Abstract

In particle size measurement with dynamic light scattering (DLS), it is difficult to get an accurate recovery of a bimodal particle size distribution (PSD) with a peak position ratio less than ~2:1, especially when large particles (>350nm) are present. This is due to the inherent noise in the autocorrelation function (ACF) data and the scarce utilization of PSD information during the inversion process. In this paper, the PSD information distribution in the ACF data is investigated. It was found that the initial decay section of the ACF contains more information, especially for a bimodal PSD. Based on this, an information-weighted constrained regularization (IWCR) method is proposed in this paper and applied in multiangle DLS analysis for bimodal PSD recovery. By using larger (or smaller) coefficients for weighting the ACF data, more (or less) weight can then be given to the initial part of the ACF. In this way, the IWCR method can enhance utilization of the PSD information in the ACF data, and effectively weaken the effect of noise at large delay time on PSD recovery. Using this method, bimodal PSDs (with nominal diameters of 400:608 nm, 448:608 nm, 500:600 nm) were recovered successfully from simulated data and it appears that the IWCR method can improve the recovery resolution for closely spaced bimodal particles. Results of the PSD recovery from experimental DLS data confirm the performance of this method.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2016 (1)

X. Zhu, J. Shen, and L. Song, “Accurate retrieval of bimodal particle size distribution in dynamic light scattering,” IEEE Photonics Technol. Lett. 28(3), 311–314 (2016).
[Crossref]

2015 (2)

M. Naiim, A. Boualem, C. Ferre, M. Jabloun, A. Jalocha, and P. Ravier, “Multiangle dynamic light scattering for the improvement of multimodal particle size distribution measurements,” Soft Matter 11(1), 28–32 (2015).
[Crossref] [PubMed]

A. G. Mailer, P. S. Clegg, and P. N. Pusey, “Particle sizing by dynamic light scattering: non-linear cumulant analysis,” J. Phys. Condens. Matter 27(14), 145102 (2015).
[Crossref] [PubMed]

2012 (1)

2011 (2)

J. Shen, J. C. Thomas, X. Zhu, and Y. Wang, “Wavelet denoising experiments in dynamic light scattering,” Opt. Express 19(13), 12284–12290 (2011).
[Crossref] [PubMed]

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]

2009 (1)

L. M. Gugliotta, G. S. Stegmayer, L. A. Clementi, V. D. G. Gonzalez, R. J. Minari, J. R. Leiza, and J. R. Vega, “A neural network model for estimating the particle size distribution of dilute latex from multiangle dynamic light scattering measurements,” Part. Part. Syst. Charact. 26(1-2), 41–52 (2009).
[Crossref]

2008 (1)

M. G. Rasteiro, C. C. Lemos, and A. Vasquez, “Nanoparticle Characterization by PCS: The Analysis of Bimodal Distributions,” Particul. Sci. Technol. 26(5), 413–437 (2008).
[Crossref]

2003 (1)

J. R. Vega, L. M. Gugliotta, V. D. G. Gonzalez, and G. R. Meira, “Latex particle size distribution by dynamic light scattering: novel data processing for multiangle measurements,” J. Colloid Interface Sci. 261(1), 74–81 (2003).
[Crossref] [PubMed]

2001 (2)

R. Buttgereit, T. Roths, J. Honerkamp, and L. B. Aberle, “Simultaneous regularization method for the determination of radius distributions from experimental multiangle correlation functions,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(4), 041404 (2001).
[Crossref] [PubMed]

B. J. Frisken, “Revisiting the method of cumulants for the analysis of dynamic light-scattering data,” Appl. Opt. 40(24), 4087–4091 (2001).
[Crossref] [PubMed]

2000 (2)

H. Ruf, “Effects of experimental errors in dynamic light scattering data on the results from regularized inversions,” Prog. Colloid Polym. Sci. 115, 255–258 (2000).

L. M. Gugliotta, J. R. Vega, and G. R. Meira, “Latex particle size distribution by dynamic light scattering: computer evaluation of two alternative calculation paths,” J. Colloid Interface Sci. 228(1), 14–17 (2000).
[Crossref] [PubMed]

1998 (1)

H. Ruf and B. J. Gould, “Size distributions of chylomicrons from human lymph from dynamic light scattering measurements,” Eur. Biophys. J. 28(1), 1–11 (1998).
[Crossref] [PubMed]

1996 (1)

G. Bryant, C. Abeynayake, and J. C. Thomas, “Improved particle size distribution measurements using multiangle dynamic light scattering. 2. refinements and applications,” Langmuir 12(26), 6224–6228 (1996).
[Crossref]

1995 (1)

G. Bryant and J. C. Thomas, “Improved particle size distribution measurements using multiangle dynamic light scattering,” Langmuir 11(7), 2480–2485 (1995).
[Crossref]

1994 (1)

1993 (1)

D. A. Ross and N. Dimas, “Particle Sizing by Dynamic Light Scattering: Noise and distortion in correlation data,” Part. Part. Syst. Charact. 1(2), 62–69 (1993).
[Crossref]

1991 (2)

M. Bertero and E. R. Pike, “Exponential sampling method for Laplace and other dilationally invariant tranforms: II. Examples in photon correlation spectroscopy and Fraunhofer diffraction,” Inverse Probl. 7(1), 21–41 (1991).
[Crossref]

