Abstract

A secondary optimization technique is proposed that allows the complex refractive index and particle size distribution (PSD) to be retrieved simultaneously by using the diffuse transmittance (T), diffuse reflectance (R), and collimated transmittance (T c) of a 1-D spherical particle systems as measured values. In the proposed method, two 1-D experimental samples of different thicknesses were exposed to continuous wave lasers of two different wavelengths. First, T, R, and T c were calculated by solving the radiative transfer equation. Then, the complex refractive index and PSDs were retrieved simultaneously by applying the inversion technique, quantum particle swarm optimization. However, the estimated results of the PSDs proved to be inaccurate. Hence, a secondary optimization was performed to improve the accuracy of the PSDs on the basis of the first optimization process. The results showed that the proposed technique can estimate the complex refractive index and particle size distribution accurately.

© 2015 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Simultaneous retrieval of aerosol refractive index and particle size distribution from ground-based measurements of direct and scattered solar radiation

Peter Romanov, Norman T. O’Neill, Alain Royer, and Bruce L. J. McArthur
Appl. Opt. 38(36) 7305-7320 (1999)

Simultaneous determination of the aerosol complex index of refraction and size distribution from scattering measurements of polarized light

Fengsheng Zhao, Zhiben Gong, Huanling Hu, Masayuki Tanaka, and Tadahiro Hayasaka
Appl. Opt. 36(30) 7992-8001 (1997)

References

  • View by:
  • |
  • |
  • |

  1. Y. Takano and K. N. Liou, “Solar radiative transfer in cirrus clouds. Part I: Single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46(1), 3–19 (1989).
    [Crossref]
  2. K. D. Kanniah, J. Beringer, P. North, and L. Hutley, “Control of atmospheric particles on diffuse radiation and terrestrial plant productivity A review,” Prog. Phys. Geogr. 36(2), 209–237 (2012).
    [Crossref]
  3. L. Pilon, H. Berberoğlu, and R. Kandilian, “Radiation transfer in photobiological carbon dioxide fixation and fuel production by microalgae,” J. Quant. Spectrosc. Ra. 112(17), 2639–2660 (2011).
    [Crossref]
  4. M. Su, M. Xue, X. Cai, Z. Shang, and F. Xu, “Particle size characterization by ultrasonic attenuation spectra,” Particuology 6(4), 276–281 (2008).
    [Crossref]
  5. D. Doxaran, J. Ehn, S. Bélanger, A. Matsuoka, S. Hooker, and M. Babin, “Optical characterisation of suspended particles in the Mackenzie River plume (Canadian Arctic Ocean) and implications for ocean colour remote sensing,” Biogeosciences 9(8), 3213–3229 (2012).
    [Crossref]
  6. S. Pfeifer, W. Birmili, A. Schladitz, T. Müller, A. Nowak, and A. Wiedensohler, “A fast and easy-to-implement inversion algorithm for mobility particle size spectrometers considering particle number size distribution information outside of the detection range,” Atmos. Meas. Tech. 7(1), 95–105 (2014).
    [Crossref]
  7. X. Sun, H. Tang, and J. Dai, “Retrieval of particle size distribution in the dependent model using the moment method,” Opt. Express 15(18), 11507–11516 (2007).
    [Crossref] [PubMed]
  8. K. J. Zarzana, C. D. Cappa, and M. A. Tolbert, “Sensitivity of aerosol refractive index retrievals using optical spectroscopy,” Aerosol Sci. Technol. 48(11), 1133–1144 (2014).
    [Crossref]
  9. X. Wu, Y. Wu, J. Yang, Z. Wang, B. Zhou, G. Gréhan, and K. Cen, “Modified convolution method to reconstruct particle hologram with an elliptical Gaussian Beam illumination,” Opt. Express 21(10), 12803–12814 (2013).
    [Crossref] [PubMed]
  10. M. Ye, S. Wang, Y. Lu, T. Hu, Z. Zhu, and Y. Xu, “Inversion of particle-size distribution from angular light-scattering data with genetic algorithms,” Appl. Opt. 38(12), 2677–2685 (1999).
    [Crossref] [PubMed]
  11. L. M. Ruan, H. Qi, W. An, and H. P. Tan, “Inverse radiation problem for determination of optical constants of fly-ash particles,” Int. J. Thermophys. 28(4), 1322–1341 (2007).
    [Crossref]
  12. X. Zhang, Y. Huang, R. Rao, and Z. Wang, “Retrieval of effective complex refractive index from intensive measurements of characteristics of ambient aerosols in the boundary layer,” Opt. Express 21(15), 17849–17862 (2013).
    [Crossref] [PubMed]
  13. H. Tang and J. Lin, “Inversion of visible optical extinction data for spheroid particle size distribution based on PCA,” Optik 125(19), 5494–5507 (2014).
    [Crossref]
  14. M. Su, F. Xu, X. Cai, K. Ren, and J. Shen, “Optimization of regularization parameter of inversion in particle sizing using light extinction method,” China Particuology 5(4), 295–299 (2007).
    [Crossref]
  15. M. Tanaka, T. Nakajima, and T. Takamura, “Simultaneous determination of complex refractive index and size distribution of airborne and water-suspended particles from light scattering measurements,” J. Meteorol. Soc. Jpn. 60(6), 1259–1271 (1982).
  16. B. Aernouts, E. Zamora-Rojas, R. Van Beers, R. Watté, L. Wang, M. Tsuta, J. Lammertyn, and W. Saeys, “Supercontinuum laser based optical characterization of Intralipid® phantoms in the 500-2250 nm range,” Opt. Express 21(26), 32450–32467 (2013).
    [Crossref] [PubMed]
  17. B. Zhang, H. Qi, Y. T. Ren, S. C. Sun, and L. M. Ruan, “Application of homogenous continuous Ant Colony Optimization algorithm to inverse problem of one-dimensional coupled radiation and conduction heat transfer,” Int. J. Heat Mass Trans. 66, 507–516 (2013).
    [Crossref]
  18. G. Masiello and C. Serio, “Simultaneous physical retrieval of surface emissivity spectrum and atmospheric parameters from infrared atmospheric sounder interferometer spectral radiances,” Appl. Opt. 52(11), 2428–2446 (2013).
    [Crossref] [PubMed]
  19. H. Mao and D. Zhao, “Alternative phase-diverse phase retrieval algorithm based on Levenberg-Marquardt nonlinear optimization,” Opt. Express 17(6), 4540–4552 (2009).
    [Crossref] [PubMed]
  20. C. H. Huang and C. H. Wang, “The design of uniform tube flow rates for Z-type compact parallel flow heat exchangers,” Int. J. Heat Mass Trans. 57(2), 608–622 (2013).
    [Crossref]
  21. Z. Tao, N. J. McCormick, and R. Sanchez, “Ocean source and optical property estimation from explicit and implicit algorithms,” Appl. Opt. 33(15), 3265–3275 (1994).
    [Crossref] [PubMed]
  22. K. W. Kim and S. W. Baek, “Efficient inverse radiation analysis in a cylindrical geometry using a combined method of hybrid genetic algorithm and finite difference Newton method,” J. Quant. Spectrosc. Ra. 108(3), 423–439 (2007).
    [Crossref]
  23. R. Das, S. C. Mishra, M. Ajith, and R. Uppaluri, “An inverse analysis of a transient 2-D conduction–radiation problem using the lattice Boltzmann method and the finite volume method coupled with the genetic algorithm,” J. Quant. Spectrosc. Ra. 109(11), 2060–2077 (2008).
    [Crossref]
  24. R. Das, S. C. Mishra, T. B. P. Kumar, and R. Uppaluri, “An inverse analysis for parameter estimation applied to a non-fourier conduction–radiation problem,” Heat Transf. Eng. 32(6), 455–466 (2011).
    [Crossref]
  25. H. Qi, L. M. Ruan, H. C. Zhang, Y. M. Wang, and H. P. Tan, “Inverse radiation analysis of a one-dimensional participating slab by stochastic particle swarm optimizer algorithm,” Int. J. Therm. Sci. 46(7), 649–661 (2007).
    [Crossref]
  26. H. Qi, D. L. Wang, S. G. Wang, and L. M. Ruan, “Inverse transient radiation analysis in one-dimensional non-homogeneous participating slabs using particle swarm optimization algorithms,” J. Quant. Spectrosc. Ra. 112(15), 2507–2519 (2011).
    [Crossref]
  27. Y. P. Sun, C. Lou, and H. C. Zhou, “Estimating soot volume fraction and temperature in flames using stochastic particle swarm optimization algorithm, Int. J. Heat Mass Trans. 54(1–3), 217–224 (2011).
    [Crossref]
  28. S. Stephany, J. C. Becceneri, R. P. Souto, H. F. de Campos Velho, and A. J. Silva Neto, “A preregularization scheme for the reconstruction of a spatial dependent scattering albedo using a hybrid ant colony optimization implementation,” Appl. Math. Model. 34(3), 561–572 (2010).
    [Crossref]
  29. M. A. Behrang, E. Assareh, M. R. Assari, and A. Ghanbarzadeh, “Assessment of electricity demand in Iran’s industrial sector using different intelligent optimization techniques,” Appl. Artif. Intell. 25(4), 292–304 (2011).
    [Crossref]
  30. S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Found. Trends Mach. Learn. 3(1), 1–122 (2010).
    [Crossref]
  31. B. Zhang, H. Qi, S. C. Sun, L. M. Ruan, and H. P. Tan, “Solving inverse problems of radiative heat transfer and phase change in semitransparent medium by using Improved Quantum Particle Swarm Optimization,” Int. J. Heat Mass Trans. 85, 300–310 (2015).
    [Crossref]
  32. M. F. Modest, Radiative Heat Transfer (Elsevier, 2003).
  33. C. F. Bohren and D. R. Huffman, Absorption and scattering of light by small particles (John Wiley & Sons, 2008)
  34. H. Qi, L. M. Ruan, S. G. Wang, M. Shi, and H. Zhao, “Application of multi-phase particle swarm optimization technique to retrieve the particle size distribution,” Chin. Opt. Lett. 6, 346–349 (2008).
    [Crossref]
  35. Z. Z. He, H. Qi, Y. C. Yao, and L. M. Ruan, “Inverse estimation of the particle size distribution using the Fruit Fly Optimization Algorithm,” Appl. Therm. Eng.in press.
  36. E. Lee, R. L. Heng, and L. Pilon, “Spectral optical properties of selected photo synthetic microalgae producing biofuels,” J. Quant. Spectrosc. Ra. 114, 122–135 (2013).
    [Crossref]
  37. H. Qi, C.-Y. Niu, S. Gong, Y.-T. Ren, and L.-M. Ruan, “Application of the hybrid particle swarm optimization algorithms for simultaneous estimation of multi-parameters in a transient conduction-radiation problem,” Int. J. Heat Mass Trans. 83, 428–440 (2015).
    [Crossref]

