Abstract

An analytic inversion method, based on the anomalous diffraction approximation for nonabsorbing spherical particles, was developed to retrieve the size distribution from the optical turbidity or extinction spectrum. This method makes use of a differential Fourier cosine transform approach and provides a simple and fast inversion by means of fast Fourier transform and the Savitzky–Golay filter. The applicability of this algorithm was tested on the extinction data generated by the Mie solution. The effects of noise, modality, band limits, and data set size were analyzed by comparison with simulated data. This method can be used to reconstruct the original monomodal and bimodal distributions from 10% noise-corrupted data. The peak position and ratio of peak heights can be recovered with 10% or less deviation. The experiments with latex spheres showed that the inversion result from this method compares favorably with that from the dynamic light scattering measurement.

© 1996 Optical Society of America

PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. S. Shifrin, G. Tonna, “Inverse problems related to light scattering in the atmosphere and ocean,” Adv. Geophys. 34, 175–252 (1993).
    [CrossRef]
  2. L. P. Bayvel, Electromagnetic Scattering and Its Applications (Applied Science, Essex, England, 1981), Chap. 6, p. 199.
  3. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), Chap. 11, p. 172.
  4. A. L. Fymat, C. B. Smith, “Analytical inversions in remote sensing of particle size distributions. 4: Comparison of Fymat and Box-McKellar solutions in the anomalous diffraction approximation,” Appl. Opt. 18, 3595–3598 (1979).
    [CrossRef] [PubMed]
  5. M. A. Box, B. H. J. McKellar, “Relationship between two analytic inversion formulae for multispectral extinction data,” Appl. Opt. 18, 3599–3601 (1979).
    [CrossRef] [PubMed]
  6. C. B. Smith, “Inversion of the anomalous diffraction approximation for variable complex index of refraction near unity,” Appl. Opt. 21, 3363–3366 (1982).
    [CrossRef] [PubMed]
  7. J. D. Klett, “Anomalous diffraction model for inversion of multispectral extinction data including absorption effects,” Appl. Opt. 23, 4499–4508 (1984).
    [CrossRef] [PubMed]
  8. M. Bertero, C. De Mol, E. R. Pike, “Particle size distributions from spectral turbidity: a singular-system analysis,” Inverse Problems 2, 247–258 (1986).
    [CrossRef]
  9. A. L. Fymat, “Analytical inversions in remote sensing of particle size distributions. 1: Multispectral extinctions in the anomalous diffraction approximation,” Appl. Opt. 17, 1675–1676 (1978).
  10. M. A. Box, B. H. J. McKellar, “Analytic inversion of multispectral extinction data in the anomalous diffraction approximation,” Opt. Lett. 3, 91–93 (1978).
    [CrossRef] [PubMed]
  11. N. C. Ford, “Light scattering apparatus,” in Dynamic Light Scattering. Applications of Photon Correlation Spectroscopy, R. Pecora, ed. (Plenum, New York, 1985), pp. 7–58.
  12. Ref. 2, Chap. 1, p. 5.
  13. N. C. Wickramasinghe, Light Scattering Functions for Small Particles, with Applications in Astronomy (Wiley, New York, 1973), p. 26.
  14. S. W. Provencher, “CONTIN a general purpose constrained regularization program for inverting noisy linear algebraic and integral equations,” Comput. Phys. Commun. 27, 229– 242 (1982).
    [CrossRef]
  15. J. Wang, F. R. Hallett, “Vesicle sizing by static light scattering: a Fourier cosine transform approach,” Appl. Opt. 34, 5010–5015 (1995).
    [CrossRef] [PubMed]
  16. A. Savitzky, M. Golay, “Smoothing and differentiation of data by simplified least squares procedures,” Anal. Chem. 36, 1627–1639 (1964).
    [CrossRef]
  17. F. R. Hallett, J. Watton, P. Krygsman, “Vesicle sizing. Number distributions by dynamic light scattering,” Biophys. J. 59, 357–362 (1991).
    [CrossRef] [PubMed]
  18. R. Finsy, L. Deriemaeker, E. Gelade, J. Joosten, “Inversion of static light scattering measurements for particle size distributions,” J. Colloid Interface Sci. 59, 357–362 (1991).

1995 (1)

1993 (1)

K. S. Shifrin, G. Tonna, “Inverse problems related to light scattering in the atmosphere and ocean,” Adv. Geophys. 34, 175–252 (1993).
[CrossRef]

1991 (2)

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

R. Finsy, L. Deriemaeker, E. Gelade, J. Joosten, “Inversion of static light scattering measurements for particle size distributions,” J. Colloid Interface Sci. 59, 357–362 (1991).

1986 (1)

M. Bertero, C. De Mol, E. R. Pike, “Particle size distributions from spectral turbidity: a singular-system analysis,” Inverse Problems 2, 247–258 (1986).
[CrossRef]

1984 (1)

1982 (2)

C. B. Smith, “Inversion of the anomalous diffraction approximation for variable complex index of refraction near unity,” Appl. Opt. 21, 3363–3366 (1982).
[CrossRef] [PubMed]

S. W. Provencher, “CONTIN a general purpose constrained regularization program for inverting noisy linear algebraic and integral equations,” Comput. Phys. Commun. 27, 229– 242 (1982).
[CrossRef]

1979 (2)

1978 (2)

1964 (1)

A. Savitzky, M. Golay, “Smoothing and differentiation of data by simplified least squares procedures,” Anal. Chem. 36, 1627–1639 (1964).
[CrossRef]

Bayvel, L. P.

