Abstract

An experimental investigation of speckle patterns formed when a collimated beam of laser light is scattered by small spherical particles dispersed uniformly throughout a volume is reported. Double-exposure speckle photography is used to measure the decrease of correlation that occurs when the angle of incidence of the collimated beam is changed by an amount α. The results are presented graphically and in the form of empirical equations involving dimensionless groups of the following parameters: particle diameter, number of particles per unit volume, and depth of the test volume. The data form two distinct regimes—one for low numbers per unit volume and one for high numbers per unit volume. The effect of other experimental variables such as particle refractive index, film exposure characteristics, and the geometry of the recording system are studied.

© 1980 Optical Society of America

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  1. B. J. Thompson, "Holographic particle sizing techniques," J. Phys. E 7, 781–788 (1974).
  2. G. A. Hotham, "Particle sizing by laser photography," Proc. Soc. Photo-Opt. Instrum. Eng. 125, 44–76 (1977).
  3. J. Swithenbank, J. M. Beer, D. S. Taylor, D. Abbot, and G. C. McCreath, "A laser diagnostic technique for the measurement of droplet and size distribution," in Progress in Astronautics and Aeronautics, edited by B. T. Zinn (AIAA, New York 1977), Vol. 53, pp. 421–447.
  4. P. G. Felton, "In-stream measurent of particle size distribution," presented at the International Symposium on In-Stream Measurements of Particle Solid Properties, Bergen, Norway, Aug. 22–23, 1978 (unpublished).
  5. 5.G. Tribillion, "Correlation entre deux speckles obtenus avec deux longueurs d'onde—application à la mesure de la rugosite moyenne," Opt. Commun. 11, 172–174 (1974).
  6. D. Léger, E. Mathieu, and J. C. Perrin, "Optical surface roughness determination using speckle correlation technique," Appl. Opt. 14, 872–877 (1975).
  7. D. Léger and J. C. Perrin, "Real-time measurement of surface roughness by correlation of speckle patterns," J. Opt. Soc. Am. 66, 1210–1217 (1976).
  8. S. Debrus and C. P. Grover, "Correlation of light beams scattered at different angles by a ground glass," Opt. Commun. 3, 340–342 (1971).
  9. J. A. Méndez and M. L. Roblin, "Variations du speckle en presence d'une rotation de 1'objet diffusant," Opt. Commun. 15, 226–230 (1975).
  10. A. K. Chakraborty, "The effect of polarization of the illuminating beam on the microstructure of speckles produced by a random diffuser," Opt. Commun. 8, 366–368 (1973).
  11. N. George, A. Jain, and R. D. S. Melville, "Speckle, diffusers, and depolarization," Appl. Phys. 6, 65–70 (1975).
  12. N. George, A. Jain, and R. D.S. Melville, "Experiments on the space and wavelength dependence of speckle," Appl. Phys. 7, 157–169 (1975).
  13. J. A. Méndez and M. L. Roblin, "Contraste des franges d'interferences produites par l'enregistrement photographique de deux speckles en présence d'un dépointage longitudinal entre les deux poses," Nouv. Rev. Opt. 7, 105–112 (1976).
  14. J. W. Goodman, "Statistical properties of laser speckle patterns," in Laser Speckle and Related Phenomena, edited by J. C. Dainty (Springer-Verlag, New York, 1975), p. 42.
  15. K. A. Stetson, "Film nonlinearities in speckle photography," J. Opt. Soc. Am. 68, 1406–1407 (1978).
  16. (Nd3) = 0.01 is approximately the boundary separating the two regimes for the current experimental parameters. This boundary is more precisely disclosed by a sharp change in slope of curves of constant (L/d) on a plot of the log of the angular change α to attain a given fringe visibility versus the log of (Nd3). An experimental determination of the regime is also possible because, as is subsequently indicated in this paper, Regime I data are sensitive to changes in R, but Regime II data are not.

1978 (1)

K. A. Stetson, "Film nonlinearities in speckle photography," J. Opt. Soc. Am. 68, 1406–1407 (1978).

1977 (1)

G. A. Hotham, "Particle sizing by laser photography," Proc. Soc. Photo-Opt. Instrum. Eng. 125, 44–76 (1977).

1976 (2)

D. Léger and J. C. Perrin, "Real-time measurement of surface roughness by correlation of speckle patterns," J. Opt. Soc. Am. 66, 1210–1217 (1976).

J. A. Méndez and M. L. Roblin, "Contraste des franges d'interferences produites par l'enregistrement photographique de deux speckles en présence d'un dépointage longitudinal entre les deux poses," Nouv. Rev. Opt. 7, 105–112 (1976).

1975 (4)

N. George, A. Jain, and R. D. S. Melville, "Speckle, diffusers, and depolarization," Appl. Phys. 6, 65–70 (1975).

N. George, A. Jain, and R. D.S. Melville, "Experiments on the space and wavelength dependence of speckle," Appl. Phys. 7, 157–169 (1975).

