Abstract

We demonstrate that unspeckled images of coherently illuminated, diffuse objects can be formed from measurements of backscattered laser-speckle intensity. The theoretical basis for this imaging technique is outlined, and results of computer experiments that successfully construct images from digitally simulated laser-speckle measurements are presented.

© 1987 Optical Society of America

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References

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  1. J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, 2nd ed.,J. C. Dainty, ed. (Springer-Verlag, New York, 1984), pp. 9–75.
  2. L. I. Goldfischer, J. Opt. Soc. Am. 55, 247 (1965).
    [CrossRef]
  3. R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, San Francisco, 1978), p. 115.
  4. J. R. Fienup, Opt. Lett. 3, 27 (1978).
    [CrossRef] [PubMed]
  5. J. R. Fienup, Appl. Opt. 21, 2758 (1982).
    [CrossRef] [PubMed]
  6. J. R. Fienup, C. C. Wackerman, J. Opt. Soc. Am. A 3, 1897 (1986).
    [CrossRef]
  7. J. R. Fienup, J. Opt. Soc. Am. A 4, 118 (1987).
    [CrossRef]
  8. S. Lowenthal, H. Arsenault, J. Opt. Soc. Am. 60, 1478 (1970).
    [CrossRef]
  9. R. Hanbury Brown, The Intensity Interferometer (Taylor and Francis, London, 1974).

1987 (1)

1986 (1)

1982 (1)

1978 (1)

1970 (1)

1965 (1)

Arsenault, H.

Bracewell, R. N.

R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, San Francisco, 1978), p. 115.

Fienup, J. R.

Goldfischer, L. I.

Goodman, J. W.

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, 2nd ed.,J. C. Dainty, ed. (Springer-Verlag, New York, 1984), pp. 9–75.

Hanbury Brown, R.

R. Hanbury Brown, The Intensity Interferometer (Taylor and Francis, London, 1974).

Lowenthal, S.

Wackerman, C. C.

Appl. Opt. (1)

J. Opt. Soc. Am. (2)

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

Opt. Lett. (1)

Other (3)

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, 2nd ed.,J. C. Dainty, ed. (Springer-Verlag, New York, 1984), pp. 9–75.

R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, San Francisco, 1978), p. 115.

R. Hanbury Brown, The Intensity Interferometer (Taylor and Francis, London, 1974).

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Figures (2)

Fig. 1
Fig. 1

Estimating the energy spectrum of speckle intensity by noncoherently averaging many coherent speckled image autocorrelations. (A) Noncoherent average of N = 4 autocorrelations; (B) estimate of dc term; (C), (A) minus (B); (D)–(F) N = 32; (G)–(I) N = 128; (J)–(L) N = 1024.

Fig. 2
Fig. 2

Image recovery from noncoherently average autocorrelation data (N = 10,000): (A) dc-adjusted, noncoherently averaged autocorrelations, (B) estimate of the Fourier modulus of the incoherent object, (C) image reconstructed from (B) using the iterative transform (phase-retrieval) algorithm, (D) Wiener filter, (E) filtered Fourier modulus estimate, (F) image reconstructed from (E), (G) original incoherent object, (H) Wiener filtered, incoherent object, (I) result of Wiener filtering (C).

Equations (6)

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I n ( u ) = | F n ( u ) | 2 = | { f n ( x ) } | 2 ,
r n ( x ) = 1 { | F n ( u ) | 2 H ( u ) } = [ f n ( x ) f n ( x ) ] * h ( x ) ,
lim N N 1 n = 1 N | r n ( x ) | 2 = b | h ( x ) | 2 + c r 0 ( x ) * | h ( x ) | 2 ,
b = c [ | f 0 ( x ) | 2 d 2 x ] 2
r 0 ( x ) | f 0 ( x ) | 2 | f 0 ( x ) | 2
W ( u ) = OTF ( u ) E s ( u ) | OTF ( u ) | 2 E s ( u ) + E n ,

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