Abstract

A technique is described for ensemble-averaging the light wave emerging from a turbid medium, enabling the recovery of optical information that is otherwise lost in a speckle pattern. The technique recovers both an amplitude and a phase function for a wave that has been corrupted by severe scattering, without the use of holography. With the phase estimated, an ensemble-averaged field is constructed that can be backprojected to form an image of the object obscured by the scattering medium. Experimental results suggest that the technique can resolve two object points whose signals are unresolved on the exit surface of a diffuser.

© 1998 Optical Society of America

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References

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  1. R. R. Alfano and James G. Fujimoto, eds., Advances in Optical Imaging and Photon Migration, Vol. 2 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 1996).
  2. T. Wilson and C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, London, 1984).
  3. E. Leith, P. Naulleau, and D. Dilworth, “Ensemble-averaged imaging through highly scattering media,” Opt. Lett. 21, 1691–1693 (1996).
    [CrossRef] [PubMed]
  4. P. Naulleau, E. Leith, H. Chen, B. Hoover, and J. Lopez, “Time-gated ensemble-averaged imaging through highly scattering media,” Appl. Opt. 36, 3889–3894 (1997).
    [CrossRef] [PubMed]
  5. G. Y. Yoon, T. Jitsuno, M. Nakatsuka, and S. Nakai, “Shack–Hartmann wave-front measurement with large F-number plastic microlens array,” Appl. Opt. 35, 188–192 (1996).
    [CrossRef] [PubMed]
  6. J. D. Gonglewski, P. S. Idell, D. G. Voelz, D. C. Dayton, B. K. Spielbusch, and R. E. Pierson, “Coherent image synthesis from wave-front sensor measurements of a nonimaged laser speckle field: a laboratory demonstration,” Opt. Lett. 16, 1893–1895 (1991).
    [CrossRef] [PubMed]
  7. G. A. Chanan, “Design of the Keck Observatory alignment camera,” in Precision Instrument Design, T. C. Bristow and A. E. Hatheway, eds., Proc. SPIE 1036, 59–69 (1988).
    [CrossRef]
  8. J. W. Hardy, “Active optics: a new technology for the control of light,” Proc. IEEE 66, 651–697 (1978).
    [CrossRef]
  9. I. Ghozeil, “Hartmann and other screen tests,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), pp. 323–349.
  10. W. H. Southwell, “Wave-front estimation from wave-front slope measurements,” J. Opt. Soc. Am. 70, 998–1006 (1980).
    [CrossRef]
  11. Joseph W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), Chap. 2.
  12. A. Labeyrie, “Attainment of diffraction limited resolution in large telescopes by Fourier analysing speckle patterns in star images,” Astron. Astrophys. 6, 85–87 (1970).
  13. J. R. Fienup, “Reconstruction of an object from the modulus of its Fourier transform,” Opt. Lett. 3, 27–29 (1978).
    [CrossRef] [PubMed]

1997 (1)

1996 (2)

1991 (1)

1980 (1)

1978 (2)

J. R. Fienup, “Reconstruction of an object from the modulus of its Fourier transform,” Opt. Lett. 3, 27–29 (1978).
[CrossRef] [PubMed]

J. W. Hardy, “Active optics: a new technology for the control of light,” Proc. IEEE 66, 651–697 (1978).
[CrossRef]

1970 (1)

A. Labeyrie, “Attainment of diffraction limited resolution in large telescopes by Fourier analysing speckle patterns in star images,” Astron. Astrophys. 6, 85–87 (1970).

Chanan, G. A.

G. A. Chanan, “Design of the Keck Observatory alignment camera,” in Precision Instrument Design, T. C. Bristow and A. E. Hatheway, eds., Proc. SPIE 1036, 59–69 (1988).
[CrossRef]

Chen, H.

Dayton, D. C.

Dilworth, D.

Fienup, J. R.

Ghozeil, I.

I. Ghozeil, “Hartmann and other screen tests,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), pp. 323–349.

Gonglewski, J. D.

