Abstract

In retrieving particle size distribution from spectral extinction data, a critical issue is the calculation of extinction efficiency, which affects the accuracy and rapidity of the whole retrieval. The generalized eikonal approximation (GEA) method, used as an alternative to the rigorous Mie theory, is introduced for retrieval of the unparameterized shape-independent particle size distribution (PSD). To compute the extinction efficiency more efficiently, the combination of GEA method and Mie theory is adopted in this paper, which not only extends the applicable range of the approximation method but also improves the speed of the whole retrieval. Within the framework of the combined approximation method, the accuracy and limitations of the retrieval are investigated. Moreover, the retrieval time and memory requirement are also discussed. Both simulations and experimental results show that the combined approximation method can be successfully applied to retrieval of PSD when the refractive index is within the validity range. The retrieval results we present demonstrate the high reliability and stability of the method. By using this method, we find the complexity and computation time of the retrieval are significantly reduced and the memory resources can also be saved effectively, thus making this method more suitable for online particle sizing.

© 2012 Optical Society of America

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  1. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).
  2. V. V. Berdnik and V. A. Loiko, “Retrieval of size and refractive index of spherical particles by multiangle light scattering: neural network method application,” Appl. Opt. 48, 6178–6187 (2009).
    [CrossRef]
  3. S. Gordon, R. Hammond, K. Roberts, N. Savelli, and D. Wilkinson, “In-process particle characterization by spectral extinction,” Trans. IChemE. 78, 1147–1152 (2000).
    [CrossRef]
  4. M. Z. Li and D. Wilkinson, “Particle size distribution determination from spectral extinction using evolutionary programming,” Chem. Eng. Sci. 56, 3045–3052 (2001).
    [CrossRef]
  5. J. P. Jalava, V. M. Taavitsainen, H. Haario, and L. Lamberg, “Determination of particle and crystal size distribution from turbidity spectrum of TiO2 pigments by means of T-matrix,” J. Quant. Spectrosc. Radiat. Transfer 60, 399–409 (1998).
    [CrossRef]
  6. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption and Emission of Light by Small Particles(Cambridge University, 2006).
  7. J. P. Wang, S. Z. Xie, Y. M. Zhang, and L. Wei, “Improved projection algorithm to invert forward scattered light for particle sizing,” Appl. Opt. 40, 3937–3945 (2001).
    [CrossRef]
  8. J. Vargas-Ubera, J. J. Sanchez-Escobar, J. F. Aguilar, and D. M. Gale, “Numerical study of particle-size distributions retrieved from angular light-scattering data using an evolution strategy with the Fraunhofer approximation,” Appl. Opt. 46, 3602–3610 (2007).
    [CrossRef]
  9. F. Xu, X. S. Cai, and J. Shen, “Geometric approximation of light scattering in arbitrary diffraction regime for absorbing particles: application in laser particle sizing,” Acta Opt. Sin. 23, 1464–1469 (2003).
  10. J. G. Devore, “The truncated geometric approximation and the size distribution of small atmospheric particles,” J. Atmos. Oceanic Tech. 28, 779–786 (2011).
    [CrossRef]
  11. A. Y. Perelman, “Extinction and scattering by soft spheres,” Appl. Opt. 30, 475–484 (1991).
    [CrossRef]
  12. A. Y. Perelman and N. V. Voshchinnikov, “Improved S-approximation for dielectric particles,” J. Quant. Spectrosc. Radiat. Transfer 72, 607–621 (2002).
    [CrossRef]
  13. G. R. Franssens, “Retrieval of the aerosol size distribution in the complex anomalous diffraction approximation,” Atmos. Environ. 35, 5099–5104 (2001).
    [CrossRef]
