Abstract

A method of one-way image transmission through a turbulent medium is presented using four-wave mixing in BSO crystal. In this method, a pointlike reflector is placed on the observation plane to return part of the incident wave, giving the instantaneous wave propagation function of the turbulent medium to the image transmission side. The returned wave together with the plane reference wave and the Fourier-transformed input image wave is impinged in BSO crystal to modulate the image wave by the phase-conjugate wave, so that transmission of the image with reduced turbulence effects is achieved. The principle and laboratory experimental results are given.

© 1983 Optical Society of America

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References

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  1. J. Upatnieks, A. VanderLugt, E. Leith, Appl. Opt. 5, 589 (1966).
    [CrossRef] [PubMed]
  2. J. W. Goodman, W. H. Huntley, D. W. Jackson, M. Lehmann, Appl. Phys. Lett. 8, 311 (1966).
    [CrossRef]
  3. H. Kogelnik, K. S. Pennington, J. Opt. Soc. Am. 58, 273 (1968).
    [CrossRef]
  4. A. Yariv, T. L. Koch, Opt. Lett. 7, 113 (1982).
    [CrossRef] [PubMed]
  5. B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, Appl. Phys. Lett. 41, 141 (1982).
    [CrossRef]
  6. J. W. Goodman, D. W. Jackson, M. Lehmann, J. Knotts, Appl. Opt. 8, 1581 (1969).
    [CrossRef] [PubMed]
  7. J. P. Huignard, J. P. Herriau, P. Aubourg, E. Spitz, Opt. Lett. 4, 21 (1979).
    [CrossRef] [PubMed]
  8. H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
  9. F. M. Küchel, H. J. Tiziani, Opt. Commun. 38, 17 (1981).
    [CrossRef]
  10. T. Sato, Y. Nagura, O. Ikeda, T. Hatsuzawa, Appl. Opt. 21, 1778 (1982).
    [CrossRef] [PubMed]

1982

1981

F. M. Küchel, H. J. Tiziani, Opt. Commun. 38, 17 (1981).
[CrossRef]

1979

1969

1968

1966

J. Upatnieks, A. VanderLugt, E. Leith, Appl. Opt. 5, 589 (1966).
[CrossRef] [PubMed]

J. W. Goodman, W. H. Huntley, D. W. Jackson, M. Lehmann, Appl. Phys. Lett. 8, 311 (1966).
[CrossRef]

Aubourg, P.

Cronin-Golomb, M.

B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, Appl. Phys. Lett. 41, 141 (1982).
[CrossRef]

Fischer, B.

B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, Appl. Phys. Lett. 41, 141 (1982).
[CrossRef]

Goodman, J. W.

J. W. Goodman, D. W. Jackson, M. Lehmann, J. Knotts, Appl. Opt. 8, 1581 (1969).
[CrossRef] [PubMed]

J. W. Goodman, W. H. Huntley, D. W. Jackson, M. Lehmann, Appl. Phys. Lett. 8, 311 (1966).
[CrossRef]

Hatsuzawa, T.

Herriau, J. P.

Huignard, J. P.

Huntley, W. H.

J. W. Goodman, W. H. Huntley, D. W. Jackson, M. Lehmann, Appl. Phys. Lett. 8, 311 (1966).
[CrossRef]

Ikeda, O.

Jackson, D. W.

J. W. Goodman, D. W. Jackson, M. Lehmann, J. Knotts, Appl. Opt. 8, 1581 (1969).
[CrossRef] [PubMed]

J. W. Goodman, W. H. Huntley, D. W. Jackson, M. Lehmann, Appl. Phys. Lett. 8, 311 (1966).
[CrossRef]

Knotts, J.

Koch, T. L.

Kogelnik, H.

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

H. Kogelnik, K. S. Pennington, J. Opt. Soc. Am. 58, 273 (1968).
[CrossRef]

Küchel, F. M.

F. M. Küchel, H. J. Tiziani, Opt. Commun. 38, 17 (1981).
[CrossRef]

Lehmann, M.

J. W. Goodman, D. W. Jackson, M. Lehmann, J. Knotts, Appl. Opt. 8, 1581 (1969).
[CrossRef] [PubMed]

J. W. Goodman, W. H. Huntley, D. W. Jackson, M. Lehmann, Appl. Phys. Lett. 8, 311 (1966).
[CrossRef]

Leith, E.