2015 (2)

B. Zhang, H. Qi, S. C. Sun, L. M. Ruan, and H. P. Tan, “Solving inverse problems of radiative heat transfer and phase change in semitransparent medium by using Improved Quantum Particle Swarm Optimization,” Int. J. Heat Mass Trans. 85, 300–310 (2015).
[Crossref]

H. Qi, C.-Y. Niu, S. Gong, Y.-T. Ren, and L.-M. Ruan, “Application of the hybrid particle swarm optimization algorithms for simultaneous estimation of multi-parameters in a transient conduction-radiation problem,” Int. J. Heat Mass Trans. 83, 428–440 (2015).
[Crossref]

2014 (3)

S. Pfeifer, W. Birmili, A. Schladitz, T. Müller, A. Nowak, and A. Wiedensohler, “A fast and easy-to-implement inversion algorithm for mobility particle size spectrometers considering particle number size distribution information outside of the detection range,” Atmos. Meas. Tech. 7(1), 95–105 (2014).
[Crossref]

K. J. Zarzana, C. D. Cappa, and M. A. Tolbert, “Sensitivity of aerosol refractive index retrievals using optical spectroscopy,” Aerosol Sci. Technol. 48(11), 1133–1144 (2014).
[Crossref]

H. Tang and J. Lin, “Inversion of visible optical extinction data for spheroid particle size distribution based on PCA,” Optik 125(19), 5494–5507 (2014).
[Crossref]

2013 (7)

B. Zhang, H. Qi, Y. T. Ren, S. C. Sun, and L. M. Ruan, “Application of homogenous continuous Ant Colony Optimization algorithm to inverse problem of one-dimensional coupled radiation and conduction heat transfer,” Int. J. Heat Mass Trans. 66, 507–516 (2013).
[Crossref]

C. H. Huang and C. H. Wang, “The design of uniform tube flow rates for Z-type compact parallel flow heat exchangers,” Int. J. Heat Mass Trans. 57(2), 608–622 (2013).
[Crossref]

E. Lee, R. L. Heng, and L. Pilon, “Spectral optical properties of selected photo synthetic microalgae producing biofuels,” J. Quant. Spectrosc. Ra. 114, 122–135 (2013).
[Crossref]

G. Masiello and C. Serio, “Simultaneous physical retrieval of surface emissivity spectrum and atmospheric parameters from infrared atmospheric sounder interferometer spectral radiances,” Appl. Opt. 52(11), 2428–2446 (2013).
[Crossref] [PubMed]

X. Wu, Y. Wu, J. Yang, Z. Wang, B. Zhou, G. Gréhan, and K. Cen, “Modified convolution method to reconstruct particle hologram with an elliptical Gaussian Beam illumination,” Opt. Express 21(10), 12803–12814 (2013).
[Crossref] [PubMed]

X. Zhang, Y. Huang, R. Rao, and Z. Wang, “Retrieval of effective complex refractive index from intensive measurements of characteristics of ambient aerosols in the boundary layer,” Opt. Express 21(15), 17849–17862 (2013).
[Crossref] [PubMed]

B. Aernouts, E. Zamora-Rojas, R. Van Beers, R. Watté, L. Wang, M. Tsuta, J. Lammertyn, and W. Saeys, “Supercontinuum laser based optical characterization of Intralipid® phantoms in the 500-2250 nm range,” Opt. Express 21(26), 32450–32467 (2013).
[Crossref] [PubMed]

2012 (2)

K. D. Kanniah, J. Beringer, P. North, and L. Hutley, “Control of atmospheric particles on diffuse radiation and terrestrial plant productivity A review,” Prog. Phys. Geogr. 36(2), 209–237 (2012).
[Crossref]

D. Doxaran, J. Ehn, S. Bélanger, A. Matsuoka, S. Hooker, and M. Babin, “Optical characterisation of suspended particles in the Mackenzie River plume (Canadian Arctic Ocean) and implications for ocean colour remote sensing,” Biogeosciences 9(8), 3213–3229 (2012).
[Crossref]

2011 (5)

