Abstract

We demonstrate that images of laser-illuminated objects can be formed from measurements of the wave-front slope (gradient) associated with the backscattered, coherent laser-speckle field. A digital wave-front recovery and image synthesis procedure is described, and the results of computer-simulation experiments are presented in which coherent images are reconstructed from digitally simulated Fourier-plane laser-speckle measurements. Images are recovered from noisy wave-front-difference data to illustrate the effect that measurement noise has on recovered image quality.

© 1990 Optical Society of America

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References

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  1. J. W. Hardy, Proc. IEEE 66, 651 (1978).
    [Crossref]
  2. R. U. Shack, B. C. Platt, J. Opt. Soc. Am. 61, 656 (1971).
  3. R. H. Hudgin, J. Opt. Soc. Am. 67, 375 (1977).
    [Crossref]
  4. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  5. M. S. Scivier, M. A. Fiddy, J. Opt. Soc. Am. A 2, 693 (1985).
    [Crossref]
  6. H. Takajo, T. Takahashi, J. Opt. Soc. Am. A 5, 416 (1988).
    [Crossref]
  7. J. W. Goodman, in Laser Speckle and Related Phenomena, 2nd ed., J. C. Dainty, ed. (Springer-Verlag, New York, 1985), p. 9.

1988 (1)

1985 (1)

1978 (1)

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

1977 (1)

1971 (1)

R. U. Shack, B. C. Platt, J. Opt. Soc. Am. 61, 656 (1971).

Fiddy, M. A.

Goodman, J. W.

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

J. W. Goodman, in Laser Speckle and Related Phenomena, 2nd ed., J. C. Dainty, ed. (Springer-Verlag, New York, 1985), p. 9.

Hardy, J. W.

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

Hudgin, R. H.

Platt, B. C.

R. U. Shack, B. C. Platt, J. Opt. Soc. Am. 61, 656 (1971).

Scivier, M. S.

Shack, R. U.

R. U. Shack, B. C. Platt, J. Opt. Soc. Am. 61, 656 (1971).

Takahashi, T.

Takajo, H.

J. Opt. Soc. Am. (2)

R. U. Shack, B. C. Platt, J. Opt. Soc. Am. 61, 656 (1971).

R. H. Hudgin, J. Opt. Soc. Am. 67, 375 (1977).
[Crossref]

J. Opt. Soc. Am. A (2)

Proc. IEEE (1)

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

Other (2)

J. W. Goodman, in Laser Speckle and Related Phenomena, 2nd ed., J. C. Dainty, ed. (Springer-Verlag, New York, 1985), p. 9.

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

Illustration of the process of averaging multiple path integrals of phase used in phase reconstruction. Here the phase values integrated over the four nearest-neighbor paths (labeled 1, 2, 3, and 4) are averaged to form the average path-integrated phase value ϕi,j at the central grid point.

Fig. 3
Fig. 3

Steps in recovering a coherent image from measurements of laser-speckle field amplitude and phase difference: (A) unspeckled bar target source amplitude, (B) measurement (aperture) plane field amplitude resulting from speckled object field, (C) phase map of the aperture-plane field reconstructed from phase-difference data, and (D) recovered coherent image, formed by inverse Fourier transforming the aperture-plane field specified by the data in (B) and (C).

Fig. 4
Fig. 4

Effect that measurement noise has on recovered image quality. Shown are coherent images recovered from phase-difference data corrupted with additive Gaussian phase-difference errors having standard deviations of (A) 0.1, (B) 0.2, (C) 0.4, and (D) 0.8 rad.

Equations (10)

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ϕ i , j = p = 1 4 w p ϕ i , j ( p ) ,
ϕ i , j ( 1 ) = ϕ i 1 , j + Δ ϕ i 1 , j x ,
ϕ i , j ( 2 ) = ϕ i , j + 1 Δ ϕ i , j y ,
ϕ i , j ( 3 ) = ϕ i + 1 , j Δ ϕ i , j x ,
ϕ i , j ( 4 ) = ϕ i , j 1 + Δ ϕ i , j 1 y
ϕ i , j = arg { p = 1 4 w p exp i , j ( p ) } ,
Δ ϕ i , j x = arg { U ( x i + 1 , y j ) | U ( x i + 1 , y j ) | U * ( x i , y j ) | U * ( x i , y j ) | }
Δ ϕ i , j y = arg { U ( x i , y j + 1 ) | U ( x i , y j + 1 ) | U * ( x i , y j ) | U * ( x i , y j ) | } ,
ϕ i + 1 , j = arg { exp j [ ϕ i , j + Δ ϕ i , j x ] }
ϕ i , j + 1 = arg { exp j [ ϕ i , j + Δ ϕ i , j y ] } .

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