Abstract

The speckle grain close to a diffuser medium carries information about the angles at which light is scattered. We propose the extension of a technique that allows obtaining the angular distribution of the scattered intensity in the far-field speckle pattern from the near-field speckle pattern produced by strong diffusers (whose roughness is greater than the illuminating wavelength). To illustrate this technique we applied it to the light scattered from ground glass diffusers. The experimental results are compared with those obtained by direct measurement of the angular distribution of the mean scattered intensity in the far field showing good agreement with each other. The advantages over the classical far-field methods are outlined.

© 2010 Optical Society of America

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References

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  1. H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).
  2. M. Carpineti, F. Ferri, M. Giglio, E. Paganin, and U. Perini, “Salt-induced fast aggregation of polystyrene latex,” Phys. Rev. A 42, 7347-7354 (1990).
    [CrossRef] [PubMed]
  3. F. Ferri, “Use of a charge coupled device camera for low-angle elastic light scattering,” Rev. Sci. Instrum. 68, 2265-2274(1997).
    [CrossRef]
  4. P. Beckmann and A. Spizzichino, Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, 1963).
  5. J. M. Bennett, Surface Finish and Its Measurement, Collected Works in Optics (Optical Society of America, 1992).
  6. J. C. Stover, Optical Scattering (SPIE Press, 1995).
    [CrossRef]
  7. N. G. Gaggioli and M. L. Roblin, “Détermination de la longueur de covariance d'une surface rugueuse par l'étude de la diffusion résiduelle à l'infini,” Opt. Commun. 54, 201-206 (1985).
    [CrossRef]
  8. K. A. O'Donnell and E. R. Méndez, “Experimental study of scattering from characterized random surfaces,” J. Opt. Soc. Am. A 4, 1194-1205 (1987).
    [CrossRef]
  9. F. Perez Quintián, M. A. Rebollo, and N. G. Gaggioli, “Diffusion of light transmitted from rough surfaces,” J. Mod. Opt. 44, 447-460 (1997).
    [CrossRef]
  10. D. Brogioli, A. Vailati, and M. Giglio, “Heterodyne near-field scattering,” Appl. Phys. Lett. 81, 4109-4111(2002).
    [CrossRef]
  11. F. Ferri, D. Magatti, D. Pescini, M. A. C. Potenza, and M. Giglio, “Heterodyne near-field scattering: a technique for complex fluids,” Phys. Rev. E 70, 041405 (2004).
    [CrossRef]
  12. J. W. Goodman, Statistical Optics (Wiley, 1985).
  13. J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, 1975).
    [CrossRef]
  14. R. Berlasso, F. Perez Quintián, M. A. Rebollo, C. A. Raffo, and N. G. Gaggioli, “Study of speckle size of light scattered from cylindrical rough surfaces,” Appl. Opt. 39, 5811-5819 (2000).
    [CrossRef]
  15. R. G. Berlasso, F. Perez Quintián, M. A. Rebollo, N. G. Gaggioli, L. M. Sánnchez Brea, and E. Bernabeu Martínez, “Speckle size of light scattered from slightly rough cylindrical surfaces,” Appl. Opt. 41, 2020-2027 (2002).
    [CrossRef] [PubMed]

2004 (1)

F. Ferri, D. Magatti, D. Pescini, M. A. C. Potenza, and M. Giglio, “Heterodyne near-field scattering: a technique for complex fluids,” Phys. Rev. E 70, 041405 (2004).
[CrossRef]

2002 (2)

2000 (1)

1997 (2)

F. Perez Quintián, M. A. Rebollo, and N. G. Gaggioli, “Diffusion of light transmitted from rough surfaces,” J. Mod. Opt. 44, 447-460 (1997).
[CrossRef]

F. Ferri, “Use of a charge coupled device camera for low-angle elastic light scattering,” Rev. Sci. Instrum. 68, 2265-2274(1997).
[CrossRef]

1990 (1)

M. Carpineti, F. Ferri, M. Giglio, E. Paganin, and U. Perini, “Salt-induced fast aggregation of polystyrene latex,” Phys. Rev. A 42, 7347-7354 (1990).
[CrossRef] [PubMed]

1987 (1)

1985 (1)

N. G. Gaggioli and M. L. Roblin, “Détermination de la longueur de covariance d'une surface rugueuse par l'étude de la diffusion résiduelle à l'infini,” Opt. Commun. 54, 201-206 (1985).
[CrossRef]

Beckmann, P.

P. Beckmann and A. Spizzichino, Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, 1963).

Bennett, J. M.

J. M. Bennett, Surface Finish and Its Measurement, Collected Works in Optics (Optical Society of America, 1992).

Berlasso, R.

Berlasso, R. G.

Bernabeu Martínez, E.

Brogioli, D.