L. Pilon, H. Berberoğlu, and R. Kandilian, “Radiation transfer in photobiological carbon dioxide fixation and fuel production by microalgae,” J. Quant. Spectrosc. Ra. 112(17), 2639–2660 (2011).
[Crossref]

R. Das, S. C. Mishra, T. B. P. Kumar, and R. Uppaluri, “An inverse analysis for parameter estimation applied to a non-fourier conduction–radiation problem,” Heat Transf. Eng. 32(6), 455–466 (2011).
[Crossref]

H. Qi, D. L. Wang, S. G. Wang, and L. M. Ruan, “Inverse transient radiation analysis in one-dimensional non-homogeneous participating slabs using particle swarm optimization algorithms,” J. Quant. Spectrosc. Ra. 112(15), 2507–2519 (2011).
[Crossref]

Y. P. Sun, C. Lou, and H. C. Zhou, “Estimating soot volume fraction and temperature in flames using stochastic particle swarm optimization algorithm, Int. J. Heat Mass Trans. 54(1–3), 217–224 (2011).
[Crossref]

M. A. Behrang, E. Assareh, M. R. Assari, and A. Ghanbarzadeh, “Assessment of electricity demand in Iran’s industrial sector using different intelligent optimization techniques,” Appl. Artif. Intell. 25(4), 292–304 (2011).
[Crossref]

2010 (2)

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Found. Trends Mach. Learn. 3(1), 1–122 (2010).
[Crossref]

S. Stephany, J. C. Becceneri, R. P. Souto, H. F. de Campos Velho, and A. J. Silva Neto, “A preregularization scheme for the reconstruction of a spatial dependent scattering albedo using a hybrid ant colony optimization implementation,” Appl. Math. Model. 34(3), 561–572 (2010).
[Crossref]

2009 (1)

2008 (3)

R. Das, S. C. Mishra, M. Ajith, and R. Uppaluri, “An inverse analysis of a transient 2-D conduction–radiation problem using the lattice Boltzmann method and the finite volume method coupled with the genetic algorithm,” J. Quant. Spectrosc. Ra. 109(11), 2060–2077 (2008).
[Crossref]

H. Qi, L. M. Ruan, S. G. Wang, M. Shi, and H. Zhao, “Application of multi-phase particle swarm optimization technique to retrieve the particle size distribution,” Chin. Opt. Lett. 6, 346–349 (2008).
[Crossref]

M. Su, M. Xue, X. Cai, Z. Shang, and F. Xu, “Particle size characterization by ultrasonic attenuation spectra,” Particuology 6(4), 276–281 (2008).
[Crossref]

2007 (5)

M. Su, F. Xu, X. Cai, K. Ren, and J. Shen, “Optimization of regularization parameter of inversion in particle sizing using light extinction method,” China Particuology 5(4), 295–299 (2007).
[Crossref]

L. M. Ruan, H. Qi, W. An, and H. P. Tan, “Inverse radiation problem for determination of optical constants of fly-ash particles,” Int. J. Thermophys. 28(4), 1322–1341 (2007).
[Crossref]

H. Qi, L. M. Ruan, H. C. Zhang, Y. M. Wang, and H. P. Tan, “Inverse radiation analysis of a one-dimensional participating slab by stochastic particle swarm optimizer algorithm,” Int. J. Therm. Sci. 46(7), 649–661 (2007).
[Crossref]

K. W. Kim and S. W. Baek, “Efficient inverse radiation analysis in a cylindrical geometry using a combined method of hybrid genetic algorithm and finite difference Newton method,” J. Quant. Spectrosc. Ra. 108(3), 423–439 (2007).
[Crossref]

X. Sun, H. Tang, and J. Dai, “Retrieval of particle size distribution in the dependent model using the moment method,” Opt. Express 15(18), 11507–11516 (2007).
[Crossref] [PubMed]

1999 (1)

1994 (1)

1989 (1)

Y. Takano and K. N. Liou, “Solar radiative transfer in cirrus clouds. Part I: Single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46(1), 3–19 (1989).
[Crossref]

1982 (1)

M. Tanaka, T. Nakajima, and T. Takamura, “Simultaneous determination of complex refractive index and size distribution of airborne and water-suspended particles from light scattering measurements,” J. Meteorol. Soc. Jpn. 60(6), 1259–1271 (1982).

Aernouts, B.

Ajith, M.

R. Das, S. C. Mishra, M. Ajith, and R. Uppaluri, “An inverse analysis of a transient 2-D conduction–radiation problem using the lattice Boltzmann method and the finite volume method coupled with the genetic algorithm,” J. Quant. Spectrosc. Ra. 109(11), 2060–2077 (2008).
[Crossref]

An, W.

L. M. Ruan, H. Qi, W. An, and H. P. Tan, “Inverse radiation problem for determination of optical constants of fly-ash particles,” Int. J. Thermophys. 28(4), 1322–1341 (2007).
[Crossref]

Assareh, E.

M. A. Behrang, E. Assareh, M. R. Assari, and A. Ghanbarzadeh, “Assessment of electricity demand in Iran’s industrial sector using different intelligent optimization techniques,” Appl. Artif. Intell. 25(4), 292–304 (2011).
[Crossref]

Assari, M. R.

M. A. Behrang, E. Assareh, M. R. Assari, and A. Ghanbarzadeh, “Assessment of electricity demand in Iran’s industrial sector using different intelligent optimization techniques,” Appl. Artif. Intell. 25(4), 292–304 (2011).
[Crossref]

Babin, M.

D. Doxaran, J. Ehn, S. Bélanger, A. Matsuoka, S. Hooker, and M. Babin, “Optical characterisation of suspended particles in the Mackenzie River plume (Canadian Arctic Ocean) and implications for ocean colour remote sensing,” Biogeosciences 9(8), 3213–3229 (2012).
[Crossref]

Baek, S. W.

K. W. Kim and S. W. Baek, “Efficient inverse radiation analysis in a cylindrical geometry using a combined method of hybrid genetic algorithm and finite difference Newton method,” J. Quant. Spectrosc. Ra. 108(3), 423–439 (2007).
[Crossref]

Becceneri, J. C.

S. Stephany, J. C. Becceneri, R. P. Souto, H. F. de Campos Velho, and A. J. Silva Neto, “A preregularization scheme for the reconstruction of a spatial dependent scattering albedo using a hybrid ant colony optimization implementation,” Appl. Math. Model. 34(3), 561–572 (2010).
[Crossref]

Behrang, M. A.

M. A. Behrang, E. Assareh, M. R. Assari, and A. Ghanbarzadeh, “Assessment of electricity demand in Iran’s industrial sector using different intelligent optimization techniques,” Appl. Artif. Intell. 25(4), 292–304 (2011).
[Crossref]

Bélanger, S.

D. Doxaran, J. Ehn, S. Bélanger, A. Matsuoka, S. Hooker, and M. Babin, “Optical characterisation of suspended particles in the Mackenzie River plume (Canadian Arctic Ocean) and implications for ocean colour remote sensing,” Biogeosciences 9(8), 3213–3229 (2012).
[Crossref]

Berberoglu, H.

L. Pilon, H. Berberoğlu, and R. Kandilian, “Radiation transfer in photobiological carbon dioxide fixation and fuel production by microalgae,” J. Quant. Spectrosc. Ra. 112(17), 2639–2660 (2011).
[Crossref]

Beringer, J.

K. D. Kanniah, J. Beringer, P. North, and L. Hutley, “Control of atmospheric particles on diffuse radiation and terrestrial plant productivity A review,” Prog. Phys. Geogr. 36(2), 209–237 (2012).
[Crossref]

Birmili, W.

