Abstract

A compact, passive, holographic system is proposed which compensates arbitrary phase distortion in an incoherently illuminated imaging system.

© 1983 Optical Society of America

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References

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  1. J. W. Goodman, Appl. Phys. Lett. 8, 311 (1966).
    [CrossRef]
  2. E. N. Leith, J. Upatnieks, J. Opt. Soc. Am. 56, 523 (1966).
    [CrossRef]
  3. H. Kogelnik, Bell Syst. Tech. J. 44, 2451 (1965).
  4. J. Upatnieks, A. VanderLugt, E. Leith, Appl. Opt. 5, 589 (1966).
    [CrossRef] [PubMed]
  5. H. Kogelnik, K. S. Pennington, J. Opt. Soc. Am. 58, 273 (1968).
    [CrossRef]
  6. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 80.
  7. L. Rosen, Appl. Phys. Lett. 9, 337 (1966).
    [CrossRef]
  8. G. W. Stroke, Phys. Lett. 23, 325 (1966).
    [CrossRef]
  9. G. B. Brandt, Appl. Opt. 8, 1421 (1969).
    [CrossRef] [PubMed]
  10. W. T. Cathey, Optical Information Processing and Holography (Wiley, New York, 1974), p. 148.
  11. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 241.
  12. C. B. Burckhardt, Bell Syst. Tech. J. 45, 1841 (1966).
  13. D. J. DeBitetto, Appl. Phys. Lett. 9, 417 (1966).
    [CrossRef]
  14. P. L. Ransom, Appl. Opt. 11, 2554 (1972).
    [CrossRef] [PubMed]

1972

1969

1968

1966

E. N. Leith, J. Upatnieks, J. Opt. Soc. Am. 56, 523 (1966).
[CrossRef]

J. W. Goodman, Appl. Phys. Lett. 8, 311 (1966).
[CrossRef]

L. Rosen, Appl. Phys. Lett. 9, 337 (1966).
[CrossRef]

G. W. Stroke, Phys. Lett. 23, 325 (1966).
[CrossRef]

C. B. Burckhardt, Bell Syst. Tech. J. 45, 1841 (1966).

D. J. DeBitetto, Appl. Phys. Lett. 9, 417 (1966).
[CrossRef]

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

1965

H. Kogelnik, Bell Syst. Tech. J. 44, 2451 (1965).

Brandt, G. B.

Burckhardt, C. B.

C. B. Burckhardt, Bell Syst. Tech. J. 45, 1841 (1966).

Cathey, W. T.

W. T. Cathey, Optical Information Processing and Holography (Wiley, New York, 1974), p. 148.

DeBitetto, D. J.

D. J. DeBitetto, Appl. Phys. Lett. 9, 417 (1966).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Appl. Phys. Lett. 8, 311 (1966).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 241.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 80.

Kogelnik, H.

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

H. Kogelnik, Bell Syst. Tech. J. 44, 2451 (1965).

Leith, E.

Leith, E. N.

Pennington, K. S.

Ransom, P. L.

Rosen, L.

L. Rosen, Appl. Phys. Lett. 9, 337 (1966).
[CrossRef]

Stroke, G. W.

G. W. Stroke, Phys. Lett. 23, 325 (1966).
[CrossRef]

Upatnieks, J.

VanderLugt, A.

Appl. Opt.

Appl. Phys. Lett.

L. Rosen, Appl. Phys. Lett. 9, 337 (1966).
[CrossRef]

J. W. Goodman, Appl. Phys. Lett. 8, 311 (1966).
[CrossRef]

D. J. DeBitetto, Appl. Phys. Lett. 9, 417 (1966).
[CrossRef]

Bell Syst. Tech. J.

C. B. Burckhardt, Bell Syst. Tech. J. 45, 1841 (1966).

H. Kogelnik, Bell Syst. Tech. J. 44, 2451 (1965).

J. Opt. Soc. Am.

Phys. Lett.

G. W. Stroke, Phys. Lett. 23, 325 (1966).
[CrossRef]

Other

W. T. Cathey, Optical Information Processing and Holography (Wiley, New York, 1974), p. 148.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 241.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 80.

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Figures (11)

Fig. 1
Fig. 1

Viewing a phase-distorted object.

Fig. 2
Fig. 2

Configuration for recording a phase-compensating hologram (PCH) with a single lens and monochromatic plane-wave illumination.