  14. S. A. Ackerman and G. L. Stephens, “The absorption of solar radiation by cloud droplets: an application of anomalous diffraction theory,” J. Atmos. Sci. 44, 1574–1588 (1987).
    [CrossRef]
  15. X. G. Sun, H. Tang, and G. B. Yuan, “Anomalous diffraction approximation method for retrieval of spherical and spheroidal particle size distributions in total light scattering,” J. Quant. Spectrosc. Radiat. Transfer 109, 89–106 (2008).
    [CrossRef]
  16. G. Crawley, M. Cournil, and D. D. Benedetto, “Size analysis of fine particle suspensions by spectral turbidimetry: potential and limits,” Powder Technol. 91, 197–208 (1997).
    [CrossRef]
  17. X. G. Sun, H. Tang, and J. M. Dai, “Retrieval of particle size distribution in the dependent model using the moment method,” Optic Express 15, 11507–11516 (2007).
    [CrossRef]
  18. S. K. Sharma and D. J. Somerford, Light Scattering by Optically Soft Particles: Theory and Applications (Springer-Praxis, 2006).
  19. T. W. Chen, “High energy light scattering in the generalized eikonal approximation,” Appl. Opt. 28, 4096–4102 (1989).
    [CrossRef]
  20. L. M. Yang, “The GEA method for light scattering by dielectric spheroids and ellipsoids with fixed and random orientations,” Ph.D. thesis (New Mexico State University, 1999).
  21. H. Y. Zuo, Q. J. Liu, J. Y. Wang, L. Yang, and S. R. Luo, “Technique to improve the accuracy of the retrieval of aerosol size-distribution,” Opt. Lett. 35, 1380–1382 (2010).
    [CrossRef]
  22. N. Riefler and T. Wriedt, “Intercomparison of inversion algorithms for particle-sizing using Mie scattering,” Part. Part. Syst. Charact. 25, 216–230 (2008).
    [CrossRef]
  23. D. Muller, U. Wandinger, and A. Ansmann, “Microphysical particle parameters from extinction and backscatter lidar data by inversion with regularization: theory,” Appl. Opt. 38, 2346–2355 (1999).
    [CrossRef]
  24. M. Kandlikar and G. Ramachandran, “Inverse methods for analysing aerosol spectrometer measurements: a critical review,” J. Aerosol Sci. 30, 413–437 (1999).
    [CrossRef]
  25. M.-T. Celis and L. H. Garcia-Rubio, “Stability of emulsions from multiwavelength transmission measurements,” Ind. Eng. Chem. Res. 43, 2067–2072 (2004).
    [CrossRef]
  26. M. X. Su, F. Xu, X. S. Cai, K. F. Ren, and J. Q. Shen, “Optimization of regularization parameter of inversion in particle sizing using light extinction method,” China Particuol. 5, 295–299 (2007).
    [CrossRef]
  27. L. Hespel and A. Delfour, “Mie light-scattering granulometer with adaptive numerical filtering. I. Theory,” Appl. Opt. 39, 6897–6917 (2000).
    [CrossRef]
  28. I. Veselovskii, A. Kolgotin, V. Griaznov, D. Muller, K. Franke, and D. N. Whiteman, “Inversion of multiwavelength Raman lidar data for retrieval of bimodal aerosol size distribution,” Appl. Opt. 43, 1180–1195 (2004).
    [CrossRef]
  29. X. G. Sun, H. Tang, and J. M. Dai, “Inversion of particle size distribution from spectral extinction data using the modified beta function,” Powder Technol. 190, 292–296 (2009).
    [CrossRef]
  30. G. Ramachandran and D. Leith, “Extraction of aerosol-size distributions from multispectral light extinction data,” Aerosol Sci. Technol. 17, 303–325 (1992).
    [CrossRef]
  31. A. K. Roy and S. K. Sharma, “A simple parameterized phase function for small non-absorbing spheres,” J. Quant. Spectrosc. Radiat. Transfer 109, 2804–2812 (2008).
    [CrossRef]
  32. Z. Cao, L. J. Xu, and J. Ding, “Integral inversion to Fraunhofer diffraction for particle sizing,” Appl. Opt. 48, 4842–4850 (2009).
    [CrossRef]
  33. J. D. Klett and R. A. Sutherland, “Approximate methods for modeling the scattering properties of nonspherical particles: evaluation of the Wentzel-Kramers-Brillouin method,” Appl. Opt. 31, 373–386 (1992).
    [CrossRef]
  34. N. N. Wang, Optic Measurement Technology of Particle Size and Its Application (Atomic Energy Press, 2000).

