Abstract

Imaging through scattering media such as fog is a problem with few known viable solutions. Holographic techniques have been demonstrated successfully in the laboratory, but their usefulness is often limited in field conditions by the requirement of a separate coherent reference beam. In this paper, an interferometric imaging technique that utilizes a grating interferometer is presented. Experimental results obtained with this technique show substantial improvement in image contrast over that obtained via direct imaging.

© 1981 Optical Society of America

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References

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    [CrossRef]
  8. A. W. Lohmann, C. A. Schmalfuss, Opt. Commun. 26, 318 (1978).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  13. R. J. Collier, C. B. Burchardt, L. H. Lin, Optical Holography (Academic, New York, 1971), Chap. 12.
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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1980 (1)

B. J. Chang, K. Winick, Proc. Soc. Photo-Opt. Instrum. Eng. 215, 172 (1980).

1979 (2)

1978 (2)

J. W. Hardy, Proc. IEEE 66, 651 (1978).
[CrossRef]

A. W. Lohmann, C. A. Schmalfuss, Opt. Commun. 26, 318 (1978).
[CrossRef]

1977 (2)

T. R. O'Meara, J. Opt. Soc. Am. 67, 306 (1977).
[CrossRef]

E. Leith, B. J. Chang, Opt. Commun. 23, 217 (1977).
[CrossRef]

1975 (1)

1974 (1)

1973 (1)

1970 (1)

1969 (1)

1967 (2)

E. Spitz, C. R. Acad. Sci. Ser. B: 264, 1449 (1967).

K. A. Stetson, J. Opt. Soc. Am. 57, 1060 (1967).
[CrossRef]

Alferness, R.

Bridges, W. B.

Burchardt, C. B.

R. J. Collier, C. B. Burchardt, L. H. Lin, Optical Holography (Academic, New York, 1971), Chap. 12.

Chang, B. J.

Chang, J. S.

Collier, R. J.

R. J. Collier, C. B. Burchardt, L. H. Lin, Optical Holography (Academic, New York, 1971), Chap. 12.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Hardy, J. W.

J. W. Hardy, Proc. IEEE 66, 651 (1978).
[CrossRef]

Leith, E.

E. Leith, B. J. Chang, Opt. Commun. 23, 217 (1977).
[CrossRef]

Leith, E. N.

Leonard, C. D.

Lin, L. H.

R. J. Collier, C. B. Burchardt, L. H. Lin, Optical Holography (Academic, New York, 1971), Chap. 12.

Lohmann, A. W.

A. W. Lohmann, C. A. Schmalfuss, Opt. Commun. 26, 318 (1978).
[CrossRef]

Middleton, W. E. K.

W. E. K. Middleton, Vision Through the Atmosphere (University Press, Toronto, Canada, 1963).

O'Meara, T. R.

Schmalfuss, C. A.

A. W. Lohmann, C. A. Schmalfuss, Opt. Commun. 26, 318 (1978).
[CrossRef]

Spitz, E.

E. Spitz, C. R. Acad. Sci. Ser. B: 264, 1449 (1967).

Stetson, K. A.

Upatnieks, J.

Vilkomerson, D. H. R.

Winick, K.

B. J. Chang, K. Winick, Proc. Soc. Photo-Opt. Instrum. Eng. 215, 172 (1980).

Wyant, J. C.

Appl. Opt. (6)

C. R. Acad. Sci. Ser. B: (1)

E. Spitz, C. R. Acad. Sci. Ser. B: 264, 1449 (1967).

J. Opt. Soc. Am. (2)

Opt. Commun. (2)

A. W. Lohmann, C. A. Schmalfuss, Opt. Commun. 26, 318 (1978).
[CrossRef]

E. Leith, B. J. Chang, Opt. Commun. 23, 217 (1977).
[CrossRef]

Opt. Lett. (1)

Proc. IEEE (1)

J. W. Hardy, Proc. IEEE 66, 651 (1978).
[CrossRef]

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

B. J. Chang, K. Winick, Proc. Soc. Photo-Opt. Instrum. Eng. 215, 172 (1980).

Other (4)

World Meteorological Organization, Code 4377, Horizontal Visibility at Surface, Geneva, Switzerland.

