Abstract

A new technique is developed to retrieve the fractal dimension and size distribution of soot aggregates simultaneously from the relative intensities of multi-wavelength angular-resolved light scattering. Compared with other techniques, the main advantage of this method is its independence of knowing complex refractive index, number density of aggregate, fractal prefactor and primary particle diameter. The forward light scattering procedure of soot aggregate is described by Rayleigh-Debye-Gans polydisperse fractal aggregate (RDG-PFA) scattering theory, and the retrieval process is performed by using the covariance matrix adaption-evolution strategy algorithm (CMA-ES). Three different measurement models, i.e. absolute scattering and transmittance, absolute scattering, relative scattering (RS), are investigated in present research. Numerical experiments have been performed to test the feasibility of the CMA-ES algorithm. Combined with the multi-wavelength RDG-PFA strategy, the retrieval accuracy of soot aggregate size distribution is proved to be more effectively by using the RS model. Satisfactory results under 10% Gaussian measurement noise have demonstrated the feasibility of the proposed method.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (5)

J. Luo, Y. Zhang, Q. Zhang, F. Wang, J. Liu, and J. Wang, “Sensitivity analysis of morphology on radiative properties of soot aerosols,” Opt. Express 26(10), A420–A432 (2018).
[Crossref] [PubMed]

J. Y. Zhang, H. Qi, Y. T. Ren, and L. M. Ruan, “Simultaneous identification of optical constants and PSD of spherical particles by multi-wavelength scattering–transmittance measurement,” Opt. Commun. 413, 317–328 (2018).
[Crossref]

O. B. Ericok and H. Erturk, “Optical characterization limits of nanoparticle aggregates at different wavelengths using approximate Bayesian computation,” J. Quant. Spectrosco. Ra. 213, 113–118 (2018).
[Crossref]

J. Luo, Y. Zhang, F. Wang, J. Wang, and Q. Zhang, “Applying machine learning to estimate the optical properties of black carbon fractal aggregates,” J. Quant. Spectrosc. Ra. 215, 1–8 (2018).
[Crossref]

O. B. Ericok, A. T. Cemgil, and H. Erturk, “Approximate Bayesian computation techniques for optical characterization of nanoparticle clusters,” J. Opt. Soc. Am. A 35(1), 88–97 (2018).
[Crossref] [PubMed]

2017 (5)

Z. He, J. Mao, and X. Han, “Non-parametric estimation of particle size distribution from spectral extinction data with PCA approach,” Powder Technol. 325, 510 (2017).

J. Cai, X. Hu, B. Xiao, Y. Zhou, and W. Wei, ““Recent developments on fractal-based approaches to nanofluids and nanoparticle aggregation,” Int,” J. Heat Mass Tran. 105, 623–637 (2017).
[Crossref]

S. Talebi, P. J. Hadwin, and K. J. Daun, “Soot aggregate sizing through multiangle elastic light scattering: Influence of model error,” J. Aerosol Sci. 111, 36–50 (2017).
[Crossref]

M. Sirignano, D. Bartos, M. Conturso, M. Dunn, A. D’Anna, and A. R. Masri, “Detection of nanostructures and soot in laminar premixed flames,” Combust. Flame 176, 299–308 (2017).
[Crossref]

R. Mansmann, K. Thomson, G. Smallwood, T. Dreier, and C. Schulz, “Sequential signal detection for high dynamic range time-resolved laser-induced incandescence,” Opt. Express 25(3), 2413–2421 (2017).
[Crossref] [PubMed]

2016 (5)

G. Okyay, E. Héripré, T. Reiss, P. Haghi-Ashtiani, T. Auger, and F. Enguehard, “Soot aggregate complex morphology: 3D geometry reconstruction by SEM tomography applied on soot issued from propane combustion,” J. Aerosol Sci. 93, 63–79 (2016).
[Crossref]

M. L. Botero, E. M. Adkins, S. González-Calera, H. Miller, and M. Kraft, “PAH structure analysis of soot in a non-premixed flame using high-resolution transmission electron microscopy and optical band gap analysis,” Combust. Flame 164, 250–258 (2016).
[Crossref]

T. R. Meyer, B. R. Halls, N. Jiang, M. N. Slipchenko, S. Roy, and J. R. Gord, “High-speed, three-dimensional tomographic laser-induced incandescence imaging of soot volume fraction in turbulent flames,” Opt. Express 24(26), 29547–29555 (2016).
[Crossref] [PubMed]

H. Qi, Z. Z. He, F. Z. Zhao, and L. M. Ruan, “Determination of the spectral complex refractive indices of microalgae cells by light reflectance-transmittance measurement,” Int. J. Hydrogen Energy 41(9), 4941–4956 (2016).
[Crossref]

F. J. T. Huber, S. Will, and K. J. Daun, “Sizing aerosolized fractal nanoparticle aggregates through Bayesian analysis of wide-angle light scattering (WALS) data,” J. Quant. Spectrosco. Ra. 184, 27–39 (2016).
[Crossref]

2015 (4)

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 Tran. 85(1), 300–310 (2015).
[Crossref]

F. A. Otero, H. R. B. Orlande, G. L. Frontini, and G. E. Eliçabe, “Bayesian approach to the inverse problem in a light scattering application,” J. Appl. Stat. 42(5), 994–1016 (2015).
[Crossref]

A. Pandey, R. K. Chakrabarty, L. Liu, and M. I. Mishchenko, “Empirical relationships between optical properties and equivalent diameters of fractal soot aggregates at 550 nm wavelength,” Opt. Express 23(24), A1354–A1362 (2015).
[Crossref] [PubMed]

J. Yon, A. Bescond, and F. Liu, “On the radiative properties of soot aggregates part 1: Necking and overlapping,” J. Quant. Spectrosco. Ra. 162, 197–206 (2015).
[Crossref]

2014 (1)

A. J. A. Smith and R. G. Grainger, “Simplifying the calculation of light scattering properties for black carbon fractal aggregates,” Atmos. Chem. Phys. 14(15), 7825–7836 (2014).
[Crossref]

2013 (5)

C. Caumont-Prim, J. Yon, A. Coppalle, F. X. Ouf, and K. F. Ren, “Measurement of aggregates’ size distribution by angular light scattering,” J. Quant. Spectrosco. Ra. 126(S1), 140–149 (2013).
[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 Tran. 66(3), 507–516 (2013).
[Crossref]

T. Geijtenbeek, M. V. D. Panne, and A. F. V. D. Stappen, “Flexible muscle-based locomotion for bipedal creatures,” ACM Trans. Graphic. 32(6), 1–11 (2013).
[Crossref]

P. Desgroux, X. Mercier, and K. A. Thomson, “Study of the formation of soot and its precursors in flames using optical diagnostics,” Proc. Combust. Inst. 34(1), 1713–1738 (2013).
[Crossref]

S. China, C. Mazzoleni, K. Gorkowski, A. C. Aiken, and M. K. Dubey, “Morphology and mixing state of individual freshly emitted wildfire carbonaceous particles,” Nat. Commun. 4, 2122 (2013).
[Crossref] [PubMed]

2012 (5)

H. Oltmann, J. Reimann, and S. Will, “Single-shot measurement of soot aggregate sizes by wide-angle light scattering (WALS),” Appl. Phys. B. 106(1), 171–183 (2012).
[Crossref]

M. Kashif, J. Bonnety, P. Guibert, C. Morin, and G. Legros, “Soot volume fraction fields in unsteady axis-symmetric flames by continuous laser extinction technique,” Opt. Express 20(27), 28742–28751 (2012).
[Crossref] [PubMed]

D. W. Burr, K. J. Daun, K. A. Thomson, and G. J. Smallwood, “Optimization of measurement angles for soot aggregate sizing by elastic light scattering, through design-of-experiment theory,” J. Quant. Spectrosco. Ra. 113(5), 355–365 (2012).
[Crossref]

Q. Niu, Z. Zhou, H. Y. Zhang, and J. Deng, “An Improved Quantum-Behaved Particle Swarm Optimization Method for Economic Dispatch Problems with Multiple Fuel Options and Valve-Points Effects,” Energies 5(9), 240–250 (2012).
[Crossref]

R. Charnigo, M. Francoeur, P. Kenkel, M. P. Menguc, B. Hall, and C. Srinivasan, “Credible intervals for nanoparticle characteristics,” J. Quant. Spectrosco. Ra. 113(2), 182–193 (2012).
[Crossref]