2011 (1)

J. G. Devore, “The truncated geometric approximation and the size distribution of small atmospheric particles,” J. Atmos. Oceanic Tech. 28, 779–786 (2011).
[CrossRef]

2010 (1)

2009 (3)

2008 (3)

A. K. Roy and S. K. Sharma, “A simple parameterized phase function for small non-absorbing spheres,” J. Quant. Spectrosc. Radiat. Transfer 109, 2804–2812 (2008).
[CrossRef]

N. Riefler and T. Wriedt, “Intercomparison of inversion algorithms for particle-sizing using Mie scattering,” Part. Part. Syst. Charact. 25, 216–230 (2008).
[CrossRef]

X. G. Sun, H. Tang, and G. B. Yuan, “Anomalous diffraction approximation method for retrieval of spherical and spheroidal particle size distributions in total light scattering,” J. Quant. Spectrosc. Radiat. Transfer 109, 89–106 (2008).
[CrossRef]

2007 (3)

J. Vargas-Ubera, J. J. Sanchez-Escobar, J. F. Aguilar, and D. M. Gale, “Numerical study of particle-size distributions retrieved from angular light-scattering data using an evolution strategy with the Fraunhofer approximation,” Appl. Opt. 46, 3602–3610 (2007).
[CrossRef]

M. X. Su, F. Xu, X. S. Cai, K. F. Ren, and J. Q. Shen, “Optimization of regularization parameter of inversion in particle sizing using light extinction method,” China Particuol. 5, 295–299 (2007).
[CrossRef]

X. G. Sun, H. Tang, and J. M. Dai, “Retrieval of particle size distribution in the dependent model using the moment method,” Optic Express 15, 11507–11516 (2007).
[CrossRef]

2004 (2)

2003 (1)

F. Xu, X. S. Cai, and J. Shen, “Geometric approximation of light scattering in arbitrary diffraction regime for absorbing particles: application in laser particle sizing,” Acta Opt. Sin. 23, 1464–1469 (2003).

2002 (1)

A. Y. Perelman and N. V. Voshchinnikov, “Improved S-approximation for dielectric particles,” J. Quant. Spectrosc. Radiat. Transfer 72, 607–621 (2002).
[CrossRef]

2001 (3)

G. R. Franssens, “Retrieval of the aerosol size distribution in the complex anomalous diffraction approximation,” Atmos. Environ. 35, 5099–5104 (2001).
[CrossRef]

M. Z. Li and D. Wilkinson, “Particle size distribution determination from spectral extinction using evolutionary programming,” Chem. Eng. Sci. 56, 3045–3052 (2001).
[CrossRef]

J. P. Wang, S. Z. Xie, Y. M. Zhang, and L. Wei, “Improved projection algorithm to invert forward scattered light for particle sizing,” Appl. Opt. 40, 3937–3945 (2001).
[CrossRef]

2000 (2)

L. Hespel and A. Delfour, “Mie light-scattering granulometer with adaptive numerical filtering. I. Theory,” Appl. Opt. 39, 6897–6917 (2000).
[CrossRef]

S. Gordon, R. Hammond, K. Roberts, N. Savelli, and D. Wilkinson, “In-process particle characterization by spectral extinction,” Trans. IChemE. 78, 1147–1152 (2000).
[CrossRef]

1999 (2)

D. Muller, U. Wandinger, and A. Ansmann, “Microphysical particle parameters from extinction and backscatter lidar data by inversion with regularization: theory,” Appl. Opt. 38, 2346–2355 (1999).
[CrossRef]

M. Kandlikar and G. Ramachandran, “Inverse methods for analysing aerosol spectrometer measurements: a critical review,” J. Aerosol Sci. 30, 413–437 (1999).
[CrossRef]

1998 (1)

J. P. Jalava, V. M. Taavitsainen, H. Haario, and L. Lamberg, “Determination of particle and crystal size distribution from turbidity spectrum of TiO2 pigments by means of T-matrix,” J. Quant. Spectrosc. Radiat. Transfer 60, 399–409 (1998).
[CrossRef]

1997 (1)

