Abstract

Distortion-free imaging through a system with aberrations is possible for a certain class of input. The input spatial spectrum must be restricted to spatial frequencies which are equally affected by the aberrations (i.e., which experience identical phase shifts mod 2π). We demonstrate experimentally that if the aberrations can be localized in the pupil plane, an arbitrary input can be prefiltered to produce a distribution which is imaged without distortion by an aberrant system. Equivalently, the output of the system can be postfiltered to select the information which was imaged without distortion.

© 1990 Optical Society of America

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References

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  1. J. Tsujiuchi, “Restitution des images aberrantes par le filtrage des frequences spatiales,” Opt. Acta 7, 243–261 (1960).
    [CrossRef]
  2. E. N. Leith, J. Upatnieks, “Holograms: Their Properties and Uses,” SPIE J. 4, 3–6 (1965).
  3. H. Kogelnik, “Holographic Image Projection Through Inhomogeneous Media,” Bell Syst. Tech. J. 44, 2451–2455 (1965).
  4. O. Yu Nosach, V. Il Popovichev, V. V. Ragulsky, F. S. Faizullow, “Compensation of Phase Distortions in an Amplifying Medium by a Brillouin Mirror,” JETP Lett. 16, 435–437 (1972).
  5. R. W. Hellwarth, “Generation of Time Reversed Wavefronts by Nonlinear Reflection,” J. Opt. Soc. Am. 67, 1–3 (1977).
    [CrossRef]
  6. R. Risher, Ed., Optical Phase Conjugation (Academic, New York, 1983).
  7. J. Munch, R. Wuerker, L. Heflinger, “Wideband Holographic Correction of an Aberrated Telescope Objective,” Appl. Opt. 29, 2440–2445 (1990).
    [CrossRef] [PubMed]
  8. J. Upatnieks, A. Vander Lugt, E. Leith, “Correction of Lens Aberrations by Means of Holograms,” Appl. Opt. 5, 589–593 (1966).
    [CrossRef] [PubMed]
  9. A. Yariv, T. L. Koch, “One-Way Coherent Imaging Through a Distorting Medium Using Four-Wave Mixing,” Opt. Lett. 7, 113–115 (1982).
    [CrossRef] [PubMed]
  10. K. R. MacDonald, W. R. Tompkin, R. W. Boyd, “Passive One-Way Aberration Correction Using Four-Wave Mixing,” Opt. Lett. 13, 485–487 (1988).
    [CrossRef] [PubMed]
  11. E. N. Leith, D. K. Angell, C.-P. Kuei, “Superresolution by Incoherent-to-Coherent Conversion,” J. Opt. Soc. Am. A 4, 1050–1054 (1987).
    [CrossRef]
  12. A. Cunha, E. N. Leith, “Generalized One-Way Phase-Conjugation Systems,” J. Opt. Soc. Am. B 6, 1803–1812 (1989).
    [CrossRef]
  13. F. Merkle, “New Adaptive Optics Results from ESO,” in ICO 15, Garmish-Partenkirchen (1990), postdeadline paper; see also “Successful Test of Adaptive Optics,” EO Reports 75, 1 (Mar.1990).
  14. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968), Chap. 6.

1990 (1)

1989 (1)

1988 (1)

1987 (1)

1982 (1)

1977 (1)

1972 (1)

O. Yu Nosach, V. Il Popovichev, V. V. Ragulsky, F. S. Faizullow, “Compensation of Phase Distortions in an Amplifying Medium by a Brillouin Mirror,” JETP Lett. 16, 435–437 (1972).

1966 (1)

1965 (2)

E. N. Leith, J. Upatnieks, “Holograms: Their Properties and Uses,” SPIE J. 4, 3–6 (1965).

H. Kogelnik, “Holographic Image Projection Through Inhomogeneous Media,” Bell Syst. Tech. J. 44, 2451–2455 (1965).

1960 (1)

J. Tsujiuchi, “Restitution des images aberrantes par le filtrage des frequences spatiales,” Opt. Acta 7, 243–261 (1960).
[CrossRef]

Angell, D. K.

Boyd, R. W.

Cunha, A.

Faizullow, F. S.

O. Yu Nosach, V. Il Popovichev, V. V. Ragulsky, F. S. Faizullow, “Compensation of Phase Distortions in an Amplifying Medium by a Brillouin Mirror,” JETP Lett. 16, 435–437 (1972).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968), Chap. 6.

Heflinger, L.

Hellwarth, R. W.

Il Popovichev, V.

O. Yu Nosach, V. Il Popovichev, V. V. Ragulsky, F. S. Faizullow, “Compensation of Phase Distortions in an Amplifying Medium by a Brillouin Mirror,” JETP Lett. 16, 435–437 (1972).

Koch, T. L.

Kogelnik, H.

