Abstract

A proposal and an analysis are presented for imaging through a distorting medium using field multiplication by four-wave mixing.

© 1982 Optical Society of America

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References

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  1. E. N. Leith, J. Upatnieks, “Holographic imagery through diffusing media,” J. Opt. Soc. Am. 56, 523 (1966).
    [CrossRef]
  2. H. Kogelnik, “Holographic image projection through inhomogenious media,” Bell Syst. Tech. J. 44, 2451 (1965).
  3. J. W. Goodman et al., “Wavefront reconstruction imaging through random media,” Appl. Phys. Lett. 8, 311 (1966).
    [CrossRef]
  4. B. I. Stepanov, E. V. Ivakin, A. S. Rubanov, “On registration of plane wave and volume dynamic holograms in bleachable substances,” Dokl. Akad. Nauk SSSR 196, 567 (1971).
  5. J. P. Woerdman, “Some optical and electrical properties of a laser generated free carrier plasma in Si,” Ph.D. Thesis, U. of Amsterdam (Dec.1971). Also republished in Philips Res. Dept. Suppl. 1971, No. 7.
  6. A. Yariv, “On transmission and recovery of three dimensional image information in optical waveguides,” J. Opt. Soc. Am. 66, 301 (1976).
    [CrossRef]
  7. T. R. O’Meara, “Applications of nonlinear phase conjugation in compensated active media,” Proc. Soc. Photo-Opt. Instrum. Eng. 168, 542 (1979).

1979 (1)

T. R. O’Meara, “Applications of nonlinear phase conjugation in compensated active media,” Proc. Soc. Photo-Opt. Instrum. Eng. 168, 542 (1979).

1976 (1)

1971 (1)

B. I. Stepanov, E. V. Ivakin, A. S. Rubanov, “On registration of plane wave and volume dynamic holograms in bleachable substances,” Dokl. Akad. Nauk SSSR 196, 567 (1971).

1966 (2)

E. N. Leith, J. Upatnieks, “Holographic imagery through diffusing media,” J. Opt. Soc. Am. 56, 523 (1966).
[CrossRef]

J. W. Goodman et al., “Wavefront reconstruction imaging through random media,” Appl. Phys. Lett. 8, 311 (1966).
[CrossRef]

1965 (1)

H. Kogelnik, “Holographic image projection through inhomogenious media,” Bell Syst. Tech. J. 44, 2451 (1965).

Goodman, J. W.

J. W. Goodman et al., “Wavefront reconstruction imaging through random media,” Appl. Phys. Lett. 8, 311 (1966).
[CrossRef]

Ivakin, E. V.

B. I. Stepanov, E. V. Ivakin, A. S. Rubanov, “On registration of plane wave and volume dynamic holograms in bleachable substances,” Dokl. Akad. Nauk SSSR 196, 567 (1971).

Kogelnik, H.

H. Kogelnik, “Holographic image projection through inhomogenious media,” Bell Syst. Tech. J. 44, 2451 (1965).

Leith, E. N.

O’Meara, T. R.

T. R. O’Meara, “Applications of nonlinear phase conjugation in compensated active media,” Proc. Soc. Photo-Opt. Instrum. Eng. 168, 542 (1979).

Rubanov, A. S.

B. I. Stepanov, E. V. Ivakin, A. S. Rubanov, “On registration of plane wave and volume dynamic holograms in bleachable substances,” Dokl. Akad. Nauk SSSR 196, 567 (1971).

Stepanov, B. I.

B. I. Stepanov, E. V. Ivakin, A. S. Rubanov, “On registration of plane wave and volume dynamic holograms in bleachable substances,” Dokl. Akad. Nauk SSSR 196, 567 (1971).

Upatnieks, J.

Woerdman, J. P.

J. P. Woerdman, “Some optical and electrical properties of a laser generated free carrier plasma in Si,” Ph.D. Thesis, U. of Amsterdam (Dec.1971). Also republished in Philips Res. Dept. Suppl. 1971, No. 7.

Yariv, A.

Appl. Phys. Lett. (1)

J. W. Goodman et al., “Wavefront reconstruction imaging through random media,” Appl. Phys. Lett. 8, 311 (1966).
[CrossRef]

Bell Syst. Tech. J. (1)

H. Kogelnik, “Holographic image projection through inhomogenious media,” Bell Syst. Tech. J. 44, 2451 (1965).

Dokl. Akad. Nauk SSSR (1)

B. I. Stepanov, E. V. Ivakin, A. S. Rubanov, “On registration of plane wave and volume dynamic holograms in bleachable substances,” Dokl. Akad. Nauk SSSR 196, 567 (1971).