G. Crawley, M. Cournil, and D. D. Benedetto, “Size analysis of fine particle suspensions by spectral turbidimetry: potential and limits,” Powder Technol. 91, 197–208 (1997).
[CrossRef]

1992 (2)

G. Ramachandran and D. Leith, “Extraction of aerosol-size distributions from multispectral light extinction data,” Aerosol Sci. Technol. 17, 303–325 (1992).
[CrossRef]

J. D. Klett and R. A. Sutherland, “Approximate methods for modeling the scattering properties of nonspherical particles: evaluation of the Wentzel-Kramers-Brillouin method,” Appl. Opt. 31, 373–386 (1992).
[CrossRef]

1991 (1)

1989 (1)

1987 (1)

S. A. Ackerman and G. L. Stephens, “The absorption of solar radiation by cloud droplets: an application of anomalous diffraction theory,” J. Atmos. Sci. 44, 1574–1588 (1987).
[CrossRef]

Ackerman, S. A.

S. A. Ackerman and G. L. Stephens, “The absorption of solar radiation by cloud droplets: an application of anomalous diffraction theory,” J. Atmos. Sci. 44, 1574–1588 (1987).
[CrossRef]

Aguilar, J. F.

Ansmann, A.

Benedetto, D. D.

G. Crawley, M. Cournil, and D. D. Benedetto, “Size analysis of fine particle suspensions by spectral turbidimetry: potential and limits,” Powder Technol. 91, 197–208 (1997).
[CrossRef]

Berdnik, V. V.

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).

Cai, X. S.

M. X. Su, F. Xu, X. S. Cai, K. F. Ren, and J. Q. Shen, “Optimization of regularization parameter of inversion in particle sizing using light extinction method,” China Particuol. 5, 295–299 (2007).
[CrossRef]

F. Xu, X. S. Cai, and J. Shen, “Geometric approximation of light scattering in arbitrary diffraction regime for absorbing particles: application in laser particle sizing,” Acta Opt. Sin. 23, 1464–1469 (2003).

Cao, Z.

Celis, M.-T.

M.-T. Celis and L. H. Garcia-Rubio, “Stability of emulsions from multiwavelength transmission measurements,” Ind. Eng. Chem. Res. 43, 2067–2072 (2004).
[CrossRef]

Chen, T. W.

Cournil, M.

G. Crawley, M. Cournil, and D. D. Benedetto, “Size analysis of fine particle suspensions by spectral turbidimetry: potential and limits,” Powder Technol. 91, 197–208 (1997).
[CrossRef]

Crawley, G.

G. Crawley, M. Cournil, and D. D. Benedetto, “Size analysis of fine particle suspensions by spectral turbidimetry: potential and limits,” Powder Technol. 91, 197–208 (1997).
[CrossRef]

Dai, J. M.

X. G. Sun, H. Tang, and J. M. Dai, “Inversion of particle size distribution from spectral extinction data using the modified beta function,” Powder Technol. 190, 292–296 (2009).
[CrossRef]

X. G. Sun, H. Tang, and J. M. Dai, “Retrieval of particle size distribution in the dependent model using the moment method,” Optic Express 15, 11507–11516 (2007).
[CrossRef]

Delfour, A.

Devore, J. G.

J. G. Devore, “The truncated geometric approximation and the size distribution of small atmospheric particles,” J. Atmos. Oceanic Tech. 28, 779–786 (2011).
[CrossRef]

Ding, J.

Franke, K.

Franssens, G. R.

G. R. Franssens, “Retrieval of the aerosol size distribution in the complex anomalous diffraction approximation,” Atmos. Environ. 35, 5099–5104 (2001).
[CrossRef]

Gale, D. M.

Garcia-Rubio, L. H.

M.-T. Celis and L. H. Garcia-Rubio, “Stability of emulsions from multiwavelength transmission measurements,” Ind. Eng. Chem. Res. 43, 2067–2072 (2004).
[CrossRef]

Gordon, S.

S. Gordon, R. Hammond, K. Roberts, N. Savelli, and D. Wilkinson, “In-process particle characterization by spectral extinction,” Trans. IChemE. 78, 1147–1152 (2000).
[CrossRef]

Griaznov, V.

Haario, H.