2011 (6)

D. W. Burr, K. J. Daun, O. Link, K. A. Thomson, and G. J. Smallwood, “Determination of the soot aggregate size distribution from elastic light scattering through Bayesian inference,” J. Quant. Spectrosco. Ra. 112(6), 1099–1107 (2011).
[Crossref]

L. A. Clementi, J. R. Vega, L. M. Gugliotta, and H. R. B. Orlande, “A Bayesian Inversion Method for Estimating the Particle Size Distribution of Latexes from Multiangle Dynamic Light Scattering Measurements,” Chemometr. Intell. Lab. 107(1), 165–173 (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 Tran. 54(1), 217–224 (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. Spectrosco. Ra. 112(15), 2507–2519 (2011).
[Crossref]

A. R. Coderre, K. A. Thomson, D. R. Snelling, and M. R. Johnson, “Spectrally resolved light absorption properties of cooled soot from a methane flame,” Appl. Phys. B. 104(1), 175–188 (2011).
[Crossref]

O. Link, D. R. Snelling, K. A. Thomson, and G. J. Smallwood, “Development of absolute intensity multi-angle light scattering for the determination of polydisperse soot aggregate properties,” Proc. Combust. Inst. 33(1), 847–854 (2011).
[Crossref]

2010 (5)

F. X. Ouf, J. Yon, P. Ausset, A. Coppalle, and M. Maillé, “Influence of Sampling and Storage Protocol on Fractal Morphology of Soot Studied by Transmission Electron Microscopy,” Aerosol Sci. Technol. 44(11), 1005–1017 (2010).
[Crossref]

T. J. Grahame and R. B. Schlesinger, “Cardiovascular health and particulate vehicular emissions: a critical evaluation of the evidence,” Air Qual. Atmos. Health 3(1), 3–27 (2010).
[Crossref] [PubMed]

H. Oltmann, J. Reimann, and S. Will, “Wide-angle light scattering (WALS) for soot aggregate characterization,” Combust. Flame 157(3), 516–522 (2010).
[Crossref]

L. D. S. Coelho, “Gaussian quantum-behaved particle swarm optimization approaches for constrained engineering design problems,” Expert Syst. Appl. 37(2), 1676–1683 (2010).
[Crossref]

M. Kahnert, “Modelling the optical and radiative properties of freshly emitted light absorbing carbon within an atmospheric chemical transport model,” Atmos. Chem. Phys. 10(3), 1403–1416 (2010).
[Crossref]

2008 (3)

F. Liu, K. A. Thomson, and G. J. Smallwood, “Effects of soot absorption and scattering on LII intensities in laminar coflow diffusion flames,” J. Quant. Spectrosco. Ra. 109(2), 337–348 (2008).
[Crossref]

K. J. Daun, G. J. Smallwood, and F. Liu, “Investigation of Thermal Accommodation Coefficients in Time-Resolved Laser-Induced Incandescence,” J. Heat Trans-Transf. 130(12), 320–327 (2008).
[Crossref]

V. Ramanathan and G. Carmichael, “Global and regional climate changes due to black carbon,” Nat. Geosci. 36, 335–358 (2008).
[Crossref]

2007 (2)

R. K. Chakrabarty, H. Moosmüller, W. P. Arnott, M. A. Garro, J. G. Slowik, E. S. Cross, J.-H. Han, P. Davidovits, T. B. Onasch, and D. R. Worsnop, “Light scattering and absorption by fractal-like carbonaceous chain aggregates: comparison of theories and experiment,” Appl. Opt. 46(28), 6990–7006 (2007).
[Crossref] [PubMed]

H. A. Michelsen, F. Liu, B. F. Kock, H. Bladh, A. Boiarciuc, M. Charwath, T. Dreier, R. Hadef, M. Hofmann, J. Reimann, S. Will, P. E. Bengtsson, H. Bockhorn, F. Foucher, K. P. Geigle, C. Mounaïm-Rousselle, C. Schulz, R. Stirn, B. Tribalet, and R. Suntz, “Modeling laser-induced incandescence of soot: a summary and comparison of LII models,” Appl. Phys. B. 87(3), 503–521 (2007).
[Crossref]

2006 (3)

C. Schulz, B. F. Kock, M. Hofmann, H. Michelsen, S. Will, R. Suntz, and G. Smallwood, “Laser-induced incandescence: recent trends and current questions,” Appl. Phys. B. 83(3), 333–354 (2006).
[Crossref]

T. C. Bond and R. W. Bergstrom, “Light Absorption by Carbonaceous Particles: An Investigative Review,” Aerosol Sci. Technol. 40(1), 27–67 (2006).
[Crossref]

N. Hansen, “The CMA Evolution Strategy: A Comparing Review,” Stud Fuzz. Soft Comput. 192, 75–102 (2006).

2005 (2)

Y. Deng, R. Hu, Q. Luo, and Q. Lu, “Float genetic algorithm for determination of particle size distribution and refractive index in polarized LSS,” Proc. SPIE 5693, 10–16 (2005).
[Crossref]

B. Yang and Ü. Ö. Köylü, “Detailed soot field in a turbulent non-premixed ethylene/air flame from laser scattering and extinction experiments,” Combust. Flame 141(1), 55–65 (2005).
[Crossref]

2004 (1)

2003 (1)

2001 (2)

C. M. Sorensen, “Light Scattering by Fractal Aggregates: A Review,” Aerosol Sci. Technol. 35(2), 648–687 (2001).
[Crossref]

N. Hansen and A. Ostermeier, “Completely derandomized self-adaptation in evolution strategies,” Evol. Comput. 9(2), 159–195 (2001).
[Crossref] [PubMed]

1999 (1)

R. L. V. Wal, T. M. Ticich, and A. B. Stephens, “Can soot primary particle size be determined using laser-induced incandescence?” Combust. Flame 116(1–2), 291–296 (1999).

1997 (1)

Ü. Ö. Köylü, “Quantitative analysis of in situ optical diagnostics for inferring particle/aggregate parameters in flames: Implications for soot surface growth and total emissivity,” Combust. Flame 109(3), 488–500 (1997).
[Crossref]

1996 (2)

T. L. Farias, U. Ö. Köylü, and M. G. Carvalho, “Range of validity of the Rayleigh-Debye-Gans theory for optics of fractal aggregates,” Appl. Opt. 35(33), 6560–6567 (1996).
[Crossref] [PubMed]

K. C. Smyth and C. R. Shaddix, “The elusive history of m∼= 1.57 – 0.56i for the refractive index of soot,” Combust. Flame 107(3), 314–320 (1996).
[Crossref]

1994 (1)

A. Ostermeier, A. Gawelczyk, and N. Hansen, “A Derandomized Approach to Self-Adaptation of Evolution Strategies,” Evol. Comput. 2(4), 369–380 (1994).
[Crossref]

1992 (2)

Ü. Ö. Köylü and G. M. Faeth, “Structure of overfire soot in buoyant turbulent diffusion flames at long residence times,” Combust. Flame 89(2), 140–156 (1992).
[Crossref]

C. M. Sorensen, J. Cai, and N. Lu, “Light-scattering measurements of monomer size, monomers per aggregate, and fractal dimension for soot aggregates in flames,” Appl. Opt. 31(30), 6547–6557 (1992).
[Crossref] [PubMed]

1991 (1)

1990 (1)

M. Y. Lin, R. Klein, H. M. Lindsay, D. A. Weitz, R. C. Ball, and P. Meakin, “The Structure of Fractal Colloidal Aggregates of Finite Extent,” J. Colloid Interface Sci. 137(1), 263–280 (1990).
[Crossref]

Adkins, E. M.

M. L. Botero, E. M. Adkins, S. González-Calera, H. Miller, and M. Kraft, “PAH structure analysis of soot in a non-premixed flame using high-resolution transmission electron microscopy and optical band gap analysis,” Combust. Flame 164, 250–258 (2016).
[Crossref]

Aiken, A. C.

S. China, C. Mazzoleni, K. Gorkowski, A. C. Aiken, and M. K. Dubey, “Morphology and mixing state of individual freshly emitted wildfire carbonaceous particles,” Nat. Commun. 4, 2122 (2013).
[Crossref] [PubMed]

Arnott, W. P.

