Abstract

A random grating is a periodic structure whose unit cell has random variations. Hence, its autocorrelation function shows high periodic peaks, which may be useful for implementing holographic sensors for in-plane lateral displacements or phase-gradient detection. We report what we believe to be the first experimental verification of this finding.

© 1997 Optical Society of America

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References

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  1. J. Ojeda-Castañeda and V. Arrizón, Microwave Opt. Technol. Lett. 5, 429 (1992).
  2. E. Klotz and M. Kock, Opt. Commun. 6, 130 (1964).

1992 (1)

J. Ojeda-Castañeda and V. Arrizón, Microwave Opt. Technol. Lett. 5, 429 (1992).

1964 (1)

E. Klotz and M. Kock, Opt. Commun. 6, 130 (1964).

Arrizón, V.

J. Ojeda-Castañeda and V. Arrizón, Microwave Opt. Technol. Lett. 5, 429 (1992).

Klotz, E.

E. Klotz and M. Kock, Opt. Commun. 6, 130 (1964).

Kock, M.

E. Klotz and M. Kock, Opt. Commun. 6, 130 (1964).

Ojeda-Castañeda, J.

J. Ojeda-Castañeda and V. Arrizón, Microwave Opt. Technol. Lett. 5, 429 (1992).

Microwave Opt. Technol. Lett. (1)

J. Ojeda-Castañeda and V. Arrizón, Microwave Opt. Technol. Lett. 5, 429 (1992).

Opt. Commun. (1)

E. Klotz and M. Kock, Opt. Commun. 6, 130 (1964).

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Figures (3)

Fig. 1
Fig. 1

Random phase grating: (a) Negative binary input, (b) interferogram of the output, (c) out-of-focus irradiance distribution.

Fig. 2
Fig. 2

Schematic diagrams of the optical setups for generating (a) a random phase grating and (b) a holographic correlator.

Fig. 3
Fig. 3

Square modules of the correlation function of (a) two equal one-dimensional random signals and (b) two equal random phase gratings.

Equations (5)

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t(x,y)=m=Cm expi2π[yR(x)]mp,
p(x,y)=δ(x)exp(i2πΩy).
u(x,y)=t(x,y)*p(x,y)=A exp[i2πΩR(x)],
v(xy)=[u(x+x,y)u(x, y)]ϕ(x, y;x0,y0).
w(x0,y0)=v(x,y)ϕ(x,y;x0,y0)dxdy=Bexpi2π[x0x0)x]/λr×expi2πΩ[R(x+x)R(x)]dxδ(y0y0).

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