S. Pfeifer, W. Birmili, A. Schladitz, T. Müller, A. Nowak, and A. Wiedensohler, “A fast and easy-to-implement inversion algorithm for mobility particle size spectrometers considering particle number size distribution information outside of the detection range,” Atmos. Meas. Tech. 7(1), 95–105 (2014).
[Crossref]

Boyd, S.

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Found. Trends Mach. Learn. 3(1), 1–122 (2010).
[Crossref]

Cai, X.

M. Su, M. Xue, X. Cai, Z. Shang, and F. Xu, “Particle size characterization by ultrasonic attenuation spectra,” Particuology 6(4), 276–281 (2008).
[Crossref]

M. Su, F. Xu, X. Cai, K. Ren, and J. Shen, “Optimization of regularization parameter of inversion in particle sizing using light extinction method,” China Particuology 5(4), 295–299 (2007).
[Crossref]

Cappa, C. D.

K. J. Zarzana, C. D. Cappa, and M. A. Tolbert, “Sensitivity of aerosol refractive index retrievals using optical spectroscopy,” Aerosol Sci. Technol. 48(11), 1133–1144 (2014).
[Crossref]

Cen, K.

Chu, E.

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Found. Trends Mach. Learn. 3(1), 1–122 (2010).
[Crossref]

Dai, J.

Das, R.

R. Das, S. C. Mishra, T. B. P. Kumar, and R. Uppaluri, “An inverse analysis for parameter estimation applied to a non-fourier conduction–radiation problem,” Heat Transf. Eng. 32(6), 455–466 (2011).
[Crossref]

R. Das, S. C. Mishra, M. Ajith, and R. Uppaluri, “An inverse analysis of a transient 2-D conduction–radiation problem using the lattice Boltzmann method and the finite volume method coupled with the genetic algorithm,” J. Quant. Spectrosc. Ra. 109(11), 2060–2077 (2008).
[Crossref]

de Campos Velho, H. F.

S. Stephany, J. C. Becceneri, R. P. Souto, H. F. de Campos Velho, and A. J. Silva Neto, “A preregularization scheme for the reconstruction of a spatial dependent scattering albedo using a hybrid ant colony optimization implementation,” Appl. Math. Model. 34(3), 561–572 (2010).
[Crossref]

Doxaran, D.

D. Doxaran, J. Ehn, S. Bélanger, A. Matsuoka, S. Hooker, and M. Babin, “Optical characterisation of suspended particles in the Mackenzie River plume (Canadian Arctic Ocean) and implications for ocean colour remote sensing,” Biogeosciences 9(8), 3213–3229 (2012).
[Crossref]

Eckstein, J.

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Found. Trends Mach. Learn. 3(1), 1–122 (2010).
[Crossref]

Ehn, J.

D. Doxaran, J. Ehn, S. Bélanger, A. Matsuoka, S. Hooker, and M. Babin, “Optical characterisation of suspended particles in the Mackenzie River plume (Canadian Arctic Ocean) and implications for ocean colour remote sensing,” Biogeosciences 9(8), 3213–3229 (2012).
[Crossref]

Ghanbarzadeh, A.

M. A. Behrang, E. Assareh, M. R. Assari, and A. Ghanbarzadeh, “Assessment of electricity demand in Iran’s industrial sector using different intelligent optimization techniques,” Appl. Artif. Intell. 25(4), 292–304 (2011).
[Crossref]

Gong, S.

H. Qi, C.-Y. Niu, S. Gong, Y.-T. Ren, and L.-M. Ruan, “Application of the hybrid particle swarm optimization algorithms for simultaneous estimation of multi-parameters in a transient conduction-radiation problem,” Int. J. Heat Mass Trans. 83, 428–440 (2015).
[Crossref]

Gréhan, G.

He, Z. Z.

Z. Z. He, H. Qi, Y. C. Yao, and L. M. Ruan, “Inverse estimation of the particle size distribution using the Fruit Fly Optimization Algorithm,” Appl. Therm. Eng.in press.

Heng, R. L.

E. Lee, R. L. Heng, and L. Pilon, “Spectral optical properties of selected photo synthetic microalgae producing biofuels,” J. Quant. Spectrosc. Ra. 114, 122–135 (2013).
[Crossref]

Hooker, S.

D. Doxaran, J. Ehn, S. Bélanger, A. Matsuoka, S. Hooker, and M. Babin, “Optical characterisation of suspended particles in the Mackenzie River plume (Canadian Arctic Ocean) and implications for ocean colour remote sensing,” Biogeosciences 9(8), 3213–3229 (2012).
[Crossref]

Hu, T.

Huang, C. H.

C. H. Huang and C. H. Wang, “The design of uniform tube flow rates for Z-type compact parallel flow heat exchangers,” Int. J. Heat Mass Trans. 57(2), 608–622 (2013).
[Crossref]

Huang, Y.

Hutley, L.

K. D. Kanniah, J. Beringer, P. North, and L. Hutley, “Control of atmospheric particles on diffuse radiation and terrestrial plant productivity A review,” Prog. Phys. Geogr. 36(2), 209–237 (2012).
[Crossref]

Kandilian, R.

L. Pilon, H. Berberoğlu, and R. Kandilian, “Radiation transfer in photobiological carbon dioxide fixation and fuel production by microalgae,” J. Quant. Spectrosc. Ra. 112(17), 2639–2660 (2011).
[Crossref]

Kanniah, K. D.

K. D. Kanniah, J. Beringer, P. North, and L. Hutley, “Control of atmospheric particles on diffuse radiation and terrestrial plant productivity A review,” Prog. Phys. Geogr. 36(2), 209–237 (2012).
[Crossref]

Kim, K. W.

K. W. Kim and S. W. Baek, “Efficient inverse radiation analysis in a cylindrical geometry using a combined method of hybrid genetic algorithm and finite difference Newton method,” J. Quant. Spectrosc. Ra. 108(3), 423–439 (2007).
[Crossref]

Kumar, T. B. P.

R. Das, S. C. Mishra, T. B. P. Kumar, and R. Uppaluri, “An inverse analysis for parameter estimation applied to a non-fourier conduction–radiation problem,” Heat Transf. Eng. 32(6), 455–466 (2011).
[Crossref]

Lammertyn, J.

Lee, E.

E. Lee, R. L. Heng, and L. Pilon, “Spectral optical properties of selected photo synthetic microalgae producing biofuels,” J. Quant. Spectrosc. Ra. 114, 122–135 (2013).
[Crossref]

Lin, J.

H. Tang and J. Lin, “Inversion of visible optical extinction data for spheroid particle size distribution based on PCA,” Optik 125(19), 5494–5507 (2014).
[Crossref]

Liou, K. N.

Y. Takano and K. N. Liou, “Solar radiative transfer in cirrus clouds. Part I: Single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46(1), 3–19 (1989).
[Crossref]

Lou, C.

Y. P. Sun, C. Lou, and H. C. Zhou, “Estimating soot volume fraction and temperature in flames using stochastic particle swarm optimization algorithm, Int. J. Heat Mass Trans. 54(1–3), 217–224 (2011).
[Crossref]

Lu, Y.

Mao, H.

Masiello, G.

Matsuoka, A.

D. Doxaran, J. Ehn, S. Bélanger, A. Matsuoka, S. Hooker, and M. Babin, “Optical characterisation of suspended particles in the Mackenzie River plume (Canadian Arctic Ocean) and implications for ocean colour remote sensing,” Biogeosciences 9(8), 3213–3229 (2012).
[Crossref]

McCormick, N. J.

