Abstract

We report what are to our knowledge the first coherent images recovered in the laboratory from measurements made with a Shack–Hartmann wave-front sensor of the phase and amplitude of a laser speckle wave front. We discuss the design of our wave-front sensor, which can obtain the phase and amplitude of an optical field with a single intensity measurement, and we point out a particular type of phase jump that cannot be detected by the Shack–Hartmann sensor. We also discuss implementations of this technique that may permit near-diffraction-limited imaging through turbulent media.

© 1991 Optical Society of America

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References

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  1. P. S. Idell, J. D. Gonglewski, Opt. Lett. 15, 1309 (1990).
    [CrossRef] [PubMed]
  2. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  3. J. C. Wyant, Appl. Opt. 14, 2622 (1975).
    [CrossRef] [PubMed]
  4. J. W. Hardy, Proc. IEEE 66, 651 (1978).
    [CrossRef]
  5. J. C. Bortz, J. Opt. Soc. Am. A 1, 35 (1984).
    [CrossRef]
  6. P. S. Idell, J. D. Gonglewski, in Digest of Meeting on Signal Recovery and Synthesis, Vol. 15 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), p. 160.
  7. J. C. Fontanella, J. Opt. (Paris) 16, 257 (1985).
    [CrossRef]
  8. E. Ochoa, J. W. Goodman, J. Opt. Soc. Am. 73, 943 (1983).
    [CrossRef]
  9. D. G. Voelz, J. D. Gonglewski, P. S. Idell, Proc. Soc. Photo-Opt. Instrum. Eng. 1351, 780 (1990).
  10. D. G. Voelz, D. C. Dayton, Opt. Lett. 16, 1635 (1991).
    [CrossRef] [PubMed]
  11. G. A. Tyler, Report TR634, The Optical Sciences Company, Placentia, Calif. (April1985).
  12. R. H. Hudgin, J. Opt. Soc. Am. 67, 375 (1977).
    [CrossRef]
  13. W. H. Southwell, J. Opt. Soc. Am. 70, 998 (1980).
    [CrossRef]
  14. T. J. Kane, Proc. Soc. Photo-Opt. Instrum. Eng. 1114, 160 (1989).
  15. F. Roddier, Distributions et transformation de Fourier (McGraw-Hill, New York, 1982) (in French).
  16. R. Lane, W. R. Fright, R. H. T. Bates, IEEE Trans. Acoust. Speech Signal Process. ASSP-35, 520 (1987).
    [CrossRef]
  17. R. H. Hutchin, U.S. patent4,688,086 (1987).

1991 (1)

1990 (2)

P. S. Idell, J. D. Gonglewski, Opt. Lett. 15, 1309 (1990).
[CrossRef] [PubMed]

D. G. Voelz, J. D. Gonglewski, P. S. Idell, Proc. Soc. Photo-Opt. Instrum. Eng. 1351, 780 (1990).

1989 (1)

T. J. Kane, Proc. Soc. Photo-Opt. Instrum. Eng. 1114, 160 (1989).

1987 (1)

R. Lane, W. R. Fright, R. H. T. Bates, IEEE Trans. Acoust. Speech Signal Process. ASSP-35, 520 (1987).
[CrossRef]

1985 (1)

J. C. Fontanella, J. Opt. (Paris) 16, 257 (1985).
[CrossRef]

1984 (1)

1983 (1)

1980 (1)

1978 (1)

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

1977 (1)

1975 (1)

Bates, R. H. T.

R. Lane, W. R. Fright, R. H. T. Bates, IEEE Trans. Acoust. Speech Signal Process. ASSP-35, 520 (1987).
[CrossRef]

Bortz, J. C.

Dayton, D. C.

Fontanella, J. C.

J. C. Fontanella, J. Opt. (Paris) 16, 257 (1985).
[CrossRef]

Fright, W. R.

R. Lane, W. R. Fright, R. H. T. Bates, IEEE Trans. Acoust. Speech Signal Process. ASSP-35, 520 (1987).
[CrossRef]

Gonglewski, J. D.

P. S. Idell, J. D. Gonglewski, Opt. Lett. 15, 1309 (1990).
[CrossRef] [PubMed]

D. G. Voelz, J. D. Gonglewski, P. S. Idell, Proc. Soc. Photo-Opt. Instrum. Eng. 1351, 780 (1990).

P. S. Idell, J. D. Gonglewski, in Digest of Meeting on Signal Recovery and Synthesis, Vol. 15 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), p. 160.

