Abstract

The concept of femtosecond laser speckles is put forward. The theory of a speckle pattern in light of finite bandwidth is applied to describe femtosecond laser speckles. Basic representations of the contrast and the spectral correlation of femtosecond laser speckles are presented. The relationship between the speckle contrast and the bandwidth of a femtosecond laser is given. Experimental results are given that indicate an obvious difference between the speckle patterns produced by a continuous-wave laser and those produced by a femtosecond laser.

© 2005 Optical Society of America

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  1. J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, L. Wöste, “White-light filaments for atmosphere analysis,” Science 301, 61–64 (2003).
    [CrossRef] [PubMed]
  2. H. Ihee, V. A. Lobastov, U. M. Gomez, B. M. Goodson, R. Srinivasan, C. Y. Ruan, A. H. Zewail, “Direct imaging of transient molecular structure with ultrafast diffraction,” Science 291, 458–462 (2001).
    [CrossRef] [PubMed]
  3. P. R. Herz, Y. Chen, A. D. Aguirre, J. G. Fujimoto, H. Mashimo, J. Schmitt, A. Koski, J. Goodnow, C. Petersen, “Ultrahigh resolution optical biopsy with endoscope optical coherence tomography,” Opt. Express 12, 3532–3542 (2004).
    [CrossRef] [PubMed]
  4. T. Yasui, K. Minoshima, H. Matsumoto, “Three-dimensional shape measurement of a diffusing surface by use of a femtosecond amplifying optical Kerr gate,” Appl. Opt. 39, 65–71 (2000).
    [CrossRef]
  5. J. Scaffidi, J. Pender, W. Pearman, S. R. Goode, B. W. Colston, J. C. Carter, S. M. Angel, “Dual-pulse laser-induced breakdown spectroscopy with combinations of pemtosecond and nanosecond laser pulses,” Appl. Opt. 42, 6099–6106 (2003).
    [CrossRef] [PubMed]
  6. M. A. Webster, K. J. Webb, A. M. Weiner, “Temporal response of a random medium from third-order laser speckle frequency correlations,” Phys. Rev. Lett. 88, 033901 (2002).
    [CrossRef] [PubMed]
  7. M. A. Webster, T. D. Gerke, A. M. Weiner, K. J. Webb, “Spectral and temporal speckle field measurement of a random medium,” Opt. Lett. 29, 1491–1493 (2004).
    [CrossRef] [PubMed]
  8. J. D. McKinney, M. A. Webster, K. J. Webb, A. M. Weiner, “Characterization and imaging in optically scattering media by use of laser speckle and a variable-coherence source,” Opt. Lett. 25, 4–6 (2000).
    [CrossRef]
  9. J. Pearce, Z. Jian, D. M. Mittleman, “Statistics of multiply scattered broadband terahertz pulses,” Phys. Rev. Lett. 91, 043903 (2003).
    [CrossRef] [PubMed]
  10. J. C. Dainty, Laser Speckle and Related Phenomena (Springer-Verlag, 1984).
  11. G. Parry, “Some effects of temporal coherence on the first order statistics of speckle,” Opt. Acta 21, 763–772 (1974).
    [CrossRef]
  12. H. M. Pedersen, “On the contrast of polychromatic speckle patterns and its dependence on surface roughness,” Opt. Acta 22, 15–24 (1975).
    [CrossRef]

2004

2003

J. Scaffidi, J. Pender, W. Pearman, S. R. Goode, B. W. Colston, J. C. Carter, S. M. Angel, “Dual-pulse laser-induced breakdown spectroscopy with combinations of pemtosecond and nanosecond laser pulses,” Appl. Opt. 42, 6099–6106 (2003).
[CrossRef] [PubMed]

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, L. Wöste, “White-light filaments for atmosphere analysis,” Science 301, 61–64 (2003).
[CrossRef] [PubMed]

J. Pearce, Z. Jian, D. M. Mittleman, “Statistics of multiply scattered broadband terahertz pulses,” Phys. Rev. Lett. 91, 043903 (2003).
[CrossRef] [PubMed]

2002

M. A. Webster, K. J. Webb, A. M. Weiner, “Temporal response of a random medium from third-order laser speckle frequency correlations,” Phys. Rev. Lett. 88, 033901 (2002).
[CrossRef] [PubMed]

2001

H. Ihee, V. A. Lobastov, U. M. Gomez, B. M. Goodson, R. Srinivasan, C. Y. Ruan, A. H. Zewail, “Direct imaging of transient molecular structure with ultrafast diffraction,” Science 291, 458–462 (2001).
[CrossRef] [PubMed]

2000

1975

H. M. Pedersen, “On the contrast of polychromatic speckle patterns and its dependence on surface roughness,” Opt. Acta 22, 15–24 (1975).
[CrossRef]

1974

G. Parry, “Some effects of temporal coherence on the first order statistics of speckle,” Opt. Acta 21, 763–772 (1974).
[CrossRef]

Aguirre, A. D.