Mishra, S. C.

R. Das, S. C. Mishra, T. B. P. Kumar, and R. Uppaluri, “An inverse analysis for parameter estimation applied to a non-fourier conduction–radiation problem,” Heat Transf. Eng. 32(6), 455–466 (2011).
[Crossref]

R. Das, S. C. Mishra, M. Ajith, and R. Uppaluri, “An inverse analysis of a transient 2-D conduction–radiation problem using the lattice Boltzmann method and the finite volume method coupled with the genetic algorithm,” J. Quant. Spectrosc. Ra. 109(11), 2060–2077 (2008).
[Crossref]

Müller, T.

S. Pfeifer, W. Birmili, A. Schladitz, T. Müller, A. Nowak, and A. Wiedensohler, “A fast and easy-to-implement inversion algorithm for mobility particle size spectrometers considering particle number size distribution information outside of the detection range,” Atmos. Meas. Tech. 7(1), 95–105 (2014).
[Crossref]

Nakajima, T.

M. Tanaka, T. Nakajima, and T. Takamura, “Simultaneous determination of complex refractive index and size distribution of airborne and water-suspended particles from light scattering measurements,” J. Meteorol. Soc. Jpn. 60(6), 1259–1271 (1982).

Niu, C.-Y.

H. Qi, C.-Y. Niu, S. Gong, Y.-T. Ren, and L.-M. Ruan, “Application of the hybrid particle swarm optimization algorithms for simultaneous estimation of multi-parameters in a transient conduction-radiation problem,” Int. J. Heat Mass Trans. 83, 428–440 (2015).
[Crossref]

North, P.

K. D. Kanniah, J. Beringer, P. North, and L. Hutley, “Control of atmospheric particles on diffuse radiation and terrestrial plant productivity A review,” Prog. Phys. Geogr. 36(2), 209–237 (2012).
[Crossref]

Nowak, A.

S. Pfeifer, W. Birmili, A. Schladitz, T. Müller, A. Nowak, and A. Wiedensohler, “A fast and easy-to-implement inversion algorithm for mobility particle size spectrometers considering particle number size distribution information outside of the detection range,” Atmos. Meas. Tech. 7(1), 95–105 (2014).
[Crossref]

Parikh, N.

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Found. Trends Mach. Learn. 3(1), 1–122 (2010).
[Crossref]

Peleato, B.

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Found. Trends Mach. Learn. 3(1), 1–122 (2010).
[Crossref]

Pfeifer, S.

S. Pfeifer, W. Birmili, A. Schladitz, T. Müller, A. Nowak, and A. Wiedensohler, “A fast and easy-to-implement inversion algorithm for mobility particle size spectrometers considering particle number size distribution information outside of the detection range,” Atmos. Meas. Tech. 7(1), 95–105 (2014).
[Crossref]

Pilon, L.

E. Lee, R. L. Heng, and L. Pilon, “Spectral optical properties of selected photo synthetic microalgae producing biofuels,” J. Quant. Spectrosc. Ra. 114, 122–135 (2013).
[Crossref]

L. Pilon, H. Berberoğlu, and R. Kandilian, “Radiation transfer in photobiological carbon dioxide fixation and fuel production by microalgae,” J. Quant. Spectrosc. Ra. 112(17), 2639–2660 (2011).
[Crossref]

Qi, H.

H. Qi, C.-Y. Niu, S. Gong, Y.-T. Ren, and L.-M. Ruan, “Application of the hybrid particle swarm optimization algorithms for simultaneous estimation of multi-parameters in a transient conduction-radiation problem,” Int. J. Heat Mass Trans. 83, 428–440 (2015).
[Crossref]

B. Zhang, H. Qi, S. C. Sun, L. M. Ruan, and H. P. Tan, “Solving inverse problems of radiative heat transfer and phase change in semitransparent medium by using Improved Quantum Particle Swarm Optimization,” Int. J. Heat Mass Trans. 85, 300–310 (2015).
[Crossref]

B. Zhang, H. Qi, Y. T. Ren, S. C. Sun, and L. M. Ruan, “Application of homogenous continuous Ant Colony Optimization algorithm to inverse problem of one-dimensional coupled radiation and conduction heat transfer,” Int. J. Heat Mass Trans. 66, 507–516 (2013).
[Crossref]

H. Qi, D. L. Wang, S. G. Wang, and L. M. Ruan, “Inverse transient radiation analysis in one-dimensional non-homogeneous participating slabs using particle swarm optimization algorithms,” J. Quant. Spectrosc. Ra. 112(15), 2507–2519 (2011).
[Crossref]

H. Qi, L. M. Ruan, S. G. Wang, M. Shi, and H. Zhao, “Application of multi-phase particle swarm optimization technique to retrieve the particle size distribution,” Chin. Opt. Lett. 6, 346–349 (2008).
[Crossref]

H. Qi, L. M. Ruan, H. C. Zhang, Y. M. Wang, and H. P. Tan, “Inverse radiation analysis of a one-dimensional participating slab by stochastic particle swarm optimizer algorithm,” Int. J. Therm. Sci. 46(7), 649–661 (2007).
[Crossref]

L. M. Ruan, H. Qi, W. An, and H. P. Tan, “Inverse radiation problem for determination of optical constants of fly-ash particles,” Int. J. Thermophys. 28(4), 1322–1341 (2007).
[Crossref]

Z. Z. He, H. Qi, Y. C. Yao, and L. M. Ruan, “Inverse estimation of the particle size distribution using the Fruit Fly Optimization Algorithm,” Appl. Therm. Eng.in press.

Rao, R.

Ren, K.

M. Su, F. Xu, X. Cai, K. Ren, and J. Shen, “Optimization of regularization parameter of inversion in particle sizing using light extinction method,” China Particuology 5(4), 295–299 (2007).
[Crossref]

Ren, Y. T.

B. Zhang, H. Qi, Y. T. Ren, S. C. Sun, and L. M. Ruan, “Application of homogenous continuous Ant Colony Optimization algorithm to inverse problem of one-dimensional coupled radiation and conduction heat transfer,” Int. J. Heat Mass Trans. 66, 507–516 (2013).
[Crossref]

Ren, Y.-T.

H. Qi, C.-Y. Niu, S. Gong, Y.-T. Ren, and L.-M. Ruan, “Application of the hybrid particle swarm optimization algorithms for simultaneous estimation of multi-parameters in a transient conduction-radiation problem,” Int. J. Heat Mass Trans. 83, 428–440 (2015).
[Crossref]

Ruan, L. M.

B. Zhang, H. Qi, S. C. Sun, L. M. Ruan, and H. P. Tan, “Solving inverse problems of radiative heat transfer and phase change in semitransparent medium by using Improved Quantum Particle Swarm Optimization,” Int. J. Heat Mass Trans. 85, 300–310 (2015).
[Crossref]

B. Zhang, H. Qi, Y. T. Ren, S. C. Sun, and L. M. Ruan, “Application of homogenous continuous Ant Colony Optimization algorithm to inverse problem of one-dimensional coupled radiation and conduction heat transfer,” Int. J. Heat Mass Trans. 66, 507–516 (2013).
[Crossref]

H. Qi, D. L. Wang, S. G. Wang, and L. M. Ruan, “Inverse transient radiation analysis in one-dimensional non-homogeneous participating slabs using particle swarm optimization algorithms,” J. Quant. Spectrosc. Ra. 112(15), 2507–2519 (2011).
[Crossref]

H. Qi, L. M. Ruan, S. G. Wang, M. Shi, and H. Zhao, “Application of multi-phase particle swarm optimization technique to retrieve the particle size distribution,” Chin. Opt. Lett. 6, 346–349 (2008).
[Crossref]

H. Qi, L. M. Ruan, H. C. Zhang, Y. M. Wang, and H. P. Tan, “Inverse radiation analysis of a one-dimensional participating slab by stochastic particle swarm optimizer algorithm,” Int. J. Therm. Sci. 46(7), 649–661 (2007).
[Crossref]

L. M. Ruan, H. Qi, W. An, and H. P. Tan, “Inverse radiation problem for determination of optical constants of fly-ash particles,” Int. J. Thermophys. 28(4), 1322–1341 (2007).
[Crossref]

Z. Z. He, H. Qi, Y. C. Yao, and L. M. Ruan, “Inverse estimation of the particle size distribution using the Fruit Fly Optimization Algorithm,” Appl. Therm. Eng.in press.