J. Opt. Soc. Am. (2)

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

T. R. O’Meara, “Applications of nonlinear phase conjugation in compensated active media,” Proc. Soc. Photo-Opt. Instrum. Eng. 168, 542 (1979).

Other (1)

J. P. Woerdman, “Some optical and electrical properties of a laser generated free carrier plasma in Si,” Ph.D. Thesis, U. of Amsterdam (Dec.1971). Also republished in Philips Res. Dept. Suppl. 1971, No. 7.

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Figures (1)

Fig. 1
Fig. 1

The configuration for propagating an image from plane (3) through a distorting medium to plane (1) with no distortion.

Equations (14)

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E 2 ( x , z ) = A 2 λ ( l 2 z ) e ikz d 2 x f ( x ) × exp [ i k 2 ( l 2 z ) | x x | 2 ] .
E 3 ( x , z ) = A 3 ( z ) exp [ ikz i k 2 ( d 2 + z ) | x | 2 ] .
E 1 ( s ) = A 1 λ d 1 d 2 x exp [ Φ ( x ) i k 2 d 1 | x s | 2 ] .
E 1 ( x , z ) = A 1 λ 2 d 1 ( l 1 + z ) e ikz d 2 x d 2 s × exp [ i Φ ( x ) i k 2 d 1 | x s | 2 ] × exp [ i k 2 f | s | 2 i k 2 ( l 1 + z ) | x s | 2 ] .
1 d 2 + z 1 d 2 z d 2 2 , 1 l 1 + z 1 l 1 z l 1 2 , 1 l 2 z 1 l 2 + z l 2 2
P NL = χ ( 3 ) E 1 * E 2 E 3 ,
P NL ( x , z ) = χ ( 3 ) A 1 * A 2 A 3 ( z = 0 ) λ 3 d 1 l 1 l 2 e ikz × d 2 x d 2 x d 2 s f ( x ) e i Φ ( x ) × exp ( i k 2 d 2 | x | 2 ikz 2 d 2 2 | x | 2 ) × exp ( i k 2 l 2 | x x | 2 ikz 2 l 2 2 | x x | 2 ) × exp [ i k 2 d 1 | x | 2 + i k 2 l 1 | x | 2 i k d 1 ( x + d 1 l 1 x ) · s ikz 2 l 1 2 | x s | 2 ] .
E ( s ) = 4 π 2 λ 2 υ P NL ( x , z ) e i k r r d 2 x d z ,
E ( s ) = 4 π 2 λ 2 l 1 υ d 2 x d z P NL ( x , z ) × exp ( ikz i k 2 l 1 | x s | 2 + ikz 2 l 1 2 | x s | 2 ) .
E ( η ) = 4 π 2 χ ( 3 ) A 1 * A 2 A 3 λ 6 d 1 l 1 l 2 e i Φ ( η ) × d z d 2 x d 2 x d 2 x d 2 s d 2 s × e j Φ ( x ) f ( x ) exp ( i k 2 d 1 | η | 2 i k 2 d 2 | x | 2 + i k 2 d 1 | x | 2 i k 2 l 2 | x x | 2 ) × exp [ i k d 1 ( x + d 1 l 1 x ) · s ] × exp [ i k d 1 ( η + d 1 l 1 x ) · s ] × { exp ( ikz 2 d 2 2 | x | 2 ikz 2 l 2 2 | x x | 2 + ikz 2 l 1 2 | x s | 2 ikz 2 l 1 2 | x s | 2 ) } .
k z | x or x or s or s | 2 ( l 1 or l 2 or d 2 ) 2 π
( d 1 λ ) 2 δ ( x + d 1 l 1 x ) and ( l 1 λ ) 2 δ ( x + l 1 d 1 η ) ,
E ( η ) = [ 4 π 2 χ ( 3 ) A 1 * A 3 t / λ ] exp ( i k l 1 2 2 d 2 d 1 2 | η | 2 ) × A 2 λ l 2 d 2 x f ( x ) exp ( i k 2 l 2 | l 1 d 1 η + x | 2 ) ,
G 4 π 2 χ ( 3 ) A 1 * A 3 t / λ

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