André, Y.-B.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, L. Wöste, “White-light filaments for atmosphere analysis,” Science 301, 61–64 (2003).
[CrossRef] [PubMed]

Angel, S. M.

Bourayou, R.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, L. Wöste, “White-light filaments for atmosphere analysis,” Science 301, 61–64 (2003).
[CrossRef] [PubMed]

Carter, J. C.

Chen, Y.

Colston, B. W.

Dainty, J. C.

J. C. Dainty, Laser Speckle and Related Phenomena (Springer-Verlag, 1984).

Frey, S.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, L. Wöste, “White-light filaments for atmosphere analysis,” Science 301, 61–64 (2003).
[CrossRef] [PubMed]

Fujimoto, J. G.

Gerke, T. D.

Gomez, U. M.

H. Ihee, V. A. Lobastov, U. M. Gomez, B. M. Goodson, R. Srinivasan, C. Y. Ruan, A. H. Zewail, “Direct imaging of transient molecular structure with ultrafast diffraction,” Science 291, 458–462 (2001).
[CrossRef] [PubMed]

Goode, S. R.

Goodnow, J.

Goodson, B. M.

H. Ihee, V. A. Lobastov, U. M. Gomez, B. M. Goodson, R. Srinivasan, C. Y. Ruan, A. H. Zewail, “Direct imaging of transient molecular structure with ultrafast diffraction,” Science 291, 458–462 (2001).
[CrossRef] [PubMed]

Herz, P. R.

Ihee, H.

H. Ihee, V. A. Lobastov, U. M. Gomez, B. M. Goodson, R. Srinivasan, C. Y. Ruan, A. H. Zewail, “Direct imaging of transient molecular structure with ultrafast diffraction,” Science 291, 458–462 (2001).
[CrossRef] [PubMed]

Jian, Z.

J. Pearce, Z. Jian, D. M. Mittleman, “Statistics of multiply scattered broadband terahertz pulses,” Phys. Rev. Lett. 91, 043903 (2003).
[CrossRef] [PubMed]

Kasparian, J.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, L. Wöste, “White-light filaments for atmosphere analysis,” Science 301, 61–64 (2003).
[CrossRef] [PubMed]

Koski, A.

Lobastov, V. A.

H. Ihee, V. A. Lobastov, U. M. Gomez, B. M. Goodson, R. Srinivasan, C. Y. Ruan, A. H. Zewail, “Direct imaging of transient molecular structure with ultrafast diffraction,” Science 291, 458–462 (2001).
[CrossRef] [PubMed]

Mashimo, H.

Matsumoto, H.

McKinney, J. D.

Méjean, G.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, L. Wöste, “White-light filaments for atmosphere analysis,” Science 301, 61–64 (2003).
[CrossRef] [PubMed]

Minoshima, K.

Mittleman, D. M.

J. Pearce, Z. Jian, D. M. Mittleman, “Statistics of multiply scattered broadband terahertz pulses,” Phys. Rev. Lett. 91, 043903 (2003).
[CrossRef] [PubMed]

Mysyrowicz, A.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, L. Wöste, “White-light filaments for atmosphere analysis,” Science 301, 61–64 (2003).
[CrossRef] [PubMed]

Parry, G.

G. Parry, “Some effects of temporal coherence on the first order statistics of speckle,” Opt. Acta 21, 763–772 (1974).
[CrossRef]

Pearce, J.

J. Pearce, Z. Jian, D. M. Mittleman, “Statistics of multiply scattered broadband terahertz pulses,” Phys. Rev. Lett. 91, 043903 (2003).
[CrossRef] [PubMed]

Pearman, W.

Pedersen, H. M.

H. M. Pedersen, “On the contrast of polychromatic speckle patterns and its dependence on surface roughness,” Opt. Acta 22, 15–24 (1975).
[CrossRef]

Pender, J.

Petersen, C.

Rodriguez, M.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, L. Wöste, “White-light filaments for atmosphere analysis,” Science 301, 61–64 (2003).
[CrossRef] [PubMed]

Ruan, C. Y.

H. Ihee, V. A. Lobastov, U. M. Gomez, B. M. Goodson, R. Srinivasan, C. Y. Ruan, A. H. Zewail, “Direct imaging of transient molecular structure with ultrafast diffraction,” Science 291, 458–462 (2001).
[CrossRef] [PubMed]

Salmon, E.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, L. Wöste, “White-light filaments for atmosphere analysis,” Science 301, 61–64 (2003).
[CrossRef] [PubMed]

Sauerbrey, R.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, L. Wöste, “White-light filaments for atmosphere analysis,” Science 301, 61–64 (2003).
[CrossRef] [PubMed]

Scaffidi, J.

