Abstract

Spectra of intensity fluctuations of dynamic non-Gaussian speckles formed with a small number of scattering events have been studied theoretically and experimentally. A new type of manifestation of the Doppler effect has been observed. The dependence of frequency position of the Doppler peak and the shape of the Doppler spectrum on the number of scatterers has been analyzed.

© 2014 Optical Society of America

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  1. J. C. Dainty, Laser Speckle and Related Phenomena, Vol. 9 of Topics in Applied Physics (Springer, 1975).
  2. J. W. Goodman, Statistical Optics, (Wiley, 1985).
  3. T. Yoshimura, “Statistical properties of dynamic speckles,” J. Opt. Soc. Am. A 3, 1032–1054 (1986).
  4. P. J. Chandley and H. M. Escamilla, “Speckle from a rough surface when the illuminated region contains few correlation areas: the effect of changing the surface height variance,” Opt. Commun. 29, 151–154 (1979).
    [CrossRef]
  5. E. Jakeman, “Speckle statistics with a small number of scatterers,” Opt. Eng. 23, 453–461 (1984).
    [CrossRef]
  6. B. Saleh, Photoelectron Statistics with Applications to Spectroscopy and Optical Communication (Springer-Verlag, 1991), pp. 145–149.
  7. S. S. Ulyanov, D. A. Zimnyakov, and V. V. Tuchin, “Fundamentals and applications of dynamic speckles induced by focused laser beam scattering,” Opt. Eng. 33, 3189–3201 (1994).
    [CrossRef]
  8. S. S. Ulyanov, “Speckled speckles statistics with a small number of scatterers. An implication for blood flow measurements,” J. Biomed. Opt. 3, 237–245 (1998).
    [CrossRef]
  9. M. Kowalczyk and P. Zalicki, “Small-N speckle: phase-contrast approach,” Proc. SPIE 556, 50–54 (1985).
    [CrossRef]
  10. G. Goodman, “Speckle with a finite number of steps,” Appl. Opt. 47, A111–A118 (2008).
    [CrossRef]
  11. E. R. Mendez, “Speckle contrast variation in the confocal scanning microscope. Hard-edged aperture,” Opt. Acta 33, 269–278 (1986).
    [CrossRef]
  12. T. Wilson, “Optical aspects of confocal microscopy,” in Confocal Microscopy, T. Wilson, ed. (Academic, 1990), pp. 93–139.
  13. S. S. Ulyanov, “High resolution speckle-microscopy: study of the spatial structure of a bioflow,” Physiol. Meas. 22, 681–691 (2001).
    [CrossRef]
  14. E. I. Galanzha, G. E. Brill, Y. Aizu, S. S. Ulyanov, and V. V. Tuchin, “Speckle and Doppler methods of blood and lymph flow monitoring,” in Handbook of Optical Biomedical Diagnostics, V. Tuchin, ed. (SPIE, 2002), pp. 875–937.
  15. S. S. Ulyanov, “Diffusing wave spectroscopy with a small number of scattering events: an implication for microflow diagnostics,” Phys. Rev. E 72, 052902 (2005).
    [CrossRef]
  16. S. S. Ulyanov, Yu. A. Ganilova, D. Zhu, J. Qiu, P. Li, O. V. Ulianova, and Q. Luo, “LASCA with a small number of scatterers: application for monitoring of microflow,” Europhys. Lett. 82, 18005 (2008).
    [CrossRef]
  17. S. S. Ulyanov and V. V. Tuchin, “Using of low-coherent speckled speckles for bioflow measurements,” Appl. Opt. 39, 6385–6389 (2000).
    [CrossRef]
  18. S. S. Ulyanov, “New type of manifestation of the Doppler effect: an applications to blood and lymph flow measurements,” Opt. Eng. 34, 2850–2855 (1995).