J. P. Jalava, V. M. Taavitsainen, H. Haario, and L. Lamberg, “Determination of particle and crystal size distribution from turbidity spectrum of TiO2 pigments by means of T-matrix,” J. Quant. Spectrosc. Radiat. Transfer 60, 399–409 (1998).
[CrossRef]

Hammond, R.

S. Gordon, R. Hammond, K. Roberts, N. Savelli, and D. Wilkinson, “In-process particle characterization by spectral extinction,” Trans. IChemE. 78, 1147–1152 (2000).
[CrossRef]

Hespel, L.

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).

Jalava, J. P.

J. P. Jalava, V. M. Taavitsainen, H. Haario, and L. Lamberg, “Determination of particle and crystal size distribution from turbidity spectrum of TiO2 pigments by means of T-matrix,” J. Quant. Spectrosc. Radiat. Transfer 60, 399–409 (1998).
[CrossRef]

Kandlikar, M.

M. Kandlikar and G. Ramachandran, “Inverse methods for analysing aerosol spectrometer measurements: a critical review,” J. Aerosol Sci. 30, 413–437 (1999).
[CrossRef]

Klett, J. D.

Kolgotin, A.

Lacis, A. A.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption and Emission of Light by Small Particles(Cambridge University, 2006).

Lamberg, L.

J. P. Jalava, V. M. Taavitsainen, H. Haario, and L. Lamberg, “Determination of particle and crystal size distribution from turbidity spectrum of TiO2 pigments by means of T-matrix,” J. Quant. Spectrosc. Radiat. Transfer 60, 399–409 (1998).
[CrossRef]

Leith, D.

G. Ramachandran and D. Leith, “Extraction of aerosol-size distributions from multispectral light extinction data,” Aerosol Sci. Technol. 17, 303–325 (1992).
[CrossRef]

Li, M. Z.

M. Z. Li and D. Wilkinson, “Particle size distribution determination from spectral extinction using evolutionary programming,” Chem. Eng. Sci. 56, 3045–3052 (2001).
[CrossRef]

Liu, Q. J.

Loiko, V. A.

Luo, S. R.

Mishchenko, M. I.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption and Emission of Light by Small Particles(Cambridge University, 2006).

Muller, D.

Perelman, A. Y.

A. Y. Perelman and N. V. Voshchinnikov, “Improved S-approximation for dielectric particles,” J. Quant. Spectrosc. Radiat. Transfer 72, 607–621 (2002).
[CrossRef]

A. Y. Perelman, “Extinction and scattering by soft spheres,” Appl. Opt. 30, 475–484 (1991).
[CrossRef]

Ramachandran, G.

M. Kandlikar and G. Ramachandran, “Inverse methods for analysing aerosol spectrometer measurements: a critical review,” J. Aerosol Sci. 30, 413–437 (1999).
[CrossRef]

G. Ramachandran and D. Leith, “Extraction of aerosol-size distributions from multispectral light extinction data,” Aerosol Sci. Technol. 17, 303–325 (1992).
[CrossRef]

Ren, K. F.

M. X. Su, F. Xu, X. S. Cai, K. F. Ren, and J. Q. Shen, “Optimization of regularization parameter of inversion in particle sizing using light extinction method,” China Particuol. 5, 295–299 (2007).
[CrossRef]

Riefler, N.

N. Riefler and T. Wriedt, “Intercomparison of inversion algorithms for particle-sizing using Mie scattering,” Part. Part. Syst. Charact. 25, 216–230 (2008).
[CrossRef]

Roberts, K.

S. Gordon, R. Hammond, K. Roberts, N. Savelli, and D. Wilkinson, “In-process particle characterization by spectral extinction,” Trans. IChemE. 78, 1147–1152 (2000).
[CrossRef]

Roy, A. K.

A. K. Roy and S. K. Sharma, “A simple parameterized phase function for small non-absorbing spheres,” J. Quant. Spectrosc. Radiat. Transfer 109, 2804–2812 (2008).
[CrossRef]

Sanchez-Escobar, J. J.

Savelli, N.

