laterally displaced by amount δ given by Eq. (9).

Equations (9)

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p = p / 2 sin ( θ / 2 ) ~ p / θ .
A = p / [ p / cos ( θ / 2 ) ] = ½ cot ( θ / 2 ) ~ ( 1 / θ ) .
δ = 2 H cos α .
H = T θ / 2 cos α .
p F 2 H min cos α θ .
H min = P 2 F cos α .
β = ( h θ ) / ( 2 Δ ) ,
β min = p θ 2 Δ F = p 2 Δ F .
δ = H cos α ( 1 - sin α n 2 - cos 2 α ) .

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