    [CrossRef]
  19. S. S. Ulyanov, “Dynamics of statistically inhomogeneous speckles: a new type of manifestation of the Doppler effect,” Opt. Lett. 20, 1313–1315 (1995).
    [CrossRef]
  20. Y. Aizu, T. Asakura, K. Ogino, and T. Sugita, “Evaluation of flow volume in a capillary using dynamic laser speckles based on the photon correlation,” Opt. Commun. 80, 1–6 (1990).
    [CrossRef]
  21. Y. Aizu, K. Ogino, T. Sugita, T. Yamamoto, and T. Asakura, “Noninvasive evaluation of the retinal blood circulation using laser speckle phenomena,” J. Clinical Laser Med. Surgery 8, 35–45 (1990).
  22. T. Eiju, N. Nagai, K. Matsuda, J. Ohtsubo, K. Homma, and K. Shimizu, “Microscopic laser Doppler velocimeter for blood velocity measurement,” Opt. Eng. 32, 15–20 (1993).
    [CrossRef]
  23. J. S. Koelle, C. E. Riva, B. L. Petrig, and S. D. Cranstoun, “Depth of tissue sampling in the optic nerve head using laser Doppler flowmetry,” Lasers Med. Sci. 8, 49–54 (1993).
    [CrossRef]
  24. C. E. Riva and B. L. Petrig, “Choroidal blood flow by laser Doppler flowmetry,” Opt. Eng. 34, 746–752 (1995).
    [CrossRef]
  25. D. L. Fried, “Laser eye safety: the implications of ordinary speckle statistics and speckled-speckle statistics,” J. Opt. Soc. Am. 71, 914–916 (1981).
    [CrossRef]
  26. S. S. Ulyanov, “Statistical models for speckles with a small number of scatterers,” Asian J. Phys. 11, 1–15 (2002).
  27. E. Jakeman, “On the statistics of K-distributed noise,” J. Phys. A 13, 31–48 (1980).
    [CrossRef]
  28. J. Uozumi and T. Asakura, “The first-order statistics of partially developed non-Gaussian speckle patterns,” J. Opt. 12, 177–186 (1981).
    [CrossRef]
  29. S. Yu. Kuzmin and S. S. Ulyanov, “Dynamic speckles formed by focused coherent field scattering from rough surfaces with non-Gaussian statistics,” Proc. SPIE 2544, 317–326 (1995).
    [CrossRef]
  30. S. S. Ulyanov, “Statistical properties of dynamic small-N speckles within highly scattering media,” J. Opt. Soc. Am. A 25, 2207–2214 (2008).
    [CrossRef]
  31. S. S. Ulyanov, “The peculiarities of manifestation of the Doppler effect at the scattering of focused Gaussian beams on moving random inhomogeneous media,” Rep. Russ. Acad. Sci. 59, 133–137 (1995), Physical Issue.
  32. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996), pp. 63–90.
  33. S. M. Rytov, Yu. A. Kravtsov, and V. I. Tatarsky, Principles of Statistical Radiophysics, Part 2 (Springer, 1989).
  34. I. S. Gonorovsky, Radiotechnical Circuits and Signals (Sovietskoe Radio, 1977).
  35. I. S. Gradshtein and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, 1994).
  36. J. S. Bendat and A. G. Piersol, Random Data: Analysis and Measurements Procedures (Wiley, 1986).
  37. S. C. Wu, M. F. Chen, and A. K. Fung, “Non-Gaussian surface generation,” IEEE Trans. Geosci. Remote Sens. 26, 885–888 (1988).
    [CrossRef]
  38. I. V. Fedosov and S. S. Ulyanov, “Specific features of the manifestation of the Doppler effect in diffraction of focused coherent beams in a scattering flow,” Opt. Spectrosc. 91, 278–282 (2001).
    [CrossRef]