J. C. Thomas, “Photon correlation spectroscopy: technique and instrumentation,” Proc. SPIE 1430, 2–18 (1991).
[Crossref]

1990 (1)

A. B. Yu and N. Standish, “A study of particle size distribution,” Powder Technol. 62(2), 101–118 (1990).
[Crossref]

1987 (2)

K. Schatzel, “Correlation techniques in dynamic light scattering,” Appl. Phys. B-Lasers O. 42, 193–213 (1987).

P. G. Cummins and E. J. Staples, “Particle size distributions determined by a “multiangle” analysis of photon correlation spectroscopy data,” Langmuir 3(6), 1109–1113 (1987).
[Crossref]

1985 (1)

I. D. Morrison, E. F. Grabowski, and C. A. Herb, “Improved techniques for particle size determination by quasi-elastic light scattering,” Langmuir 1(4), 496–501 (1985).
[Crossref]

1983 (1)

K. Schatzel, “Noise in photon correlation and photon structure functions,” J. Mod. Opt. 30, 155–166 (1983).

1982 (2)

S. W. Provencher, “A constrained regularization method for inverting data represented by linear algebraic or integral equations,” Comput. Phys. Commun. 27(3), 213–227 (1982).
[Crossref]

S. W. Provencher, “CONTIN: A general purpose constrained regularization program for inverting noisy linear algebraic and integral equations,” Comput. Phys. Commun. 27(3), 229–242 (1982).
[Crossref]

1981 (1)

N. Ostrowiky, D. Sornette, P. Parker, and E. R. Pike, “Exponential-sampling method for light scattering polydisperity analysis,” J. Mod. Opt. 28, 1059–1070 (1981).

1979 (1)

E. Gulari, E. Gulari, Y. Tsunashima, and B. Chu, “Photon correlation spectroscopy of particle distributions,” J. Chem. Phys. 70(8), 3965–3972 (1979).
[Crossref]

1977 (1)

A. N. Tikhonov and V. Y. Arsenin, “Solutions of ill-posed problems,” Math. Comput. 32, 491 (1977).

1970 (1)

R. Foord, E. Jakeman, C. J. Oliver, E. R. Pike, R. J. Blagrove, E. Wood, and A. R. Peacocke, “Determination of diffusion coefficients of haemocyanin at low concentration by intensity fluctuation spectroscopy of scattered laser light,” Nature 227(5255), 242–245 (1970).
[Crossref] [PubMed]

1908 (1)

G. Mie, “Contributions to the optics of turbid media, especially colloidal metal solutions,” Ann. Phys. 25, 377–445 (1908).
[Crossref]

Aberle, L. B.

R. Buttgereit, T. Roths, J. Honerkamp, and L. B. Aberle, “Simultaneous regularization method for the determination of radius distributions from experimental multiangle correlation functions,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(4), 041404 (2001).
[Crossref] [PubMed]

Abeynayake, C.

G. Bryant, C. Abeynayake, and J. C. Thomas, “Improved particle size distribution measurements using multiangle dynamic light scattering. 2. refinements and applications,” Langmuir 12(26), 6224–6228 (1996).
[Crossref]

Arsenin, V. Y.

A. N. Tikhonov and V. Y. Arsenin, “Solutions of ill-posed problems,” Math. Comput. 32, 491 (1977).

Bertero, M.

M. Bertero and E. R. Pike, “Exponential sampling method for Laplace and other dilationally invariant tranforms: II. Examples in photon correlation spectroscopy and Fraunhofer diffraction,” Inverse Probl. 7(1), 21–41 (1991).
[Crossref]

Blagrove, R. J.

R. Foord, E. Jakeman, C. J. Oliver, E. R. Pike, R. J. Blagrove, E. Wood, and A. R. Peacocke, “Determination of diffusion coefficients of haemocyanin at low concentration by intensity fluctuation spectroscopy of scattered laser light,” Nature 227(5255), 242–245 (1970).
[Crossref] [PubMed]

Boualem, A.

M. Naiim, A. Boualem, C. Ferre, M. Jabloun, A. Jalocha, and P. Ravier, “Multiangle dynamic light scattering for the improvement of multimodal particle size distribution measurements,” Soft Matter 11(1), 28–32 (2015).
[Crossref] [PubMed]

Bryant, G.

G. Bryant, C. Abeynayake, and J. C. Thomas, “Improved particle size distribution measurements using multiangle dynamic light scattering. 2. refinements and applications,” Langmuir 12(26), 6224–6228 (1996).
[Crossref]

G. Bryant and J. C. Thomas, “Improved particle size distribution measurements using multiangle dynamic light scattering,” Langmuir 11(7), 2480–2485 (1995).
[Crossref]

Buttgereit, R.

R. Buttgereit, T. Roths, J. Honerkamp, and L. B. Aberle, “Simultaneous regularization method for the determination of radius distributions from experimental multiangle correlation functions,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(4), 041404 (2001).
[Crossref] [PubMed]

Chu, B.

E. Gulari, E. Gulari, Y. Tsunashima, and B. Chu, “Photon correlation spectroscopy of particle distributions,” J. Chem. Phys. 70(8), 3965–3972 (1979).
[Crossref]

Clegg, P. S.