Schmitt, J.

Srinivasan, R.

H. Ihee, V. A. Lobastov, U. M. Gomez, B. M. Goodson, R. Srinivasan, C. Y. Ruan, A. H. Zewail, “Direct imaging of transient molecular structure with ultrafast diffraction,” Science 291, 458–462 (2001).
[CrossRef] [PubMed]

Webb, K. J.

Webster, M. A.

Weiner, A. M.

Wille, H.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, L. Wöste, “White-light filaments for atmosphere analysis,” Science 301, 61–64 (2003).
[CrossRef] [PubMed]

Wolf, J.-P.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, L. Wöste, “White-light filaments for atmosphere analysis,” Science 301, 61–64 (2003).
[CrossRef] [PubMed]

Wöste, L.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, L. Wöste, “White-light filaments for atmosphere analysis,” Science 301, 61–64 (2003).
[CrossRef] [PubMed]

Yasui, T.

Yu, J.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, L. Wöste, “White-light filaments for atmosphere analysis,” Science 301, 61–64 (2003).
[CrossRef] [PubMed]

Zewail, A. H.

H. Ihee, V. A. Lobastov, U. M. Gomez, B. M. Goodson, R. Srinivasan, C. Y. Ruan, A. H. Zewail, “Direct imaging of transient molecular structure with ultrafast diffraction,” Science 291, 458–462 (2001).
[CrossRef] [PubMed]

Appl. Opt.

Opt. Acta

G. Parry, “Some effects of temporal coherence on the first order statistics of speckle,” Opt. Acta 21, 763–772 (1974).
[CrossRef]

H. M. Pedersen, “On the contrast of polychromatic speckle patterns and its dependence on surface roughness,” Opt. Acta 22, 15–24 (1975).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

M. A. Webster, K. J. Webb, A. M. Weiner, “Temporal response of a random medium from third-order laser speckle frequency correlations,” Phys. Rev. Lett. 88, 033901 (2002).
[CrossRef] [PubMed]

J. Pearce, Z. Jian, D. M. Mittleman, “Statistics of multiply scattered broadband terahertz pulses,” Phys. Rev. Lett. 91, 043903 (2003).
[CrossRef] [PubMed]

Science

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. André, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, L. Wöste, “White-light filaments for atmosphere analysis,” Science 301, 61–64 (2003).
[CrossRef] [PubMed]

H. Ihee, V. A. Lobastov, U. M. Gomez, B. M. Goodson, R. Srinivasan, C. Y. Ruan, A. H. Zewail, “Direct imaging of transient molecular structure with ultrafast diffraction,” Science 291, 458–462 (2001).
[CrossRef] [PubMed]

Other

J. C. Dainty, Laser Speckle and Related Phenomena (Springer-Verlag, 1984).

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Figures (3)

Fig. 1
Fig. 1

Experimental setup for measuring femtosecond laser speckles.

Fig. 2
Fig. 2

Speckle patterns reflected from two aluminum sheets with surface roughnesses (a) σh = 921.8 nm and (b) σh = 1159.5 nm were produced by a cw laser (left) and by a femtosecond laser with a pulse duration of 12 fs (right).

Fig. 3
Fig. 3

Theoretical curves of normalized speckle contrast produced by a cw laser and a femtosecond laser with a pulse duration of 12 fs, and experimental results for eight speckle patterns produced by four aluminum sheets illuminated by a cw laser (squares) and by a femtosecond 12 fs laser (circles). k0 is the wavenumber and σh is the standard deviation of the surface roughness.

Tables (1)

Tables Icon

Table 1 Experimental Means and Standard Deviations of the Gray Scale for the Eight Speckle Patterns on Four Aluminum Sheets

Equations (23)