2008 (3)

S. S. Ulyanov, Yu. A. Ganilova, D. Zhu, J. Qiu, P. Li, O. V. Ulianova, and Q. Luo, “LASCA with a small number of scatterers: application for monitoring of microflow,” Europhys. Lett. 82, 18005 (2008).
[CrossRef]

G. Goodman, “Speckle with a finite number of steps,” Appl. Opt. 47, A111–A118 (2008).
[CrossRef]

S. S. Ulyanov, “Statistical properties of dynamic small-N speckles within highly scattering media,” J. Opt. Soc. Am. A 25, 2207–2214 (2008).
[CrossRef]

2005 (1)

S. S. Ulyanov, “Diffusing wave spectroscopy with a small number of scattering events: an implication for microflow diagnostics,” Phys. Rev. E 72, 052902 (2005).
[CrossRef]

2002 (1)

S. S. Ulyanov, “Statistical models for speckles with a small number of scatterers,” Asian J. Phys. 11, 1–15 (2002).

2001 (2)

S. S. Ulyanov, “High resolution speckle-microscopy: study of the spatial structure of a bioflow,” Physiol. Meas. 22, 681–691 (2001).
[CrossRef]

I. V. Fedosov and S. S. Ulyanov, “Specific features of the manifestation of the Doppler effect in diffraction of focused coherent beams in a scattering flow,” Opt. Spectrosc. 91, 278–282 (2001).
[CrossRef]

2000 (1)

1998 (1)

S. S. Ulyanov, “Speckled speckles statistics with a small number of scatterers. An implication for blood flow measurements,” J. Biomed. Opt. 3, 237–245 (1998).
[CrossRef]

1995 (5)

C. E. Riva and B. L. Petrig, “Choroidal blood flow by laser Doppler flowmetry,” Opt. Eng. 34, 746–752 (1995).
[CrossRef]

S. S. Ulyanov, “Dynamics of statistically inhomogeneous speckles: a new type of manifestation of the Doppler effect,” Opt. Lett. 20, 1313–1315 (1995).
[CrossRef]

S. Yu. Kuzmin and S. S. Ulyanov, “Dynamic speckles formed by focused coherent field scattering from rough surfaces with non-Gaussian statistics,” Proc. SPIE 2544, 317–326 (1995).
[CrossRef]

S. S. Ulyanov, “New type of manifestation of the Doppler effect: an applications to blood and lymph flow measurements,” Opt. Eng. 34, 2850–2855 (1995).
[CrossRef]

S. S. Ulyanov, “The peculiarities of manifestation of the Doppler effect at the scattering of focused Gaussian beams on moving random inhomogeneous media,” Rep. Russ. Acad. Sci. 59, 133–137 (1995), Physical Issue.

1994 (1)

S. S. Ulyanov, D. A. Zimnyakov, and V. V. Tuchin, “Fundamentals and applications of dynamic speckles induced by focused laser beam scattering,” Opt. Eng. 33, 3189–3201 (1994).
[CrossRef]

1993 (2)

T. Eiju, N. Nagai, K. Matsuda, J. Ohtsubo, K. Homma, and K. Shimizu, “Microscopic laser Doppler velocimeter for blood velocity measurement,” Opt. Eng. 32, 15–20 (1993).
[CrossRef]

J. S. Koelle, C. E. Riva, B. L. Petrig, and S. D. Cranstoun, “Depth of tissue sampling in the optic nerve head using laser Doppler flowmetry,” Lasers Med. Sci. 8, 49–54 (1993).
[CrossRef]

1990 (2)

Y. Aizu, T. Asakura, K. Ogino, and T. Sugita, “Evaluation of flow volume in a capillary using dynamic laser speckles based on the photon correlation,” Opt. Commun. 80, 1–6 (1990).
[CrossRef]

Y. Aizu, K. Ogino, T. Sugita, T. Yamamoto, and T. Asakura, “Noninvasive evaluation of the retinal blood circulation using laser speckle phenomena,” J. Clinical Laser Med. Surgery 8, 35–45 (1990).

1988 (1)

S. C. Wu, M. F. Chen, and A. K. Fung, “Non-Gaussian surface generation,” IEEE Trans. Geosci. Remote Sens. 26, 885–888 (1988).
[CrossRef]

1986 (2)

T. Yoshimura, “Statistical properties of dynamic speckles,” J. Opt. Soc. Am. A 3, 1032–1054 (1986).

E. R. Mendez, “Speckle contrast variation in the confocal scanning microscope. Hard-edged aperture,” Opt. Acta 33, 269–278 (1986).
[CrossRef]

1985 (1)

M. Kowalczyk and P. Zalicki, “Small-N speckle: phase-contrast approach,” Proc. SPIE 556, 50–54 (1985).
[CrossRef]

1984 (1)

E. Jakeman, “Speckle statistics with a small number of scatterers,” Opt. Eng. 23, 453–461 (1984).
[CrossRef]

1981 (2)

