Abstract

The diffraction of a focused Gaussian beam from a moving random phase screen is discussed. The correlation function of intensity fluctuations of statistically inhomogeneous dynamic speckles is studied. A theoretical and experimental analysis of the peculiarities of a new type of manifestation of the Doppler effect for focused Gaussian beam scattering is carried out.

© 1995 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. E. Jakeman, Opt. Eng. 23, 453 (1984).
  2. S. S. Ul’yanov, J. Tech. Phys. 61, 106 (1991) (in Russian, translated into English).
  3. S. S. Ul’yanov, Measurements 10, 93 (1992).
  4. S. S. Ul’yanov, D. A. Zimnyakov, V. V. Tuchin, Opt. Eng. 33, 3189 (1994).
    [CrossRef]
  5. S. Ma, X. Peng, Optik 80, 184 (1988).
  6. V. P. Ryabukho, S. S. Ul’yanov, Measurements 10, 39 (1992).
  7. S. S. Ul’yanov, V. P. Ryabukho, V. V. Tuchin, Opt. Eng. 33, 908 (1994).
    [CrossRef]
  8. M. Nieto-Vesperinas, J. M. Soto-Crespo, Phys. Rev. B 39, 8193 (1989).
    [CrossRef]
  9. A. R. McGurn, A. A. Maradudin, Phys. Rev. B 39, 13,160 (1989).
  10. M. Saillard, D. Maystre, J. Opt. Soc. Am. A 7, 982 (1990).
    [CrossRef]
  11. C. Macaskill, B. J. Kachoyan, J. Acoust. Soc. Am. 84, 1826 (1988).
    [CrossRef]
  12. S. M. Rytov, Yu. A. Kravtsov, V. I. Tatarskiy, Introduction to Statistical Radiophysics, Part II, Random Fields (Nauka, Moscow, 1978) (in Russian, translated into English).
  13. R. L. Fante, J. Opt. Soc. Am. A 2, 2318 (1985).
    [CrossRef]
  14. I. S. Gonorovsky, Radiotechnical Circuits and Signals (Sovietskoe Radio, Moscow, 1977) (in Russian).
  15. I. S. Gradstein, I. M. Ryzhyk, Tables of Integrals, Sums, Series and Products (Physical and Mathemetical Literature General Publisher, Moscow, 1971) (in Russian, translated into English).

1994

S. S. Ul’yanov, D. A. Zimnyakov, V. V. Tuchin, Opt. Eng. 33, 3189 (1994).
[CrossRef]

S. S. Ul’yanov, V. P. Ryabukho, V. V. Tuchin, Opt. Eng. 33, 908 (1994).
[CrossRef]

1992

S. S. Ul’yanov, Measurements 10, 93 (1992).

V. P. Ryabukho, S. S. Ul’yanov, Measurements 10, 39 (1992).

1991

S. S. Ul’yanov, J. Tech. Phys. 61, 106 (1991) (in Russian, translated into English).

1990

1989

M. Nieto-Vesperinas, J. M. Soto-Crespo, Phys. Rev. B 39, 8193 (1989).
[CrossRef]

A. R. McGurn, A. A. Maradudin, Phys. Rev. B 39, 13,160 (1989).

1988

C. Macaskill, B. J. Kachoyan, J. Acoust. Soc. Am. 84, 1826 (1988).
[CrossRef]

S. Ma, X. Peng, Optik 80, 184 (1988).

1985

1984

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

Fante, R. L.

Gonorovsky, I. S.

I. S. Gonorovsky, Radiotechnical Circuits and Signals (Sovietskoe Radio, Moscow, 1977) (in Russian).

Gradstein, I. S.

I. S. Gradstein, I. M. Ryzhyk, Tables of Integrals, Sums, Series and Products (Physical and Mathemetical Literature General Publisher, Moscow, 1971) (in Russian, translated into English).

Jakeman, E.

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

Kachoyan, B. J.

C. Macaskill, B. J. Kachoyan, J. Acoust. Soc. Am. 84, 1826 (1988).
[CrossRef]

Kravtsov, Yu. A.