Goodman, J. W.

E. Ochoa, J. W. Goodman, J. Opt. Soc. Am. 73, 943 (1983).
[CrossRef]

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

Hardy, J. W.

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

Hudgin, R. H.

Hutchin, R. H.

R. H. Hutchin, U.S. patent4,688,086 (1987).

Idell, P. S.

D. G. Voelz, J. D. Gonglewski, P. S. Idell, Proc. Soc. Photo-Opt. Instrum. Eng. 1351, 780 (1990).

P. S. Idell, J. D. Gonglewski, Opt. Lett. 15, 1309 (1990).
[CrossRef] [PubMed]

P. S. Idell, J. D. Gonglewski, in Digest of Meeting on Signal Recovery and Synthesis, Vol. 15 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), p. 160.

Kane, T. J.

T. J. Kane, Proc. Soc. Photo-Opt. Instrum. Eng. 1114, 160 (1989).

Lane, R.

R. Lane, W. R. Fright, R. H. T. Bates, IEEE Trans. Acoust. Speech Signal Process. ASSP-35, 520 (1987).
[CrossRef]

Ochoa, E.

Roddier, F.

F. Roddier, Distributions et transformation de Fourier (McGraw-Hill, New York, 1982) (in French).

Southwell, W. H.

Tyler, G. A.

G. A. Tyler, Report TR634, The Optical Sciences Company, Placentia, Calif. (April1985).

Voelz, D. G.

D. G. Voelz, D. C. Dayton, Opt. Lett. 16, 1635 (1991).
[CrossRef] [PubMed]

D. G. Voelz, J. D. Gonglewski, P. S. Idell, Proc. Soc. Photo-Opt. Instrum. Eng. 1351, 780 (1990).

Wyant, J. C.

Appl. Opt. (1)

IEEE Trans. Acoust. Speech Signal Process. (1)

R. Lane, W. R. Fright, R. H. T. Bates, IEEE Trans. Acoust. Speech Signal Process. ASSP-35, 520 (1987).
[CrossRef]

J. Opt. (Paris) (1)

J. C. Fontanella, J. Opt. (Paris) 16, 257 (1985).
[CrossRef]

J. Opt. Soc. Am. (3)

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

Opt. Lett. (2)

Proc. IEEE (1)

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

Proc. Soc. Photo-Opt. Instrum. Eng. (2)

D. G. Voelz, J. D. Gonglewski, P. S. Idell, Proc. Soc. Photo-Opt. Instrum. Eng. 1351, 780 (1990).

T. J. Kane, Proc. Soc. Photo-Opt. Instrum. Eng. 1114, 160 (1989).

Other (5)

F. Roddier, Distributions et transformation de Fourier (McGraw-Hill, New York, 1982) (in French).

G. A. Tyler, Report TR634, The Optical Sciences Company, Placentia, Calif. (April1985).

R. H. Hutchin, U.S. patent4,688,086 (1987).

P. S. Idell, J. D. Gonglewski, in Digest of Meeting on Signal Recovery and Synthesis, Vol. 15 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), p. 160.

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

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Figures (4)

Fig. 1
Fig. 1

Schematic of a Shack–Hartmann wave-front sensor used to collect wave-front slope and field amplitude measurements of a coherent diffraction field.

Fig. 2
Fig. 2

Laboratory setup for the IWS experiment.

Fig. 3
Fig. 3

Laboratory reconstruction of bar target group. (A) Measured speckle field amplitude, (B) x-direction phase gradient, (C) y-direction phase gradient, (D) recovered image, (E) truth image.

Fig. 4
Fig. 4

Laboratory reconstruction of bar target group through turbulence. (A) Measured point-spread function of turbulence, (B) truth image through a lens without turbulence, (C) turbulence-degraded image, (D) turbulence-compensated image.

Equations (4)

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δ c = λ f / # 2 π T A 2 ( x , y ) ϕ ( x , y ) d x d y ,
δ c = λ f / # A 2 2 π T ϕ ( x , y ) d x d y = λ f / # 2 π ϕ ( x , y ) ¯ ,
p ( ϕ x ) = 3 ( w sp / π ) 2 [ 1 + 3 ( w sp / π ) 2 ϕ x 2 ] 3 / 2 ,
δ cx = λ f / # 2 π T sin 2 x x [ π rect ( x π ) ] d x d y = 0 ,

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