J. Uozumi and T. Asakura, “The first-order statistics of partially developed non-Gaussian speckle patterns,” J. Opt. 12, 177–186 (1981).
[CrossRef]

D. L. Fried, “Laser eye safety: the implications of ordinary speckle statistics and speckled-speckle statistics,” J. Opt. Soc. Am. 71, 914–916 (1981).
[CrossRef]

1980 (1)

E. Jakeman, “On the statistics of K-distributed noise,” J. Phys. A 13, 31–48 (1980).
[CrossRef]

1979 (1)

P. J. Chandley and H. M. Escamilla, “Speckle from a rough surface when the illuminated region contains few correlation areas: the effect of changing the surface height variance,” Opt. Commun. 29, 151–154 (1979).
[CrossRef]

Aizu, Y.

Y. Aizu, T. Asakura, K. Ogino, and T. Sugita, “Evaluation of flow volume in a capillary using dynamic laser speckles based on the photon correlation,” Opt. Commun. 80, 1–6 (1990).
[CrossRef]

Y. Aizu, K. Ogino, T. Sugita, T. Yamamoto, and T. Asakura, “Noninvasive evaluation of the retinal blood circulation using laser speckle phenomena,” J. Clinical Laser Med. Surgery 8, 35–45 (1990).

E. I. Galanzha, G. E. Brill, Y. Aizu, S. S. Ulyanov, and V. V. Tuchin, “Speckle and Doppler methods of blood and lymph flow monitoring,” in Handbook of Optical Biomedical Diagnostics, V. Tuchin, ed. (SPIE, 2002), pp. 875–937.

Asakura, T.

Y. Aizu, T. Asakura, K. Ogino, and T. Sugita, “Evaluation of flow volume in a capillary using dynamic laser speckles based on the photon correlation,” Opt. Commun. 80, 1–6 (1990).
[CrossRef]

Y. Aizu, K. Ogino, T. Sugita, T. Yamamoto, and T. Asakura, “Noninvasive evaluation of the retinal blood circulation using laser speckle phenomena,” J. Clinical Laser Med. Surgery 8, 35–45 (1990).

J. Uozumi and T. Asakura, “The first-order statistics of partially developed non-Gaussian speckle patterns,” J. Opt. 12, 177–186 (1981).
[CrossRef]

Bendat, J. S.

J. S. Bendat and A. G. Piersol, Random Data: Analysis and Measurements Procedures (Wiley, 1986).

Brill, G. E.

E. I. Galanzha, G. E. Brill, Y. Aizu, S. S. Ulyanov, and V. V. Tuchin, “Speckle and Doppler methods of blood and lymph flow monitoring,” in Handbook of Optical Biomedical Diagnostics, V. Tuchin, ed. (SPIE, 2002), pp. 875–937.

Chandley, P. J.

P. J. Chandley and H. M. Escamilla, “Speckle from a rough surface when the illuminated region contains few correlation areas: the effect of changing the surface height variance,” Opt. Commun. 29, 151–154 (1979).
[CrossRef]

Chen, M. F.

S. C. Wu, M. F. Chen, and A. K. Fung, “Non-Gaussian surface generation,” IEEE Trans. Geosci. Remote Sens. 26, 885–888 (1988).
[CrossRef]

Cranstoun, S. D.

J. S. Koelle, C. E. Riva, B. L. Petrig, and S. D. Cranstoun, “Depth of tissue sampling in the optic nerve head using laser Doppler flowmetry,” Lasers Med. Sci. 8, 49–54 (1993).
[CrossRef]

Dainty, J. C.

J. C. Dainty, Laser Speckle and Related Phenomena, Vol. 9 of Topics in Applied Physics (Springer, 1975).

Eiju, T.

T. Eiju, N. Nagai, K. Matsuda, J. Ohtsubo, K. Homma, and K. Shimizu, “Microscopic laser Doppler velocimeter for blood velocity measurement,” Opt. Eng. 32, 15–20 (1993).
[CrossRef]

Escamilla, H. M.

P. J. Chandley and H. M. Escamilla, “Speckle from a rough surface when the illuminated region contains few correlation areas: the effect of changing the surface height variance,” Opt. Commun. 29, 151–154 (1979).
[CrossRef]

Fedosov, I. V.

