Abstract

We have developed an experimental method based on the visibility factor of light-scattering minima to obtain size-polydispersity information from contaminants upon a flat substrate. We verify the method by using double-interaction-model calculations and use this technique to examine experimentally the radial variation of a micrometer-sized fiber and the size polydispersity of spherical particles upon a substrate.

© 1999 Optical Society of America

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  1. P. Lilienfeld, Aerosol Sci. Technol. 5, 145 (1986).
    [CrossRef]
  2. M. L. Liswith, E. J. Bawolek, and E. D. Hirleman, Opt. Eng. 35, 858 (1996).
    [CrossRef]
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    [CrossRef]
  4. F. Moreno, J. M. Saiz, P. J. Valle, and F. González, Appl. Phys. Lett. 68, 3087 (1996).
    [CrossRef]
  5. J. L. de la Peña, F. González, J. M. Saiz, F. Moreno, and P. J. Valle, J. Appl. Phys. 85, 432 (1999).
    [CrossRef]
  6. J. L. de la Peña, J. M. Saiz, P. J. Valle, F. González, and F. Moreno, Part. Part. Syst. Charact. 16, 1 (1999).
    [CrossRef]
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    [CrossRef] [PubMed]
  8. B. R. Johnson, J. Opt. Soc. Am. A 9, 1341 (1992); errata 10, 766 (1993).
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  9. G. Videen, J. Opt. Soc. Am. A 8, 483 (1991); errata 9, 844 (1992).
    [CrossRef]
  10. G. Videen, Opt. Commun. 115, 1 (1995).
    [CrossRef]
  11. T. Allen, Particle Size Measurements, 5th ed. (Chapman & Hall, London, 1997), Vol. 1.
  12. F. González, J. M. Saiz, P. J. Valle, and F. Moreno, Opt. Eng. 34, 1200 (1995).
    [CrossRef]
  13. P. J. Valle, F. Moreno, J. M. Saiz, and F. Gonzalez, IEEE Trans. Antennas Propag. 44, 321 (1996).
    [CrossRef]
  14. Y.-L. Xu, Appl. Opt. 36, 9496 (1997).
    [CrossRef]
  15. J. M. Saiz, P. J. Valle, F. González, and F. Moreno, Opt. Eng. 33, 1261 (1994).
    [CrossRef]

1999 (2)

J. L. de la Peña, F. González, J. M. Saiz, F. Moreno, and P. J. Valle, J. Appl. Phys. 85, 432 (1999).
[CrossRef]

J. L. de la Peña, J. M. Saiz, P. J. Valle, F. González, and F. Moreno, Part. Part. Syst. Charact. 16, 1 (1999).
[CrossRef]

1997 (2)

F. González, J. M. Saiz, P. J. Valle, and F. Moreno, Opt. Commun. 137, 359 (1997).
[CrossRef]

Y.-L. Xu, Appl. Opt. 36, 9496 (1997).
[CrossRef]

1996 (3)

P. J. Valle, F. Moreno, J. M. Saiz, and F. Gonzalez, IEEE Trans. Antennas Propag. 44, 321 (1996).
[CrossRef]

F. Moreno, J. M. Saiz, P. J. Valle, and F. González, Appl. Phys. Lett. 68, 3087 (1996).
[CrossRef]

M. L. Liswith, E. J. Bawolek, and E. D. Hirleman, Opt. Eng. 35, 858 (1996).
[CrossRef]

1995 (2)

G. Videen, Opt. Commun. 115, 1 (1995).
[CrossRef]

F. González, J. M. Saiz, P. J. Valle, and F. Moreno, Opt. Eng. 34, 1200 (1995).
[CrossRef]

1994 (1)

J. M. Saiz, P. J. Valle, F. González, and F. Moreno, Opt. Eng. 33, 1261 (1994).
[CrossRef]

1992 (1)

1991 (1)

1987 (1)

1986 (1)

P. Lilienfeld, Aerosol Sci. Technol. 5, 145 (1986).
[CrossRef]

Allen, T.

T. Allen, Particle Size Measurements, 5th ed. (Chapman & Hall, London, 1997), Vol. 1.

Bawolek, E. J.

M. L. Liswith, E. J. Bawolek, and E. D. Hirleman, Opt. Eng. 35, 858 (1996).
[CrossRef]

de la Peña, J. L.