Ruan, L.-M.

H. Qi, C.-Y. Niu, S. Gong, Y.-T. Ren, and L.-M. Ruan, “Application of the hybrid particle swarm optimization algorithms for simultaneous estimation of multi-parameters in a transient conduction-radiation problem,” Int. J. Heat Mass Trans. 83, 428–440 (2015).
[Crossref]

Saeys, W.

Sanchez, R.

Schladitz, A.

S. Pfeifer, W. Birmili, A. Schladitz, T. Müller, A. Nowak, and A. Wiedensohler, “A fast and easy-to-implement inversion algorithm for mobility particle size spectrometers considering particle number size distribution information outside of the detection range,” Atmos. Meas. Tech. 7(1), 95–105 (2014).
[Crossref]

Serio, C.

Shang, Z.

M. Su, M. Xue, X. Cai, Z. Shang, and F. Xu, “Particle size characterization by ultrasonic attenuation spectra,” Particuology 6(4), 276–281 (2008).
[Crossref]

Shen, J.

M. Su, F. Xu, X. Cai, K. Ren, and J. Shen, “Optimization of regularization parameter of inversion in particle sizing using light extinction method,” China Particuology 5(4), 295–299 (2007).
[Crossref]

Shi, M.

Silva Neto, A. J.

S. Stephany, J. C. Becceneri, R. P. Souto, H. F. de Campos Velho, and A. J. Silva Neto, “A preregularization scheme for the reconstruction of a spatial dependent scattering albedo using a hybrid ant colony optimization implementation,” Appl. Math. Model. 34(3), 561–572 (2010).
[Crossref]

Souto, R. P.

S. Stephany, J. C. Becceneri, R. P. Souto, H. F. de Campos Velho, and A. J. Silva Neto, “A preregularization scheme for the reconstruction of a spatial dependent scattering albedo using a hybrid ant colony optimization implementation,” Appl. Math. Model. 34(3), 561–572 (2010).
[Crossref]

Stephany, S.

S. Stephany, J. C. Becceneri, R. P. Souto, H. F. de Campos Velho, and A. J. Silva Neto, “A preregularization scheme for the reconstruction of a spatial dependent scattering albedo using a hybrid ant colony optimization implementation,” Appl. Math. Model. 34(3), 561–572 (2010).
[Crossref]

Su, M.

M. Su, M. Xue, X. Cai, Z. Shang, and F. Xu, “Particle size characterization by ultrasonic attenuation spectra,” Particuology 6(4), 276–281 (2008).
[Crossref]

M. Su, F. Xu, X. Cai, K. Ren, and J. Shen, “Optimization of regularization parameter of inversion in particle sizing using light extinction method,” China Particuology 5(4), 295–299 (2007).
[Crossref]

Sun, S. C.

B. Zhang, H. Qi, S. C. Sun, L. M. Ruan, and H. P. Tan, “Solving inverse problems of radiative heat transfer and phase change in semitransparent medium by using Improved Quantum Particle Swarm Optimization,” Int. J. Heat Mass Trans. 85, 300–310 (2015).
[Crossref]

B. Zhang, H. Qi, Y. T. Ren, S. C. Sun, and L. M. Ruan, “Application of homogenous continuous Ant Colony Optimization algorithm to inverse problem of one-dimensional coupled radiation and conduction heat transfer,” Int. J. Heat Mass Trans. 66, 507–516 (2013).
[Crossref]

Sun, X.

Sun, Y. P.

Y. P. Sun, C. Lou, and H. C. Zhou, “Estimating soot volume fraction and temperature in flames using stochastic particle swarm optimization algorithm, Int. J. Heat Mass Trans. 54(1–3), 217–224 (2011).
[Crossref]

Takamura, T.

M. Tanaka, T. Nakajima, and T. Takamura, “Simultaneous determination of complex refractive index and size distribution of airborne and water-suspended particles from light scattering measurements,” J. Meteorol. Soc. Jpn. 60(6), 1259–1271 (1982).

Takano, Y.

Y. Takano and K. N. Liou, “Solar radiative transfer in cirrus clouds. Part I: Single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46(1), 3–19 (1989).
[Crossref]

Tan, H. P.

B. Zhang, H. Qi, S. C. Sun, L. M. Ruan, and H. P. Tan, “Solving inverse problems of radiative heat transfer and phase change in semitransparent medium by using Improved Quantum Particle Swarm Optimization,” Int. J. Heat Mass Trans. 85, 300–310 (2015).
[Crossref]

L. M. Ruan, H. Qi, W. An, and H. P. Tan, “Inverse radiation problem for determination of optical constants of fly-ash particles,” Int. J. Thermophys. 28(4), 1322–1341 (2007).
[Crossref]

H. Qi, L. M. Ruan, H. C. Zhang, Y. M. Wang, and H. P. Tan, “Inverse radiation analysis of a one-dimensional participating slab by stochastic particle swarm optimizer algorithm,” Int. J. Therm. Sci. 46(7), 649–661 (2007).
[Crossref]

Tanaka, M.

M. Tanaka, T. Nakajima, and T. Takamura, “Simultaneous determination of complex refractive index and size distribution of airborne and water-suspended particles from light scattering measurements,” J. Meteorol. Soc. Jpn. 60(6), 1259–1271 (1982).

Tang, H.

H. Tang and J. Lin, “Inversion of visible optical extinction data for spheroid particle size distribution based on PCA,” Optik 125(19), 5494–5507 (2014).
[Crossref]

X. Sun, H. Tang, and J. Dai, “Retrieval of particle size distribution in the dependent model using the moment method,” Opt. Express 15(18), 11507–11516 (2007).
[Crossref] [PubMed]

Tao, Z.

Tolbert, M. A.

K. J. Zarzana, C. D. Cappa, and M. A. Tolbert, “Sensitivity of aerosol refractive index retrievals using optical spectroscopy,” Aerosol Sci. Technol. 48(11), 1133–1144 (2014).
[Crossref]

Tsuta, M.

Uppaluri, R.

R. Das, S. C. Mishra, T. B. P. Kumar, and R. Uppaluri, “An inverse analysis for parameter estimation applied to a non-fourier conduction–radiation problem,” Heat Transf. Eng. 32(6), 455–466 (2011).
[Crossref]

R. Das, S. C. Mishra, M. Ajith, and R. Uppaluri, “An inverse analysis of a transient 2-D conduction–radiation problem using the lattice Boltzmann method and the finite volume method coupled with the genetic algorithm,” J. Quant. Spectrosc. Ra. 109(11), 2060–2077 (2008).
[Crossref]

Van Beers, R.

Wang, C. H.