I. V. Fedosov and S. S. Ulyanov, “Specific features of the manifestation of the Doppler effect in diffraction of focused coherent beams in a scattering flow,” Opt. Spectrosc. 91, 278–282 (2001).
[CrossRef]

Fried, D. L.

Fung, A. K.

S. C. Wu, M. F. Chen, and A. K. Fung, “Non-Gaussian surface generation,” IEEE Trans. Geosci. Remote Sens. 26, 885–888 (1988).
[CrossRef]

Galanzha, E. I.

E. I. Galanzha, G. E. Brill, Y. Aizu, S. S. Ulyanov, and V. V. Tuchin, “Speckle and Doppler methods of blood and lymph flow monitoring,” in Handbook of Optical Biomedical Diagnostics, V. Tuchin, ed. (SPIE, 2002), pp. 875–937.

Ganilova, Yu. A.

S. S. Ulyanov, Yu. A. Ganilova, D. Zhu, J. Qiu, P. Li, O. V. Ulianova, and Q. Luo, “LASCA with a small number of scatterers: application for monitoring of microflow,” Europhys. Lett. 82, 18005 (2008).
[CrossRef]

Gonorovsky, I. S.

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

Goodman, G.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996), pp. 63–90.

J. W. Goodman, Statistical Optics, (Wiley, 1985).

Gradshtein, I. S.

I. S. Gradshtein and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, 1994).

Homma, K.

T. Eiju, N. Nagai, K. Matsuda, J. Ohtsubo, K. Homma, and K. Shimizu, “Microscopic laser Doppler velocimeter for blood velocity measurement,” Opt. Eng. 32, 15–20 (1993).
[CrossRef]

Jakeman, E.

E. Jakeman, “Speckle statistics with a small number of scatterers,” Opt. Eng. 23, 453–461 (1984).
[CrossRef]

E. Jakeman, “On the statistics of K-distributed noise,” J. Phys. A 13, 31–48 (1980).
[CrossRef]

Koelle, J. S.

J. S. Koelle, C. E. Riva, B. L. Petrig, and S. D. Cranstoun, “Depth of tissue sampling in the optic nerve head using laser Doppler flowmetry,” Lasers Med. Sci. 8, 49–54 (1993).
[CrossRef]

Kowalczyk, M.

M. Kowalczyk and P. Zalicki, “Small-N speckle: phase-contrast approach,” Proc. SPIE 556, 50–54 (1985).
[CrossRef]

Kravtsov, Yu. A.

S. M. Rytov, Yu. A. Kravtsov, and V. I. Tatarsky, Principles of Statistical Radiophysics, Part 2 (Springer, 1989).

Kuzmin, S. Yu.

S. Yu. Kuzmin and S. S. Ulyanov, “Dynamic speckles formed by focused coherent field scattering from rough surfaces with non-Gaussian statistics,” Proc. SPIE 2544, 317–326 (1995).
[CrossRef]

Li, P.

S. S. Ulyanov, Yu. A. Ganilova, D. Zhu, J. Qiu, P. Li, O. V. Ulianova, and Q. Luo, “LASCA with a small number of scatterers: application for monitoring of microflow,” Europhys. Lett. 82, 18005 (2008).
[CrossRef]

Luo, Q.

S. S. Ulyanov, Yu. A. Ganilova, D. Zhu, J. Qiu, P. Li, O. V. Ulianova, and Q. Luo, “LASCA with a small number of scatterers: application for monitoring of microflow,” Europhys. Lett. 82, 18005 (2008).
[CrossRef]

Matsuda, K.

T. Eiju, N. Nagai, K. Matsuda, J. Ohtsubo, K. Homma, and K. Shimizu, “Microscopic laser Doppler velocimeter for blood velocity measurement,” Opt. Eng. 32, 15–20 (1993).
[CrossRef]

Mendez, E. R.

E. R. Mendez, “Speckle contrast variation in the confocal scanning microscope. Hard-edged aperture,” Opt. Acta 33, 269–278 (1986).
[CrossRef]

Nagai, N.