Fig. 3
Fig. 3

Double-lens configuration for recording a PCH with monochromatic illumination.

Fig. 4
Fig. 4

Lensless configuration for recording a PCH with monochromatic illumination.

Fig. 5
Fig. 5

Shower glass used as the layer of phase-distorting material.

Fig. 6
Fig. 6

Test chart used as the object.

Fig. 7
Fig. 7

Phase-distorted image with achromatic (white) illumination.

Fig. 8
Fig. 8

Phase-compensated (but color-dispersed) image with achromatic illumination.

Fig. 9
Fig. 9

Phase-compensated image with monochromatic illumination.

Fig. 10
Fig. 10

Configuration of PDM + PCH + hologram grating which yields an undispersed and undistorted image superimposed on an undispersed but distorted image when achromatically illuminated.

Fig. 11
Fig. 11

Configuration of the proposed holographic system for compensating arbitrary phase distortion with achromatic (white) illumination.

Equations (17)

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g 1 ( x , y ) = ϕ λ 0 f ( x , y ) exp [ jd ( x , y ) ] ,
ϕ λ 0 f ( x , y ) = exp [ j ( π / λ 0 f ) ( x 2 + y 2 ) ] .
h ( x , y ) = | exp [ j 2 π ( sin θ 0 / λ 0 ) x ] + ϕ λ 0 f ( x , y ) exp [ jd ( x , y ) ] | 2 ,
h ( x , y ) = 2 + ϕ λ 0 f ( x , y ) exp [ jd ( x , y ) ] × exp [ j 2 π ( sin θ 0 / λ 0 ) x ] + ϕ λ 0 f * ( x , y ) exp [ jd ( x , y ) ] exp [ j 2 π ( sin θ 0 / λ 0 ) x ] .
g 5 ( x , y ) = ϕ λ f ( x , y ) exp [ jd ( x , y ) ] 0 ( x , y ) .
g 6 ( x , y ) = 2 ϕ λ f ( x , y ) exp [ jd ( x , y ) ] 0 ( x , y ) ] + ϕ λ f ( x , y ) ϕ λ 0 f ( x , y ) exp [ j 2 d ( x , y ) ] × 0 ( x , y ) exp [ j 2 π ( sin θ 0 / λ 0 ) x ] + ϕ λ f ( x , y ) ϕ λ 0 f * ( x , y ) 0 ( x , y ) exp [ j 2 π ( sin θ 0 / λ 0 ) x ] .
sin θ t = ( λ / λ 0 ) sin θ 0 .
g 7 ( x , y ) = exp [ jd ( x / m , y / m ) ] ,
m = f 2 / f 1
g 8 ( x , y ) = exp [ jd ( x , y ) ] ,
exp [ jd ( x , y ) ] h ( x , y ) = 2 exp [ jd ( x , y ) ] + exp [ j 2 d ( x , y ) ] exp [ j 2 π ( sin θ 0 / λ 0 ) x ] + exp [ j 2 π ( sin θ 0 / λ 0 ) x ] .
h g ( x , y ) = 2 + exp [ j 2 π ( sin θ 0 / λ 0 ) x ] + exp [ j 2 π ( sin θ 0 / λ 0 ) x ] .
sin θ t + = sin θ i + ( λ / λ 0 ) sin θ 0 , θ t 0 = θ i , sin θ t = sin θ i ( λ / λ 0 ) sin θ 0 .
g 9 ( x , y ) = 0 ( x , y ) exp [ j 2 π ( sin θ i / λ ) x ] .
g 10 ( x , y ) = 0 ( x , y ) { exp [ j 2 d ( x , y ) ] exp [ j 2 π ( sin θ i λ + sin θ 0 λ 0 ) x ] + 2 exp [ jd ( x , y ) ] exp [ j 2 π ( sin θ i / λ ) x ] + exp [ j 2 π ( sin θ i λ sin θ 0 λ 0 ) x ] } .
g 11 ( x , y ) = 0 ( x , y ) { exp [ j 2 π ( sin θ i / λ ) x ] + 2 exp [ j 2 π ( sin θ i λ sin θ 0 λ 0 ) x ] } + exp [ j 2 π ( sin θ i λ 2 sin θ 0 λ 0 ) x ] .
sin θ m = sin θ i sin θ 0 .

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