Abstract

The problem of determining particle size distribution using the moment method in the spectral extinction technique is studied. The feasibility and reliability of the retrieval of spherical particle size distribution using the moment method are investigated. The single spherical particle extinction efficiency, which is derived theoretically using the Mie’s solution to Maxwell’s equation, is approximated with a higher order polynomial in order to apply the moment method. Simulation and experimental results indicate that a fairly reasonable representation of the particle size distribution can be obtained using the moment method in the dependent model algorithm. The method has advantages of simplicity, rapidity, and suitability for in-line particle size measurement.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. F. Ferri, A. Bassini, and E. Paganini, "Modified version of the Chahine algorithm to invert spectral extinction data for particle sizing," Appl. Opt. 34, 5829-5839 (1995).
    [CrossRef] [PubMed]
  2. A. V. Kharchenko, and D. Gresillon, "Nonparticle laser velocimetry and permanent velocity measurement by enhanced light scattering," Meas. Sci. Technol. 14, 228-233 (2003).
    [CrossRef]
  3. F. Pedocchi, and M. H. Garcia, "Noise-resolution trade-off in projection algorithms for laser diffraction particle sizing," Appl. Opt. 45, 3620-3628 (2006).
    [CrossRef] [PubMed]
  4. B. N. Khlebtsov, L. A. Kovler, V. A. Bogatyrev, N. G. Khlebtsov, and S. Y. Shchyogolev, "Studies of phosphatidylcholine vesicles by spectroturbidimetric and dynamic light scattering methods," J. Quant. Spectrosc. Radiat. Transf. 79-80, 825-838 (2003).
    [CrossRef]
  5. A. K. Roy and S. K. Sharma, "A simple analysis of the extinction spectrum of a size distritution of Mie particles," J. Opt. A: Pure Appl. Opt. 7, 675-684 (2005).
    [CrossRef]
  6. M. L. Arias, and G. L. Frontini, "Particle size distribution retrieval from elastic light scattering measurements by a modified regularization method," Part. Part. Syst. Charact. 23, 374-380 (2007).
    [CrossRef]
  7. A. P. Nefedov, O. F. Petrov, and O. S. Vaulina, "Analysis of particle sizes, concentration, and refractive index in measurement of light transmittance in the forward-scattering-angle range," Appl. Opt. 36, 1357-1366 (1997).
    [CrossRef] [PubMed]
  8. C. H. Jung and Y. P. Kim, "Numerical estimation of the effects of condensation and coagulation on visibility using the moment method," J. Aerosol Sci. 37, 143-161 (2006).
    [CrossRef]
  9. S. H. Park, R. Xiang, and K. W. Lee, "Brownian coagulation of fractal agglomerates:analytical solution using the log-normal size distribution assumption," J. Colloid Interface Sci. 231, 129-135 (2000).
    [CrossRef] [PubMed]
  10. E. Marioth, B. Koenig, H. Krause, and S. Loebbecke, "Fast particle size and droplet size measurements in supercritical CO2," Ind. Eng. Chem. Res. 339, 4853-4857 (2000).
    [CrossRef]
  11. A. Katz, A. Alimova, M. Xu, P. Gottlieb, E. Rudolph, J. C. Steiner, and R. R. Alfano, "In situ determination of refractive index and size of bacillus spores by light transmission," Opt. Lett. 30, 589-591 (2005).
    [CrossRef] [PubMed]
  12. D. Rosskamp, F. Truffer, S. Bolay, and M. Geiser, "Forward scattering measurement device with a high angular resolution," Opt. Express 15, 2683-2690 (2007).
    [CrossRef] [PubMed]
  13. W. Liang, Y. Xu, Y. Y. Huang, A. Yariv, J. G. Fleming, and S. W. Yu, "Mie scattering analysis of spherical Bragg "onion" resonators," Opt. Express 12, 657-669 (2004).
    [CrossRef] [PubMed]
  14. D. L. Wright, S. C. Yu, P. S. Kasibhatla, R. Mcgraw, S. E. Schwartz, V. K. Saxena, and G. K. Yue, "Retrieval of aerosol properties from moments of the particle size distribution for kernel involving the step function:cloud droplet activation," J. Aerosol Sci. 33, 319-337 (2002).
    [CrossRef]
  15. D. L. Wright, "Retrieval of optical properties of atmospheric aerosols from moments of the particle size distribution," J. Aerosol Sci. 31, 1-18 (2000).
    [CrossRef]
  16. J. P. Wang, S. Z. Xie, Y. M. Zhang, and W. Li, "Improved projection to invert forward scattered light for particle sizing," Appl. Opt. 40, 3937-3945 (2001).
    [CrossRef]