T. Eiju, N. Nagai, K. Matsuda, J. Ohtsubo, K. Homma, and K. Shimizu, “Microscopic laser Doppler velocimeter for blood velocity measurement,” Opt. Eng. 32, 15–20 (1993).
[CrossRef]

Ogino, K.

Y. Aizu, T. Asakura, K. Ogino, and T. Sugita, “Evaluation of flow volume in a capillary using dynamic laser speckles based on the photon correlation,” Opt. Commun. 80, 1–6 (1990).
[CrossRef]

Y. Aizu, K. Ogino, T. Sugita, T. Yamamoto, and T. Asakura, “Noninvasive evaluation of the retinal blood circulation using laser speckle phenomena,” J. Clinical Laser Med. Surgery 8, 35–45 (1990).

Ohtsubo, J.

T. Eiju, N. Nagai, K. Matsuda, J. Ohtsubo, K. Homma, and K. Shimizu, “Microscopic laser Doppler velocimeter for blood velocity measurement,” Opt. Eng. 32, 15–20 (1993).
[CrossRef]

Petrig, B. L.

C. E. Riva and B. L. Petrig, “Choroidal blood flow by laser Doppler flowmetry,” Opt. Eng. 34, 746–752 (1995).
[CrossRef]

J. S. Koelle, C. E. Riva, B. L. Petrig, and S. D. Cranstoun, “Depth of tissue sampling in the optic nerve head using laser Doppler flowmetry,” Lasers Med. Sci. 8, 49–54 (1993).
[CrossRef]

Piersol, A. G.

J. S. Bendat and A. G. Piersol, Random Data: Analysis and Measurements Procedures (Wiley, 1986).

Qiu, J.

S. S. Ulyanov, Yu. A. Ganilova, D. Zhu, J. Qiu, P. Li, O. V. Ulianova, and Q. Luo, “LASCA with a small number of scatterers: application for monitoring of microflow,” Europhys. Lett. 82, 18005 (2008).
[CrossRef]

Riva, C. E.

C. E. Riva and B. L. Petrig, “Choroidal blood flow by laser Doppler flowmetry,” Opt. Eng. 34, 746–752 (1995).
[CrossRef]

J. S. Koelle, C. E. Riva, B. L. Petrig, and S. D. Cranstoun, “Depth of tissue sampling in the optic nerve head using laser Doppler flowmetry,” Lasers Med. Sci. 8, 49–54 (1993).
[CrossRef]

Rytov, S. M.

S. M. Rytov, Yu. A. Kravtsov, and V. I. Tatarsky, Principles of Statistical Radiophysics, Part 2 (Springer, 1989).

Ryzhik, I. M.

I. S. Gradshtein and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, 1994).

Saleh, B.

B. Saleh, Photoelectron Statistics with Applications to Spectroscopy and Optical Communication (Springer-Verlag, 1991), pp. 145–149.

Shimizu, K.

T. Eiju, N. Nagai, K. Matsuda, J. Ohtsubo, K. Homma, and K. Shimizu, “Microscopic laser Doppler velocimeter for blood velocity measurement,” Opt. Eng. 32, 15–20 (1993).
[CrossRef]

Sugita, T.

Y. Aizu, K. Ogino, T. Sugita, T. Yamamoto, and T. Asakura, “Noninvasive evaluation of the retinal blood circulation using laser speckle phenomena,” J. Clinical Laser Med. Surgery 8, 35–45 (1990).

Y. Aizu, T. Asakura, K. Ogino, and T. Sugita, “Evaluation of flow volume in a capillary using dynamic laser speckles based on the photon correlation,” Opt. Commun. 80, 1–6 (1990).
[CrossRef]

Tatarsky, V. I.

S. M. Rytov, Yu. A. Kravtsov, and V. I. Tatarsky, Principles of Statistical Radiophysics, Part 2 (Springer, 1989).

Tuchin, V. V.