Auger, T.

G. Okyay, E. Héripré, T. Reiss, P. Haghi-Ashtiani, T. Auger, and F. Enguehard, “Soot aggregate complex morphology: 3D geometry reconstruction by SEM tomography applied on soot issued from propane combustion,” J. Aerosol Sci. 93, 63–79 (2016).
[Crossref]

Ausset, P.

F. X. Ouf, J. Yon, P. Ausset, A. Coppalle, and M. Maillé, “Influence of Sampling and Storage Protocol on Fractal Morphology of Soot Studied by Transmission Electron Microscopy,” Aerosol Sci. Technol. 44(11), 1005–1017 (2010).
[Crossref]

Ball, R. C.

M. Y. Lin, R. Klein, H. M. Lindsay, D. A. Weitz, R. C. Ball, and P. Meakin, “The Structure of Fractal Colloidal Aggregates of Finite Extent,” J. Colloid Interface Sci. 137(1), 263–280 (1990).
[Crossref]

Bartos, D.

M. Sirignano, D. Bartos, M. Conturso, M. Dunn, A. D’Anna, and A. R. Masri, “Detection of nanostructures and soot in laminar premixed flames,” Combust. Flame 176, 299–308 (2017).
[Crossref]

Bengtsson, P. E.

H. A. Michelsen, F. Liu, B. F. Kock, H. Bladh, A. Boiarciuc, M. Charwath, T. Dreier, R. Hadef, M. Hofmann, J. Reimann, S. Will, P. E. Bengtsson, H. Bockhorn, F. Foucher, K. P. Geigle, C. Mounaïm-Rousselle, C. Schulz, R. Stirn, B. Tribalet, and R. Suntz, “Modeling laser-induced incandescence of soot: a summary and comparison of LII models,” Appl. Phys. B. 87(3), 503–521 (2007).
[Crossref]

Bergstrom, R. W.

T. C. Bond and R. W. Bergstrom, “Light Absorption by Carbonaceous Particles: An Investigative Review,” Aerosol Sci. Technol. 40(1), 27–67 (2006).
[Crossref]

Bescond, A.

J. Yon, A. Bescond, and F. Liu, “On the radiative properties of soot aggregates part 1: Necking and overlapping,” J. Quant. Spectrosco. Ra. 162, 197–206 (2015).
[Crossref]

Bladh, H.

H. A. Michelsen, F. Liu, B. F. Kock, H. Bladh, A. Boiarciuc, M. Charwath, T. Dreier, R. Hadef, M. Hofmann, J. Reimann, S. Will, P. E. Bengtsson, H. Bockhorn, F. Foucher, K. P. Geigle, C. Mounaïm-Rousselle, C. Schulz, R. Stirn, B. Tribalet, and R. Suntz, “Modeling laser-induced incandescence of soot: a summary and comparison of LII models,” Appl. Phys. B. 87(3), 503–521 (2007).
[Crossref]

Bockhorn, H.

H. A. Michelsen, F. Liu, B. F. Kock, H. Bladh, A. Boiarciuc, M. Charwath, T. Dreier, R. Hadef, M. Hofmann, J. Reimann, S. Will, P. E. Bengtsson, H. Bockhorn, F. Foucher, K. P. Geigle, C. Mounaïm-Rousselle, C. Schulz, R. Stirn, B. Tribalet, and R. Suntz, “Modeling laser-induced incandescence of soot: a summary and comparison of LII models,” Appl. Phys. B. 87(3), 503–521 (2007).
[Crossref]

T. Lehre, B. Jungfleisch, R. Suntz, and H. Bockhorn, “Size distributions of nanoscaled particles and gas temperatures from time-resolved laser-induced-incandescence measurements,” Appl. Opt. 42(12), 2021–2030 (2003).
[Crossref] [PubMed]

Boiarciuc, A.

H. A. Michelsen, F. Liu, B. F. Kock, H. Bladh, A. Boiarciuc, M. Charwath, T. Dreier, R. Hadef, M. Hofmann, J. Reimann, S. Will, P. E. Bengtsson, H. Bockhorn, F. Foucher, K. P. Geigle, C. Mounaïm-Rousselle, C. Schulz, R. Stirn, B. Tribalet, and R. Suntz, “Modeling laser-induced incandescence of soot: a summary and comparison of LII models,” Appl. Phys. B. 87(3), 503–521 (2007).
[Crossref]

Bond, T. C.

T. C. Bond and R. W. Bergstrom, “Light Absorption by Carbonaceous Particles: An Investigative Review,” Aerosol Sci. Technol. 40(1), 27–67 (2006).
[Crossref]

Bonnety, J.

Botero, M. L.

M. L. Botero, E. M. Adkins, S. González-Calera, H. Miller, and M. Kraft, “PAH structure analysis of soot in a non-premixed flame using high-resolution transmission electron microscopy and optical band gap analysis,” Combust. Flame 164, 250–258 (2016).
[Crossref]

Burr, D. W.

D. W. Burr, K. J. Daun, K. A. Thomson, and G. J. Smallwood, “Optimization of measurement angles for soot aggregate sizing by elastic light scattering, through design-of-experiment theory,” J. Quant. Spectrosco. Ra. 113(5), 355–365 (2012).
[Crossref]

D. W. Burr, K. J. Daun, O. Link, K. A. Thomson, and G. J. Smallwood, “Determination of the soot aggregate size distribution from elastic light scattering through Bayesian inference,” J. Quant. Spectrosco. Ra. 112(6), 1099–1107 (2011).
[Crossref]

Cai, J.

J. Cai, X. Hu, B. Xiao, Y. Zhou, and W. Wei, ““Recent developments on fractal-based approaches to nanofluids and nanoparticle aggregation,” Int,” J. Heat Mass Tran. 105, 623–637 (2017).
[Crossref]

C. M. Sorensen, J. Cai, and N. Lu, “Light-scattering measurements of monomer size, monomers per aggregate, and fractal dimension for soot aggregates in flames,” Appl. Opt. 31(30), 6547–6557 (1992).
[Crossref] [PubMed]

Carmichael, G.

V. Ramanathan and G. Carmichael, “Global and regional climate changes due to black carbon,” Nat. Geosci. 36, 335–358 (2008).
[Crossref]

Carvalho, M. G.

Caumont-Prim, C.

C. Caumont-Prim, J. Yon, A. Coppalle, F. X. Ouf, and K. F. Ren, “Measurement of aggregates’ size distribution by angular light scattering,” J. Quant. Spectrosco. Ra. 126(S1), 140–149 (2013).
[Crossref]

Cemgil, A. T.

Chakrabarty, R. K.

Charnigo, R.

R. Charnigo, M. Francoeur, P. Kenkel, M. P. Menguc, B. Hall, and C. Srinivasan, “Credible intervals for nanoparticle characteristics,” J. Quant. Spectrosco. Ra. 113(2), 182–193 (2012).
[Crossref]

Charwath, M.

H. A. Michelsen, F. Liu, B. F. Kock, H. Bladh, A. Boiarciuc, M. Charwath, T. Dreier, R. Hadef, M. Hofmann, J. Reimann, S. Will, P. E. Bengtsson, H. Bockhorn, F. Foucher, K. P. Geigle, C. Mounaïm-Rousselle, C. Schulz, R. Stirn, B. Tribalet, and R. Suntz, “Modeling laser-induced incandescence of soot: a summary and comparison of LII models,” Appl. Phys. B. 87(3), 503–521 (2007).
[Crossref]

China, S.

S. China, C. Mazzoleni, K. Gorkowski, A. C. Aiken, and M. K. Dubey, “Morphology and mixing state of individual freshly emitted wildfire carbonaceous particles,” Nat. Commun. 4, 2122 (2013).
[Crossref] [PubMed]

Clementi, L. A.

L. A. Clementi, J. R. Vega, L. M. Gugliotta, and H. R. B. Orlande, “A Bayesian Inversion Method for Estimating the Particle Size Distribution of Latexes from Multiangle Dynamic Light Scattering Measurements,” Chemometr. Intell. Lab. 107(1), 165–173 (2011).
[Crossref]

Coderre, A. R.

A. R. Coderre, K. A. Thomson, D. R. Snelling, and M. R. Johnson, “Spectrally resolved light absorption properties of cooled soot from a methane flame,” Appl. Phys. B. 104(1), 175–188 (2011).
[Crossref]

Coelho, L. D. S.