S. Gordon, R. Hammond, K. Roberts, N. Savelli, and D. Wilkinson, “In-process particle characterization by spectral extinction,” Trans. IChemE. 78, 1147–1152 (2000).
[CrossRef]

Sharma, S. K.

A. K. Roy and S. K. Sharma, “A simple parameterized phase function for small non-absorbing spheres,” J. Quant. Spectrosc. Radiat. Transfer 109, 2804–2812 (2008).
[CrossRef]

S. K. Sharma and D. J. Somerford, Light Scattering by Optically Soft Particles: Theory and Applications (Springer-Praxis, 2006).

Shen, J.

F. Xu, X. S. Cai, and J. Shen, “Geometric approximation of light scattering in arbitrary diffraction regime for absorbing particles: application in laser particle sizing,” Acta Opt. Sin. 23, 1464–1469 (2003).

Shen, J. Q.

M. X. Su, F. Xu, X. S. Cai, K. F. Ren, and J. Q. Shen, “Optimization of regularization parameter of inversion in particle sizing using light extinction method,” China Particuol. 5, 295–299 (2007).
[CrossRef]

Somerford, D. J.

S. K. Sharma and D. J. Somerford, Light Scattering by Optically Soft Particles: Theory and Applications (Springer-Praxis, 2006).

Stephens, G. L.

S. A. Ackerman and G. L. Stephens, “The absorption of solar radiation by cloud droplets: an application of anomalous diffraction theory,” J. Atmos. Sci. 44, 1574–1588 (1987).
[CrossRef]

Su, M. X.

M. X. Su, F. Xu, X. S. Cai, K. F. Ren, and J. Q. Shen, “Optimization of regularization parameter of inversion in particle sizing using light extinction method,” China Particuol. 5, 295–299 (2007).
[CrossRef]

Sun, X. G.

X. G. Sun, H. Tang, and J. M. Dai, “Inversion of particle size distribution from spectral extinction data using the modified beta function,” Powder Technol. 190, 292–296 (2009).
[CrossRef]

X. G. Sun, H. Tang, and G. B. Yuan, “Anomalous diffraction approximation method for retrieval of spherical and spheroidal particle size distributions in total light scattering,” J. Quant. Spectrosc. Radiat. Transfer 109, 89–106 (2008).
[CrossRef]

X. G. Sun, H. Tang, and J. M. Dai, “Retrieval of particle size distribution in the dependent model using the moment method,” Optic Express 15, 11507–11516 (2007).
[CrossRef]

Sutherland, R. A.

Taavitsainen, V. M.

J. P. Jalava, V. M. Taavitsainen, H. Haario, and L. Lamberg, “Determination of particle and crystal size distribution from turbidity spectrum of TiO2 pigments by means of T-matrix,” J. Quant. Spectrosc. Radiat. Transfer 60, 399–409 (1998).
[CrossRef]

Tang, H.

X. G. Sun, H. Tang, and J. M. Dai, “Inversion of particle size distribution from spectral extinction data using the modified beta function,” Powder Technol. 190, 292–296 (2009).
[CrossRef]

X. G. Sun, H. Tang, and G. B. Yuan, “Anomalous diffraction approximation method for retrieval of spherical and spheroidal particle size distributions in total light scattering,” J. Quant. Spectrosc. Radiat. Transfer 109, 89–106 (2008).
[CrossRef]

X. G. Sun, H. Tang, and J. M. Dai, “Retrieval of particle size distribution in the dependent model using the moment method,” Optic Express 15, 11507–11516 (2007).
[CrossRef]

Travis, L. D.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption and Emission of Light by Small Particles(Cambridge University, 2006).

Vargas-Ubera, J.

Veselovskii, I.

Voshchinnikov, N. V.

A. Y. Perelman and N. V. Voshchinnikov, “Improved S-approximation for dielectric particles,” J. Quant. Spectrosc. Radiat. Transfer 72, 607–621 (2002).
[CrossRef]

Wandinger, U.

Wang, J. P.

Wang, J. Y.

Wang, N. N.

N. N. Wang, Optic Measurement Technology of Particle Size and Its Application (Atomic Energy Press, 2000).

Wei, L.

Whiteman, D. N.

Wilkinson, D.