A. G. Mailer, P. S. Clegg, and P. N. Pusey, “Particle sizing by dynamic light scattering: non-linear cumulant analysis,” J. Phys. Condens. Matter 27(14), 145102 (2015).
[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]

L. M. Gugliotta, G. S. Stegmayer, L. A. Clementi, V. D. G. Gonzalez, R. J. Minari, J. R. Leiza, and J. R. Vega, “A neural network model for estimating the particle size distribution of dilute latex from multiangle dynamic light scattering measurements,” Part. Part. Syst. Charact. 26(1-2), 41–52 (2009).
[Crossref]

Cummins, P. G.

P. G. Cummins and E. J. Staples, “Particle size distributions determined by a “multiangle” analysis of photon correlation spectroscopy data,” Langmuir 3(6), 1109–1113 (1987).
[Crossref]

Deurloo, K.

Dimas, N.

D. A. Ross and N. Dimas, “Particle Sizing by Dynamic Light Scattering: Noise and distortion in correlation data,” Part. Part. Syst. Charact. 1(2), 62–69 (1993).
[Crossref]

Ferre, C.

M. Naiim, A. Boualem, C. Ferre, M. Jabloun, A. Jalocha, and P. Ravier, “Multiangle dynamic light scattering for the improvement of multimodal particle size distribution measurements,” Soft Matter 11(1), 28–32 (2015).
[Crossref] [PubMed]

Foord, R.

R. Foord, E. Jakeman, C. J. Oliver, E. R. Pike, R. J. Blagrove, E. Wood, and A. R. Peacocke, “Determination of diffusion coefficients of haemocyanin at low concentration by intensity fluctuation spectroscopy of scattered laser light,” Nature 227(5255), 242–245 (1970).
[Crossref] [PubMed]

Frisken, B. J.

Gonzalez, V. D. G.

L. M. Gugliotta, G. S. Stegmayer, L. A. Clementi, V. D. G. Gonzalez, R. J. Minari, J. R. Leiza, and J. R. Vega, “A neural network model for estimating the particle size distribution of dilute latex from multiangle dynamic light scattering measurements,” Part. Part. Syst. Charact. 26(1-2), 41–52 (2009).
[Crossref]

J. R. Vega, L. M. Gugliotta, V. D. G. Gonzalez, and G. R. Meira, “Latex particle size distribution by dynamic light scattering: novel data processing for multiangle measurements,” J. Colloid Interface Sci. 261(1), 74–81 (2003).
[Crossref] [PubMed]

Gould, B. J.

H. Ruf and B. J. Gould, “Size distributions of chylomicrons from human lymph from dynamic light scattering measurements,” Eur. Biophys. J. 28(1), 1–11 (1998).
[Crossref] [PubMed]

Grabowski, E. F.

I. D. Morrison, E. F. Grabowski, and C. A. Herb, “Improved techniques for particle size determination by quasi-elastic light scattering,” Langmuir 1(4), 496–501 (1985).
[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]

L. M. Gugliotta, G. S. Stegmayer, L. A. Clementi, V. D. G. Gonzalez, R. J. Minari, J. R. Leiza, and J. R. Vega, “A neural network model for estimating the particle size distribution of dilute latex from multiangle dynamic light scattering measurements,” Part. Part. Syst. Charact. 26(1-2), 41–52 (2009).
[Crossref]

J. R. Vega, L. M. Gugliotta, V. D. G. Gonzalez, and G. R. Meira, “Latex particle size distribution by dynamic light scattering: novel data processing for multiangle measurements,” J. Colloid Interface Sci. 261(1), 74–81 (2003).
[Crossref] [PubMed]

L. M. Gugliotta, J. R. Vega, and G. R. Meira, “Latex particle size distribution by dynamic light scattering: computer evaluation of two alternative calculation paths,” J. Colloid Interface Sci. 228(1), 14–17 (2000).
[Crossref] [PubMed]

Gulari, E.

E. Gulari, E. Gulari, Y. Tsunashima, and B. Chu, “Photon correlation spectroscopy of particle distributions,” J. Chem. Phys. 70(8), 3965–3972 (1979).
[Crossref]

E. Gulari, E. Gulari, Y. Tsunashima, and B. Chu, “Photon correlation spectroscopy of particle distributions,” J. Chem. Phys. 70(8), 3965–3972 (1979).
[Crossref]

Herb, C. A.

I. D. Morrison, E. F. Grabowski, and C. A. Herb, “Improved techniques for particle size determination by quasi-elastic light scattering,” Langmuir 1(4), 496–501 (1985).
[Crossref]

Honerkamp, J.

R. Buttgereit, T. Roths, J. Honerkamp, and L. B. Aberle, “Simultaneous regularization method for the determination of radius distributions from experimental multiangle correlation functions,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(4), 041404 (2001).
[Crossref] [PubMed]

Jabloun, M.

M. Naiim, A. Boualem, C. Ferre, M. Jabloun, A. Jalocha, and P. Ravier, “Multiangle dynamic light scattering for the improvement of multimodal particle size distribution measurements,” Soft Matter 11(1), 28–32 (2015).
[Crossref] [PubMed]

Jakeman, E.

R. Foord, E. Jakeman, C. J. Oliver, E. R. Pike, R. J. Blagrove, E. Wood, and A. R. Peacocke, “Determination of diffusion coefficients of haemocyanin at low concentration by intensity fluctuation spectroscopy of scattered laser light,” Nature 227(5255), 242–245 (1970).
[Crossref] [PubMed]

Jalocha, A.