C. H. Huang and C. H. Wang, “The design of uniform tube flow rates for Z-type compact parallel flow heat exchangers,” Int. J. Heat Mass Trans. 57(2), 608–622 (2013).
[Crossref]

Wang, D. L.

H. Qi, D. L. Wang, S. G. Wang, and L. M. Ruan, “Inverse transient radiation analysis in one-dimensional non-homogeneous participating slabs using particle swarm optimization algorithms,” J. Quant. Spectrosc. Ra. 112(15), 2507–2519 (2011).
[Crossref]

Wang, L.

Wang, S.

Wang, S. G.

H. Qi, D. L. Wang, S. G. Wang, and L. M. Ruan, “Inverse transient radiation analysis in one-dimensional non-homogeneous participating slabs using particle swarm optimization algorithms,” J. Quant. Spectrosc. Ra. 112(15), 2507–2519 (2011).
[Crossref]

H. Qi, L. M. Ruan, S. G. Wang, M. Shi, and H. Zhao, “Application of multi-phase particle swarm optimization technique to retrieve the particle size distribution,” Chin. Opt. Lett. 6, 346–349 (2008).
[Crossref]

Wang, Y. M.

H. Qi, L. M. Ruan, H. C. Zhang, Y. M. Wang, and H. P. Tan, “Inverse radiation analysis of a one-dimensional participating slab by stochastic particle swarm optimizer algorithm,” Int. J. Therm. Sci. 46(7), 649–661 (2007).
[Crossref]

Wang, Z.

Watté, R.

Wiedensohler, A.

S. Pfeifer, W. Birmili, A. Schladitz, T. Müller, A. Nowak, and A. Wiedensohler, “A fast and easy-to-implement inversion algorithm for mobility particle size spectrometers considering particle number size distribution information outside of the detection range,” Atmos. Meas. Tech. 7(1), 95–105 (2014).
[Crossref]

Wu, X.

Wu, Y.

Xu, F.

M. Su, M. Xue, X. Cai, Z. Shang, and F. Xu, “Particle size characterization by ultrasonic attenuation spectra,” Particuology 6(4), 276–281 (2008).
[Crossref]

M. Su, F. Xu, X. Cai, K. Ren, and J. Shen, “Optimization of regularization parameter of inversion in particle sizing using light extinction method,” China Particuology 5(4), 295–299 (2007).
[Crossref]

Xu, Y.

Xue, M.

M. Su, M. Xue, X. Cai, Z. Shang, and F. Xu, “Particle size characterization by ultrasonic attenuation spectra,” Particuology 6(4), 276–281 (2008).
[Crossref]

Yang, J.

Yao, Y. C.

Z. Z. He, H. Qi, Y. C. Yao, and L. M. Ruan, “Inverse estimation of the particle size distribution using the Fruit Fly Optimization Algorithm,” Appl. Therm. Eng.in press.

Ye, M.

Zamora-Rojas, E.

Zarzana, K. J.

K. J. Zarzana, C. D. Cappa, and M. A. Tolbert, “Sensitivity of aerosol refractive index retrievals using optical spectroscopy,” Aerosol Sci. Technol. 48(11), 1133–1144 (2014).
[Crossref]

Zhang, B.

B. Zhang, H. Qi, S. C. Sun, L. M. Ruan, and H. P. Tan, “Solving inverse problems of radiative heat transfer and phase change in semitransparent medium by using Improved Quantum Particle Swarm Optimization,” Int. J. Heat Mass Trans. 85, 300–310 (2015).
[Crossref]

B. Zhang, H. Qi, Y. T. Ren, S. C. Sun, and L. M. Ruan, “Application of homogenous continuous Ant Colony Optimization algorithm to inverse problem of one-dimensional coupled radiation and conduction heat transfer,” Int. J. Heat Mass Trans. 66, 507–516 (2013).
[Crossref]

Zhang, H. C.

H. Qi, L. M. Ruan, H. C. Zhang, Y. M. Wang, and H. P. Tan, “Inverse radiation analysis of a one-dimensional participating slab by stochastic particle swarm optimizer algorithm,” Int. J. Therm. Sci. 46(7), 649–661 (2007).
[Crossref]

Zhang, X.

Zhao, D.

Zhao, H.

Zhou, B.

Zhou, H. C.

Y. P. Sun, C. Lou, and H. C. Zhou, “Estimating soot volume fraction and temperature in flames using stochastic particle swarm optimization algorithm, Int. J. Heat Mass Trans. 54(1–3), 217–224 (2011).
[Crossref]

Zhu, Z.

Aerosol Sci. Technol. (1)

K. J. Zarzana, C. D. Cappa, and M. A. Tolbert, “Sensitivity of aerosol refractive index retrievals using optical spectroscopy,” Aerosol Sci. Technol. 48(11), 1133–1144 (2014).
[Crossref]

Appl. Artif. Intell. (1)

M. A. Behrang, E. Assareh, M. R. Assari, and A. Ghanbarzadeh, “Assessment of electricity demand in Iran’s industrial sector using different intelligent optimization techniques,” Appl. Artif. Intell. 25(4), 292–304 (2011).
[Crossref]

Appl. Math. Model. (1)

S. Stephany, J. C. Becceneri, R. P. Souto, H. F. de Campos Velho, and A. J. Silva Neto, “A preregularization scheme for the reconstruction of a spatial dependent scattering albedo using a hybrid ant colony optimization implementation,” Appl. Math. Model. 34(3), 561–572 (2010).
[Crossref]

Appl. Opt. (3)

Atmos. Meas. Tech. (1)

S. Pfeifer, W. Birmili, A. Schladitz, T. Müller, A. Nowak, and A. Wiedensohler, “A fast and easy-to-implement inversion algorithm for mobility particle size spectrometers considering particle number size distribution information outside of the detection range,” Atmos. Meas. Tech. 7(1), 95–105 (2014).
[Crossref]

Biogeosciences (1)

D. Doxaran, J. Ehn, S. Bélanger, A. Matsuoka, S. Hooker, and M. Babin, “Optical characterisation of suspended particles in the Mackenzie River plume (Canadian Arctic Ocean) and implications for ocean colour remote sensing,” Biogeosciences 9(8), 3213–3229 (2012).
[Crossref]

Chin. Opt. Lett. (1)

China Particuology (1)

M. Su, F. Xu, X. Cai, K. Ren, and J. Shen, “Optimization of regularization parameter of inversion in particle sizing using light extinction method,” China Particuology 5(4), 295–299 (2007).
[Crossref]

Found. Trends Mach. Learn. (1)

S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Found. Trends Mach. Learn. 3(1), 1–122 (2010).
[Crossref]

Heat Transf. Eng. (1)

R. Das, S. C. Mishra, T. B. P. Kumar, and R. Uppaluri, “An inverse analysis for parameter estimation applied to a non-fourier conduction–radiation problem,” Heat Transf. Eng. 32(6), 455–466 (2011).
[Crossref]

Int. J. Heat Mass Trans. (5)

C. H. Huang and C. H. Wang, “The design of uniform tube flow rates for Z-type compact parallel flow heat exchangers,” Int. J. Heat Mass Trans. 57(2), 608–622 (2013).
[Crossref]

Y. P. Sun, C. Lou, and H. C. Zhou, “Estimating soot volume fraction and temperature in flames using stochastic particle swarm optimization algorithm, Int. J. Heat Mass Trans. 54(1–3), 217–224 (2011).
[Crossref]