L. P. Bayvel, Electromagnetic Scattering and Its Applications (Applied Science, Essex, England, 1981), Chap. 6, p. 199.

Bertero, M.

M. Bertero, C. De Mol, E. R. Pike, “Particle size distributions from spectral turbidity: a singular-system analysis,” Inverse Problems 2, 247–258 (1986).
[CrossRef]

Box, M. A.

De Mol, C.

M. Bertero, C. De Mol, E. R. Pike, “Particle size distributions from spectral turbidity: a singular-system analysis,” Inverse Problems 2, 247–258 (1986).
[CrossRef]

Deriemaeker, L.

R. Finsy, L. Deriemaeker, E. Gelade, J. Joosten, “Inversion of static light scattering measurements for particle size distributions,” J. Colloid Interface Sci. 59, 357–362 (1991).

Finsy, R.

R. Finsy, L. Deriemaeker, E. Gelade, J. Joosten, “Inversion of static light scattering measurements for particle size distributions,” J. Colloid Interface Sci. 59, 357–362 (1991).

Ford, N. C.

N. C. Ford, “Light scattering apparatus,” in Dynamic Light Scattering. Applications of Photon Correlation Spectroscopy, R. Pecora, ed. (Plenum, New York, 1985), pp. 7–58.

Fymat, A. L.

Gelade, E.

R. Finsy, L. Deriemaeker, E. Gelade, J. Joosten, “Inversion of static light scattering measurements for particle size distributions,” J. Colloid Interface Sci. 59, 357–362 (1991).

Golay, M.

A. Savitzky, M. Golay, “Smoothing and differentiation of data by simplified least squares procedures,” Anal. Chem. 36, 1627–1639 (1964).
[CrossRef]

Hallett, F. R.

J. Wang, F. R. Hallett, “Vesicle sizing by static light scattering: a Fourier cosine transform approach,” Appl. Opt. 34, 5010–5015 (1995).
[CrossRef] [PubMed]

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

Joosten, J.

R. Finsy, L. Deriemaeker, E. Gelade, J. Joosten, “Inversion of static light scattering measurements for particle size distributions,” J. Colloid Interface Sci. 59, 357–362 (1991).

Klett, J. D.

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]

McKellar, B. H. J.

Pike, E. R.

M. Bertero, C. De Mol, E. R. Pike, “Particle size distributions from spectral turbidity: a singular-system analysis,” Inverse Problems 2, 247–258 (1986).
[CrossRef]

Provencher, S. W.

S. W. Provencher, “CONTIN a general purpose constrained regularization program for inverting noisy linear algebraic and integral equations,” Comput. Phys. Commun. 27, 229– 242 (1982).
[CrossRef]

Savitzky, A.

A. Savitzky, M. Golay, “Smoothing and differentiation of data by simplified least squares procedures,” Anal. Chem. 36, 1627–1639 (1964).
[CrossRef]

Shifrin, K. S.

K. S. Shifrin, G. Tonna, “Inverse problems related to light scattering in the atmosphere and ocean,” Adv. Geophys. 34, 175–252 (1993).
[CrossRef]

Smith, C. B.

Tonna, G.

K. S. Shifrin, G. Tonna, “Inverse problems related to light scattering in the atmosphere and ocean,” Adv. Geophys. 34, 175–252 (1993).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), Chap. 11, p. 172.

Wang, J.

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]

Wickramasinghe, N. C.

N. C. Wickramasinghe, Light Scattering Functions for Small Particles, with Applications in Astronomy (Wiley, New York, 1973), p. 26.

Adv. Geophys. (1)

K. S. Shifrin, G. Tonna, “Inverse problems related to light scattering in the atmosphere and ocean,” Adv. Geophys. 34, 175–252 (1993).
[CrossRef]

Anal. Chem. (1)

A. Savitzky, M. Golay, “Smoothing and differentiation of data by simplified least squares procedures,” Anal. Chem. 36, 1627–1639 (1964).
[CrossRef]

Appl. Opt. (6)

Biophys. J. (1)

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

Comput. Phys. Commun. (1)

S. W. Provencher, “CONTIN a general purpose constrained regularization program for inverting noisy linear algebraic and integral equations,” Comput. Phys. Commun. 27, 229– 242 (1982).
[CrossRef]

Inverse Problems (1)

M. Bertero, C. De Mol, E. R. Pike, “Particle size distributions from spectral turbidity: a singular-system analysis,” Inverse Problems 2, 247–258 (1986).
[CrossRef]

J. Colloid Interface Sci. (1)

R. Finsy, L. Deriemaeker, E. Gelade, J. Joosten, “Inversion of static light scattering measurements for particle size distributions,” J. Colloid Interface Sci. 59, 357–362 (1991).

Opt. Lett. (1)

Other (5)

L. P. Bayvel, Electromagnetic Scattering and Its Applications (Applied Science, Essex, England, 1981), Chap. 6, p. 199.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), Chap. 11, p. 172.

N. C. Ford, “Light scattering apparatus,” in Dynamic Light Scattering. Applications of Photon Correlation Spectroscopy, R. Pecora, ed. (Plenum, New York, 1985), pp. 7–58.

Ref. 2, Chap. 1, p. 5.

N. C. Wickramasinghe, Light Scattering Functions for Small Particles, with Applications in Astronomy (Wiley, New York, 1973), p. 26.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Metrics