S. S. Ulyanov and V. V. Tuchin, “Using of low-coherent speckled speckles for bioflow measurements,” Appl. Opt. 39, 6385–6389 (2000).
[CrossRef]

S. S. Ulyanov, D. A. Zimnyakov, and V. V. Tuchin, “Fundamentals and applications of dynamic speckles induced by focused laser beam scattering,” Opt. Eng. 33, 3189–3201 (1994).
[CrossRef]

E. I. Galanzha, G. E. Brill, Y. Aizu, S. S. Ulyanov, and V. V. Tuchin, “Speckle and Doppler methods of blood and lymph flow monitoring,” in Handbook of Optical Biomedical Diagnostics, V. Tuchin, ed. (SPIE, 2002), pp. 875–937.

Ulianova, O. V.

S. S. Ulyanov, Yu. A. Ganilova, D. Zhu, J. Qiu, P. Li, O. V. Ulianova, and Q. Luo, “LASCA with a small number of scatterers: application for monitoring of microflow,” Europhys. Lett. 82, 18005 (2008).
[CrossRef]

Ulyanov, S. S.

S. S. Ulyanov, Yu. A. Ganilova, D. Zhu, J. Qiu, P. Li, O. V. Ulianova, and Q. Luo, “LASCA with a small number of scatterers: application for monitoring of microflow,” Europhys. Lett. 82, 18005 (2008).
[CrossRef]

S. S. Ulyanov, “Statistical properties of dynamic small-N speckles within highly scattering media,” J. Opt. Soc. Am. A 25, 2207–2214 (2008).
[CrossRef]

S. S. Ulyanov, “Diffusing wave spectroscopy with a small number of scattering events: an implication for microflow diagnostics,” Phys. Rev. E 72, 052902 (2005).
[CrossRef]

S. S. Ulyanov, “Statistical models for speckles with a small number of scatterers,” Asian J. Phys. 11, 1–15 (2002).

S. S. Ulyanov, “High resolution speckle-microscopy: study of the spatial structure of a bioflow,” Physiol. Meas. 22, 681–691 (2001).
[CrossRef]

I. V. Fedosov and S. S. Ulyanov, “Specific features of the manifestation of the Doppler effect in diffraction of focused coherent beams in a scattering flow,” Opt. Spectrosc. 91, 278–282 (2001).
[CrossRef]

S. S. Ulyanov and V. V. Tuchin, “Using of low-coherent speckled speckles for bioflow measurements,” Appl. Opt. 39, 6385–6389 (2000).
[CrossRef]

S. S. Ulyanov, “Speckled speckles statistics with a small number of scatterers. An implication for blood flow measurements,” J. Biomed. Opt. 3, 237–245 (1998).
[CrossRef]

S. S. Ulyanov, “New type of manifestation of the Doppler effect: an applications to blood and lymph flow measurements,” Opt. Eng. 34, 2850–2855 (1995).
[CrossRef]

S. Yu. Kuzmin and S. S. Ulyanov, “Dynamic speckles formed by focused coherent field scattering from rough surfaces with non-Gaussian statistics,” Proc. SPIE 2544, 317–326 (1995).
[CrossRef]

S. S. Ulyanov, “The peculiarities of manifestation of the Doppler effect at the scattering of focused Gaussian beams on moving random inhomogeneous media,” Rep. Russ. Acad. Sci. 59, 133–137 (1995), Physical Issue.

S. S. Ulyanov, “Dynamics of statistically inhomogeneous speckles: a new type of manifestation of the Doppler effect,” Opt. Lett. 20, 1313–1315 (1995).
[CrossRef]

S. S. Ulyanov, D. A. Zimnyakov, and V. V. Tuchin, “Fundamentals and applications of dynamic speckles induced by focused laser beam scattering,” Opt. Eng. 33, 3189–3201 (1994).
[CrossRef]

E. I. Galanzha, G. E. Brill, Y. Aizu, S. S. Ulyanov, and V. V. Tuchin, “Speckle and Doppler methods of blood and lymph flow monitoring,” in Handbook of Optical Biomedical Diagnostics, V. Tuchin, ed. (SPIE, 2002), pp. 875–937.

Uozumi, J.

J. Uozumi and T. Asakura, “The first-order statistics of partially developed non-Gaussian speckle patterns,” J. Opt. 12, 177–186 (1981).
[CrossRef]

Wilson, T.

T. Wilson, “Optical aspects of confocal microscopy,” in Confocal Microscopy, T. Wilson, ed. (Academic, 1990), pp. 93–139.