M. Naiim, A. Boualem, C. Ferre, M. Jabloun, A. Jalocha, and P. Ravier, “Multiangle dynamic light scattering for the improvement of multimodal particle size distribution measurements,” Soft Matter 11(1), 28–32 (2015).
[Crossref] [PubMed]

Leiza, J. R.

L. M. Gugliotta, G. S. Stegmayer, L. A. Clementi, V. D. G. Gonzalez, R. J. Minari, J. R. Leiza, and J. R. Vega, “A neural network model for estimating the particle size distribution of dilute latex from multiangle dynamic light scattering measurements,” Part. Part. Syst. Charact. 26(1-2), 41–52 (2009).
[Crossref]

Lemos, C. C.

M. G. Rasteiro, C. C. Lemos, and A. Vasquez, “Nanoparticle Characterization by PCS: The Analysis of Bimodal Distributions,” Particul. Sci. Technol. 26(5), 413–437 (2008).
[Crossref]

Liu, W.

Liu, X.

Mailer, A. G.

A. G. Mailer, P. S. Clegg, and P. N. Pusey, “Particle sizing by dynamic light scattering: non-linear cumulant analysis,” J. Phys. Condens. Matter 27(14), 145102 (2015).
[Crossref] [PubMed]

Meira, G. R.

J. R. Vega, L. M. Gugliotta, V. D. G. Gonzalez, and G. R. Meira, “Latex particle size distribution by dynamic light scattering: novel data processing for multiangle measurements,” J. Colloid Interface Sci. 261(1), 74–81 (2003).
[Crossref] [PubMed]

L. M. Gugliotta, J. R. Vega, and G. R. Meira, “Latex particle size distribution by dynamic light scattering: computer evaluation of two alternative calculation paths,” J. Colloid Interface Sci. 228(1), 14–17 (2000).
[Crossref] [PubMed]

Mie, G.

G. Mie, “Contributions to the optics of turbid media, especially colloidal metal solutions,” Ann. Phys. 25, 377–445 (1908).
[Crossref]

Minari, R. J.

L. M. Gugliotta, G. S. Stegmayer, L. A. Clementi, V. D. G. Gonzalez, R. J. Minari, J. R. Leiza, and J. R. Vega, “A neural network model for estimating the particle size distribution of dilute latex from multiangle dynamic light scattering measurements,” Part. Part. Syst. Charact. 26(1-2), 41–52 (2009).
[Crossref]

Morrison, I. D.

I. D. Morrison, E. F. Grabowski, and C. A. Herb, “Improved techniques for particle size determination by quasi-elastic light scattering,” Langmuir 1(4), 496–501 (1985).
[Crossref]

Naiim, M.

M. Naiim, A. Boualem, C. Ferre, M. Jabloun, A. Jalocha, and P. Ravier, “Multiangle dynamic light scattering for the improvement of multimodal particle size distribution measurements,” Soft Matter 11(1), 28–32 (2015).
[Crossref] [PubMed]

Oliver, C. J.

R. Foord, E. Jakeman, C. J. Oliver, E. R. Pike, R. J. Blagrove, E. Wood, and A. R. Peacocke, “Determination of diffusion coefficients of haemocyanin at low concentration by intensity fluctuation spectroscopy of scattered laser light,” Nature 227(5255), 242–245 (1970).
[Crossref] [PubMed]

Orlande, H. R. B.

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]

Ostrowiky, N.

N. Ostrowiky, D. Sornette, P. Parker, and E. R. Pike, “Exponential-sampling method for light scattering polydisperity analysis,” J. Mod. Opt. 28, 1059–1070 (1981).

Parker, P.

N. Ostrowiky, D. Sornette, P. Parker, and E. R. Pike, “Exponential-sampling method for light scattering polydisperity analysis,” J. Mod. Opt. 28, 1059–1070 (1981).

Peacocke, A. R.

R. Foord, E. Jakeman, C. J. Oliver, E. R. Pike, R. J. Blagrove, E. Wood, and A. R. Peacocke, “Determination of diffusion coefficients of haemocyanin at low concentration by intensity fluctuation spectroscopy of scattered laser light,” Nature 227(5255), 242–245 (1970).
[Crossref] [PubMed]

Pike, E. R.

M. Bertero and E. R. Pike, “Exponential sampling method for Laplace and other dilationally invariant tranforms: II. Examples in photon correlation spectroscopy and Fraunhofer diffraction,” Inverse Probl. 7(1), 21–41 (1991).
[Crossref]

N. Ostrowiky, D. Sornette, P. Parker, and E. R. Pike, “Exponential-sampling method for light scattering polydisperity analysis,” J. Mod. Opt. 28, 1059–1070 (1981).

R. Foord, E. Jakeman, C. J. Oliver, E. R. Pike, R. J. Blagrove, E. Wood, and A. R. Peacocke, “Determination of diffusion coefficients of haemocyanin at low concentration by intensity fluctuation spectroscopy of scattered laser light,” Nature 227(5255), 242–245 (1970).
[Crossref] [PubMed]

Provder, T.

T. Provder, Particle Size Distribution: Assessment and Characterization, (ACS Symposium Series, 1987).

Provencher, S. W.

S. W. Provencher, “CONTIN: A general purpose constrained regularization program for inverting noisy linear algebraic and integral equations,” Comput. Phys. Commun. 27(3), 229–242 (1982).
[Crossref]

S. W. Provencher, “A constrained regularization method for inverting data represented by linear algebraic or integral equations,” Comput. Phys. Commun. 27(3), 213–227 (1982).
[Crossref]

Pusey, P. N.

