Abstract

Speckle image contrasts from a fractal rough-surface object are investigated in simulation, where the image surface is conjugate to the object surface. It is observed that the Hurst exponent H of fractal roughness affects speckle contrast and statistics dramatically. For example, a strong rough surface (σh>λ) exhibits Rayleigh statistics over increasing ranges of point spread function widths as H decreases. Conceptual explanations are also presented for effects of H and the coherence factor on speckle in imaging systems.

© 2009 Optical Society of America

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References

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  1. J. C. Dainty, A. E. Ennos, M. Francon, J. W. Goodman, T. S. McKechnie, and G. Parry, Laser Speckle and Related Phenomena (Springer-Verlag, 1984).
  2. J. W. Goodman, Speckle Phenomena in Optics (Roberts & Company, 2007).
  3. E. Jakeman, Opt. Eng. 23, 453 (1984).
  4. P. J. Chandley and H. M. Escamilla, Opt. Commun. 29, 151 (1979).
    [CrossRef]
  5. M. V. Berry, J. Phys. A 12, 781 (1979).
    [CrossRef]
  6. E. Jakeman, J. Opt. Soc. Am. 72, 1034 (1982).
    [CrossRef]
  7. I. A. Popov, N. V. Sidorovsky, and L. M. Veselov, Opt. Commun. 134, 289 (1997).
    [CrossRef]
  8. J. Krim, I. Heyvaert, C. Van Haesendonck, and Y. Bruynseraede, Phys. Rev. Lett. 70, 57 (1993).
    [CrossRef] [PubMed]
  9. G. Palasantzas and J. Krim, Phys. Rev. B 48, 2873 (1993).
    [CrossRef]
  10. D. Y. Kang and T. D. Milster, J. Opt. Soc. Am. A 26, 1954 (2009).
    [CrossRef]
  11. B. M. Levine and J. C. Dainty, Opt. Commun. 45, 252 (1983).
    [CrossRef]
  12. H. Kadono, T. Asakura, and N. Takai, Appl. Phys. B 44, 167 (1987).
    [CrossRef]
  13. D. J. Schertler and N. George, Opt. Lett. 18, 391 (1993).
    [CrossRef] [PubMed]

2009 (1)

1997 (1)

I. A. Popov, N. V. Sidorovsky, and L. M. Veselov, Opt. Commun. 134, 289 (1997).
[CrossRef]

1993 (3)

J. Krim, I. Heyvaert, C. Van Haesendonck, and Y. Bruynseraede, Phys. Rev. Lett. 70, 57 (1993).
[CrossRef] [PubMed]

G. Palasantzas and J. Krim, Phys. Rev. B 48, 2873 (1993).
[CrossRef]

D. J. Schertler and N. George, Opt. Lett. 18, 391 (1993).
[CrossRef] [PubMed]

1987 (1)

H. Kadono, T. Asakura, and N. Takai, Appl. Phys. B 44, 167 (1987).
[CrossRef]

1984 (1)

E. Jakeman, Opt. Eng. 23, 453 (1984).

1983 (1)

B. M. Levine and J. C. Dainty, Opt. Commun. 45, 252 (1983).
[CrossRef]

1982 (1)

1979 (2)

P. J. Chandley and H. M. Escamilla, Opt. Commun. 29, 151 (1979).
[CrossRef]

M. V. Berry, J. Phys. A 12, 781 (1979).
[CrossRef]

Asakura, T.

H. Kadono, T. Asakura, and N. Takai, Appl. Phys. B 44, 167 (1987).
[CrossRef]

Berry, M. V.

M. V. Berry, J. Phys. A 12, 781 (1979).
[CrossRef]

Bruynseraede, Y.

J. Krim, I. Heyvaert, C. Van Haesendonck, and Y. Bruynseraede, Phys. Rev. Lett. 70, 57 (1993).
[CrossRef] [PubMed]

Chandley, P. J.

P. J. Chandley and H. M. Escamilla, Opt. Commun. 29, 151 (1979).
[CrossRef]

Dainty, J. C.

B. M. Levine and J. C. Dainty, Opt. Commun. 45, 252 (1983).
[CrossRef]

J. C. Dainty, A. E. Ennos, M. Francon, J. W. Goodman, T. S. McKechnie, and G. Parry, Laser Speckle and Related Phenomena (Springer-Verlag, 1984).

Ennos, A. E.

J. C. Dainty, A. E. Ennos, M. Francon, J. W. Goodman, T. S. McKechnie, and G. Parry, Laser Speckle and Related Phenomena (Springer-Verlag, 1984).

Escamilla, H. M.

P. J. Chandley and H. M. Escamilla, Opt. Commun. 29, 151 (1979).
[CrossRef]

Francon, M.

J. C. Dainty, A. E. Ennos, M. Francon, J. W. Goodman, T. S. McKechnie, and G. Parry, Laser Speckle and Related Phenomena (Springer-Verlag, 1984).

George, N.

Goodman, J. W.

J. W. Goodman, Speckle Phenomena in Optics (Roberts & Company, 2007).

J. C. Dainty, A. E. Ennos, M. Francon, J. W. Goodman, T. S. McKechnie, and G. Parry, Laser Speckle and Related Phenomena (Springer-Verlag, 1984).

Heyvaert, I.

J. Krim, I. Heyvaert, C. Van Haesendonck, and Y. Bruynseraede, Phys. Rev. Lett. 70, 57 (1993).
[CrossRef] [PubMed]

Jakeman, E.