J. A. Méndez and M. L. Roblin, "Variations du speckle en presence d'une rotation de 1'objet diffusant," Opt. Commun. 15, 226–230 (1975).

D. Léger, E. Mathieu, and J. C. Perrin, "Optical surface roughness determination using speckle correlation technique," Appl. Opt. 14, 872–877 (1975).

1974 (2)

B. J. Thompson, "Holographic particle sizing techniques," J. Phys. E 7, 781–788 (1974).

5.G. Tribillion, "Correlation entre deux speckles obtenus avec deux longueurs d'onde—application à la mesure de la rugosite moyenne," Opt. Commun. 11, 172–174 (1974).

1973 (1)

A. K. Chakraborty, "The effect of polarization of the illuminating beam on the microstructure of speckles produced by a random diffuser," Opt. Commun. 8, 366–368 (1973).

1971 (1)

S. Debrus and C. P. Grover, "Correlation of light beams scattered at different angles by a ground glass," Opt. Commun. 3, 340–342 (1971).

Abbot, D.

J. Swithenbank, J. M. Beer, D. S. Taylor, D. Abbot, and G. C. McCreath, "A laser diagnostic technique for the measurement of droplet and size distribution," in Progress in Astronautics and Aeronautics, edited by B. T. Zinn (AIAA, New York 1977), Vol. 53, pp. 421–447.

Beer, J. M.

J. Swithenbank, J. M. Beer, D. S. Taylor, D. Abbot, and G. C. McCreath, "A laser diagnostic technique for the measurement of droplet and size distribution," in Progress in Astronautics and Aeronautics, edited by B. T. Zinn (AIAA, New York 1977), Vol. 53, pp. 421–447.

Chakraborty, A. K.

A. K. Chakraborty, "The effect of polarization of the illuminating beam on the microstructure of speckles produced by a random diffuser," Opt. Commun. 8, 366–368 (1973).

Debrus, S.

S. Debrus and C. P. Grover, "Correlation of light beams scattered at different angles by a ground glass," Opt. Commun. 3, 340–342 (1971).

Felton, P. G.

P. G. Felton, "In-stream measurent of particle size distribution," presented at the International Symposium on In-Stream Measurements of Particle Solid Properties, Bergen, Norway, Aug. 22–23, 1978 (unpublished).

George, N.

N. George, A. Jain, and R. D. S. Melville, "Speckle, diffusers, and depolarization," Appl. Phys. 6, 65–70 (1975).

N. George, A. Jain, and R. D.S. Melville, "Experiments on the space and wavelength dependence of speckle," Appl. Phys. 7, 157–169 (1975).

Goodman, J. W.

J. W. Goodman, "Statistical properties of laser speckle patterns," in Laser Speckle and Related Phenomena, edited by J. C. Dainty (Springer-Verlag, New York, 1975), p. 42.

Grover, C. P.

S. Debrus and C. P. Grover, "Correlation of light beams scattered at different angles by a ground glass," Opt. Commun. 3, 340–342 (1971).

Hotham, G. A.

G. A. Hotham, "Particle sizing by laser photography," Proc. Soc. Photo-Opt. Instrum. Eng. 125, 44–76 (1977).

Jain, A.

N. George, A. Jain, and R. D. S. Melville, "Speckle, diffusers, and depolarization," Appl. Phys. 6, 65–70 (1975).

N. George, A. Jain, and R. D.S. Melville, "Experiments on the space and wavelength dependence of speckle," Appl. Phys. 7, 157–169 (1975).

Léger, D.

Mathieu, E.

McCreath, G. C.

J. Swithenbank, J. M. Beer, D. S. Taylor, D. Abbot, and G. C. McCreath, "A laser diagnostic technique for the measurement of droplet and size distribution," in Progress in Astronautics and Aeronautics, edited by B. T. Zinn (AIAA, New York 1977), Vol. 53, pp. 421–447.

Melville, R. D. S.

N. George, A. Jain, and R. D. S. Melville, "Speckle, diffusers, and depolarization," Appl. Phys. 6, 65–70 (1975).

Melville, R. D.S.

N. George, A. Jain, and R. D.S. Melville, "Experiments on the space and wavelength dependence of speckle," Appl. Phys. 7, 157–169 (1975).

Méndez, J. A.

J. A. Méndez and M. L. Roblin, "Contraste des franges d'interferences produites par l'enregistrement photographique de deux speckles en présence d'un dépointage longitudinal entre les deux poses," Nouv. Rev. Opt. 7, 105–112 (1976).

J. A. Méndez and M. L. Roblin, "Variations du speckle en presence d'une rotation de 1'objet diffusant," Opt. Commun. 15, 226–230 (1975).

