Abstract

A small-angle integrated light-scattering (SAILS) instrument was designed with the innovative use of a diffusing plate and a charge-coupled device (CCD) camera. In contrast to previous small-angle light-scattering instruments, SAILS has few optical surfaces, allowing the direct recovery of scattering data. Although this approach bypasses the need for aberration corrections that are due to lenses, geometric corrections still apply and are described in detail. The image on the diffusing plate, when photographed by the CCD camera, yields a digitized two-dimensional array, covering the observed scattering angles from 10 to 20 deg. The size distribution of the scattering particles can be obtained by a discrete inversion of the experimentally obtained intensity versus angle-scattering curve. The mean radii obtained from this inversion of SAILS data are compared with nominal sizes given by the manufacturer, and standard errors are computed. The results indicate that SAILS is an ideal instrument for the study of particulates and, because of its fast readout time, is suitable for studying aggregation phenomena. However, because of the limited Q range of SAILS it is currently not suited for the direct determination of particle diameters smaller than approximately 300 nm.

© 1999 Optical Society of America

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References

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  1. Lord Rayleigh, “On the electromagnetic theory of light,” Philos. Mag. 12, 81–101 (1881).
    [CrossRef]
  2. Lord Rayleigh, “Aerial plane waves of finite amplitude,” Proc. R. Soc. London Ser. A 84, 247–284 (1910).
    [CrossRef]
  3. Lord Rayleigh, “On the propagation of waves through a stratified medium with special reference to the question of reflection,” Proc. R. Soc. London Ser. A 86, 207–266 (1912).
    [CrossRef]
  4. L. Rayleigh, “On the scattering of light by a cloud of similar small particles of any shape and oriented at random,” Philos. Mag. 35, 373–381 (1918).
    [CrossRef]
  5. P. Debye, “Interferentz von Rontgenstrahlen und Warmebewegun,” Ann. Phys. (Leipzig) 43, 49–95 (1915).
  6. R. Gans, “Molecular light dispersion in solid isotropic bodies,” Ann. Phys. (Leipzig) 77, 317–324 (1925).
    [CrossRef]
  7. C. F. Bohren, D. R. Huffman, Adsorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  8. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  9. C. Tanford, Physical Chemistry of Macromolecules (Wiley, New York, 1961).
  10. F. R. Hallett, J. Watton, P. Krygsman, “Vesicle sizing: number distributions by dynamic light scattering,” Biophys. J. 59, 357–362 (1991).
    [CrossRef] [PubMed]
  11. W. Kaye, “Low angle laser light scattering,” Anal. Chem. 45, 221A–225A (1973).
    [CrossRef]
  12. M. S. McCracken, M. C. Sammons, “Sizing of a vesicle drug formulation by quasielastic light scattering and comparison with electron microscopy and ultracentrifugation,” J. Pharm. Sci. 76, 56–59 (1987).
    [CrossRef] [PubMed]
  13. A. L. Koch, “Calculation of surface area of sacculi from low angle light scattering measurements,” J. Microbiol. Methods 9, 139–150 (1989).
    [CrossRef]
  14. J. Holoubek, “Small angle light scattering from an anisotropic sphere: anisotropy and size effects,” J. Polym. Sci. 32, 351–357 (1994).
    [CrossRef]
  15. K. Kubota, N. Kuwahara, “Low angle light scattering measurement using Fourier transform lens,” Jpn. J. Appl. Phys. 31, 3740–3743 (1992).
    [CrossRef]
  16. W. T. Culberson, M. R. Tant, “A dynamic small angle scattering device for study of polymer crystallization kinetics,” J. Am. Chem. Soc. 31, 143–144 (1990).
  17. M. A. Coil, P. V. Farrell, “Full-field diffraction particle sizing,” Appl. Opt. 34, 7771–7785 (1995).
    [CrossRef] [PubMed]
  18. A. P. Y. Wong, P. Wiltzius, “Dynamic light scattering with a CCD camera,” Rev. Sci. Instrum. 64, 2547–2549 (1993).
    [CrossRef]
  19. M. R. Tant, W. T. Culberson, “Effect of molecular weight on spherulite growth rate of poly via real time small angle light scattering,” Polym. Eng. Sci. 33, 1152–1156 (1993).
    [CrossRef]
  20. W. T. Culberson, M. R. Tant, “A device for study of polymer crystallization kinetics via real time image analysis of small angle light scattering,” J. Appl. Polym. Sci. 47, 395–405 (1993).
    [CrossRef]
  21. A. Cumming, P. Wiltzius, F. S. Bates, J. H. Rosedale, “Light scattering experiments on phase separation dynamics in binary fluid mixtures,” Phys. Rev. A 45, 885–897 (1992).
    [CrossRef] [PubMed]
  22. B. Chu, Basic Principles and Practice (Academic, San Diego, Calif., 1991).
  23. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
  24. F. L. Pedrotti, L. S. Pedrotti, Introduction to Optics (Prentice-Hall, Englewood Cliffs, N.J., 1987).
  25. M. Born, E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Pergamon, Oxford, UK, 1975).
  26. K. B. Strawbridge, F. R. Hallett, “Size distribution obtained from the inversion of I(Q) using integrated light scattering spectroscopy,” Macromolecules 27, 2283–2290 (1994).
    [CrossRef]