L. D. S. Coelho, “Gaussian quantum-behaved particle swarm optimization approaches for constrained engineering design problems,” Expert Syst. Appl. 37(2), 1676–1683 (2010).
[Crossref]

Conturso, M.

M. Sirignano, D. Bartos, M. Conturso, M. Dunn, A. D’Anna, and A. R. Masri, “Detection of nanostructures and soot in laminar premixed flames,” Combust. Flame 176, 299–308 (2017).
[Crossref]

Coppalle, A.

C. Caumont-Prim, J. Yon, A. Coppalle, F. X. Ouf, and K. F. Ren, “Measurement of aggregates’ size distribution by angular light scattering,” J. Quant. Spectrosco. Ra. 126(S1), 140–149 (2013).
[Crossref]

F. X. Ouf, J. Yon, P. Ausset, A. Coppalle, and M. Maillé, “Influence of Sampling and Storage Protocol on Fractal Morphology of Soot Studied by Transmission Electron Microscopy,” Aerosol Sci. Technol. 44(11), 1005–1017 (2010).
[Crossref]

Cross, E. S.

D’Anna, A.

M. Sirignano, D. Bartos, M. Conturso, M. Dunn, A. D’Anna, and A. R. Masri, “Detection of nanostructures and soot in laminar premixed flames,” Combust. Flame 176, 299–308 (2017).
[Crossref]

Daun, K. J.

S. Talebi, P. J. Hadwin, and K. J. Daun, “Soot aggregate sizing through multiangle elastic light scattering: Influence of model error,” J. Aerosol Sci. 111, 36–50 (2017).
[Crossref]

F. J. T. Huber, S. Will, and K. J. Daun, “Sizing aerosolized fractal nanoparticle aggregates through Bayesian analysis of wide-angle light scattering (WALS) data,” J. Quant. Spectrosco. Ra. 184, 27–39 (2016).
[Crossref]

D. W. Burr, K. J. Daun, K. A. Thomson, and G. J. Smallwood, “Optimization of measurement angles for soot aggregate sizing by elastic light scattering, through design-of-experiment theory,” J. Quant. Spectrosco. Ra. 113(5), 355–365 (2012).
[Crossref]

D. W. Burr, K. J. Daun, O. Link, K. A. Thomson, and G. J. Smallwood, “Determination of the soot aggregate size distribution from elastic light scattering through Bayesian inference,” J. Quant. Spectrosco. Ra. 112(6), 1099–1107 (2011).
[Crossref]

K. J. Daun, G. J. Smallwood, and F. Liu, “Investigation of Thermal Accommodation Coefficients in Time-Resolved Laser-Induced Incandescence,” J. Heat Trans-Transf. 130(12), 320–327 (2008).
[Crossref]

Davidovits, P.

Deng, J.

Q. Niu, Z. Zhou, H. Y. Zhang, and J. Deng, “An Improved Quantum-Behaved Particle Swarm Optimization Method for Economic Dispatch Problems with Multiple Fuel Options and Valve-Points Effects,” Energies 5(9), 240–250 (2012).
[Crossref]

Deng, Y.

Y. Deng, R. Hu, Q. Luo, and Q. Lu, “Float genetic algorithm for determination of particle size distribution and refractive index in polarized LSS,” Proc. SPIE 5693, 10–16 (2005).
[Crossref]

Desgroux, P.

P. Desgroux, X. Mercier, and K. A. Thomson, “Study of the formation of soot and its precursors in flames using optical diagnostics,” Proc. Combust. Inst. 34(1), 1713–1738 (2013).
[Crossref]

Dobbins, R. A.

Dreier, T.

R. Mansmann, K. Thomson, G. Smallwood, T. Dreier, and C. Schulz, “Sequential signal detection for high dynamic range time-resolved laser-induced incandescence,” Opt. Express 25(3), 2413–2421 (2017).
[Crossref] [PubMed]

H. A. Michelsen, F. Liu, B. F. Kock, H. Bladh, A. Boiarciuc, M. Charwath, T. Dreier, R. Hadef, M. Hofmann, J. Reimann, S. Will, P. E. Bengtsson, H. Bockhorn, F. Foucher, K. P. Geigle, C. Mounaïm-Rousselle, C. Schulz, R. Stirn, B. Tribalet, and R. Suntz, “Modeling laser-induced incandescence of soot: a summary and comparison of LII models,” Appl. Phys. B. 87(3), 503–521 (2007).
[Crossref]

Dubey, M. K.

S. China, C. Mazzoleni, K. Gorkowski, A. C. Aiken, and M. K. Dubey, “Morphology and mixing state of individual freshly emitted wildfire carbonaceous particles,” Nat. Commun. 4, 2122 (2013).
[Crossref] [PubMed]

Dunn, M.

M. Sirignano, D. Bartos, M. Conturso, M. Dunn, A. D’Anna, and A. R. Masri, “Detection of nanostructures and soot in laminar premixed flames,” Combust. Flame 176, 299–308 (2017).
[Crossref]

Eliçabe, G. E.

F. A. Otero, H. R. B. Orlande, G. L. Frontini, and G. E. Eliçabe, “Bayesian approach to the inverse problem in a light scattering application,” J. Appl. Stat. 42(5), 994–1016 (2015).
[Crossref]

Enguehard, F.

G. Okyay, E. Héripré, T. Reiss, P. Haghi-Ashtiani, T. Auger, and F. Enguehard, “Soot aggregate complex morphology: 3D geometry reconstruction by SEM tomography applied on soot issued from propane combustion,” J. Aerosol Sci. 93, 63–79 (2016).
[Crossref]

Ericok, O. B.

O. B. Ericok and H. Erturk, “Optical characterization limits of nanoparticle aggregates at different wavelengths using approximate Bayesian computation,” J. Quant. Spectrosco. Ra. 213, 113–118 (2018).
[Crossref]

O. B. Ericok, A. T. Cemgil, and H. Erturk, “Approximate Bayesian computation techniques for optical characterization of nanoparticle clusters,” J. Opt. Soc. Am. A 35(1), 88–97 (2018).
[Crossref] [PubMed]

Erturk, H.

O. B. Ericok, A. T. Cemgil, and H. Erturk, “Approximate Bayesian computation techniques for optical characterization of nanoparticle clusters,” J. Opt. Soc. Am. A 35(1), 88–97 (2018).
[Crossref] [PubMed]

O. B. Ericok and H. Erturk, “Optical characterization limits of nanoparticle aggregates at different wavelengths using approximate Bayesian computation,” J. Quant. Spectrosco. Ra. 213, 113–118 (2018).
[Crossref]

Faeth, G. M.

Ü. Ö. Köylü and G. M. Faeth, “Structure of overfire soot in buoyant turbulent diffusion flames at long residence times,” Combust. Flame 89(2), 140–156 (1992).
[Crossref]

Farias, T. L.

Foucher, F.

H. A. Michelsen, F. Liu, B. F. Kock, H. Bladh, A. Boiarciuc, M. Charwath, T. Dreier, R. Hadef, M. Hofmann, J. Reimann, S. Will, P. E. Bengtsson, H. Bockhorn, F. Foucher, K. P. Geigle, C. Mounaïm-Rousselle, C. Schulz, R. Stirn, B. Tribalet, and R. Suntz, “Modeling laser-induced incandescence of soot: a summary and comparison of LII models,” Appl. Phys. B. 87(3), 503–521 (2007).
[Crossref]

Francoeur, M.

R. Charnigo, M. Francoeur, P. Kenkel, M. P. Menguc, B. Hall, and C. Srinivasan, “Credible intervals for nanoparticle characteristics,” J. Quant. Spectrosco. Ra. 113(2), 182–193 (2012).
[Crossref]

Frontini, G. L.

F. A. Otero, H. R. B. Orlande, G. L. Frontini, and G. E. Eliçabe, “Bayesian approach to the inverse problem in a light scattering application,” J. Appl. Stat. 42(5), 994–1016 (2015).
[Crossref]

Garro, M. A.

Gawelczyk, A.

A. Ostermeier, A. Gawelczyk, and N. Hansen, “A Derandomized Approach to Self-Adaptation of Evolution Strategies,” Evol. Comput. 2(4), 369–380 (1994).
[Crossref]

Geigle, K. P.