A. G. Mailer, P. S. Clegg, and P. N. Pusey, “Particle sizing by dynamic light scattering: non-linear cumulant analysis,” J. Phys. Condens. Matter 27(14), 145102 (2015).
[Crossref] [PubMed]

Rasteiro, M. G.

M. G. Rasteiro, C. C. Lemos, and A. Vasquez, “Nanoparticle Characterization by PCS: The Analysis of Bimodal Distributions,” Particul. Sci. Technol. 26(5), 413–437 (2008).
[Crossref]

Ravier, P.

M. Naiim, A. Boualem, C. Ferre, M. Jabloun, A. Jalocha, and P. Ravier, “Multiangle dynamic light scattering for the improvement of multimodal particle size distribution measurements,” Soft Matter 11(1), 28–32 (2015).
[Crossref] [PubMed]

Ross, D. A.

D. A. Ross and N. Dimas, “Particle Sizing by Dynamic Light Scattering: Noise and distortion in correlation data,” Part. Part. Syst. Charact. 1(2), 62–69 (1993).
[Crossref]

Roths, T.

R. Buttgereit, T. Roths, J. Honerkamp, and L. B. Aberle, “Simultaneous regularization method for the determination of radius distributions from experimental multiangle correlation functions,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(4), 041404 (2001).
[Crossref] [PubMed]

Ruf, H.

H. Ruf, “Effects of experimental errors in dynamic light scattering data on the results from regularized inversions,” Prog. Colloid Polym. Sci. 115, 255–258 (2000).

H. Ruf and B. J. Gould, “Size distributions of chylomicrons from human lymph from dynamic light scattering measurements,” Eur. Biophys. J. 28(1), 1–11 (1998).
[Crossref] [PubMed]

Schatzel, K.

K. Schatzel, “Correlation techniques in dynamic light scattering,” Appl. Phys. B-Lasers O. 42, 193–213 (1987).

K. Schatzel, “Noise in photon correlation and photon structure functions,” J. Mod. Opt. 30, 155–166 (1983).

Shen, J.

Shi, S.

Song, L.

X. Zhu, J. Shen, and L. Song, “Accurate retrieval of bimodal particle size distribution in dynamic light scattering,” IEEE Photonics Technol. Lett. 28(3), 311–314 (2016).
[Crossref]

Sornette, D.

N. Ostrowiky, D. Sornette, P. Parker, and E. R. Pike, “Exponential-sampling method for light scattering polydisperity analysis,” J. Mod. Opt. 28, 1059–1070 (1981).

Srivastva, R.

Stamatelopolous, P.

Standish, N.

A. B. Yu and N. Standish, “A study of particle size distribution,” Powder Technol. 62(2), 101–118 (1990).
[Crossref]

Staples, E. J.

P. G. Cummins and E. J. Staples, “Particle size distributions determined by a “multiangle” analysis of photon correlation spectroscopy data,” Langmuir 3(6), 1109–1113 (1987).
[Crossref]

Stegmayer, G. S.

L. M. Gugliotta, G. S. Stegmayer, L. A. Clementi, V. D. G. Gonzalez, R. J. Minari, J. R. Leiza, and J. R. Vega, “A neural network model for estimating the particle size distribution of dilute latex from multiangle dynamic light scattering measurements,” Part. Part. Syst. Charact. 26(1-2), 41–52 (2009).
[Crossref]

Sun, X.

Suparno, S.

Thomas, J. C.

X. Liu, J. Shen, J. C. Thomas, S. Shi, X. Sun, and W. Liu, “Multiangle dynamic light scattering analysis using angular intensity weighting determined by iterative recursion,” Appl. Opt. 51(7), 846–854 (2012).
[Crossref] [PubMed]

J. Shen, J. C. Thomas, X. Zhu, and Y. Wang, “Wavelet denoising experiments in dynamic light scattering,” Opt. Express 19(13), 12284–12290 (2011).
[Crossref] [PubMed]

G. Bryant, C. Abeynayake, and J. C. Thomas, “Improved particle size distribution measurements using multiangle dynamic light scattering. 2. refinements and applications,” Langmuir 12(26), 6224–6228 (1996).
[Crossref]

G. Bryant and J. C. Thomas, “Improved particle size distribution measurements using multiangle dynamic light scattering,” Langmuir 11(7), 2480–2485 (1995).
[Crossref]

S. Suparno, K. Deurloo, P. Stamatelopolous, R. Srivastva, and J. C. Thomas, “Light scattering with single-mode fiber collimators,” Appl. Opt. 33(30), 7200–7205 (1994).
[Crossref] [PubMed]

J. C. Thomas, “Photon correlation spectroscopy: technique and instrumentation,” Proc. SPIE 1430, 2–18 (1991).
[Crossref]

Tikhonov, A. N.

A. N. Tikhonov and V. Y. Arsenin, “Solutions of ill-posed problems,” Math. Comput. 32, 491 (1977).

Tsunashima, Y.

E. Gulari, E. Gulari, Y. Tsunashima, and B. Chu, “Photon correlation spectroscopy of particle distributions,” J. Chem. Phys. 70(8), 3965–3972 (1979).
[Crossref]

Vasquez, A.