B. Zhang, H. Qi, S. C. Sun, L. M. Ruan, and H. P. Tan, “Solving inverse problems of radiative heat transfer and phase change in semitransparent medium by using Improved Quantum Particle Swarm Optimization,” Int. J. Heat Mass Trans. 85, 300–310 (2015).
[Crossref]

B. Zhang, H. Qi, Y. T. Ren, S. C. Sun, and L. M. Ruan, “Application of homogenous continuous Ant Colony Optimization algorithm to inverse problem of one-dimensional coupled radiation and conduction heat transfer,” Int. J. Heat Mass Trans. 66, 507–516 (2013).
[Crossref]

H. Qi, C.-Y. Niu, S. Gong, Y.-T. Ren, and L.-M. Ruan, “Application of the hybrid particle swarm optimization algorithms for simultaneous estimation of multi-parameters in a transient conduction-radiation problem,” Int. J. Heat Mass Trans. 83, 428–440 (2015).
[Crossref]

Int. J. Therm. Sci. (1)

H. Qi, L. M. Ruan, H. C. Zhang, Y. M. Wang, and H. P. Tan, “Inverse radiation analysis of a one-dimensional participating slab by stochastic particle swarm optimizer algorithm,” Int. J. Therm. Sci. 46(7), 649–661 (2007).
[Crossref]

Int. J. Thermophys. (1)

L. M. Ruan, H. Qi, W. An, and H. P. Tan, “Inverse radiation problem for determination of optical constants of fly-ash particles,” Int. J. Thermophys. 28(4), 1322–1341 (2007).
[Crossref]

J. Atmos. Sci. (1)

Y. Takano and K. N. Liou, “Solar radiative transfer in cirrus clouds. Part I: Single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46(1), 3–19 (1989).
[Crossref]

J. Meteorol. Soc. Jpn. (1)

M. Tanaka, T. Nakajima, and T. Takamura, “Simultaneous determination of complex refractive index and size distribution of airborne and water-suspended particles from light scattering measurements,” J. Meteorol. Soc. Jpn. 60(6), 1259–1271 (1982).

J. Quant. Spectrosc. Ra. (5)

L. Pilon, H. Berberoğlu, and R. Kandilian, “Radiation transfer in photobiological carbon dioxide fixation and fuel production by microalgae,” J. Quant. Spectrosc. Ra. 112(17), 2639–2660 (2011).
[Crossref]

H. Qi, D. L. Wang, S. G. Wang, and L. M. Ruan, “Inverse transient radiation analysis in one-dimensional non-homogeneous participating slabs using particle swarm optimization algorithms,” J. Quant. Spectrosc. Ra. 112(15), 2507–2519 (2011).
[Crossref]

K. W. Kim and S. W. Baek, “Efficient inverse radiation analysis in a cylindrical geometry using a combined method of hybrid genetic algorithm and finite difference Newton method,” J. Quant. Spectrosc. Ra. 108(3), 423–439 (2007).
[Crossref]

R. Das, S. C. Mishra, M. Ajith, and R. Uppaluri, “An inverse analysis of a transient 2-D conduction–radiation problem using the lattice Boltzmann method and the finite volume method coupled with the genetic algorithm,” J. Quant. Spectrosc. Ra. 109(11), 2060–2077 (2008).
[Crossref]

E. Lee, R. L. Heng, and L. Pilon, “Spectral optical properties of selected photo synthetic microalgae producing biofuels,” J. Quant. Spectrosc. Ra. 114, 122–135 (2013).
[Crossref]

Opt. Express (5)

Optik (1)

H. Tang and J. Lin, “Inversion of visible optical extinction data for spheroid particle size distribution based on PCA,” Optik 125(19), 5494–5507 (2014).
[Crossref]

Particuology (1)

M. Su, M. Xue, X. Cai, Z. Shang, and F. Xu, “Particle size characterization by ultrasonic attenuation spectra,” Particuology 6(4), 276–281 (2008).
[Crossref]

Prog. Phys. Geogr. (1)

K. D. Kanniah, J. Beringer, P. North, and L. Hutley, “Control of atmospheric particles on diffuse radiation and terrestrial plant productivity A review,” Prog. Phys. Geogr. 36(2), 209–237 (2012).
[Crossref]

Other (3)

Z. Z. He, H. Qi, Y. C. Yao, and L. M. Ruan, “Inverse estimation of the particle size distribution using the Fruit Fly Optimization Algorithm,” Appl. Therm. Eng.in press.

M. F. Modest, Radiative Heat Transfer (Elsevier, 2003).

C. F. Bohren and D. R. Huffman, Absorption and scattering of light by small particles (John Wiley & Sons, 2008)

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 (6)

Fig. 1
Fig. 1 The schematic of a 1-D slab absorbing, scattering, but non-emitting particle system exposed to collimated continuous wave laser. The signals that need to be measured include: the diffuse reflectance (R), diffuse transmittance (T), and collimated transmittance (T c).
Fig. 2
Fig. 2 The sensitivity coefficients of (a) n, (b) k, (c) D ¯ , and (d) σ under different thicknesses. The PSDs for R-R, S-N, and L-N distributions are (8.3, 5.6), (5.2, 4.5), and (6.1, 3.4), respectively. Note that the sensitivity coefficients of the PSDs are much lower than those of the complex refractive index.
Fig. 3
Fig. 3 The retrieved results of (a) n, (b) k, (c) D ¯ , and (d) σ for each independent run.
Fig. 4
Fig. 4 The sensitivity coefficients of the collimated transmittance to (a) n and k, and (b) PSDs for different thicknesses.
Fig. 5
Fig. 5 The flowchart for the whole optimization procedure.
Fig. 6
Fig. 6 The retrieved results of the PSDs: (a) volume frequency distribution, and (b) relative error. The legends ‘1st’ and ‘2nd’ correspond to the results of the first and second optimization. The description ‘Ori’ in (a) denotes the original distribution of the particle size.

Tables (4)

Tables Icon

Table 1 Original Value of PSDs

Tables Icon

Table 2 Control Parameters of QPSO

Tables Icon

Table 3 Retrieved Results of the Complex Refractive Index and PSDs

Tables Icon

Table 4 Retrieved Results for the PSDs

Equations (10)

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

I ( x , θ ) x = β λ I ( x , θ ) + σ s λ 2 0 π I ( x , θ ) Φ λ ( θ , θ ) sin θ d θ ,
κ λ = 0 C a λ ( D ) N ( D ) d D ,
σ s λ = 0 C s λ ( D ) N ( D ) d D ,
f R-R ( D ) = σ D ¯ × ( D D ¯ ) σ 1 × exp [ ( D D ¯ ) σ ] ,
f S-N ( D ) = 1 2 π σ × exp [ ( D D ¯ ) 2 2 σ 2 ] ,
f L-N ( D ) = 1 2 π D ln σ × exp [ ( ln D ln D ¯ ) 2 2 ( ln σ ) 2 ] ,
F obj = i = 1 2 j = 1 2 { [ R est ( L i , λ j ) R mea ( L i , λ j ) R mea ( L i , λ j ) ] 2 + [ T est ( L i , λ j ) T mea ( L i , λ j ) T mea ( L i , λ j ) ] 2 } ,
S m i ( ρ ) = ρ m i | m i = m 0 = ρ ( m 0 + m 0 Δ ) ρ ( m 0 m 0 Δ ) 2 m 0 Δ ,
ε rel = | z est z ori | z ori × 100 % ,
F obj = i = 1 2 j = 1 2 { [ T c, est ( L i , λ j ) T c, mea ( L i , λ j ) T c, mea ( L i , λ j ) ] 2 } ,

Metrics