H. A. Michelsen, F. Liu, B. F. Kock, H. Bladh, A. Boiarciuc, M. Charwath, T. Dreier, R. Hadef, M. Hofmann, J. Reimann, S. Will, P. E. Bengtsson, H. Bockhorn, F. Foucher, K. P. Geigle, C. Mounaïm-Rousselle, C. Schulz, R. Stirn, B. Tribalet, and R. Suntz, “Modeling laser-induced incandescence of soot: a summary and comparison of LII models,” Appl. Phys. B. 87(3), 503–521 (2007).
[Crossref]

Geijtenbeek, T.

T. Geijtenbeek, M. V. D. Panne, and A. F. V. D. Stappen, “Flexible muscle-based locomotion for bipedal creatures,” ACM Trans. Graphic. 32(6), 1–11 (2013).
[Crossref]

González-Calera, S.

M. L. Botero, E. M. Adkins, S. González-Calera, H. Miller, and M. Kraft, “PAH structure analysis of soot in a non-premixed flame using high-resolution transmission electron microscopy and optical band gap analysis,” Combust. Flame 164, 250–258 (2016).
[Crossref]

Gord, J. R.

Gorkowski, K.

S. China, C. Mazzoleni, K. Gorkowski, A. C. Aiken, and M. K. Dubey, “Morphology and mixing state of individual freshly emitted wildfire carbonaceous particles,” Nat. Commun. 4, 2122 (2013).
[Crossref] [PubMed]

Grahame, T. J.

T. J. Grahame and R. B. Schlesinger, “Cardiovascular health and particulate vehicular emissions: a critical evaluation of the evidence,” Air Qual. Atmos. Health 3(1), 3–27 (2010).
[Crossref] [PubMed]

Grainger, R. G.

A. J. A. Smith and R. G. Grainger, “Simplifying the calculation of light scattering properties for black carbon fractal aggregates,” Atmos. Chem. Phys. 14(15), 7825–7836 (2014).
[Crossref]

Gugliotta, L. M.

L. A. Clementi, J. R. Vega, L. M. Gugliotta, and H. R. B. Orlande, “A Bayesian Inversion Method for Estimating the Particle Size Distribution of Latexes from Multiangle Dynamic Light Scattering Measurements,” Chemometr. Intell. Lab. 107(1), 165–173 (2011).
[Crossref]

Guibert, P.

Hadef, R.

H. A. Michelsen, F. Liu, B. F. Kock, H. Bladh, A. Boiarciuc, M. Charwath, T. Dreier, R. Hadef, M. Hofmann, J. Reimann, S. Will, P. E. Bengtsson, H. Bockhorn, F. Foucher, K. P. Geigle, C. Mounaïm-Rousselle, C. Schulz, R. Stirn, B. Tribalet, and R. Suntz, “Modeling laser-induced incandescence of soot: a summary and comparison of LII models,” Appl. Phys. B. 87(3), 503–521 (2007).
[Crossref]

Hadwin, P. J.

S. Talebi, P. J. Hadwin, and K. J. Daun, “Soot aggregate sizing through multiangle elastic light scattering: Influence of model error,” J. Aerosol Sci. 111, 36–50 (2017).
[Crossref]

Haghi-Ashtiani, P.

G. Okyay, E. Héripré, T. Reiss, P. Haghi-Ashtiani, T. Auger, and F. Enguehard, “Soot aggregate complex morphology: 3D geometry reconstruction by SEM tomography applied on soot issued from propane combustion,” J. Aerosol Sci. 93, 63–79 (2016).
[Crossref]

Hall, B.

R. Charnigo, M. Francoeur, P. Kenkel, M. P. Menguc, B. Hall, and C. Srinivasan, “Credible intervals for nanoparticle characteristics,” J. Quant. Spectrosco. Ra. 113(2), 182–193 (2012).
[Crossref]

Halls, B. R.

Han, J.-H.

Han, X.

Z. He, J. Mao, and X. Han, “Non-parametric estimation of particle size distribution from spectral extinction data with PCA approach,” Powder Technol. 325, 510 (2017).

Hansen, N.

N. Hansen, “The CMA Evolution Strategy: A Comparing Review,” Stud Fuzz. Soft Comput. 192, 75–102 (2006).

N. Hansen and A. Ostermeier, “Completely derandomized self-adaptation in evolution strategies,” Evol. Comput. 9(2), 159–195 (2001).
[Crossref] [PubMed]

A. Ostermeier, A. Gawelczyk, and N. Hansen, “A Derandomized Approach to Self-Adaptation of Evolution Strategies,” Evol. Comput. 2(4), 369–380 (1994).
[Crossref]

He, Z.

Z. He, J. Mao, and X. Han, “Non-parametric estimation of particle size distribution from spectral extinction data with PCA approach,” Powder Technol. 325, 510 (2017).

He, Z. Z.

H. Qi, Z. Z. He, F. Z. Zhao, and L. M. Ruan, “Determination of the spectral complex refractive indices of microalgae cells by light reflectance-transmittance measurement,” Int. J. Hydrogen Energy 41(9), 4941–4956 (2016).
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[Crossref]

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 Tran. 54(1), 217–224 (2011).
[Crossref]

Suntz, R.

H. A. Michelsen, F. Liu, B. F. Kock, H. Bladh, A. Boiarciuc, M. Charwath, T. Dreier, R. Hadef, M. Hofmann, J. Reimann, S. Will, P. E. Bengtsson, H. Bockhorn, F. Foucher, K. P. Geigle, C. Mounaïm-Rousselle, C. Schulz, R. Stirn, B. Tribalet, and R. Suntz, “Modeling laser-induced incandescence of soot: a summary and comparison of LII models,” Appl. Phys. B. 87(3), 503–521 (2007).
[Crossref]

C. Schulz, B. F. Kock, M. Hofmann, H. Michelsen, S. Will, R. Suntz, and G. Smallwood, “Laser-induced incandescence: recent trends and current questions,” Appl. Phys. B. 83(3), 333–354 (2006).
[Crossref]

T. Lehre, B. Jungfleisch, R. Suntz, and H. Bockhorn, “Size distributions of nanoscaled particles and gas temperatures from time-resolved laser-induced-incandescence measurements,” Appl. Opt. 42(12), 2021–2030 (2003).
[Crossref] [PubMed]

Talebi, S.

S. Talebi, P. J. Hadwin, and K. J. Daun, “Soot aggregate sizing through multiangle elastic light scattering: Influence of model error,” J. Aerosol Sci. 111, 36–50 (2017).
[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 Tran. 85(1), 300–310 (2015).
[Crossref]

Thomson, K.

Thomson, K. A.

P. Desgroux, X. Mercier, and K. A. Thomson, “Study of the formation of soot and its precursors in flames using optical diagnostics,” Proc. Combust. Inst. 34(1), 1713–1738 (2013).
[Crossref]

D. W. Burr, K. J. Daun, K. A. Thomson, and G. J. Smallwood, “Optimization of measurement angles for soot aggregate sizing by elastic light scattering, through design-of-experiment theory,” J. Quant. Spectrosco. Ra. 113(5), 355–365 (2012).
[Crossref]

D. W. Burr, K. J. Daun, O. Link, K. A. Thomson, and G. J. Smallwood, “Determination of the soot aggregate size distribution from elastic light scattering through Bayesian inference,” J. Quant. Spectrosco. Ra. 112(6), 1099–1107 (2011).
[Crossref]

O. Link, D. R. Snelling, K. A. Thomson, and G. J. Smallwood, “Development of absolute intensity multi-angle light scattering for the determination of polydisperse soot aggregate properties,” Proc. Combust. Inst. 33(1), 847–854 (2011).
[Crossref]

A. R. Coderre, K. A. Thomson, D. R. Snelling, and M. R. Johnson, “Spectrally resolved light absorption properties of cooled soot from a methane flame,” Appl. Phys. B. 104(1), 175–188 (2011).
[Crossref]

F. Liu, K. A. Thomson, and G. J. Smallwood, “Effects of soot absorption and scattering on LII intensities in laminar coflow diffusion flames,” J. Quant. Spectrosco. Ra. 109(2), 337–348 (2008).
[Crossref]

Ticich, T. M.