D. Brogioli, A. Vailati, and M. Giglio, “Heterodyne near-field scattering,” Appl. Phys. Lett. 81, 4109-4111(2002).
[CrossRef]

Carpineti, M.

M. Carpineti, F. Ferri, M. Giglio, E. Paganin, and U. Perini, “Salt-induced fast aggregation of polystyrene latex,” Phys. Rev. A 42, 7347-7354 (1990).
[CrossRef] [PubMed]

Ferri, F.

F. Ferri, D. Magatti, D. Pescini, M. A. C. Potenza, and M. Giglio, “Heterodyne near-field scattering: a technique for complex fluids,” Phys. Rev. E 70, 041405 (2004).
[CrossRef]

F. Ferri, “Use of a charge coupled device camera for low-angle elastic light scattering,” Rev. Sci. Instrum. 68, 2265-2274(1997).
[CrossRef]

M. Carpineti, F. Ferri, M. Giglio, E. Paganin, and U. Perini, “Salt-induced fast aggregation of polystyrene latex,” Phys. Rev. A 42, 7347-7354 (1990).
[CrossRef] [PubMed]

Gaggioli, N. G.

R. G. Berlasso, F. Perez Quintián, M. A. Rebollo, N. G. Gaggioli, L. M. Sánnchez Brea, and E. Bernabeu Martínez, “Speckle size of light scattered from slightly rough cylindrical surfaces,” Appl. Opt. 41, 2020-2027 (2002).
[CrossRef] [PubMed]

R. Berlasso, F. Perez Quintián, M. A. Rebollo, C. A. Raffo, and N. G. Gaggioli, “Study of speckle size of light scattered from cylindrical rough surfaces,” Appl. Opt. 39, 5811-5819 (2000).
[CrossRef]

F. Perez Quintián, M. A. Rebollo, and N. G. Gaggioli, “Diffusion of light transmitted from rough surfaces,” J. Mod. Opt. 44, 447-460 (1997).
[CrossRef]

N. G. Gaggioli and M. L. Roblin, “Détermination de la longueur de covariance d'une surface rugueuse par l'étude de la diffusion résiduelle à l'infini,” Opt. Commun. 54, 201-206 (1985).
[CrossRef]

Giglio, M.

F. Ferri, D. Magatti, D. Pescini, M. A. C. Potenza, and M. Giglio, “Heterodyne near-field scattering: a technique for complex fluids,” Phys. Rev. E 70, 041405 (2004).
[CrossRef]

D. Brogioli, A. Vailati, and M. Giglio, “Heterodyne near-field scattering,” Appl. Phys. Lett. 81, 4109-4111(2002).
[CrossRef]

M. Carpineti, F. Ferri, M. Giglio, E. Paganin, and U. Perini, “Salt-induced fast aggregation of polystyrene latex,” Phys. Rev. A 42, 7347-7354 (1990).
[CrossRef] [PubMed]

Goodman, J. W.

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

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, 1975).
[CrossRef]

Magatti, D.

F. Ferri, D. Magatti, D. Pescini, M. A. C. Potenza, and M. Giglio, “Heterodyne near-field scattering: a technique for complex fluids,” Phys. Rev. E 70, 041405 (2004).
[CrossRef]

Méndez, E. R.

O'Donnell, K. A.

Paganin, E.

M. Carpineti, F. Ferri, M. Giglio, E. Paganin, and U. Perini, “Salt-induced fast aggregation of polystyrene latex,” Phys. Rev. A 42, 7347-7354 (1990).
[CrossRef] [PubMed]

Perez Quintián, F.

Perini, U.

M. Carpineti, F. Ferri, M. Giglio, E. Paganin, and U. Perini, “Salt-induced fast aggregation of polystyrene latex,” Phys. Rev. A 42, 7347-7354 (1990).
[CrossRef] [PubMed]

Pescini, D.

F. Ferri, D. Magatti, D. Pescini, M. A. C. Potenza, and M. Giglio, “Heterodyne near-field scattering: a technique for complex fluids,” Phys. Rev. E 70, 041405 (2004).
[CrossRef]

Potenza, M. A. C.

F. Ferri, D. Magatti, D. Pescini, M. A. C. Potenza, and M. Giglio, “Heterodyne near-field scattering: a technique for complex fluids,” Phys. Rev. E 70, 041405 (2004).
[CrossRef]

Raffo, C. A.

Rebollo, M. A.

Roblin, M. L.

N. G. Gaggioli and M. L. Roblin, “Détermination de la longueur de covariance d'une surface rugueuse par l'étude de la diffusion résiduelle à l'infini,” Opt. Commun. 54, 201-206 (1985).
[CrossRef]

Sánnchez Brea, L. M.

Spizzichino, A.

P. Beckmann and A. Spizzichino, Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, 1963).

Stover, J. C.

J. C. Stover, Optical Scattering (SPIE Press, 1995).
[CrossRef]

Vailati, A.