1995

1994

K. B. Strawbridge, F. R. Hallett, “Size distribution obtained from the inversion of I(Q) using integrated light scattering spectroscopy,” Macromolecules 27, 2283–2290 (1994).
[CrossRef]

J. Holoubek, “Small angle light scattering from an anisotropic sphere: anisotropy and size effects,” J. Polym. Sci. 32, 351–357 (1994).
[CrossRef]

1993

A. P. Y. Wong, P. Wiltzius, “Dynamic light scattering with a CCD camera,” Rev. Sci. Instrum. 64, 2547–2549 (1993).
[CrossRef]

M. R. Tant, W. T. Culberson, “Effect of molecular weight on spherulite growth rate of poly via real time small angle light scattering,” Polym. Eng. Sci. 33, 1152–1156 (1993).
[CrossRef]

W. T. Culberson, M. R. Tant, “A device for study of polymer crystallization kinetics via real time image analysis of small angle light scattering,” J. Appl. Polym. Sci. 47, 395–405 (1993).
[CrossRef]

1992

A. Cumming, P. Wiltzius, F. S. Bates, J. H. Rosedale, “Light scattering experiments on phase separation dynamics in binary fluid mixtures,” Phys. Rev. A 45, 885–897 (1992).
[CrossRef] [PubMed]

K. Kubota, N. Kuwahara, “Low angle light scattering measurement using Fourier transform lens,” Jpn. J. Appl. Phys. 31, 3740–3743 (1992).
[CrossRef]

1991

F. R. Hallett, J. Watton, P. Krygsman, “Vesicle sizing: number distributions by dynamic light scattering,” Biophys. J. 59, 357–362 (1991).
[CrossRef] [PubMed]

1990

W. T. Culberson, M. R. Tant, “A dynamic small angle scattering device for study of polymer crystallization kinetics,” J. Am. Chem. Soc. 31, 143–144 (1990).

1989

A. L. Koch, “Calculation of surface area of sacculi from low angle light scattering measurements,” J. Microbiol. Methods 9, 139–150 (1989).
[CrossRef]

1987

M. S. McCracken, M. C. Sammons, “Sizing of a vesicle drug formulation by quasielastic light scattering and comparison with electron microscopy and ultracentrifugation,” J. Pharm. Sci. 76, 56–59 (1987).
[CrossRef] [PubMed]

1973

W. Kaye, “Low angle laser light scattering,” Anal. Chem. 45, 221A–225A (1973).
[CrossRef]

1925

R. Gans, “Molecular light dispersion in solid isotropic bodies,” Ann. Phys. (Leipzig) 77, 317–324 (1925).
[CrossRef]

1918

L. Rayleigh, “On the scattering of light by a cloud of similar small particles of any shape and oriented at random,” Philos. Mag. 35, 373–381 (1918).
[CrossRef]

1915

P. Debye, “Interferentz von Rontgenstrahlen und Warmebewegun,” Ann. Phys. (Leipzig) 43, 49–95 (1915).

1912

Lord Rayleigh, “On the propagation of waves through a stratified medium with special reference to the question of reflection,” Proc. R. Soc. London Ser. A 86, 207–266 (1912).
[CrossRef]

1910

Lord Rayleigh, “Aerial plane waves of finite amplitude,” Proc. R. Soc. London Ser. A 84, 247–284 (1910).
[CrossRef]

1881

Lord Rayleigh, “On the electromagnetic theory of light,” Philos. Mag. 12, 81–101 (1881).
[CrossRef]

Bates, F. S.