R. L. V. Wal, T. M. Ticich, and A. B. Stephens, “Can soot primary particle size be determined using laser-induced incandescence?” Combust. Flame 116(1–2), 291–296 (1999).

Tribalet, B.

H. A. Michelsen, F. Liu, B. F. Kock, H. Bladh, A. Boiarciuc, M. Charwath, T. Dreier, R. Hadef, M. Hofmann, J. Reimann, S. Will, P. E. Bengtsson, H. Bockhorn, F. Foucher, K. P. Geigle, C. Mounaïm-Rousselle, C. Schulz, R. Stirn, B. Tribalet, and R. Suntz, “Modeling laser-induced incandescence of soot: a summary and comparison of LII models,” Appl. Phys. B. 87(3), 503–521 (2007).
[Crossref]

Vega, J. R.

L. A. Clementi, J. R. Vega, L. M. Gugliotta, and H. R. B. Orlande, “A Bayesian Inversion Method for Estimating the Particle Size Distribution of Latexes from Multiangle Dynamic Light Scattering Measurements,” Chemometr. Intell. Lab. 107(1), 165–173 (2011).
[Crossref]

Wal, R. L. V.

R. L. V. Wal, T. M. Ticich, and A. B. Stephens, “Can soot primary particle size be determined using laser-induced incandescence?” Combust. Flame 116(1–2), 291–296 (1999).

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. Spectrosco. Ra. 112(15), 2507–2519 (2011).
[Crossref]

Wang, F.

J. Luo, Y. Zhang, F. Wang, J. Wang, and Q. Zhang, “Applying machine learning to estimate the optical properties of black carbon fractal aggregates,” J. Quant. Spectrosc. Ra. 215, 1–8 (2018).
[Crossref]

J. Luo, Y. Zhang, Q. Zhang, F. Wang, J. Liu, and J. Wang, “Sensitivity analysis of morphology on radiative properties of soot aerosols,” Opt. Express 26(10), A420–A432 (2018).
[Crossref] [PubMed]

Wang, J.

J. Luo, Y. Zhang, Q. Zhang, F. Wang, J. Liu, and J. Wang, “Sensitivity analysis of morphology on radiative properties of soot aerosols,” Opt. Express 26(10), A420–A432 (2018).
[Crossref] [PubMed]

J. Luo, Y. Zhang, F. Wang, J. Wang, and Q. Zhang, “Applying machine learning to estimate the optical properties of black carbon fractal aggregates,” J. Quant. Spectrosc. Ra. 215, 1–8 (2018).
[Crossref]

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. Spectrosco. Ra. 112(15), 2507–2519 (2011).
[Crossref]

Wei, W.

J. Cai, X. Hu, B. Xiao, Y. Zhou, and W. Wei, ““Recent developments on fractal-based approaches to nanofluids and nanoparticle aggregation,” Int,” J. Heat Mass Tran. 105, 623–637 (2017).
[Crossref]

Weitz, D. A.

M. Y. Lin, R. Klein, H. M. Lindsay, D. A. Weitz, R. C. Ball, and P. Meakin, “The Structure of Fractal Colloidal Aggregates of Finite Extent,” J. Colloid Interface Sci. 137(1), 263–280 (1990).
[Crossref]

Will, S.

F. J. T. Huber, S. Will, and K. J. Daun, “Sizing aerosolized fractal nanoparticle aggregates through Bayesian analysis of wide-angle light scattering (WALS) data,” J. Quant. Spectrosco. Ra. 184, 27–39 (2016).
[Crossref]

H. Oltmann, J. Reimann, and S. Will, “Single-shot measurement of soot aggregate sizes by wide-angle light scattering (WALS),” Appl. Phys. B. 106(1), 171–183 (2012).
[Crossref]

H. Oltmann, J. Reimann, and S. Will, “Wide-angle light scattering (WALS) for soot aggregate characterization,” Combust. Flame 157(3), 516–522 (2010).
[Crossref]

H. A. Michelsen, F. Liu, B. F. Kock, H. Bladh, A. Boiarciuc, M. Charwath, T. Dreier, R. Hadef, M. Hofmann, J. Reimann, S. Will, P. E. Bengtsson, H. Bockhorn, F. Foucher, K. P. Geigle, C. Mounaïm-Rousselle, C. Schulz, R. Stirn, B. Tribalet, and R. Suntz, “Modeling laser-induced incandescence of soot: a summary and comparison of LII models,” Appl. Phys. B. 87(3), 503–521 (2007).
[Crossref]

C. Schulz, B. F. Kock, M. Hofmann, H. Michelsen, S. Will, R. Suntz, and G. Smallwood, “Laser-induced incandescence: recent trends and current questions,” Appl. Phys. B. 83(3), 333–354 (2006).
[Crossref]

Worsnop, D. R.

Xiao, B.

J. Cai, X. Hu, B. Xiao, Y. Zhou, and W. Wei, ““Recent developments on fractal-based approaches to nanofluids and nanoparticle aggregation,” Int,” J. Heat Mass Tran. 105, 623–637 (2017).
[Crossref]

Yang, B.

B. Yang and Ü. Ö. Köylü, “Detailed soot field in a turbulent non-premixed ethylene/air flame from laser scattering and extinction experiments,” Combust. Flame 141(1), 55–65 (2005).
[Crossref]

Yon, J.

J. Yon, A. Bescond, and F. Liu, “On the radiative properties of soot aggregates part 1: Necking and overlapping,” J. Quant. Spectrosco. Ra. 162, 197–206 (2015).
[Crossref]

C. Caumont-Prim, J. Yon, A. Coppalle, F. X. Ouf, and K. F. Ren, “Measurement of aggregates’ size distribution by angular light scattering,” J. Quant. Spectrosco. Ra. 126(S1), 140–149 (2013).
[Crossref]

F. X. Ouf, J. Yon, P. Ausset, A. Coppalle, and M. Maillé, “Influence of Sampling and Storage Protocol on Fractal Morphology of Soot Studied by Transmission Electron Microscopy,” Aerosol Sci. Technol. 44(11), 1005–1017 (2010).
[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 Tran. 85(1), 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 Tran. 66(3), 507–516 (2013).
[Crossref]

Zhang, H. Y.

Q. Niu, Z. Zhou, H. Y. Zhang, and J. Deng, “An Improved Quantum-Behaved Particle Swarm Optimization Method for Economic Dispatch Problems with Multiple Fuel Options and Valve-Points Effects,” Energies 5(9), 240–250 (2012).
[Crossref]

Zhang, J. Y.

J. Y. Zhang, H. Qi, Y. T. Ren, and L. M. Ruan, “Simultaneous identification of optical constants and PSD of spherical particles by multi-wavelength scattering–transmittance measurement,” Opt. Commun. 413, 317–328 (2018).
[Crossref]

Zhang, Q.

J. Luo, Y. Zhang, F. Wang, J. Wang, and Q. Zhang, “Applying machine learning to estimate the optical properties of black carbon fractal aggregates,” J. Quant. Spectrosc. Ra. 215, 1–8 (2018).
[Crossref]

J. Luo, Y. Zhang, Q. Zhang, F. Wang, J. Liu, and J. Wang, “Sensitivity analysis of morphology on radiative properties of soot aerosols,” Opt. Express 26(10), A420–A432 (2018).
[Crossref] [PubMed]

Zhang, Y.

J. Luo, Y. Zhang, Q. Zhang, F. Wang, J. Liu, and J. Wang, “Sensitivity analysis of morphology on radiative properties of soot aerosols,” Opt. Express 26(10), A420–A432 (2018).
[Crossref] [PubMed]

J. Luo, Y. Zhang, F. Wang, J. Wang, and Q. Zhang, “Applying machine learning to estimate the optical properties of black carbon fractal aggregates,” J. Quant. Spectrosc. Ra. 215, 1–8 (2018).
[Crossref]

Zhao, F. Z.

H. Qi, Z. Z. He, F. Z. Zhao, and L. M. Ruan, “Determination of the spectral complex refractive indices of microalgae cells by light reflectance-transmittance measurement,” Int. J. Hydrogen Energy 41(9), 4941–4956 (2016).
[Crossref]

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 Tran. 54(1), 217–224 (2011).
[Crossref]

Zhou, Y.