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A ( t ) = exp ( - i ω 0 t ) n = 1 exp { - [ ( t - t n ) / T ] 2 } .
I ( ξ , η ) = 0 S ( λ ) I ( ξ , η , λ ) d λ ,
I ( ξ , η ) = 0 S ( λ ) I ( ξ , η , λ ) d λ ,
I 2 ( ξ , η ) = 0 S ( λ 1 ) ( λ 2 ) I ( ξ , η , λ 1 ) × I ( ξ , η , λ 2 ) d λ 1 d λ 2 ,
I ( ξ , η ) I ( ξ + ξ , η + η ) = 0 S ( λ 1 ) S ( λ 2 ) × I ( ξ , η , λ 1 ) I ( ξ + ξ , η + η , λ 2 ) d λ 1 d λ 2 .
I ( ξ , η , λ 1 ) I ( ξ + ξ , η + η , λ 2 ) = U ( ξ , η , λ 1 ) U * ( ξ , η , λ 1 ) U ( ξ + ξ , η + η , λ 2 ) U * ( ξ + ξ , η + η , λ 2 ) = I ( ξ , η , λ 1 ) I ( ξ + ξ , η + η , λ 2 ) + U ( ξ , η , λ 1 ) U * ( ξ + ξ , η + η , λ 2 ) 2 .
I ( ξ , η ) = 0 S ( λ ) I ( ξ , η , λ ) d λ ,
σ 2 [ I ( ξ , η ) ] = 0 S ( λ 1 ) S ( λ 2 ) U ( ξ , η , λ 1 ) × U * ( ξ , η , λ 2 ) 2 d λ 1 d λ 2 ,
C I ( ξ , η , ξ , η ) = 0 S ( λ 1 ) S ( λ 2 ) U ( ξ , η , λ 1 ) × U * ( ξ + ξ , η + η , λ 2 ) 2 d λ 1 d λ 2 .
U ( λ ) = U 0 ( λ ) + U s ( λ ) .
I ( λ ) = U ( λ ) U * ( λ ) , = I 0 ( λ ) + I s ( λ ) + U 0 ( λ ) U s * ( λ ) + U 0 * ( λ ) U s ( λ ) = I 0 ( λ ) + I s ( λ ) + 2 Re [ U 0 * ( λ ) U s ( λ ) ] ,
I ( λ ) = I 0 ( λ ) + I s ( λ ) + 2 Re [ U 0 * ( λ ) U s ( λ ) ] ,
Δ I ( λ ) = Δ I s ( λ ) + 2 Re [ U 0 * ( λ ) Δ U s ( λ ) ] .
I ( λ ) = I 0 ( λ ) + I s ( λ ) .
Δ I ( λ 1 ) Δ I ( λ 2 ) = Δ I s ( λ 1 ) Δ I s ( λ 2 ) + 2 Re [ U 0 * ( λ 1 ) U 0 * ( λ 2 ) Δ U s ( λ 1 ) Δ U s * ( λ 2 ) ] + 2 Re [ Δ U s ( λ 1 ) 2 U 0 * ( λ 2 ) U s ( λ 2 ) + Δ U s ( λ 2 ) 2 U 0 * ( λ 1 ) U s ( λ 1 ) ] = Γ ( λ 1 , λ 2 ) 2 + 2 Re [ U 0 * ( λ 1 ) U 0 * ( λ 2 ) Δ U s ( λ 1 ) Δ U s * ( λ 2 ) ] + 2 Re [ Δ U s ( λ 1 ) 2 U 0 * ( λ 2 ) U s ( λ 2 ) + Δ U s ( λ 2 ) 2 U 0 * ( λ 1 ) U s ( λ 1 ) ] ,
Δ I s ( λ 1 ) Δ I s ( λ 2 ) = Γ ( λ 1 , λ 2 ) 2 ,
Γ ( λ 1 , λ 2 ) = U s ( λ 1 ) U s * ( λ 2 ) .
Γ 0 ( λ 1 , λ 2 ) = U 0 ( λ 1 ) U 0 * ( λ 2 ) .
Δ I ( λ 1 ) Δ I ( λ 2 ) = Γ ( λ 1 , λ 2 ) 2 + 2 Re [ Γ 0 * ( λ 1 , λ 2 ) Γ ( λ 1 , λ 2 ) ] .
U 1 ( ξ , η ) = U 0 ( x , y ) K ( x , y ) .
U 1 ( ξ 1 , η 1 , λ 1 ) U 1 * ( ξ 2 , η 2 , λ 2 ) = U 0 ( x 1 , y 1 , λ 1 ) K ( x 1 , y 1 , λ 1 ) × U 0 * ( x 2 , y 2 , λ 2 ) K * ( x 2 , y 2 , λ 2 ) = U 0 ( x 1 , y 1 , λ 1 ) U 0 * ( x 2 , y 2 , λ 2 ) [ K ( x 1 , y 1 , λ 1 ) K * ( x 2 , y 2 , λ 2 ) ] = C exp [ - π σ z 2 ( 1 λ 1 - 1 λ 2 ) ] [ K ( x 1 , y 1 , λ 1 ) × K * ( x 2 , y 2 , λ 2 ) ] ,
ρ 2 = Δ I 2 / I 2 = ρ ( k 0 ) 2 δ 2 = ρ ( k 0 ) 2 [ 1 + ( 2 W σ ) 2 ] - ( 1 / 2 ) ,
ρ ( k 0 ) 2 = 1 - { 1 + N - 1 [ exp ( σ 2 k 0 2 ) - 1 ] } - 2 ,

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