Wu, S. C.

S. C. Wu, M. F. Chen, and A. K. Fung, “Non-Gaussian surface generation,” IEEE Trans. Geosci. Remote Sens. 26, 885–888 (1988).
[CrossRef]

Yamamoto, T.

Y. Aizu, K. Ogino, T. Sugita, T. Yamamoto, and T. Asakura, “Noninvasive evaluation of the retinal blood circulation using laser speckle phenomena,” J. Clinical Laser Med. Surgery 8, 35–45 (1990).

Yoshimura, T.

Zalicki, P.

M. Kowalczyk and P. Zalicki, “Small-N speckle: phase-contrast approach,” Proc. SPIE 556, 50–54 (1985).
[CrossRef]

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Figures (8)

Fig. 1.
Fig. 1.

Examples of 2D computer simulation realizations of speckles with SNS.

Fig. 2.
Fig. 2.

Illustration of the process of scattering of Gaussian beam from a random screen. (a) Formation of static speckles; coordinate of the center of the waist beam is (0, 0, 0). (b) Formation of dynamic speckles. Beam scans the screen. The center of the beam is shifted along the ζ axis on the distance shift=vt.

Fig. 3.
Fig. 3.

Dependence of position of Doppler peak on the number Nscatt of scatterers, parameter (Xo/Zo)=1.

Fig. 4.
Fig. 4.

Dependence of the shape of Doppler spectra on the number of scatterers. (a) Nscatt=0.095, (b) Nscatt=0.1, (c) Nscatt=0.125, (d) Nscatt=0.15, (e) Nscatt=0.2, and (f) Nscatt=0.5; parameter Xo/Zo=1.

Fig. 5.
Fig. 5.

Normalized spectra of intensity fluctuations of dynamic speckles. Observation of false Doppler peak on the basis of computer simulation. (a) Result of sample error. Rectangular temporal window; 5 averaging of spectra. (b) Result of spectral leakage. Rectangular temporal window; 100 averaging of spectra. (c) Result of wrong sampling (large step of integration). Hann temporal window; 200 averaging of spectra. (d) Relief of the screen contains quasi-monochromatic component.

Fig. 6.
Fig. 6.

Observation of real Doppler peak dependence on observation angle; computer simulation. (a) Observation angle=0° (corresponds to the value of parameter Xo/Zo=0). (b) Observation angle=45° (corresponds to the value of parameter Xo/Zo=1).

Fig. 7.
Fig. 7.

Observation of real Doppler peak dependence on number of scatterers; computer simulation. (a) Nscatt=0.2, (b) Nscatt=0.5, and (c) Nscatt=2.

Fig. 8.
Fig. 8.

Experimental observation of Doppler peak with SNS. (a) Observation on the optical axis (observation angle=0°, which corresponds to the value of parameter Xo/Zo=0). (b) Observation angle=45° (which corresponds to the value of parameter Xo/Zo=1).

Equations (18)

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Us(Xo)Uv(ξ)·G(ξ,Xo,Zo)dξ,
G(ξ,Xo,Zo)=exp[2π·i·XoZo·ξλ]·exp[ξ2w02].
x=v·tλ,
Us(x)Uv(xξ)·G(ξ)dξ.
Uv(x)=exp[2·π·i·h(x)λ],
h(x)=0,
h(x)h(x)=σ2exp[(xx)2lc2],
Ψv(x)=4π2σ2·exp{x2lc2}.
Γv(x)=Ψv(x)+Uv2=4π2σ2·exp{x2lc2}+exp(4π2σ2),
Uv=exp(2π2σ2).
Bg(x)=G(ξ)·G(ξ+x)*dξ.
Bg(x)=[π2]2·w0·exp{x22w02}·exp{2πi·X0Z0x}.
Γu=ΓvBg,
ΨI(x)=|ΓU(x)|2|ΓU()|2|ΓU(0)|2|ΓU()|2.
ΨI(x)exp(βx2)·{1+cos(ω0x)},
β=2lc2+2wo2,
ω0=2π1+2(w0lc)2·[2w0lc]2·[XoZo].
ΨI(v·tλ)exp[β(v·tλ)2]·{1+cos(ω0v·tλ)}.

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