J. Cai, X. Hu, B. Xiao, Y. Zhou, and W. Wei, ““Recent developments on fractal-based approaches to nanofluids and nanoparticle aggregation,” Int,” J. Heat Mass Tran. 105, 623–637 (2017).
[Crossref]

Zhou, Z.

Q. Niu, Z. Zhou, H. Y. Zhang, and J. Deng, “An Improved Quantum-Behaved Particle Swarm Optimization Method for Economic Dispatch Problems with Multiple Fuel Options and Valve-Points Effects,” Energies 5(9), 240–250 (2012).
[Crossref]

ACM Trans. Graphic. (1)

T. Geijtenbeek, M. V. D. Panne, and A. F. V. D. Stappen, “Flexible muscle-based locomotion for bipedal creatures,” ACM Trans. Graphic. 32(6), 1–11 (2013).
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T. C. Bond and R. W. Bergstrom, “Light Absorption by Carbonaceous Particles: An Investigative Review,” Aerosol Sci. Technol. 40(1), 27–67 (2006).
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F. X. Ouf, J. Yon, P. Ausset, A. Coppalle, and M. Maillé, “Influence of Sampling and Storage Protocol on Fractal Morphology of Soot Studied by Transmission Electron Microscopy,” Aerosol Sci. Technol. 44(11), 1005–1017 (2010).
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C. M. Sorensen, “Light Scattering by Fractal Aggregates: A Review,” Aerosol Sci. Technol. 35(2), 648–687 (2001).
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Air Qual. Atmos. Health (1)

T. J. Grahame and R. B. Schlesinger, “Cardiovascular health and particulate vehicular emissions: a critical evaluation of the evidence,” Air Qual. Atmos. Health 3(1), 3–27 (2010).
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Appl. Opt. (6)

Appl. Phys. B. (4)

H. Oltmann, J. Reimann, and S. Will, “Single-shot measurement of soot aggregate sizes by wide-angle light scattering (WALS),” Appl. Phys. B. 106(1), 171–183 (2012).
[Crossref]

C. Schulz, B. F. Kock, M. Hofmann, H. Michelsen, S. Will, R. Suntz, and G. Smallwood, “Laser-induced incandescence: recent trends and current questions,” Appl. Phys. B. 83(3), 333–354 (2006).
[Crossref]

H. A. Michelsen, F. Liu, B. F. Kock, H. Bladh, A. Boiarciuc, M. Charwath, T. Dreier, R. Hadef, M. Hofmann, J. Reimann, S. Will, P. E. Bengtsson, H. Bockhorn, F. Foucher, K. P. Geigle, C. Mounaïm-Rousselle, C. Schulz, R. Stirn, B. Tribalet, and R. Suntz, “Modeling laser-induced incandescence of soot: a summary and comparison of LII models,” Appl. Phys. B. 87(3), 503–521 (2007).
[Crossref]

A. R. Coderre, K. A. Thomson, D. R. Snelling, and M. R. Johnson, “Spectrally resolved light absorption properties of cooled soot from a methane flame,” Appl. Phys. B. 104(1), 175–188 (2011).
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A. J. A. Smith and R. G. Grainger, “Simplifying the calculation of light scattering properties for black carbon fractal aggregates,” Atmos. Chem. Phys. 14(15), 7825–7836 (2014).
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M. Kahnert, “Modelling the optical and radiative properties of freshly emitted light absorbing carbon within an atmospheric chemical transport model,” Atmos. Chem. Phys. 10(3), 1403–1416 (2010).
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L. A. Clementi, J. R. Vega, L. M. Gugliotta, and H. R. B. Orlande, “A Bayesian Inversion Method for Estimating the Particle Size Distribution of Latexes from Multiangle Dynamic Light Scattering Measurements,” Chemometr. Intell. Lab. 107(1), 165–173 (2011).
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M. Sirignano, D. Bartos, M. Conturso, M. Dunn, A. D’Anna, and A. R. Masri, “Detection of nanostructures and soot in laminar premixed flames,” Combust. Flame 176, 299–308 (2017).
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R. L. V. Wal, T. M. Ticich, and A. B. Stephens, “Can soot primary particle size be determined using laser-induced incandescence?” Combust. Flame 116(1–2), 291–296 (1999).

Ü. Ö. Köylü, “Quantitative analysis of in situ optical diagnostics for inferring particle/aggregate parameters in flames: Implications for soot surface growth and total emissivity,” Combust. Flame 109(3), 488–500 (1997).
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B. Yang and Ü. Ö. Köylü, “Detailed soot field in a turbulent non-premixed ethylene/air flame from laser scattering and extinction experiments,” Combust. Flame 141(1), 55–65 (2005).
[Crossref]

H. Oltmann, J. Reimann, and S. Will, “Wide-angle light scattering (WALS) for soot aggregate characterization,” Combust. Flame 157(3), 516–522 (2010).
[Crossref]

Energies (1)

Q. Niu, Z. Zhou, H. Y. Zhang, and J. Deng, “An Improved Quantum-Behaved Particle Swarm Optimization Method for Economic Dispatch Problems with Multiple Fuel Options and Valve-Points Effects,” Energies 5(9), 240–250 (2012).
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Int. J. Heat Mass Tran. (3)

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 Tran. 85(1), 300–310 (2015).
[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 Tran. 54(1), 217–224 (2011).
[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 Tran. 66(3), 507–516 (2013).
[Crossref]

Int. J. Hydrogen Energy (1)

H. Qi, Z. Z. He, F. Z. Zhao, and L. M. Ruan, “Determination of the spectral complex refractive indices of microalgae cells by light reflectance-transmittance measurement,” Int. J. Hydrogen Energy 41(9), 4941–4956 (2016).
[Crossref]

J. Aerosol Sci. (2)

S. Talebi, P. J. Hadwin, and K. J. Daun, “Soot aggregate sizing through multiangle elastic light scattering: Influence of model error,” J. Aerosol Sci. 111, 36–50 (2017).
[Crossref]

G. Okyay, E. Héripré, T. Reiss, P. Haghi-Ashtiani, T. Auger, and F. Enguehard, “Soot aggregate complex morphology: 3D geometry reconstruction by SEM tomography applied on soot issued from propane combustion,” J. Aerosol Sci. 93, 63–79 (2016).
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J. Appl. Stat. (1)

F. A. Otero, H. R. B. Orlande, G. L. Frontini, and G. E. Eliçabe, “Bayesian approach to the inverse problem in a light scattering application,” J. Appl. Stat. 42(5), 994–1016 (2015).
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J. Colloid Interface Sci. (1)

M. Y. Lin, R. Klein, H. M. Lindsay, D. A. Weitz, R. C. Ball, and P. Meakin, “The Structure of Fractal Colloidal Aggregates of Finite Extent,” J. Colloid Interface Sci. 137(1), 263–280 (1990).
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J. Heat Mass Tran. (1)

J. Cai, X. Hu, B. Xiao, Y. Zhou, and W. Wei, ““Recent developments on fractal-based approaches to nanofluids and nanoparticle aggregation,” Int,” J. Heat Mass Tran. 105, 623–637 (2017).
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J. Heat Trans-Transf. (1)

K. J. Daun, G. J. Smallwood, and F. Liu, “Investigation of Thermal Accommodation Coefficients in Time-Resolved Laser-Induced Incandescence,” J. Heat Trans-Transf. 130(12), 320–327 (2008).
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J. Opt. Soc. Am. A (1)

J. Quant. Spectrosc. Ra. (1)

J. Luo, Y. Zhang, F. Wang, J. Wang, and Q. Zhang, “Applying machine learning to estimate the optical properties of black carbon fractal aggregates,” J. Quant. Spectrosc. Ra. 215, 1–8 (2018).
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J. Quant. Spectrosco. Ra. (9)

R. Charnigo, M. Francoeur, P. Kenkel, M. P. Menguc, B. Hall, and C. Srinivasan, “Credible intervals for nanoparticle characteristics,” J. Quant. Spectrosco. Ra. 113(2), 182–193 (2012).
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F. J. T. Huber, S. Will, and K. J. Daun, “Sizing aerosolized fractal nanoparticle aggregates through Bayesian analysis of wide-angle light scattering (WALS) data,” J. Quant. Spectrosco. Ra. 184, 27–39 (2016).
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O. B. Ericok and H. Erturk, “Optical characterization limits of nanoparticle aggregates at different wavelengths using approximate Bayesian computation,” J. Quant. Spectrosco. Ra. 213, 113–118 (2018).
[Crossref]