A. Cumming, P. Wiltzius, F. S. Bates, J. H. Rosedale, “Light scattering experiments on phase separation dynamics in binary fluid mixtures,” Phys. Rev. A 45, 885–897 (1992).
[CrossRef] [PubMed]

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Adsorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Born, M.

M. Born, E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Pergamon, Oxford, UK, 1975).

Chu, B.

B. Chu, Basic Principles and Practice (Academic, San Diego, Calif., 1991).

Coil, M. A.

Culberson, W. T.

M. R. Tant, W. T. Culberson, “Effect of molecular weight on spherulite growth rate of poly via real time small angle light scattering,” Polym. Eng. Sci. 33, 1152–1156 (1993).
[CrossRef]

W. T. Culberson, M. R. Tant, “A device for study of polymer crystallization kinetics via real time image analysis of small angle light scattering,” J. Appl. Polym. Sci. 47, 395–405 (1993).
[CrossRef]

W. T. Culberson, M. R. Tant, “A dynamic small angle scattering device for study of polymer crystallization kinetics,” J. Am. Chem. Soc. 31, 143–144 (1990).

Cumming, A.

A. Cumming, P. Wiltzius, F. S. Bates, J. H. Rosedale, “Light scattering experiments on phase separation dynamics in binary fluid mixtures,” Phys. Rev. A 45, 885–897 (1992).
[CrossRef] [PubMed]

Debye, P.

P. Debye, “Interferentz von Rontgenstrahlen und Warmebewegun,” Ann. Phys. (Leipzig) 43, 49–95 (1915).

Farrell, P. V.

Gans, R.

R. Gans, “Molecular light dispersion in solid isotropic bodies,” Ann. Phys. (Leipzig) 77, 317–324 (1925).
[CrossRef]

Hallett, F. R.

K. B. Strawbridge, F. R. Hallett, “Size distribution obtained from the inversion of I(Q) using integrated light scattering spectroscopy,” Macromolecules 27, 2283–2290 (1994).
[CrossRef]

F. R. Hallett, J. Watton, P. Krygsman, “Vesicle sizing: number distributions by dynamic light scattering,” Biophys. J. 59, 357–362 (1991).
[CrossRef] [PubMed]

Holoubek, J.

J. Holoubek, “Small angle light scattering from an anisotropic sphere: anisotropy and size effects,” J. Polym. Sci. 32, 351–357 (1994).
[CrossRef]

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Adsorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Kaye, W.

W. Kaye, “Low angle laser light scattering,” Anal. Chem. 45, 221A–225A (1973).
[CrossRef]

Kerker, M.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

Koch, A. L.

A. L. Koch, “Calculation of surface area of sacculi from low angle light scattering measurements,” J. Microbiol. Methods 9, 139–150 (1989).
[CrossRef]

Krygsman, P.

F. R. Hallett, J. Watton, P. Krygsman, “Vesicle sizing: number distributions by dynamic light scattering,” Biophys. J. 59, 357–362 (1991).
[CrossRef] [PubMed]

Kubota, K.

K. Kubota, N. Kuwahara, “Low angle light scattering measurement using Fourier transform lens,” Jpn. J. Appl. Phys. 31, 3740–3743 (1992).
[CrossRef]

Kuwahara, N.

K. Kubota, N. Kuwahara, “Low angle light scattering measurement using Fourier transform lens,” Jpn. J. Appl. Phys. 31, 3740–3743 (1992).
[CrossRef]

McCracken, M. S.

M. S. McCracken, M. C. Sammons, “Sizing of a vesicle drug formulation by quasielastic light scattering and comparison with electron microscopy and ultracentrifugation,” J. Pharm. Sci. 76, 56–59 (1987).
[CrossRef] [PubMed]

Pedrotti, F. L.

F. L. Pedrotti, L. S. Pedrotti, Introduction to Optics (Prentice-Hall, Englewood Cliffs, N.J., 1987).

Pedrotti, L. S.

F. L. Pedrotti, L. S. Pedrotti, Introduction to Optics (Prentice-Hall, Englewood Cliffs, N.J., 1987).

Rayleigh, L.