D. Brogioli, A. Vailati, and M. Giglio, “Heterodyne near-field scattering,” Appl. Phys. Lett. 81, 4109-4111(2002).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).

Appl. Opt. (2)

Appl. Phys. Lett. (1)

D. Brogioli, A. Vailati, and M. Giglio, “Heterodyne near-field scattering,” Appl. Phys. Lett. 81, 4109-4111(2002).
[CrossRef]

J. Mod. Opt. (1)

F. Perez Quintián, M. A. Rebollo, and N. G. Gaggioli, “Diffusion of light transmitted from rough surfaces,” J. Mod. Opt. 44, 447-460 (1997).
[CrossRef]

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

Opt. Commun. (1)

N. G. Gaggioli and M. L. Roblin, “Détermination de la longueur de covariance d'une surface rugueuse par l'étude de la diffusion résiduelle à l'infini,” Opt. Commun. 54, 201-206 (1985).
[CrossRef]

Phys. Rev. A (1)

M. Carpineti, F. Ferri, M. Giglio, E. Paganin, and U. Perini, “Salt-induced fast aggregation of polystyrene latex,” Phys. Rev. A 42, 7347-7354 (1990).
[CrossRef] [PubMed]

Phys. Rev. E (1)

F. Ferri, D. Magatti, D. Pescini, M. A. C. Potenza, and M. Giglio, “Heterodyne near-field scattering: a technique for complex fluids,” Phys. Rev. E 70, 041405 (2004).
[CrossRef]

Rev. Sci. Instrum. (1)

F. Ferri, “Use of a charge coupled device camera for low-angle elastic light scattering,” Rev. Sci. Instrum. 68, 2265-2274(1997).
[CrossRef]

Other (6)

P. Beckmann and A. Spizzichino, Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, 1963).

J. M. Bennett, Surface Finish and Its Measurement, Collected Works in Optics (Optical Society of America, 1992).

J. C. Stover, Optical Scattering (SPIE Press, 1995).
[CrossRef]

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).

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

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, 1975).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Effective area of the diffuser that scatters light to point O.

Fig. 2
Fig. 2

Diagram of the vectors used in the description of the near-field scattering technique.

Fig. 3
Fig. 3

Definition of R A 1 , R A 2 , R B 1 , and R B 2 involved in the calculation of the phase of e ( r 1 ) e * ( r 2 ) .

Fig. 4
Fig. 4

Experimental setup for the near-field scattering technique.

Fig. 5
Fig. 5

Typical speckle pattern intensity recorded at a plane close to the sample.

Fig. 6
Fig. 6

Absolute value of the Fourier transform of the scattered intensity in Fig. 5, and a generic ring where the average over | q | is calculated.

Fig. 7
Fig. 7

Angular distribution of the mean scattered intensity for sample 1; the curves connect the experimental points.

Equations (16)

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e ( r ) = E ( q ) exp ( i q · r ) d q ,
J 12 ( r 1 , r 2 ) = e ( r 1 ) e * ( r 2 ) ,
i F ( θ , ϕ ) = E ( q ) E * ( q ) = FT ( e ( r 1 ) e * ( r 2 ) ) ,
i ( r 1 ) i ( r 2 ) i ( r 1 ) i ( r 2 ) = | e ( r 1 ) e * ( r 2 ) | 2 .
e ( r 1 ) e * ( r 2 ) = A ( r 1 ) A ( r 2 ) exp ( i φ ( r 1 ) ) exp ( i φ ( r 2 ) ) ,
exp ( i φ ( r 1 ) ) exp ( i φ ( r 2 ) ) A = exp ( i φ A ) exp [ i k ( R A 1 R A 2 ) ] exp ( i ψ ) , exp ( i φ ( r 1 ) ) exp ( i φ ( r 2 ) ) B = exp ( i φ B ) exp [ i k ( R B 1 R B 2 ) ] exp ( i ψ ) ,
e ( r 1 ) e * ( r 2 ) = | e ( r 1 ) e * ( r 2 ) | .
A e = π ( tan ( θ max ) d ) 2 ,
A i = π ( λ / sin ( θ ) ) 2 .
N i = A e A i = tan ( θ ) 2 sin ( θ ) 2 d 2 λ 2 .
L o = ( pixel size ) resolution magnification 150 μm ,
q min = 2 π / L o 4.18 × 10 2 μm 1 .
θ = a sin ( q / k ) θ min 0.24 ° .
NA = sin ( θ max ) θ max 40.5 ° .
| FT ( i ( r ) ) | 2 = FT ( i ( r ) ) [ FT ( i ( r ) ) ] * = FT ( i ( r ) i ( r ) ) = FT i ( r 1 ) i ( r 2 ) ,
[ FT 1 | FT ( i ( r ) ) | 2 ] = i ( r 1 ) i ( r 2 ) = R i ( Δ r ) .

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