Goodman, Joseph W.

Joseph W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), Chap. 2.

Hardy, J. W.

J. W. Hardy, “Active optics: a new technology for the control of light,” Proc. IEEE 66, 651–697 (1978).
[CrossRef]

Hoover, B.

Idell, P. S.

Jitsuno, T.

Labeyrie, A.

A. Labeyrie, “Attainment of diffraction limited resolution in large telescopes by Fourier analysing speckle patterns in star images,” Astron. Astrophys. 6, 85–87 (1970).

Leith, E.

Lopez, J.

Nakai, S.

Nakatsuka, M.

Naulleau, P.

Pierson, R. E.

Sheppard, C.

T. Wilson and C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, London, 1984).

Southwell, W. H.

Spielbusch, B. K.

Voelz, D. G.

Wilson, T.

T. Wilson and C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, London, 1984).

Yoon, G. Y.

Appl. Opt. (2)

Astron. Astrophys. (1)

A. Labeyrie, “Attainment of diffraction limited resolution in large telescopes by Fourier analysing speckle patterns in star images,” Astron. Astrophys. 6, 85–87 (1970).

J. Opt. Soc. Am. (1)

Opt. Lett. (3)

Proc. IEEE (1)

J. W. Hardy, “Active optics: a new technology for the control of light,” Proc. IEEE 66, 651–697 (1978).
[CrossRef]

Other (5)

I. Ghozeil, “Hartmann and other screen tests,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), pp. 323–349.

R. R. Alfano and James G. Fujimoto, eds., Advances in Optical Imaging and Photon Migration, Vol. 2 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 1996).

T. Wilson and C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, London, 1984).

G. A. Chanan, “Design of the Keck Observatory alignment camera,” in Precision Instrument Design, T. C. Bristow and A. E. Hatheway, eds., Proc. SPIE 1036, 59–69 (1988).
[CrossRef]

Joseph W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), Chap. 2.

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Figures (6)

Fig. 1
Fig. 1

Schematic of a single sample used in the imaging technique. The dotted lines and curves indicate the wave front and the Fourier plane intensity distribution in the absence of scattering material, whereas the solid lines and curves indicate the corresponding entities in the presence of severe scattering. Ensemble-averaging smoothes the high-contrast intensity fluctuations in the Fourier transform plane, as shown to the right.

Fig. 2
Fig. 2

(a) Relative amplitude (dashed curve), and phase slope or local spatial frequency (in inverse micrometers) of the test field used to demonstrate the limitations of coherent wave-front sensing. (b) Single period of the phase slope, with sampled values measured by the wave-front sensor with w = 3.33 μm, which is one half of the field period.

Fig. 3
Fig. 3

Selected sample EAFT distributions from computer simulation. Zero marks the zero spatial frequency in each distribution. See text for details.

Fig. 4
Fig. 4

Computer-simulation imaging results: (a) Ensemble-averaged intensity distribution on the diffuser exiting surface. (b) Reconstructed image intensity. Ensemble-averaged Shack–Hartmann wave-front sensing was used to recover phase information, and the ensemble-averaged field was backprojected to form the image. The truth-image intensity is indicated by the dashed curve.

Fig. 5
Fig. 5

Optical intensity distributions: (a) Ensemble-averaged intensity distribution I ¯ x of a diffused double-slit object wave showing poorly resolved signals. (b) Optically recovered image intensity distribution. The truth-image intensity is indicated by the dashed curve.

Fig. 6
Fig. 6

Optical data: (a) Mode spatial frequencies of the sample EAFT distributions. (b) The ensemble-averaged phase function ϕ̅(x) obtained by integration of the curve in (a).

Equations (4)

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ϕ x = 2 π     f lx x d x .
ϕ ¯ x = 2 π     f ¯ lx x d x ,
I f ;   x = rect f 2 f c sinc 2 wf + 4   sinc 2 w f - 150 + 4   sinc wf sinc w f - 150 cos 300 π x ,
A ¯ x = A rms x = I ¯ x .

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