E. Jakeman, Opt. Eng. 23, 453 (1984).

E. Jakeman, J. Opt. Soc. Am. 72, 1034 (1982).
[CrossRef]

Kadono, H.

H. Kadono, T. Asakura, and N. Takai, Appl. Phys. B 44, 167 (1987).
[CrossRef]

Kang, D. Y.

Krim, J.

G. Palasantzas and J. Krim, Phys. Rev. B 48, 2873 (1993).
[CrossRef]

J. Krim, I. Heyvaert, C. Van Haesendonck, and Y. Bruynseraede, Phys. Rev. Lett. 70, 57 (1993).
[CrossRef] [PubMed]

Levine, B. M.

B. M. Levine and J. C. Dainty, Opt. Commun. 45, 252 (1983).
[CrossRef]

McKechnie, T. S.

J. C. Dainty, A. E. Ennos, M. Francon, J. W. Goodman, T. S. McKechnie, and G. Parry, Laser Speckle and Related Phenomena (Springer-Verlag, 1984).

Milster, T. D.

Palasantzas, G.

G. Palasantzas and J. Krim, Phys. Rev. B 48, 2873 (1993).
[CrossRef]

Parry, G.

J. C. Dainty, A. E. Ennos, M. Francon, J. W. Goodman, T. S. McKechnie, and G. Parry, Laser Speckle and Related Phenomena (Springer-Verlag, 1984).

Popov, I. A.

I. A. Popov, N. V. Sidorovsky, and L. M. Veselov, Opt. Commun. 134, 289 (1997).
[CrossRef]

Schertler, D. J.

Sidorovsky, N. V.

I. A. Popov, N. V. Sidorovsky, and L. M. Veselov, Opt. Commun. 134, 289 (1997).
[CrossRef]

Takai, N.

H. Kadono, T. Asakura, and N. Takai, Appl. Phys. B 44, 167 (1987).
[CrossRef]

Van Haesendonck, C.

J. Krim, I. Heyvaert, C. Van Haesendonck, and Y. Bruynseraede, Phys. Rev. Lett. 70, 57 (1993).
[CrossRef] [PubMed]

Veselov, L. M.

I. A. Popov, N. V. Sidorovsky, and L. M. Veselov, Opt. Commun. 134, 289 (1997).
[CrossRef]

Appl. Phys. B (1)

H. Kadono, T. Asakura, and N. Takai, Appl. Phys. B 44, 167 (1987).
[CrossRef]

J. Opt. Soc. Am. (1)

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

J. Phys. A (1)

M. V. Berry, J. Phys. A 12, 781 (1979).
[CrossRef]

Opt. Commun. (3)

I. A. Popov, N. V. Sidorovsky, and L. M. Veselov, Opt. Commun. 134, 289 (1997).
[CrossRef]

B. M. Levine and J. C. Dainty, Opt. Commun. 45, 252 (1983).
[CrossRef]

P. J. Chandley and H. M. Escamilla, Opt. Commun. 29, 151 (1979).
[CrossRef]

Opt. Eng. (1)

E. Jakeman, Opt. Eng. 23, 453 (1984).

Opt. Lett. (1)

Phys. Rev. B (1)

G. Palasantzas and J. Krim, Phys. Rev. B 48, 2873 (1993).
[CrossRef]

Phys. Rev. Lett. (1)

J. Krim, I. Heyvaert, C. Van Haesendonck, and Y. Bruynseraede, Phys. Rev. Lett. 70, 57 (1993).
[CrossRef] [PubMed]

Other (2)

J. C. Dainty, A. E. Ennos, M. Francon, J. W. Goodman, T. S. McKechnie, and G. Parry, Laser Speckle and Related Phenomena (Springer-Verlag, 1984).

J. W. Goodman, Speckle Phenomena in Optics (Roberts & Company, 2007).

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Figures (4)

Fig. 1
Fig. 1

Laser speckle contrast variations versus k m for different H in a 2D 4 f imaging system for (a) σ h = 0.3 λ and (b) σ h = 1.5 λ . L cor = 5 μ m , indicated as dashed lines. Laser speckle contrasts are largely dependent on H, even though σ h and L cor of the rough objects do not vary. λ = 193 nm .

Fig. 2
Fig. 2

Simple scheme for explaining the concept of A c o for the speckle irradiance at x i . (a) A c i on the image plane is determined by two randomly phased coherent PSFs. (b) Object plane indicating A c o = A c i m t 2 .

Fig. 3
Fig. 3

1D profiles for simulated 2D rough surface for (a) H = 0.8 and (b) 0.6 with σ h = 1.5 λ and L cor = 5 μ m . Shaded areas indicate the width of A c o .

Fig. 4
Fig. 4

Simulated C s from rough surfaces with L cor = 5 μ m , H = 1 , (a) σ h = 0.3 λ , and (b) σ h = 1.5 λ for a partially coherent illumination onto a rough surface. Arrows in (b) indicate maximum C s . Error bars indicate variance in simulation calculations, and these variances are similar in Fig. 1, although they are not shown there.

Equations (3)

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K u ( Δ x o ) = σ h 2 exp [ ( Δ x o L cor ) 2 H ] ,
I ( x i ) = C diff M ( Δ x o ) f ( x o 1 ) f * ( x o 2 ) h coh ( x i x o 1 ) h coh * ( x i x o 2 ) d x o 1 d x o 2 ,
I ( x i ) = I Δ x o = 0 ( x i ) + Δ I Δ x o 0 ( x i ) ,

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