D. W. Burr, K. J. Daun, O. Link, K. A. Thomson, and G. J. Smallwood, “Determination of the soot aggregate size distribution from elastic light scattering through Bayesian inference,” J. Quant. Spectrosco. Ra. 112(6), 1099–1107 (2011).
[Crossref]

D. W. Burr, K. J. Daun, K. A. Thomson, and G. J. Smallwood, “Optimization of measurement angles for soot aggregate sizing by elastic light scattering, through design-of-experiment theory,” J. Quant. Spectrosco. Ra. 113(5), 355–365 (2012).
[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. Spectrosco. Ra. 112(15), 2507–2519 (2011).
[Crossref]

C. Caumont-Prim, J. Yon, A. Coppalle, F. X. Ouf, and K. F. Ren, “Measurement of aggregates’ size distribution by angular light scattering,” J. Quant. Spectrosco. Ra. 126(S1), 140–149 (2013).
[Crossref]

F. Liu, K. A. Thomson, and G. J. Smallwood, “Effects of soot absorption and scattering on LII intensities in laminar coflow diffusion flames,” J. Quant. Spectrosco. Ra. 109(2), 337–348 (2008).
[Crossref]

J. Yon, A. Bescond, and F. Liu, “On the radiative properties of soot aggregates part 1: Necking and overlapping,” J. Quant. Spectrosco. Ra. 162, 197–206 (2015).
[Crossref]

Nat. Commun. (1)

S. China, C. Mazzoleni, K. Gorkowski, A. C. Aiken, and M. K. Dubey, “Morphology and mixing state of individual freshly emitted wildfire carbonaceous particles,” Nat. Commun. 4, 2122 (2013).
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Nat. Geosci. (1)

V. Ramanathan and G. Carmichael, “Global and regional climate changes due to black carbon,” Nat. Geosci. 36, 335–358 (2008).
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Opt. Commun. (1)

J. Y. Zhang, H. Qi, Y. T. Ren, and L. M. Ruan, “Simultaneous identification of optical constants and PSD of spherical particles by multi-wavelength scattering–transmittance measurement,” Opt. Commun. 413, 317–328 (2018).
[Crossref]

Opt. Express (5)

Powder Technol. (1)

Z. He, J. Mao, and X. Han, “Non-parametric estimation of particle size distribution from spectral extinction data with PCA approach,” Powder Technol. 325, 510 (2017).

Proc. Combust. Inst. (2)

O. Link, D. R. Snelling, K. A. Thomson, and G. J. Smallwood, “Development of absolute intensity multi-angle light scattering for the determination of polydisperse soot aggregate properties,” Proc. Combust. Inst. 33(1), 847–854 (2011).
[Crossref]

P. Desgroux, X. Mercier, and K. A. Thomson, “Study of the formation of soot and its precursors in flames using optical diagnostics,” Proc. Combust. Inst. 34(1), 1713–1738 (2013).
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Proc. SPIE (1)

Y. Deng, R. Hu, Q. Luo, and Q. Lu, “Float genetic algorithm for determination of particle size distribution and refractive index in polarized LSS,” Proc. SPIE 5693, 10–16 (2005).
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Stud Fuzz. Soft Comput. (1)

N. Hansen, “The CMA Evolution Strategy: A Comparing Review,” Stud Fuzz. Soft Comput. 192, 75–102 (2006).

Other (3)

N. Hansen, “The CMA Evolution Strategy: A Tutorial,” https://lanl.arxiv.org/abs/1604.00772 .

F. Battin-Leclerc, J. M. Simmie, and E. Blurock, Cleaner Combustion (Green Energy and Technology, Springer, 2013).

A. R. Jones and A. Kokhanovsky, Springer Series in Light Scattering (Springer, 2018), Chap. 6.

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Figures (8)

Fig. 1
Fig. 1 (a) Field-emission scanning electron microscope images of soot particles [33]; (b) Fractal-like soot aggregate.
Fig. 2
Fig. 2 The flowchart of the inversion process.
Fig. 3
Fig. 3 The schematic of three different scattering signal models.
Fig. 4
Fig. 4 PSD curve based on preliminary results.
Fig. 5
Fig. 5 100 independent runs obtained by RS signals for different wavelength plotted on (Rg,geo & σg)-FVCS.
Fig. 6
Fig. 6 The no-noise (Rg,geo&σg)-FVCS obtained by using (a) 2-angle and (b) 5-angle RS signal for single wavelength.
Fig. 7
Fig. 7 The retrieval PSD based on 8-angle and 32-angle RS signals under different multi-wavelength strategies.
Fig. 8
Fig. 8 Converge curves of 50 runs obtained by 32-angle RS signals under 5 wavelength in (a) no-noise and (b) 10% Gaussian noise.

Tables (8)

Tables Icon

Table 1 Four typical structure factor functions

Tables Icon

Table 2 Comparison of three scattering signal models

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Table 3 The original values of properties in the test case

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Table 4 Other parameter settings of inversion

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Table 5 Retrieval results using single wavelength without measurement noise

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Table 6 Retrieval results with 10% Gaussian measurement noise using different multi-wavelength strategies

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Table 7 Retrieval results based on 8-angle RS signals under different multi-wavelength strategies

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Table 8 Retrieval results using CMA-ES and IQPSO algorithm based on 5-wavelength 32-angle RS signals

Equations (19)

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N= k f ( 2 R g d p ) D f
d σ sca agg dΩ = N 2 d σ sca p dΩ S(q R g )= N 2 [ k 4 a 6 F( m ) ]S(q R g ) where F(m)= | m 2 1 m 2 +2 | 2
σ sca agg = N 2 σ sca p G(k R g )= N 2 [ 8π 3 k 4 a 6 F(m) ]G(k R g ) where G(k R g )= ( 1+ 4 3 D f k 2 R g 2 ) D f /2
σ abs agg =N σ sca p =N[ 4πk a 3 E(m) ] where E( m )=Im[ m 2 1 m 2 +2 ]
σ ext agg = σ abs agg + σ sca agg
p( R g )= 1 R g 2π log σ g exp[ ( log R g log R g, geo ) 2 2 ( log σ g ) 2 ]
I A ( θ )= c 0 I 0 n agg d σ sca agg dΩ p( R g )d R g = c 0 I 0 n agg N 2 k 4 a 6 F(m)S( q(θ) R g )p( R g ) d R g
I A ( θ )= c 0 I 0 n agg k 4 a 62 D f F(m) k f 2 R g 2 D f S( q(θ) R g )p( R g ) d R g = C 0 ( n agg , d p , D f , m, k f ) R g 2 D f S( q(θ) R g )p( R g ) d R g
I T = I 0 exp( τ ext l )= I 0 exp( n agg σ ext agg l )
I R = I A (θ) I A (0) = C 0 R g 2 D f S( q(θ) R g )p( R g ) d R g C 0 R g 2 D f S( q(0) R g )p( R g ) d R g = R g 2 D f S( q(θ) R g )p( R g ) d R g R g 2 D f p( R g ) d R g
x k (g+1) m (g) + σ (g) N(0, C (g) ) for k=1,..., λ
m (g+1) = i=1 μ w i x i:λ (g+1)
C (g+1) =(1+ c 1 δ( h σ ) c 1 c μ i=1 λ w i ) can be close or equal to 0 C (g) + c 1 p c (g+1) [ p c (g+1) ] T rank-one update + c μ i=1 λ w i y i:λ (g+1) [ y i:λ (g+1) ] T rank-μ update
p c (g+1) =( 1 c c ) p c (g) + h σ c c ( 2 c c ) μ eff m (g+1) m (g) σ (g)
p σ (g+1) =( 1 c σ ) p σ (g) + c σ ( 2 c σ ) μ eff ( C (g) ) 0.5 m (g+1) m (g) σ (g)
σ (g+1) = σ (g) exp[ c σ d σ ( || p σ ( g+1 ) || E||N( 0,I )|| 1 ) ]
F obj = i=1 N λ { j=1 N θ [ S est ( θ j , λ i ) S mea ( θ j , λ i ) S mea ( θ j , λ i ) ] 2 } /( N λ N θ )
ε rel = | z est z ori | z ori ×100%
SD= 1 Num i=1 Num ( x i avg ) 2

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