J. L. de la Peña, J. M. Saiz, P. J. Valle, F. González, and F. Moreno, Part. Part. Syst. Charact. 16, 1 (1999).
[CrossRef]

J. L. de la Peña, F. González, J. M. Saiz, F. Moreno, and P. J. Valle, J. Appl. Phys. 85, 432 (1999).
[CrossRef]

Gonzalez, F.

P. J. Valle, F. Moreno, J. M. Saiz, and F. Gonzalez, IEEE Trans. Antennas Propag. 44, 321 (1996).
[CrossRef]

González, F.

J. L. de la Peña, J. M. Saiz, P. J. Valle, F. González, and F. Moreno, Part. Part. Syst. Charact. 16, 1 (1999).
[CrossRef]

J. L. de la Peña, F. González, J. M. Saiz, F. Moreno, and P. J. Valle, J. Appl. Phys. 85, 432 (1999).
[CrossRef]

F. González, J. M. Saiz, P. J. Valle, and F. Moreno, Opt. Commun. 137, 359 (1997).
[CrossRef]

F. Moreno, J. M. Saiz, P. J. Valle, and F. González, Appl. Phys. Lett. 68, 3087 (1996).
[CrossRef]

F. González, J. M. Saiz, P. J. Valle, and F. Moreno, Opt. Eng. 34, 1200 (1995).
[CrossRef]

J. M. Saiz, P. J. Valle, F. González, and F. Moreno, Opt. Eng. 33, 1261 (1994).
[CrossRef]

Hirleman, E. D.

M. L. Liswith, E. J. Bawolek, and E. D. Hirleman, Opt. Eng. 35, 858 (1996).
[CrossRef]

Johnson, B. R.

Lilienfeld, P.

P. Lilienfeld, Aerosol Sci. Technol. 5, 145 (1986).
[CrossRef]

Liswith, M. L.

M. L. Liswith, E. J. Bawolek, and E. D. Hirleman, Opt. Eng. 35, 858 (1996).
[CrossRef]

Moreno, F.

J. L. de la Peña, J. M. Saiz, P. J. Valle, F. González, and F. Moreno, Part. Part. Syst. Charact. 16, 1 (1999).
[CrossRef]

J. L. de la Peña, F. González, J. M. Saiz, F. Moreno, and P. J. Valle, J. Appl. Phys. 85, 432 (1999).
[CrossRef]

F. González, J. M. Saiz, P. J. Valle, and F. Moreno, Opt. Commun. 137, 359 (1997).
[CrossRef]

P. J. Valle, F. Moreno, J. M. Saiz, and F. Gonzalez, IEEE Trans. Antennas Propag. 44, 321 (1996).
[CrossRef]

F. Moreno, J. M. Saiz, P. J. Valle, and F. González, Appl. Phys. Lett. 68, 3087 (1996).
[CrossRef]

F. González, J. M. Saiz, P. J. Valle, and F. Moreno, Opt. Eng. 34, 1200 (1995).
[CrossRef]

J. M. Saiz, P. J. Valle, F. González, and F. Moreno, Opt. Eng. 33, 1261 (1994).
[CrossRef]

Nahm, K. B.

Saiz, J. M.

J. L. de la Peña, F. González, J. M. Saiz, F. Moreno, and P. J. Valle, J. Appl. Phys. 85, 432 (1999).
[CrossRef]

J. L. de la Peña, J. M. Saiz, P. J. Valle, F. González, and F. Moreno, Part. Part. Syst. Charact. 16, 1 (1999).
[CrossRef]

F. González, J. M. Saiz, P. J. Valle, and F. Moreno, Opt. Commun. 137, 359 (1997).
[CrossRef]

P. J. Valle, F. Moreno, J. M. Saiz, and F. Gonzalez, IEEE Trans. Antennas Propag. 44, 321 (1996).
[CrossRef]

F. Moreno, J. M. Saiz, P. J. Valle, and F. González, Appl. Phys. Lett. 68, 3087 (1996).
[CrossRef]

F. González, J. M. Saiz, P. J. Valle, and F. Moreno, Opt. Eng. 34, 1200 (1995).
[CrossRef]

J. M. Saiz, P. J. Valle, F. González, and F. Moreno, Opt. Eng. 33, 1261 (1994).
[CrossRef]

Valle, P. J.