2007 (2)

M. L. Arias, and G. L. Frontini, "Particle size distribution retrieval from elastic light scattering measurements by a modified regularization method," Part. Part. Syst. Charact. 23, 374-380 (2007).
[CrossRef]

D. Rosskamp, F. Truffer, S. Bolay, and M. Geiser, "Forward scattering measurement device with a high angular resolution," Opt. Express 15, 2683-2690 (2007).
[CrossRef] [PubMed]

2006 (2)

C. H. Jung and Y. P. Kim, "Numerical estimation of the effects of condensation and coagulation on visibility using the moment method," J. Aerosol Sci. 37, 143-161 (2006).
[CrossRef]

F. Pedocchi, and M. H. Garcia, "Noise-resolution trade-off in projection algorithms for laser diffraction particle sizing," Appl. Opt. 45, 3620-3628 (2006).
[CrossRef] [PubMed]

2005 (2)

2004 (1)

2003 (2)

B. N. Khlebtsov, L. A. Kovler, V. A. Bogatyrev, N. G. Khlebtsov, and S. Y. Shchyogolev, "Studies of phosphatidylcholine vesicles by spectroturbidimetric and dynamic light scattering methods," J. Quant. Spectrosc. Radiat. Transf. 79-80, 825-838 (2003).
[CrossRef]

A. V. Kharchenko, and D. Gresillon, "Nonparticle laser velocimetry and permanent velocity measurement by enhanced light scattering," Meas. Sci. Technol. 14, 228-233 (2003).
[CrossRef]

2002 (1)

D. L. Wright, S. C. Yu, P. S. Kasibhatla, R. Mcgraw, S. E. Schwartz, V. K. Saxena, and G. K. Yue, "Retrieval of aerosol properties from moments of the particle size distribution for kernel involving the step function:cloud droplet activation," J. Aerosol Sci. 33, 319-337 (2002).
[CrossRef]

2001 (1)

2000 (3)

D. L. Wright, "Retrieval of optical properties of atmospheric aerosols from moments of the particle size distribution," J. Aerosol Sci. 31, 1-18 (2000).
[CrossRef]

S. H. Park, R. Xiang, and K. W. Lee, "Brownian coagulation of fractal agglomerates:analytical solution using the log-normal size distribution assumption," J. Colloid Interface Sci. 231, 129-135 (2000).
[CrossRef] [PubMed]

E. Marioth, B. Koenig, H. Krause, and S. Loebbecke, "Fast particle size and droplet size measurements in supercritical CO2," Ind. Eng. Chem. Res. 339, 4853-4857 (2000).
[CrossRef]

1997 (1)

1995 (1)

Appl. Opt. (4)

Ind. Eng. Chem. Res. (1)

E. Marioth, B. Koenig, H. Krause, and S. Loebbecke, "Fast particle size and droplet size measurements in supercritical CO2," Ind. Eng. Chem. Res. 339, 4853-4857 (2000).
[CrossRef]

J. Aerosol Sci. (3)

D. L. Wright, S. C. Yu, P. S. Kasibhatla, R. Mcgraw, S. E. Schwartz, V. K. Saxena, and G. K. Yue, "Retrieval of aerosol properties from moments of the particle size distribution for kernel involving the step function:cloud droplet activation," J. Aerosol Sci. 33, 319-337 (2002).
[CrossRef]

D. L. Wright, "Retrieval of optical properties of atmospheric aerosols from moments of the particle size distribution," J. Aerosol Sci. 31, 1-18 (2000).
[CrossRef]

C. H. Jung and Y. P. Kim, "Numerical estimation of the effects of condensation and coagulation on visibility using the moment method," J. Aerosol Sci. 37, 143-161 (2006).
[CrossRef]