M. G. Rasteiro, C. C. Lemos, and A. Vasquez, “Nanoparticle Characterization by PCS: The Analysis of Bimodal Distributions,” Particul. Sci. Technol. 26(5), 413–437 (2008).
[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]

L. M. Gugliotta, G. S. Stegmayer, L. A. Clementi, V. D. G. Gonzalez, R. J. Minari, J. R. Leiza, and J. R. Vega, “A neural network model for estimating the particle size distribution of dilute latex from multiangle dynamic light scattering measurements,” Part. Part. Syst. Charact. 26(1-2), 41–52 (2009).
[Crossref]

J. R. Vega, L. M. Gugliotta, V. D. G. Gonzalez, and G. R. Meira, “Latex particle size distribution by dynamic light scattering: novel data processing for multiangle measurements,” J. Colloid Interface Sci. 261(1), 74–81 (2003).
[Crossref] [PubMed]

L. M. Gugliotta, J. R. Vega, and G. R. Meira, “Latex particle size distribution by dynamic light scattering: computer evaluation of two alternative calculation paths,” J. Colloid Interface Sci. 228(1), 14–17 (2000).
[Crossref] [PubMed]

Wang, Y.

Wood, E.

R. Foord, E. Jakeman, C. J. Oliver, E. R. Pike, R. J. Blagrove, E. Wood, and A. R. Peacocke, “Determination of diffusion coefficients of haemocyanin at low concentration by intensity fluctuation spectroscopy of scattered laser light,” Nature 227(5255), 242–245 (1970).
[Crossref] [PubMed]

Yu, A. B.

A. B. Yu and N. Standish, “A study of particle size distribution,” Powder Technol. 62(2), 101–118 (1990).
[Crossref]

Zhu, X.

X. Zhu, J. Shen, and L. Song, “Accurate retrieval of bimodal particle size distribution in dynamic light scattering,” IEEE Photonics Technol. Lett. 28(3), 311–314 (2016).
[Crossref]

J. Shen, J. C. Thomas, X. Zhu, and Y. Wang, “Wavelet denoising experiments in dynamic light scattering,” Opt. Express 19(13), 12284–12290 (2011).
[Crossref] [PubMed]

Ann. Phys. (1)

G. Mie, “Contributions to the optics of turbid media, especially colloidal metal solutions,” Ann. Phys. 25, 377–445 (1908).
[Crossref]

Appl. Opt. (3)

Appl. Phys. B-Lasers O. (1)

K. Schatzel, “Correlation techniques in dynamic light scattering,” Appl. Phys. B-Lasers O. 42, 193–213 (1987).

Chemometr. Intell. Lab. (1)

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]

Comput. Phys. Commun. (2)

S. W. Provencher, “A constrained regularization method for inverting data represented by linear algebraic or integral equations,” Comput. Phys. Commun. 27(3), 213–227 (1982).
[Crossref]

S. W. Provencher, “CONTIN: A general purpose constrained regularization program for inverting noisy linear algebraic and integral equations,” Comput. Phys. Commun. 27(3), 229–242 (1982).
[Crossref]

Eur. Biophys. J. (1)

H. Ruf and B. J. Gould, “Size distributions of chylomicrons from human lymph from dynamic light scattering measurements,” Eur. Biophys. J. 28(1), 1–11 (1998).
[Crossref] [PubMed]

IEEE Photonics Technol. Lett. (1)

X. Zhu, J. Shen, and L. Song, “Accurate retrieval of bimodal particle size distribution in dynamic light scattering,” IEEE Photonics Technol. Lett. 28(3), 311–314 (2016).
[Crossref]

Inverse Probl. (1)

M. Bertero and E. R. Pike, “Exponential sampling method for Laplace and other dilationally invariant tranforms: II. Examples in photon correlation spectroscopy and Fraunhofer diffraction,” Inverse Probl. 7(1), 21–41 (1991).
[Crossref]

J. Chem. Phys. (1)

E. Gulari, E. Gulari, Y. Tsunashima, and B. Chu, “Photon correlation spectroscopy of particle distributions,” J. Chem. Phys. 70(8), 3965–3972 (1979).
[Crossref]

J. Colloid Interface Sci. (2)

J. R. Vega, L. M. Gugliotta, V. D. G. Gonzalez, and G. R. Meira, “Latex particle size distribution by dynamic light scattering: novel data processing for multiangle measurements,” J. Colloid Interface Sci. 261(1), 74–81 (2003).
[Crossref] [PubMed]

L. M. Gugliotta, J. R. Vega, and G. R. Meira, “Latex particle size distribution by dynamic light scattering: computer evaluation of two alternative calculation paths,” J. Colloid Interface Sci. 228(1), 14–17 (2000).
[Crossref] [PubMed]

J. Mod. Opt. (2)

K. Schatzel, “Noise in photon correlation and photon structure functions,” J. Mod. Opt. 30, 155–166 (1983).

N. Ostrowiky, D. Sornette, P. Parker, and E. R. Pike, “Exponential-sampling method for light scattering polydisperity analysis,” J. Mod. Opt. 28, 1059–1070 (1981).