J. L. de la Peña, J. M. Saiz, P. J. Valle, F. González, and F. Moreno, Part. Part. Syst. Charact. 16, 1 (1999).
[CrossRef]

J. L. de la Peña, F. González, J. M. Saiz, F. Moreno, and P. J. Valle, J. Appl. Phys. 85, 432 (1999).
[CrossRef]

F. González, J. M. Saiz, P. J. Valle, and F. Moreno, Opt. Commun. 137, 359 (1997).
[CrossRef]

P. J. Valle, F. Moreno, J. M. Saiz, and F. Gonzalez, IEEE Trans. Antennas Propag. 44, 321 (1996).
[CrossRef]

F. Moreno, J. M. Saiz, P. J. Valle, and F. González, Appl. Phys. Lett. 68, 3087 (1996).
[CrossRef]

F. González, J. M. Saiz, P. J. Valle, and F. Moreno, Opt. Eng. 34, 1200 (1995).
[CrossRef]

J. M. Saiz, P. J. Valle, F. González, and F. Moreno, Opt. Eng. 33, 1261 (1994).
[CrossRef]

Videen, G.

Wolfe, W. L.

Xu, Y.-L.

Aerosol Sci. Technol. (1)

P. Lilienfeld, Aerosol Sci. Technol. 5, 145 (1986).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

F. Moreno, J. M. Saiz, P. J. Valle, and F. González, Appl. Phys. Lett. 68, 3087 (1996).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

P. J. Valle, F. Moreno, J. M. Saiz, and F. Gonzalez, IEEE Trans. Antennas Propag. 44, 321 (1996).
[CrossRef]

J. Appl. Phys. (1)

J. L. de la Peña, F. González, J. M. Saiz, F. Moreno, and P. J. Valle, J. Appl. Phys. 85, 432 (1999).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Commun. (2)

G. Videen, Opt. Commun. 115, 1 (1995).
[CrossRef]

F. González, J. M. Saiz, P. J. Valle, and F. Moreno, Opt. Commun. 137, 359 (1997).
[CrossRef]

Opt. Eng. (3)

F. González, J. M. Saiz, P. J. Valle, and F. Moreno, Opt. Eng. 34, 1200 (1995).
[CrossRef]

M. L. Liswith, E. J. Bawolek, and E. D. Hirleman, Opt. Eng. 35, 858 (1996).
[CrossRef]

J. M. Saiz, P. J. Valle, F. González, and F. Moreno, Opt. Eng. 33, 1261 (1994).
[CrossRef]

Part. Part. Syst. Charact. (1)

J. L. de la Peña, J. M. Saiz, P. J. Valle, F. González, and F. Moreno, Part. Part. Syst. Charact. 16, 1 (1999).
[CrossRef]

Other (1)

T. Allen, Particle Size Measurements, 5th ed. (Chapman & Hall, London, 1997), Vol. 1.

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Figures (3)

Fig. 1
Fig. 1

Experimental (circles), double-interaction model5 (solid curve), and empirical approximation (dashed curve) s-polarized light-scattering intensity from a cylinder R/λ=0.87 upon a substrate (both gold coated: ˆ=-11+1.5i) illuminated at normal incidence.

Fig. 2
Fig. 2

(a) Empirical and (b) double-interaction model predictions of the light-scattering intensities from small-sized polydisperse spherical particles upon a substrate illuminated at normal incidence. The mean relative value is R0/λ=2.53, A=1, and the angular resolution is 1°. Dotted curves, monodisperse sample; continuous curves, r=3%; dashed curves, r=6%.

Fig. 3
Fig. 3

Evolution of Vm for some values of r (expressed in percent) by means of relation (10). Circles correspond to the measurable points. Experimental visibilities for a substrate with spherical particles (triangles) and a substrate with a fiber (squares) are shown. Arrows show the minimum value of r by any order for a given sample (see text).

Equations (10)

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Iθs=0IR,θspR,R0,rdR,
IR,θs=A1-coskγRθs-π/2,
pRdR=amRm-1 exp-aRΓmdR,
IθsA-A cos1/r2arctanr2kγR0θs-π/21+kγR0r2θs-π/221/2r2.
IθsA-A coskγR0θs-π/21+kγR0r2θs-π/221/2r2.
Vm=Iθsmax,R0,r-Iθsmin,R0,rIθsmax,R0,r+Iθsmin,R0,r,
βs=1+kγR0θs-π/2r22-1/2r2,
Vmβsmax+βsmin2+βsmax-βsmin,
θsmin-π2-αm2R0,αm0.292+0.316m.
Vmβsmin1+2πγαmr22-1/2r2.

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