J. Colloid Interface Sci. (1)

S. H. Park, R. Xiang, and K. W. Lee, "Brownian coagulation of fractal agglomerates:analytical solution using the log-normal size distribution assumption," J. Colloid Interface Sci. 231, 129-135 (2000).
[CrossRef] [PubMed]

J. Opt. A: Pure Appl. Opt. (1)

A. K. Roy and S. K. Sharma, "A simple analysis of the extinction spectrum of a size distritution of Mie particles," J. Opt. A: Pure Appl. Opt. 7, 675-684 (2005).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transf. (1)

B. N. Khlebtsov, L. A. Kovler, V. A. Bogatyrev, N. G. Khlebtsov, and S. Y. Shchyogolev, "Studies of phosphatidylcholine vesicles by spectroturbidimetric and dynamic light scattering methods," J. Quant. Spectrosc. Radiat. Transf. 79-80, 825-838 (2003).
[CrossRef]

Meas. Sci. Technol. (1)

A. V. Kharchenko, and D. Gresillon, "Nonparticle laser velocimetry and permanent velocity measurement by enhanced light scattering," Meas. Sci. Technol. 14, 228-233 (2003).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Part. Part. Syst. Charact. (1)

M. L. Arias, and G. L. Frontini, "Particle size distribution retrieval from elastic light scattering measurements by a modified regularization method," Part. Part. Syst. Charact. 23, 374-380 (2007).
[CrossRef]

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.


Figures (5)

Fig. 1.
Fig. 1.

Fitting curve of the extinction efficiency for spherical particle in different particle size range

Fig. 2.
Fig. 2.

Same as Fig.1 but with different relative refractive indices

Fig. 3.
Fig. 3.

Comparison of the inversion results for R-R distributions with moment and numerical integration method

Fig. 4.
Fig. 4.

Comparison of the inversion results for L-N distributions with moment and numerical integration method

Fig. 5.
Fig. 5.

Comparison of the inversion results for bimodal R-R distributions with moment and numerical integration method in the range from 0.1~10 um in diameter

Tables (7)

Tables Icon

Table 1. Inversion Results of the Monomodal R-R Distributions

Tables Icon

Table 2. Comparison of Reproducibility for the Moment Method and Numerical Integration Method with R-R Distributions

Tables Icon

Table 3. Inversion Results of the Monomodal L-N Distributions

Tables Icon

Table 4. Comparison of Reproducibility for the Moment and Numerical Integration Method with L-N Distributions

Tables Icon

Table 5. Inversion Results of the Bimodal R-R Distributions

Tables Icon

Table 6. Comparison of Reproducibility for the Moment and Numerical Integration Method with Bimodal R-R Distributions

Tables Icon

Table 7. Inversion Results of Standard Particles

Equations (12)

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

ln I ( λ ) I 0 ( λ ) = 3 2 × L × N D × D min D max Q ext ( λ , m , D ) D × f ( D ) d D .
f L N ( D ) = 1 2 π D ln σ × exp ( ( ln D ln u ) 2 2 ( ln σ ) 2 ) .
M l = 0 + D l f ( D ) d D .
M l = u l exp ( l 2 2 ( ln σ ) 2 ) .
u = ( M 1 ) 2 M 2 .
σ = exp ( ln ( M 2 ( M 1 ) 2 ) ) .
f R R ( D ) = k D ¯ × ( D D ¯ ) k 1 × exp ( ( D D ¯ ) k ) .
M l = D ¯ l gamma ( ( k + l ) k ) .
Q ext ( λ j , m , D ) = i = 0 P A ij D P i .
ln ( I I O ) j = 3 2 × L × N × i = 0 P A ij M P i 1 .
f ( D ) = n * ( k 1 D ¯ 1 × ( D D ¯ 1 ) k 1 1 × exp ( ( D D ¯ 1 ) k 1 ) ) + ( 1 n ) * ( k 2 D ¯ 2 × ( D D ¯ 2 ) k 2 1 ) × exp ( ( D D ¯ 2 ) k 2 ) )
D 32 = D min D max D 3 f ( D ) d D D min D max D 2 f ( D ) d D

Metrics