J. Phys. Condens. Matter (1)

A. G. Mailer, P. S. Clegg, and P. N. Pusey, “Particle sizing by dynamic light scattering: non-linear cumulant analysis,” J. Phys. Condens. Matter 27(14), 145102 (2015).
[Crossref] [PubMed]

Langmuir (4)

I. D. Morrison, E. F. Grabowski, and C. A. Herb, “Improved techniques for particle size determination by quasi-elastic light scattering,” Langmuir 1(4), 496–501 (1985).
[Crossref]

P. G. Cummins and E. J. Staples, “Particle size distributions determined by a “multiangle” analysis of photon correlation spectroscopy data,” Langmuir 3(6), 1109–1113 (1987).
[Crossref]

G. Bryant and J. C. Thomas, “Improved particle size distribution measurements using multiangle dynamic light scattering,” Langmuir 11(7), 2480–2485 (1995).
[Crossref]

G. Bryant, C. Abeynayake, and J. C. Thomas, “Improved particle size distribution measurements using multiangle dynamic light scattering. 2. refinements and applications,” Langmuir 12(26), 6224–6228 (1996).
[Crossref]

Math. Comput. (1)

A. N. Tikhonov and V. Y. Arsenin, “Solutions of ill-posed problems,” Math. Comput. 32, 491 (1977).

Nature (1)

R. Foord, E. Jakeman, C. J. Oliver, E. R. Pike, R. J. Blagrove, E. Wood, and A. R. Peacocke, “Determination of diffusion coefficients of haemocyanin at low concentration by intensity fluctuation spectroscopy of scattered laser light,” Nature 227(5255), 242–245 (1970).
[Crossref] [PubMed]

Opt. Express (1)

Part. Part. Syst. Charact. (2)

L. M. Gugliotta, G. S. Stegmayer, L. A. Clementi, V. D. G. Gonzalez, R. J. Minari, J. R. Leiza, and J. R. Vega, “A neural network model for estimating the particle size distribution of dilute latex from multiangle dynamic light scattering measurements,” Part. Part. Syst. Charact. 26(1-2), 41–52 (2009).
[Crossref]

D. A. Ross and N. Dimas, “Particle Sizing by Dynamic Light Scattering: Noise and distortion in correlation data,” Part. Part. Syst. Charact. 1(2), 62–69 (1993).
[Crossref]

Particul. Sci. Technol. (1)

M. G. Rasteiro, C. C. Lemos, and A. Vasquez, “Nanoparticle Characterization by PCS: The Analysis of Bimodal Distributions,” Particul. Sci. Technol. 26(5), 413–437 (2008).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

R. Buttgereit, T. Roths, J. Honerkamp, and L. B. Aberle, “Simultaneous regularization method for the determination of radius distributions from experimental multiangle correlation functions,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 64(4), 041404 (2001).
[Crossref] [PubMed]

Powder Technol. (1)

A. B. Yu and N. Standish, “A study of particle size distribution,” Powder Technol. 62(2), 101–118 (1990).
[Crossref]

Proc. SPIE (1)

J. C. Thomas, “Photon correlation spectroscopy: technique and instrumentation,” Proc. SPIE 1430, 2–18 (1991).
[Crossref]

Prog. Colloid Polym. Sci. (1)

H. Ruf, “Effects of experimental errors in dynamic light scattering data on the results from regularized inversions,” Prog. Colloid Polym. Sci. 115, 255–258 (2000).

Soft Matter (1)

M. Naiim, A. Boualem, C. Ferre, M. Jabloun, A. Jalocha, and P. Ravier, “Multiangle dynamic light scattering for the improvement of multimodal particle size distribution measurements,” Soft Matter 11(1), 28–32 (2015).
[Crossref] [PubMed]

Other (4)

A. Jillavenkatesa, S. J. Dapkunas, and L. S. H. Lum, Particle Size Characterization (Helsingin Yliopisto, 2001).

T. Provder, Particle Size Distribution: Assessment and Characterization, (ACS Symposium Series, 1987).

K. Schatzel, Dynamic Light Scattering, W. Brown, ed. (Oxford University, 1993).

R. Peters, Dynamic Light Scattering, W. Brown, ed. (Oxford University, 1993).

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Figures (12)