S. M. Rytov, Yu. A. Kravtsov, V. I. Tatarskiy, Introduction to Statistical Radiophysics, Part II, Random Fields (Nauka, Moscow, 1978) (in Russian, translated into English).

Ma, S.

S. Ma, X. Peng, Optik 80, 184 (1988).

Macaskill, C.

C. Macaskill, B. J. Kachoyan, J. Acoust. Soc. Am. 84, 1826 (1988).
[CrossRef]

Maradudin, A. A.

A. R. McGurn, A. A. Maradudin, Phys. Rev. B 39, 13,160 (1989).

Maystre, D.

McGurn, A. R.

A. R. McGurn, A. A. Maradudin, Phys. Rev. B 39, 13,160 (1989).

Nieto-Vesperinas, M.

M. Nieto-Vesperinas, J. M. Soto-Crespo, Phys. Rev. B 39, 8193 (1989).
[CrossRef]

Peng, X.

S. Ma, X. Peng, Optik 80, 184 (1988).

Ryabukho, V. P.

S. S. Ul’yanov, V. P. Ryabukho, V. V. Tuchin, Opt. Eng. 33, 908 (1994).
[CrossRef]

V. P. Ryabukho, S. S. Ul’yanov, Measurements 10, 39 (1992).

Rytov, S. M.

S. M. Rytov, Yu. A. Kravtsov, V. I. Tatarskiy, Introduction to Statistical Radiophysics, Part II, Random Fields (Nauka, Moscow, 1978) (in Russian, translated into English).

Ryzhyk, I. M.

I. S. Gradstein, I. M. Ryzhyk, Tables of Integrals, Sums, Series and Products (Physical and Mathemetical Literature General Publisher, Moscow, 1971) (in Russian, translated into English).

Saillard, M.

Soto-Crespo, J. M.

M. Nieto-Vesperinas, J. M. Soto-Crespo, Phys. Rev. B 39, 8193 (1989).
[CrossRef]

Tatarskiy, V. I.

S. M. Rytov, Yu. A. Kravtsov, V. I. Tatarskiy, Introduction to Statistical Radiophysics, Part II, Random Fields (Nauka, Moscow, 1978) (in Russian, translated into English).

Tuchin, V. V.

S. S. Ul’yanov, V. P. Ryabukho, V. V. Tuchin, Opt. Eng. 33, 908 (1994).
[CrossRef]

S. S. Ul’yanov, D. A. Zimnyakov, V. V. Tuchin, Opt. Eng. 33, 3189 (1994).
[CrossRef]

Ul’yanov, S. S.

S. S. Ul’yanov, V. P. Ryabukho, V. V. Tuchin, Opt. Eng. 33, 908 (1994).
[CrossRef]

S. S. Ul’yanov, D. A. Zimnyakov, V. V. Tuchin, Opt. Eng. 33, 3189 (1994).
[CrossRef]

V. P. Ryabukho, S. S. Ul’yanov, Measurements 10, 39 (1992).

S. S. Ul’yanov, Measurements 10, 93 (1992).

S. S. Ul’yanov, J. Tech. Phys. 61, 106 (1991) (in Russian, translated into English).

Zimnyakov, D. A.

S. S. Ul’yanov, D. A. Zimnyakov, V. V. Tuchin, Opt. Eng. 33, 3189 (1994).
[CrossRef]

J. Acoust. Soc. Am.

C. Macaskill, B. J. Kachoyan, J. Acoust. Soc. Am. 84, 1826 (1988).
[CrossRef]

J. Opt. Soc. Am. A

J. Tech. Phys.

S. S. Ul’yanov, J. Tech. Phys. 61, 106 (1991) (in Russian, translated into English).

Measurements

S. S. Ul’yanov, Measurements 10, 93 (1992).

V. P. Ryabukho, S. S. Ul’yanov, Measurements 10, 39 (1992).

Opt. Eng.