Nagura, Y.

Pennington, K. S.

Sato, T.

Spitz, E.

Tiziani, H. J.

F. M. Küchel, H. J. Tiziani, Opt. Commun. 38, 17 (1981).
[CrossRef]

Upatnieks, J.

VanderLugt, A.

White, J. O.

B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, Appl. Phys. Lett. 41, 141 (1982).
[CrossRef]

Yariv, A.

B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, Appl. Phys. Lett. 41, 141 (1982).
[CrossRef]

A. Yariv, T. L. Koch, Opt. Lett. 7, 113 (1982).
[CrossRef] [PubMed]

Appl. Opt.

Appl. Phys. Lett.

B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, Appl. Phys. Lett. 41, 141 (1982).
[CrossRef]

J. W. Goodman, W. H. Huntley, D. W. Jackson, M. Lehmann, Appl. Phys. Lett. 8, 311 (1966).
[CrossRef]

Bell Syst. Tech. J.

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

J. Opt. Soc. Am.

Opt. Commun.

F. M. Küchel, H. J. Tiziani, Opt. Commun. 38, 17 (1981).
[CrossRef]

Opt. Lett.

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Figures (4)

Fig. 1
Fig. 1

Schematic showing the principle of the method of image transmission through a turbulent medium.

Fig. 2
Fig. 2

Coordinate system of the image transmission system: F, input image; f, Fourier transform of input image; f0, plane wave; h, wave returned from the reflector on the observation plane; g, transmitted image.

Fig. 3
Fig. 3

Schematic of the experimental system: Lx, expanding lens; PH, pinhole; Lc, collimating lens; BS, beam splitter; M, mirror; L, lens; ATT, attenuator; A, analyzer; T, vinyl film giving the phase distortion; Z0 = 200 mm; and Zf = 200 mm.

Fig. 4
Fig. 4

Typical experimental results: (a) input image A, (b) intensity distribution of the Fourier-transformed image; (c) transmitted image obtained using a conventional means (inverse Fourier transform) in the presence of the phase-distorting vinyl film; and (d) transmitted image obtained using the system shown in Fig. 3 in the presence of the phase-distorting vinyl film.

Equations (14)

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g ( ξ , η ) = K 1 [ f ( x , y ) + f 0 ] h * ( ξ 0 , η 0 , x , y ) h ( ξ , η , x , y ) d x d y ,
h ( ξ , η , x , y ) = K 2 exp { - j ( k / 2 Z 0 ) [ ( ξ - x ) 2 + ( η - y ) 2 ] } × exp [ j ψ ( ξ , η , x , y ) d p ] ,
ψ ( ξ , η , x , y ) d p ψ ( ξ 0 , η 0 x , y ) d p ,
g ( ξ , η ) K 3 f ( x , y ) exp { j ( k / Z 0 ) [ ( ξ - ξ 0 ) x ( η - η 0 ) y ] } d x d y + K 3 f 0 exp { j ( k / Z 0 ) [ ( ξ - ξ 0 ) x + ( η - η 0 ) y ] } d x d y ,
f ( x , y ) = F ( α , β ) exp [ j ( k / Z f ) ( α x + β y ) ] d α d β ,
g ( ξ , η ) K 4 F [ - ( Z f / Z 0 ) ( ξ - ξ 0 ) , - ( Z f / Z 0 ) ( η - η 0 ) ]
2 Δ θ Λ / d ,
2 Δ k = 2 k Δ θ k Λ / d .
k α / Z f Δ k k Λ / 2 d , i . e . , α Λ Z f / 2 d .
L α Λ Z f / d .
PSF ( ξ , η ) = K 5 sinc [ ( k D x / 2 Z 0 ) ( ξ - ξ 0 ) + ( k D x / 2 Z f ) α ] × sinc [ ( k D y / 2 Z 0 ) ( η - η 0 ) + ( k D y / 2 Z f ) β ] ,
Δ R ξ λ Z 0 / D x ,             Δ R η λ Z 0 / D y .
N I = [ L α ( Z 0 / Z f ) / Δ R ξ ] × [ L β ( Z 0 / Z f ) / Δ R η ] ( Λ D x / λ d ) × ( L β D y / λ L f ) .
N I ( Λ D / λ d ) 2 .

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