R. J. Collier, C. B. Burchardt, L. H. Lin, Optical Holography (Academic, New York, 1971), Chap. 12.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

W. E. K. Middleton, Vision Through the Atmosphere (University Press, Toronto, Canada, 1963).

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Figures (12)

Fig. 1
Fig. 1

(A) Spectral distribution of recorded image; (B) optical distribution of recorded image.

Fig. 2
Fig. 2

Imaging a scattering medium with a grating interferometer.

Fig. 3
Fig. 3

Lateral shearing of target images.

Fig. 4
Fig. 4

Coherent optical processing of target image.

Fig. 5
Fig. 5

Spectrum of transparency recorded with the grating interferometer.

Fig. 6
Fig. 6

Dimensions of grating interferometer.

Fig. 7
Fig. 7

Estimated system performances: A, 540-line/mm modulation, filter bandwidth equal to signal bandwidth; B, 540-line/mm modulation, filter bandwidth equal to 1/2 signal bandwidth; C, 1000-line/mm modulation, filter bandwidth equal to 1/2 signal bandwidth.

Fig. 8
Fig. 8

Imaging through a volume scattering medium with a grating interferometer.

Fig. 9
Fig. 9

Imaging a 3-D object through a volume scattering medium.

Fig. 10
Fig. 10

Optical arrangement utilized for simulating the effect of imaging through a scattering medium.

Fig. 11
Fig. 11

Experimental evaluation of system performance in imaging through scattering media.

Fig. 12
Fig. 12

Quantitative test with two-tone target.

Equations (21)

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E ( x , y ) = E u ( x , y ) + E s ( x , y ) ,
I u ( x , y ) = A 2 | g ( x , y ) | 2 = | A f ( x , y ) * h ( x , y ) | 2 ,
I s ( x , y ; t ) = | B N n = 1 N { [ f ( x , y ) * h n 1 ( x , y ; t ) ] × S n ( x , y ; t ) } * h n 2 ( x , y ) | 2 ,
I ( x , y ) = B 2 τ 0 τ I scat ( x , y ; t ) d t B 2 .
T A ( x , y ) = B 2 + A 2 | f ( x , y ) * h ( x , y ) | 2 .
S T A ( x , y ) exp [ i ( p x + q y ) ] dxdy = P ( x , y ) * { B δ 2 + A 2 [ F ( p , q ) H ( p , q ) * F ( p , q ) H ¯ ( p , q ) ] } ,
I ( x , y ) = B 2 + | A | g ( x , y ) | exp [ i ϕ ( x , y ) ] + C exp ( iKx sin θ ) | 2 ,
I ( x , y ) B 2 1 + A B | g ( x , y ) | cos [ K x sin θ + ϕ ( x , y ) ] .
I ( x , y ) = 2 B 2 + | A | g ( x , y ) | exp [ i ϕ ( x , y ) ] + A exp ( iKx sin θ ) | 2 .
I ( x , y ) B 2 1 + A 2 B 2 | g ( x , y ) | cos [ K x sin θ + ϕ ( x , y ) ] .
( A / B ) 2 : ( A 2 / B 2 ) 2
1 : ( A / B ) 2 .
E ( x , y ) = E R ( x , y ) exp { i [ ω ( t L R V R ) + ϕ R ( x , y ) ] } + E O ( x , y ) exp { i [ ω ( t L O V O ) + θ O ( x , y ) ] } ,
T A ( x , y ) = K 1 + K 2 cos [ ( ϕ R ( x , y ) ϕ O ( x , y ) + ω ( L R V R L O V O ) ] .
Δ [ ω ( L R V R L O V O ) ] = Δ [ ω ( n R L R C n O L O C ) ] 2 π 10 = π 5 .
Δ ω C ( L R L O ) π 5 .
Δ [ ω L C ( n 1 n 2 ) ] π 5 .
I ( x , y ) = | g ( x , y ) | 2 [ 1 + cos ( 2 π G 0 x ) ] ,
I ( x , y ) = B 2 + A 2 | g ( x , y ) | 2 { 1 + cos [ 2 π G 0 x + ϕ ( x , y ) ] } ,
C = I max I min I max + I min × 100 % .
C I = I u 2 I s + I u × 100 % ,

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