Abstract

Conventional methods for estimating particle size distribution (PSD) based on the computed field autocorrelation function (ACF) of dynamic light scattering data are prone to baseline error and random measurement errors. To reduce the effects of the errors efficiently and automatically, we propose a penalized nonlinear nonnegative least squares (NNLS) method based on the measured photon ACF that simultaneously determines the PSD and the unknown baseline. In simulations and experiments, the proposed method was able to estimate the PSD more accurately than the existing NNLS method using the computed field ACF.

© 2013 Optical Society of America

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References

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  1. R. Xu, Particle Characterization: Light Scattering Methods, Vol. 13 (Kluwer, 2001).
  2. B. Frisken, Appl. Opt. 40, 4087 (2001).
    [CrossRef]
  3. G. Bryant, C. Abeynayake, and J. Thomas, Langmuir 12, 6224 (1996).
    [CrossRef]
  4. S. Provencher, Comput. Phys. Commun. 27, 229 (1982).
    [CrossRef]
  5. X. Zhu, J. Shen, W. Liu, X. Sun, and Y. Wang, Appl. Opt. 49, 6591 (2010).
    [CrossRef]
  6. A. R. Roig and J. L. Alessandrini, Part. Part. Syst. Charact. 23, 431 (2006).
    [CrossRef]
  7. J. Vargas-Ubera, J. F. Aguilar, and D. M. Gale, Appl. Opt. 46, 124 (2007).
    [CrossRef]
  8. X. Zhu, J. Shen, and J. C. Thomas, Appl. Opt. 51, 7537 (2012).
    [CrossRef]
  9. H. Ruf, Biophys. J. 56, 67 (1989).
    [CrossRef]
  10. H. Ruf, E. Grell, and E. H. K. Stelzer, Eur. Biophys. J. 21, 21 (1992).
    [CrossRef]

2012 (1)

2010 (1)

2007 (1)

2006 (1)

A. R. Roig and J. L. Alessandrini, Part. Part. Syst. Charact. 23, 431 (2006).
[CrossRef]

2001 (1)

1996 (1)

G. Bryant, C. Abeynayake, and J. Thomas, Langmuir 12, 6224 (1996).
[CrossRef]

1992 (1)

H. Ruf, E. Grell, and E. H. K. Stelzer, Eur. Biophys. J. 21, 21 (1992).
[CrossRef]

1989 (1)

H. Ruf, Biophys. J. 56, 67 (1989).
[CrossRef]

1982 (1)

S. Provencher, Comput. Phys. Commun. 27, 229 (1982).
[CrossRef]

Abeynayake, C.

G. Bryant, C. Abeynayake, and J. Thomas, Langmuir 12, 6224 (1996).
[CrossRef]

Aguilar, J. F.

Alessandrini, J. L.

A. R. Roig and J. L. Alessandrini, Part. Part. Syst. Charact. 23, 431 (2006).
[CrossRef]

Bryant, G.

G. Bryant, C. Abeynayake, and J. Thomas, Langmuir 12, 6224 (1996).
[CrossRef]

Frisken, B.

Gale, D. M.

Grell, E.

H. Ruf, E. Grell, and E. H. K. Stelzer, Eur. Biophys. J. 21, 21 (1992).
[CrossRef]

Liu, W.

Provencher, S.

S. Provencher, Comput. Phys. Commun. 27, 229 (1982).
[CrossRef]

Roig, A. R.

A. R. Roig and J. L. Alessandrini, Part. Part. Syst. Charact. 23, 431 (2006).
[CrossRef]

Ruf, H.

H. Ruf, E. Grell, and E. H. K. Stelzer, Eur. Biophys. J. 21, 21 (1992).
[CrossRef]

H. Ruf, Biophys. J. 56, 67 (1989).
[CrossRef]

Shen, J.

Stelzer, E. H. K.

H. Ruf, E. Grell, and E. H. K. Stelzer, Eur. Biophys. J. 21, 21 (1992).
[CrossRef]

Sun, X.

Thomas, J.

G. Bryant, C. Abeynayake, and J. Thomas, Langmuir 12, 6224 (1996).
[CrossRef]

Thomas, J. C.

Vargas-Ubera, J.

Wang, Y.

Xu, R.

R. Xu, Particle Characterization: Light Scattering Methods, Vol. 13 (Kluwer, 2001).

Zhu, X.

Appl. Opt. (4)

Biophys. J. (1)

H. Ruf, Biophys. J. 56, 67 (1989).
[CrossRef]

Comput. Phys. Commun. (1)

S. Provencher, Comput. Phys. Commun. 27, 229 (1982).
[CrossRef]

Eur. Biophys. J. (1)

H. Ruf, E. Grell, and E. H. K. Stelzer, Eur. Biophys. J. 21, 21 (1992).
[CrossRef]

Langmuir (1)

G. Bryant, C. Abeynayake, and J. Thomas, Langmuir 12, 6224 (1996).
[CrossRef]

Part. Part. Syst. Charact. (1)

A. R. Roig and J. L. Alessandrini, Part. Part. Syst. Charact. 23, 431 (2006).
[CrossRef]

Other (1)

R. Xu, Particle Characterization: Light Scattering Methods, Vol. 13 (Kluwer, 2001).

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Figures (2)

Fig. 1.
Fig. 1.

Recovered PSDs using the proposed and the NNLSR methods in the simulations: (a) PSD 1, (b) PSD 2, (c) PSD 3, and (d) PSD 4.

Fig. 2.
Fig. 2.

Recovered PSD using the proposed method, the proposed method without baseline correction, and the NNLSR method in experiments: (a) sample 1, (b) sample 2, (c) sample 3, and (d) sample 4.

Tables (1)

Tables Icon

Table 1. Peak Locations and Intensity Ratios of PSDs

Equations (7)

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g(1)=Hx,
Hij=eΓiτj,i=1,,L,j=1,,M.
g(2)(τk)=1+f(A)|g(1)(τk)|2,
g^(2)(τk)=(1Be)+(1Be)f(A)|g(1)(τk)|2+ek,
|g^(1)(τk)|=(1Be)f(A)|g(1)(τk)|2Be+ek.
x^=argminx>0i=1L(g^(1)(τi)[Hx]i)2,
(x^,B^)=argminx>0,Bi=1L(g^(2)(τi)B([Hx]i)2)2+λxTRTRx,

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