S. S. Ul’yanov, V. P. Ryabukho, V. V. Tuchin, Opt. Eng. 33, 908 (1994).
[CrossRef]

S. S. Ul’yanov, D. A. Zimnyakov, V. V. Tuchin, Opt. Eng. 33, 3189 (1994).
[CrossRef]

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

Optik

S. Ma, X. Peng, Optik 80, 184 (1988).

Phys. Rev. B

M. Nieto-Vesperinas, J. M. Soto-Crespo, Phys. Rev. B 39, 8193 (1989).
[CrossRef]

A. R. McGurn, A. A. Maradudin, Phys. Rev. B 39, 13,160 (1989).

Other

S. M. Rytov, Yu. A. Kravtsov, V. I. Tatarskiy, Introduction to Statistical Radiophysics, Part II, Random Fields (Nauka, Moscow, 1978) (in Russian, translated into English).

I. S. Gonorovsky, Radiotechnical Circuits and Signals (Sovietskoe Radio, Moscow, 1977) (in Russian).

I. S. Gradstein, I. M. Ryzhyk, Tables of Integrals, Sums, Series and Products (Physical and Mathemetical Literature General Publisher, Moscow, 1971) (in Russian, translated into English).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Physical system under consideration.

Fig. 2
Fig. 2

Theoretical spectra (normalized to their maximal values) of dynamic speckle intensity fluctuations at the different observation angles. Curve 1: π W0X0/Z = 0, σ = 0.01, W0 = 10, W0/Lc = 0.5. Curve 2: πW0X0/Z = 3, σ = 0.01, W0 = 10, W0/Lc = 0.5. Curve 3: π W0X0/Z = 3, σ = 0.3, W0 = 10, W0/Lc = 0.5.

Fig. 3
Fig. 3

Experimental spectra of intensity fluctuations at the different observation angles. Scattering from random flow, with π W0X0/Z = 3 (curve 1) and π W0X0/Z = 0 (curve 2).

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

U s ( X ) = const . - U v ( X - α ) G ( α ) d α ,
G ( α ) = exp ( - 2 π i X 0 Z α ) exp ( - α 2 W 0 2 )
U v ( X ) = exp [ - 4 π i H ( X ) ] ,
Ψ v ( ξ ) = 16 π 2 σ 2 exp ( - ξ 2 L c 2 ) .
Γ v ( ξ ) = Ψ v ( ξ ) + U v 2 ,
U v = exp ( - δ π 2 σ 2 ) .
B g ( ξ ) = G ( α ) G ( α + ξ ) d α .
Ψ I ( ξ ) = Γ u ( ξ ) 2 - Γ u ( ) 2 Γ u ( 0 ) 2 - Γ u ( ) 2 ,
Γ u ( ξ ) = Γ v B g ,
Ψ I ( ξ ) = C 1 exp ( - 2 β ξ 2 ) + C 2 cos ( ω 0 ξ ) exp ( - β ξ 2 ) .
ω 0 = 4 π ( W 0 L c ) 2 ( X 0 Z ) 1 + 2 ( W 0 L c ) 2 ,
β = 1 L c 2 + 2 W 0 2 ,
C 1 C 2 = 8 π 2 σ 2 [ 1 + ( W 0 L c ) 2 ] 0.5 exp [ 4 π 2 W 0 2 ( W 0 L c ) 2 2 ( W 0 L c ) 2 + 1 ( X 0 Z ) 2 ] × exp ( 16 π 2 σ 2 ) 1.
C 2 C 1 = 2 [ 1 + 32 π 2 ( W 0 L c ) 2 σ 2 ] 0.5 × exp [ - 32 π 2 ( W 0 L c ) 2 σ 2 32 π 2 ( W 0 L c ) 2 σ 2 + 1 2 π 2 W 0 2 ( X 0 Z ) 2 ] × exp ( - 16 π 2 σ 2 ) 1.
S ( ω ) = [ C 1 ( 2 π β ) 0.5 exp ( - ω 2 δ β ) ] + ( C 2 ( π β ) 0.5 × { exp [ - ( ω - ω 0 ) 2 4 β ] + exp [ - ( ω + ω 0 ) 2 4 β ] } ) .

Metrics