Fig. 1
Fig. 1 Normalized light intensity ACF data (a), G(τ), obtained from experimental sample AE at 90°scattering angle; Normalized electric field ACF data (b), g(τ), calculated from G(τ); The noise in G(τ) (c) and g(τ) (d), nI(τ) and nf(τ), extracted by wavelet analysis.
Fig. 2
Fig. 2 Simulated light intensity ACF data for the PSDs with 95nm mean diameter (a); PSD information distribution in the simulated ACF data for the bimodal PSDs (b); PSDs estimated from the simulated ACF data by using the common CR method (c).
Fig. 3
Fig. 3 Simulated light intensity ACF data for the PSDs with 188nm mean diameter (a); PSD information distribution in the simulated ACF data for the bimodal PSDs (b); PSDs estimated from the simulated ACF data by using the common CR method (c).
Fig. 4
Fig. 4 Simulated light intensity ACF data for the PSDs with 350nm mean diameter (a); PSD information distribution in the simulated ACF data for the bimodal PSDs (b); PSDs estimated from the simulated ACF data by using the common CR method (c).
Fig. 5
Fig. 5 Simulated light intensity ACF data for the PSDs with 500nm mean diameter (a); PSD information distribution in the simulated ACF data for the bimodal PSDs (b); PSDs estimated from the simulated ACF data by using the common CR method (c).
Fig. 6
Fig. 6 Simulated light intensity ACF data for the PSDs with 800nm mean diameter (a); PSD information distribution in the simulated ACF data for the bimodal PSDs (b); PSDs estimated from the simulated ACF data by using the common CR method (c).
Fig. 7
Fig. 7 Simulated and estimated values for Sample AS, a bimodal particle size distribution with peaks at 400 nm and 608 nm. The recovery of PSD is estimated by different constrained regularization methods (W0, W1 and W2) in single-angle DLS (a), three-angle DLS (b) and six-angle DLS (c).
Fig. 8
Fig. 8 Simulated and estimated values for Sample BS, a bimodal particle size distribution with peaks at 448 nm and 608 nm. The recovery of PSD is estimated by different constrained regularization methods (W0, W1 and W2) in single-angle DLS (a), three-angle DLS (b) and six-angle DLS (c).
Fig. 9
Fig. 9 Simulated and estimated values for Sample CS, a bimodal particle size distribution with peaks at 500 nm and 600 nm. The recovery of PSD is estimated by different constrained regularization methods (W0, W1 and W2) in single-angle DLS (a), three-angle DLS (b) and six-angle DLS (c).
Fig. 10
Fig. 10 Estimated particle size distribution for Sample AE, a 306 nm and 974 nm bimodal latex sphere sample mixed in the ratio 1:1, using different constrained regularization methods (W0, W1 and W2) in single-angle DLS (a), three-angle DLS (b) and six-angle DLS (c).
Fig. 11
Fig. 11 Estimated particle size distribution for Sample BE, a 306 nm and 974 nm bimodal latex sphere sample mixed in the ratio 1:2, using different constrained regularization methods (W0, W1 and W2) in single-angle DLS (a), three-angle DLS (b) and six-angle DLS (c)
Fig. 12
Fig. 12 Estimated particle size distribution for Sample CE, a 300 nm and 502 nm bimodal latex sphere sample mixed in the ratio 5:1, using different constrained regularization methods (W0, W1 and W2) in single-angle DLS (a), three-angle DLS (b) and six-angle DLS (c)

Tables (9)

Tables Icon

Table 1 Properties of Simulated ACF Data Sets for the Unimodal and Bimodal PSDs, and a Summary of Particle Sizing Results from Single-angle DLS with a Constrained Regularization Method.

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Table 2 Parameters of Simulated Bimodal Polydisperse PSD Data Sets.

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Table 3 Properties of Simulated ACF Data Sets for the Bimodal Polydisperse PSDs.

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Table 4 Performance indices (PP, EPP, RPH and V) of the true and recovered PSDs for Sample AS.

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Table 5 Performance indices (PP, EPP, RPH and V) of the true and recovered PSDs for Sample BS.

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Table 6 Performance indices (PP, EPP, RPH and V) of the true and recovered PSDs for Sample CS

Tables Icon

Table 7 Performance indices (PP, EPP, and RPH) of the true and recovered PSDs for Sample AE

Tables Icon

Table 8 Performance indices (PP, EPP, and RPH) of the true and recovered PSDs for Sample BE

Tables Icon

Table 9 Performance indices (PP, EPP, and RPH) of the true and recovered PSDs for Sample CE

Equations (15)

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

G θ ( 2 ) ( τ )= lim T 0 0 T 0 i θ ( t ) i θ ( t+τ )dt/ T 0 .
G θ ( 2 ) ( τ j )= lim M k=1 M i θ ( τ k ) i θ ( τ k+j )/M .
G θ ( 2 ) ( τ j )=B( 1+β( θ ) | g θ ( 1 ) ( τ j ) | 2 ).
g θ ( 1 ) ( τ j )= i=1 N exp( Γ( θ, d i ) τ j ) h θ ( d i ) .
Γ( θ, d i )= 16πk T B n m 2 ( λ 0 ) sin 2 ( θ/2 ) 3η d i λ 0 2 .
h θ ( d i )= k θ C Iθ ( d i )f( d i ).
g θ (1) = k θ A θ f.
A θ ( j,i )=exp( 16π k B T n m 2 sin 2 ( θ/2 ) 3η d i λ 0 2 τ j ) C Iθ ( d i ).
G θ_noise ( 2 ) ( τ j )= G θ ( 2 ) ( τ j )+δ n I ( τ j ).
M α ( f )= W θ ( A θ f g θ ( 1 ) ) 2 +α Lf 2 ,0f1.
w θ_j = | g θ_j ( 1 ) | PI D θ_j /2 .
g W ( 1 ) =[ W 1 g θ 1 ( 1 ) W 2 g θ 2 ( 1 ) W m g θ m ( 1 ) ]=[ k 1 W 1 A θ 1 k 2 W 2 A θ 2 k m W m A θ m ]f= A W f.
M α ( f )= A W f g W ( 1 ) 2 +α Lf 2 ,0f1.
R PH = HI P 1 / HI P 2 E PP =| ( P P true P P meas )/ P P true | V= { ( 1 K [ f true (d) f meas (d) ] 2 )/K } 1/2 .
f(d)=a σ 1 ( d max - d min ) 2π [t(1t)] 1 exp{ 0.5 [ u 1 + σ 1 ln( t 1t )] 2 } +b σ 2 ( d max - d min ) 2π [t(1t)] 1 exp{ 0.5 [ u 2 + σ 2 ln( t 1t )] 2 },(a+b=1).

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