H. Kogelnik, “Holographic Image Projection Through Inhomogeneous Media,” Bell Syst. Tech. J. 44, 2451–2455 (1965).

Kuei, C.-P.

Leith, E.

Leith, E. N.

MacDonald, K. R.

Merkle, F.

F. Merkle, “New Adaptive Optics Results from ESO,” in ICO 15, Garmish-Partenkirchen (1990), postdeadline paper; see also “Successful Test of Adaptive Optics,” EO Reports 75, 1 (Mar.1990).

Munch, J.

Ragulsky, V. V.

O. Yu Nosach, V. Il Popovichev, V. V. Ragulsky, F. S. Faizullow, “Compensation of Phase Distortions in an Amplifying Medium by a Brillouin Mirror,” JETP Lett. 16, 435–437 (1972).

Tompkin, W. R.

Tsujiuchi, J.

J. Tsujiuchi, “Restitution des images aberrantes par le filtrage des frequences spatiales,” Opt. Acta 7, 243–261 (1960).
[CrossRef]

Upatnieks, J.

Vander Lugt, A.

Wuerker, R.

Yariv, A.

Yu Nosach, O.

O. Yu Nosach, V. Il Popovichev, V. V. Ragulsky, F. S. Faizullow, “Compensation of Phase Distortions in an Amplifying Medium by a Brillouin Mirror,” JETP Lett. 16, 435–437 (1972).

Appl. Opt. (2)

Bell Syst. Tech. J. (1)

H. Kogelnik, “Holographic Image Projection Through Inhomogeneous Media,” Bell Syst. Tech. J. 44, 2451–2455 (1965).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

JETP Lett. (1)

O. Yu Nosach, V. Il Popovichev, V. V. Ragulsky, F. S. Faizullow, “Compensation of Phase Distortions in an Amplifying Medium by a Brillouin Mirror,” JETP Lett. 16, 435–437 (1972).

Opt. Acta (1)

J. Tsujiuchi, “Restitution des images aberrantes par le filtrage des frequences spatiales,” Opt. Acta 7, 243–261 (1960).
[CrossRef]

Opt. Lett. (2)

SPIE J. (1)

E. N. Leith, J. Upatnieks, “Holograms: Their Properties and Uses,” SPIE J. 4, 3–6 (1965).

Other (3)

R. Risher, Ed., Optical Phase Conjugation (Academic, New York, 1983).

F. Merkle, “New Adaptive Optics Results from ESO,” in ICO 15, Garmish-Partenkirchen (1990), postdeadline paper; see also “Successful Test of Adaptive Optics,” EO Reports 75, 1 (Mar.1990).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968), Chap. 6.

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Figures (11)

Fig. 1
Fig. 1

Generic linear space-invariant imaging system. Each source element illuminates the input with a plane wave of spatial frequency us, which is scattered to a pupil element uh by an input spatial frequency u0.

Fig. 2
Fig. 2

Interferometric selection of the set of spatial frequencies {um}, which is identically affected by the inhomogeneity described by a pupil function w(u) (i.e., experiences identical phase shifts Φ0 mod2π).

Fig. 3
Fig. 3

MTF of the imaging system equipped with the pupil mask shown in Fig. 5 (sliced along a horizontal line).

Fig. 4
Fig. 4

Experimental system used for the demonstration. The dotted elements and laser beam were used only to record the spatial filter interferometrically.

Fig. 5
Fig. 5

Interferometrically recorded spatial filter. The inhomogeneity consisted of a piece of shower glass.

Fig. 6
Fig. 6

Unfiltered input imaged without the inhomogeneity (perfect image).

Fig. 7
Fig. 7

Unfiltered input imaged through the inhomogeneity (distorted image).

Fig. 8
Fig. 8

Prefiltered input imaged through the inhomogeneity. The prefiltered image is insensitive to the inhomogeneity.

Fig. 9
Fig. 9

Prefiltered input imaged without the inhomogeneity for comparison with Fig. 8.

Fig. 10
Fig. 10

Input imaged through the inhomogeneity in a direction inverse of that shown in Fig. 3.

Fig. 11
Fig. 11

Input imaged through the inhomogeneity and then postfiltered to extract a posteriori the image information which was transmitted integrally through the inhomogeneity.

Equations (6)

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P ( u ) = A ( u ) exp [ i w ( u ) ] ,
w ( u m ) = Φ 0 mod 2 π
G ( u ) = A ( u ) exp [ i w ( u ) ] F ( u ) .
I ( u ) = [ P ( u ) * P ( u ) ] · [ F ( u ) * F ( u ) ] ,
G m ( u ) = A ( u ) M ( u ) exp ( Φ 0 ) F ( u ) ,
I m ( u ) = [ A ( u ) M ( u ) * A ( u ) M ( u ) ] · [ F ( u ) * F ( u ) ] .

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