L. Rayleigh, “On the scattering of light by a cloud of similar small particles of any shape and oriented at random,” Philos. Mag. 35, 373–381 (1918).
[CrossRef]

Rayleigh, Lord

Lord Rayleigh, “On the propagation of waves through a stratified medium with special reference to the question of reflection,” Proc. R. Soc. London Ser. A 86, 207–266 (1912).
[CrossRef]

Lord Rayleigh, “Aerial plane waves of finite amplitude,” Proc. R. Soc. London Ser. A 84, 247–284 (1910).
[CrossRef]

Lord Rayleigh, “On the electromagnetic theory of light,” Philos. Mag. 12, 81–101 (1881).
[CrossRef]

Rosedale, J. H.

A. Cumming, P. Wiltzius, F. S. Bates, J. H. Rosedale, “Light scattering experiments on phase separation dynamics in binary fluid mixtures,” Phys. Rev. A 45, 885–897 (1992).
[CrossRef] [PubMed]

Sammons, M. C.

M. S. McCracken, M. C. Sammons, “Sizing of a vesicle drug formulation by quasielastic light scattering and comparison with electron microscopy and ultracentrifugation,” J. Pharm. Sci. 76, 56–59 (1987).
[CrossRef] [PubMed]

Strawbridge, K. B.

K. B. Strawbridge, F. R. Hallett, “Size distribution obtained from the inversion of I(Q) using integrated light scattering spectroscopy,” Macromolecules 27, 2283–2290 (1994).
[CrossRef]

Tanford, C.

C. Tanford, Physical Chemistry of Macromolecules (Wiley, New York, 1961).

Tant, M. R.

M. R. Tant, W. T. Culberson, “Effect of molecular weight on spherulite growth rate of poly via real time small angle light scattering,” Polym. Eng. Sci. 33, 1152–1156 (1993).
[CrossRef]

W. T. Culberson, M. R. Tant, “A device for study of polymer crystallization kinetics via real time image analysis of small angle light scattering,” J. Appl. Polym. Sci. 47, 395–405 (1993).
[CrossRef]

W. T. Culberson, M. R. Tant, “A dynamic small angle scattering device for study of polymer crystallization kinetics,” J. Am. Chem. Soc. 31, 143–144 (1990).

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

Watton, J.

F. R. Hallett, J. Watton, P. Krygsman, “Vesicle sizing: number distributions by dynamic light scattering,” Biophys. J. 59, 357–362 (1991).
[CrossRef] [PubMed]

Wiltzius, P.

A. P. Y. Wong, P. Wiltzius, “Dynamic light scattering with a CCD camera,” Rev. Sci. Instrum. 64, 2547–2549 (1993).
[CrossRef]

A. Cumming, P. Wiltzius, F. S. Bates, J. H. Rosedale, “Light scattering experiments on phase separation dynamics in binary fluid mixtures,” Phys. Rev. A 45, 885–897 (1992).
[CrossRef] [PubMed]

Wolf, E.

M. Born, E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Pergamon, Oxford, UK, 1975).

Wong, A. P. Y.

A. P. Y. Wong, P. Wiltzius, “Dynamic light scattering with a CCD camera,” Rev. Sci. Instrum. 64, 2547–2549 (1993).
[CrossRef]

Anal. Chem.

W. Kaye, “Low angle laser light scattering,” Anal. Chem. 45, 221A–225A (1973).
[CrossRef]

Ann. Phys. (Leipzig)

P. Debye, “Interferentz von Rontgenstrahlen und Warmebewegun,” Ann. Phys. (Leipzig) 43, 49–95 (1915).

R. Gans, “Molecular light dispersion in solid isotropic bodies,” Ann. Phys. (Leipzig) 77, 317–324 (1925).
[CrossRef]

Appl. Opt.

Biophys. J.

F. R. Hallett, J. Watton, P. Krygsman, “Vesicle sizing: number distributions by dynamic light scattering,” Biophys. J. 59, 357–362 (1991).
[CrossRef] [PubMed]

J. Am. Chem. Soc.

W. T. Culberson, M. R. Tant, “A dynamic small angle scattering device for study of polymer crystallization kinetics,” J. Am. Chem. Soc. 31, 143–144 (1990).