M. Z. Li and D. Wilkinson, “Particle size distribution determination from spectral extinction using evolutionary programming,” Chem. Eng. Sci. 56, 3045–3052 (2001).
[CrossRef]

S. Gordon, R. Hammond, K. Roberts, N. Savelli, and D. Wilkinson, “In-process particle characterization by spectral extinction,” Trans. IChemE. 78, 1147–1152 (2000).
[CrossRef]

Wriedt, T.

N. Riefler and T. Wriedt, “Intercomparison of inversion algorithms for particle-sizing using Mie scattering,” Part. Part. Syst. Charact. 25, 216–230 (2008).
[CrossRef]

Xie, S. Z.

Xu, F.

M. X. Su, F. Xu, X. S. Cai, K. F. Ren, and J. Q. Shen, “Optimization of regularization parameter of inversion in particle sizing using light extinction method,” China Particuol. 5, 295–299 (2007).
[CrossRef]

F. Xu, X. S. Cai, and J. Shen, “Geometric approximation of light scattering in arbitrary diffraction regime for absorbing particles: application in laser particle sizing,” Acta Opt. Sin. 23, 1464–1469 (2003).

Xu, L. J.

Yang, L.

Yang, L. M.

L. M. Yang, “The GEA method for light scattering by dielectric spheroids and ellipsoids with fixed and random orientations,” Ph.D. thesis (New Mexico State University, 1999).

Yuan, G. B.

X. G. Sun, H. Tang, and G. B. Yuan, “Anomalous diffraction approximation method for retrieval of spherical and spheroidal particle size distributions in total light scattering,” J. Quant. Spectrosc. Radiat. Transfer 109, 89–106 (2008).
[CrossRef]

Zhang, Y. M.

Zuo, H. Y.

Acta Opt. Sin. (1)

F. Xu, X. S. Cai, and J. Shen, “Geometric approximation of light scattering in arbitrary diffraction regime for absorbing particles: application in laser particle sizing,” Acta Opt. Sin. 23, 1464–1469 (2003).

Aerosol Sci. Technol. (1)

G. Ramachandran and D. Leith, “Extraction of aerosol-size distributions from multispectral light extinction data,” Aerosol Sci. Technol. 17, 303–325 (1992).
[CrossRef]

Appl. Opt. (10)

L. Hespel and A. Delfour, “Mie light-scattering granulometer with adaptive numerical filtering. I. Theory,” Appl. Opt. 39, 6897–6917 (2000).
[CrossRef]

I. Veselovskii, A. Kolgotin, V. Griaznov, D. Muller, K. Franke, and D. N. Whiteman, “Inversion of multiwavelength Raman lidar data for retrieval of bimodal aerosol size distribution,” Appl. Opt. 43, 1180–1195 (2004).
[CrossRef]

Z. Cao, L. J. Xu, and J. Ding, “Integral inversion to Fraunhofer diffraction for particle sizing,” Appl. Opt. 48, 4842–4850 (2009).
[CrossRef]

J. D. Klett and R. A. Sutherland, “Approximate methods for modeling the scattering properties of nonspherical particles: evaluation of the Wentzel-Kramers-Brillouin method,” Appl. Opt. 31, 373–386 (1992).
[CrossRef]

T. W. Chen, “High energy light scattering in the generalized eikonal approximation,” Appl. Opt. 28, 4096–4102 (1989).
[CrossRef]

D. Muller, U. Wandinger, and A. Ansmann, “Microphysical particle parameters from extinction and backscatter lidar data by inversion with regularization: theory,” Appl. Opt. 38, 2346–2355 (1999).
[CrossRef]

J. P. Wang, S. Z. Xie, Y. M. Zhang, and L. Wei, “Improved projection algorithm to invert forward scattered light for particle sizing,” Appl. Opt. 40, 3937–3945 (2001).
[CrossRef]

J. Vargas-Ubera, J. J. Sanchez-Escobar, J. F. Aguilar, and D. M. Gale, “Numerical study of particle-size distributions retrieved from angular light-scattering data using an evolution strategy with the Fraunhofer approximation,” Appl. Opt. 46, 3602–3610 (2007).
[CrossRef]

V. V. Berdnik and V. A. Loiko, “Retrieval of size and refractive index of spherical particles by multiangle light scattering: neural network method application,” Appl. Opt. 48, 6178–6187 (2009).
[CrossRef]

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Figures (9)

Fig. 1.
Fig. 1.