Perrin, J. C.

Roblin, M. L.

J. A. Méndez and M. L. Roblin, "Contraste des franges d'interferences produites par l'enregistrement photographique de deux speckles en présence d'un dépointage longitudinal entre les deux poses," Nouv. Rev. Opt. 7, 105–112 (1976).

J. A. Méndez and M. L. Roblin, "Variations du speckle en presence d'une rotation de 1'objet diffusant," Opt. Commun. 15, 226–230 (1975).

Stetson, K. A.

K. A. Stetson, "Film nonlinearities in speckle photography," J. Opt. Soc. Am. 68, 1406–1407 (1978).

Swithenbank, J.

J. Swithenbank, J. M. Beer, D. S. Taylor, D. Abbot, and G. C. McCreath, "A laser diagnostic technique for the measurement of droplet and size distribution," in Progress in Astronautics and Aeronautics, edited by B. T. Zinn (AIAA, New York 1977), Vol. 53, pp. 421–447.

Taylor, D. S.

J. Swithenbank, J. M. Beer, D. S. Taylor, D. Abbot, and G. C. McCreath, "A laser diagnostic technique for the measurement of droplet and size distribution," in Progress in Astronautics and Aeronautics, edited by B. T. Zinn (AIAA, New York 1977), Vol. 53, pp. 421–447.

Thompson, B. J.

B. J. Thompson, "Holographic particle sizing techniques," J. Phys. E 7, 781–788 (1974).

Tribillion, G.

5.G. Tribillion, "Correlation entre deux speckles obtenus avec deux longueurs d'onde—application à la mesure de la rugosite moyenne," Opt. Commun. 11, 172–174 (1974).

Appl. Opt. (1)

Appl. Phys. (2)

N. George, A. Jain, and R. D. S. Melville, "Speckle, diffusers, and depolarization," Appl. Phys. 6, 65–70 (1975).

N. George, A. Jain, and R. D.S. Melville, "Experiments on the space and wavelength dependence of speckle," Appl. Phys. 7, 157–169 (1975).

J. Opt. Soc. Am. (2)

K. A. Stetson, "Film nonlinearities in speckle photography," J. Opt. Soc. Am. 68, 1406–1407 (1978).

D. Léger and J. C. Perrin, "Real-time measurement of surface roughness by correlation of speckle patterns," J. Opt. Soc. Am. 66, 1210–1217 (1976).

J. Phys. E (1)

B. J. Thompson, "Holographic particle sizing techniques," J. Phys. E 7, 781–788 (1974).

Nouv. Rev. Opt. (1)

J. A. Méndez and M. L. Roblin, "Contraste des franges d'interferences produites par l'enregistrement photographique de deux speckles en présence d'un dépointage longitudinal entre les deux poses," Nouv. Rev. Opt. 7, 105–112 (1976).

Opt. Commun. (4)

5.G. Tribillion, "Correlation entre deux speckles obtenus avec deux longueurs d'onde—application à la mesure de la rugosite moyenne," Opt. Commun. 11, 172–174 (1974).

S. Debrus and C. P. Grover, "Correlation of light beams scattered at different angles by a ground glass," Opt. Commun. 3, 340–342 (1971).

J. A. Méndez and M. L. Roblin, "Variations du speckle en presence d'une rotation de 1'objet diffusant," Opt. Commun. 15, 226–230 (1975).

A. K. Chakraborty, "The effect of polarization of the illuminating beam on the microstructure of speckles produced by a random diffuser," Opt. Commun. 8, 366–368 (1973).

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

G. A. Hotham, "Particle sizing by laser photography," Proc. Soc. Photo-Opt. Instrum. Eng. 125, 44–76 (1977).

Other (4)

J. Swithenbank, J. M. Beer, D. S. Taylor, D. Abbot, and G. C. McCreath, "A laser diagnostic technique for the measurement of droplet and size distribution," in Progress in Astronautics and Aeronautics, edited by B. T. Zinn (AIAA, New York 1977), Vol. 53, pp. 421–447.

P. G. Felton, "In-stream measurent of particle size distribution," presented at the International Symposium on In-Stream Measurements of Particle Solid Properties, Bergen, Norway, Aug. 22–23, 1978 (unpublished).

(Nd3) = 0.01 is approximately the boundary separating the two regimes for the current experimental parameters. This boundary is more precisely disclosed by a sharp change in slope of curves of constant (L/d) on a plot of the log of the angular change α to attain a given fringe visibility versus the log of (Nd3). An experimental determination of the regime is also possible because, as is subsequently indicated in this paper, Regime I data are sensitive to changes in R, but Regime II data are not.

J. W. Goodman, "Statistical properties of laser speckle patterns," in Laser Speckle and Related Phenomena, edited by J. C. Dainty (Springer-Verlag, New York, 1975), p. 42.

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