J. Appl. Polym. Sci.

W. T. Culberson, M. R. Tant, “A device for study of polymer crystallization kinetics via real time image analysis of small angle light scattering,” J. Appl. Polym. Sci. 47, 395–405 (1993).
[CrossRef]

J. Microbiol. Methods

A. L. Koch, “Calculation of surface area of sacculi from low angle light scattering measurements,” J. Microbiol. Methods 9, 139–150 (1989).
[CrossRef]

J. Pharm. Sci.

M. S. McCracken, M. C. Sammons, “Sizing of a vesicle drug formulation by quasielastic light scattering and comparison with electron microscopy and ultracentrifugation,” J. Pharm. Sci. 76, 56–59 (1987).
[CrossRef] [PubMed]

J. Polym. Sci.

J. Holoubek, “Small angle light scattering from an anisotropic sphere: anisotropy and size effects,” J. Polym. Sci. 32, 351–357 (1994).
[CrossRef]

Jpn. J. Appl. Phys.

K. Kubota, N. Kuwahara, “Low angle light scattering measurement using Fourier transform lens,” Jpn. J. Appl. Phys. 31, 3740–3743 (1992).
[CrossRef]

Macromolecules

K. B. Strawbridge, F. R. Hallett, “Size distribution obtained from the inversion of I(Q) using integrated light scattering spectroscopy,” Macromolecules 27, 2283–2290 (1994).
[CrossRef]

Philos. Mag.

L. Rayleigh, “On the scattering of light by a cloud of similar small particles of any shape and oriented at random,” Philos. Mag. 35, 373–381 (1918).
[CrossRef]

Lord Rayleigh, “On the electromagnetic theory of light,” Philos. Mag. 12, 81–101 (1881).
[CrossRef]

Phys. Rev. A

A. Cumming, P. Wiltzius, F. S. Bates, J. H. Rosedale, “Light scattering experiments on phase separation dynamics in binary fluid mixtures,” Phys. Rev. A 45, 885–897 (1992).
[CrossRef] [PubMed]

Polym. Eng. Sci.

M. R. Tant, W. T. Culberson, “Effect of molecular weight on spherulite growth rate of poly via real time small angle light scattering,” Polym. Eng. Sci. 33, 1152–1156 (1993).
[CrossRef]

Proc. R. Soc. London Ser. A

Lord Rayleigh, “Aerial plane waves of finite amplitude,” Proc. R. Soc. London Ser. A 84, 247–284 (1910).
[CrossRef]

Lord Rayleigh, “On the propagation of waves through a stratified medium with special reference to the question of reflection,” Proc. R. Soc. London Ser. A 86, 207–266 (1912).
[CrossRef]

Rev. Sci. Instrum.

A. P. Y. Wong, P. Wiltzius, “Dynamic light scattering with a CCD camera,” Rev. Sci. Instrum. 64, 2547–2549 (1993).
[CrossRef]

Other

C. F. Bohren, D. R. Huffman, Adsorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

C. Tanford, Physical Chemistry of Macromolecules (Wiley, New York, 1961).

B. Chu, Basic Principles and Practice (Academic, San Diego, Calif., 1991).

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

F. L. Pedrotti, L. S. Pedrotti, Introduction to Optics (Prentice-Hall, Englewood Cliffs, N.J., 1987).

M. Born, E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Pergamon, Oxford, UK, 1975).

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram of SAILS showing its components in a light-tight box.

Fig. 2
Fig. 2

Placement of a black opaque wedge in the cuvette directs reflected backscattered rays away from the field of view of the CCD.

Fig. 3
Fig. 3

Diagram showing the different parameters used for the determination of correction factors.

Fig. 4
Fig. 4

Comparison between the relative weight of the three different sets of correction factors after normalization to unity at a scattering angle of 10°. Solid curve, K 1 corrections; dashed curve, K 2 corrections; dotted curve, K 3 corrections.

Fig. 5
Fig. 5

Intensity versus angle plot of the four different sizes of latex spheres. Superimposed are the fits obtained by the inversion program. The legend shows the different sizes.

Fig. 6
Fig. 6

Histograms obtained from the inversion program showing the size distributions for the four different nominal sizes.

Tables (1)

Tables Icon

Table 1 Comparison between Latex Solid-Sphere Sizes Given by the Manufacturer and those Obtained by SAILSa

Equations (6)

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

IscattQ, RI0=ks4α2r2 PQ,
Q=4πnλ sinθ2,
C1=d1cos θm+d2cos θm22.
K1θm, θm2=cos θm2cos θmd1cos θm+d2cos θm22.
K2θm=1T11T2,
T1=sin2θscattsin2θglasssin2θscatt+θglass,  T2=sin2θglasssin2θairsin2θglass+θair,

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