Comparison of extinction efficiency of some common particles by the exact Mie theory and the GEA method (λ=0.73μm). The relative error between the Mie theory and the GEA method is also plotted. (a) Marine suspended particle (m=1.12+0.1i), (b) Rain drop (m=1.33+0.0i), (c) Smoke particle (m=1.56+0.087i).

Fig. 2.
Fig. 2.

Comparison of extinction efficiency of some common particles by the exact Mie theory, the original GEA method, and the CGEA method (λ=0.73μm). The two curves in the bottom of the figure represent the relative errors of the original GEA method and the CGEA method compared with the exact Mie theory, respectively. (a) Marine suspended particle (m=1.12+0.1i), (b) Rain drop (m=1.33+0.0i), (c) Smoke particle (m=1.56+0.087i).

Fig. 3.
Fig. 3.

Contour plot of the maximum relative error (%) between the exact Mie theory and the CGEA method with different refractive indices (λ=0.73μm).

Fig. 4.
Fig. 4.

Extinction efficiency by the exact Mie theory and the CGEA method with some extreme refractive indices m (λ=0.73μm). The curves produced by the original GEA method are also plotted in order to compare them more thoroughly. (a) m=1.33+2.0i, (b) m=3.5+0.005i, (c) m=4.5+0.005i.

Fig. 5.
Fig. 5.

Retrieval results of unimodal R-R distribution in the framework of the CGEA method at m=1.235+0.0i. (a) (D¯,k)=(1.7,5.9), (b) (D¯,k)=(6.3,4.5).

Fig. 6.
Fig. 6.

Retrieval results of bimodal R-R distribution in the framework of the CGEA method at m=1.235+0.0i. (a) (D¯1,k1,D¯2,k2,n)=(1.5,6.0,6.5,11.0,0.3), (b) (D¯1,k1,D¯2,k2,n)=(3.5,8.0,6.7,6.9,0.5).

Fig. 7.
Fig. 7.

Schematic of measurement system based on the light extinction particle sizing technique.

Fig. 8.
Fig. 8.

Relationship diagram of incident wavelength and light intensity.

Fig. 9.
Fig. 9.

Retrieval results of standard polystyrene particle in the framework of the Mie theory and CGEA method.

Tables (2)

Tables Icon

Table 1. Comparison of Retrieval Error ξ in the Framework of the CGEA Method and Mie Theory (m=1.235+0.0i)

Tables Icon

Table 2. Comparison of Retrieval Time in the Framework of the CGEA Method and Mie Theory (m=1.235+0.0i), (D¯,k)=(1.7,5.9), Random Noise=0%

Equations (11)

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ln(II0)λi=32LNDminDmaxQext(λi,m,D)f(D)DdDi=1,2,M,
S=k4πiexp(ikr)V(r)ψ(r)d3r.
(2+k2)ψ(r)=V(r)ψ(r).
ψ(r)=ψ0(r)+Gk(rr)V(r)ψ(r)d3r,
Qext(λ,m,D)=4πk2PRe[S(0)]=2Re{i23α0γ(1γ)ρ+α0γ2[1+2iρeiρ+2ρ2(1eiρ)]},
E=Af+ε,
f=(ATA+γH)1ATE,
V(γ)=1M[IK(γ)E]22{1Mtrace[IK(γ)]}2,
f(D)RR-u=kD¯×(DD¯)k1×exp[(DD¯)k],
f(D)RR-b=n[k1D1¯×(DD1¯)k11×exp((DD1¯)k1)]+(1n)[k2D2¯×(DD2¯)k21×exp((DD2¯)k2)]
ξ={1Nj=1N[fpre(Dj)fret(Dj)]2}1/2{1Nj=1N[fpre(Dj)]2}1/2={j=1N[fpre(Dj)fret(Dj)]2}1/2{j=1N[fpre(Dj)]2}1/2,

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