Abstract

The paper puts forward a new method of ultrafine particle size measurement using small amounts of data of a dynamic light-scattering signal, and establishes an arithmetic model of the measurement by wavelet package transform. First, through the wavelet package transform, the ultrafine particle dynamic light-scattering signals were decomposed into multifrequency bands. Then, the noise of signals of different frequency bands were removed and the power spectrum of the wavelet packet coefficients of each frequency band was calculated. Finally, the ultrafine particle size distribution information could be deduced from inversing the power spectrum. The standard polystyrene particles of 100, 300, and 400nm were measured using this method, and the inversion results indicated that this method can effectively remove noise and improve the accuracy of particle size measurement using small amounts of data.

© 2011 Optical Society of America

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References

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  1. R. Pecora, Dynamic Light Scattering: Applications of Photon Correlation Spectroscopy (Plenum, 1985), pp. 45–50.
  2. R. Finsy, N. de Jaeger, R. Sneyers, and E. Geladé, “Particle sizing by photon correlation spectroscopy. part III: mono and bimodal distributions and data analysis,” Part. Part. Syst. Charact. 9, 125–137 (1992).
    [CrossRef]
  3. W. Krahn, M. Luckas, and K. Lucas, “Determination of particle size distribution in fluids using photon correlation spectroscopy,” Part. Part. Syst. Charact. 5, 72–76 (1988).
    [CrossRef]
  4. H. Yang, G. Zheng, and M.-C. Li, “A discussion of noise in dynamic light scattering for particle sizing,” Part. Part. Syst. Charact. 25, 406–413 (2009).
    [CrossRef]
  5. D. A. Ross and N. Dimas, “Particle sizing by dynamic light scattering: Noise and distortion in correlation data,” Part. Part. Syst. Charact. 10, 62–69 (1993).
    [CrossRef]
  6. J. Barros and R. I. Diego, “Analysis of harmonics in power systems using the wavelet-packet transform,” IEEE Trans. Instrum. Meas. 57, 63–69 (2008).
    [CrossRef]
  7. X. Fan and M. J. Zuo, “Gearbox fault detection using Hilbert and wavelet packet transform,” Mech. Sys. Sig. Process. 20, 966–982 (2006).
    [CrossRef]
  8. Y. Andreopoulos and M. van der Schaar, “Generalized phase shifting for M-band discrete wavelet packet transforms,” IEEE Trans. Signal Process. 55, 742–747(2007).
    [CrossRef]
  9. Y. Ao and G. Qiao, “Prognostics for drilling process with wavelet packet decomposition,” Int. J. Adv. Manuf. Technol. 50, 47–52 (2010).
    [CrossRef]
  10. D. L. Donoho and I. M. Johnstone , “Ideal spatial adaptation by wavelet shrinkage,” Biometrika 81, 425–455(1994).
    [CrossRef]
  11. Y.-J. Wang, G. Zheng, J. Shen, W. Liu, and X.-J. Zhu, “Simulation of dynamic light scattering signal for ultrafine particles based on the exponential model,” Optoelectron. Lett. l6, 302–305 (2010).
    [CrossRef]

2010 (2)

Y. Ao and G. Qiao, “Prognostics for drilling process with wavelet packet decomposition,” Int. J. Adv. Manuf. Technol. 50, 47–52 (2010).
[CrossRef]

Y.-J. Wang, G. Zheng, J. Shen, W. Liu, and X.-J. Zhu, “Simulation of dynamic light scattering signal for ultrafine particles based on the exponential model,” Optoelectron. Lett. l6, 302–305 (2010).
[CrossRef]

2009 (1)

H. Yang, G. Zheng, and M.-C. Li, “A discussion of noise in dynamic light scattering for particle sizing,” Part. Part. Syst. Charact. 25, 406–413 (2009).
[CrossRef]

2008 (1)

J. Barros and R. I. Diego, “Analysis of harmonics in power systems using the wavelet-packet transform,” IEEE Trans. Instrum. Meas. 57, 63–69 (2008).
[CrossRef]

2007 (1)

Y. Andreopoulos and M. van der Schaar, “Generalized phase shifting for M-band discrete wavelet packet transforms,” IEEE Trans. Signal Process. 55, 742–747(2007).
[CrossRef]

2006 (1)

X. Fan and M. J. Zuo, “Gearbox fault detection using Hilbert and wavelet packet transform,” Mech. Sys. Sig. Process. 20, 966–982 (2006).
[CrossRef]

1994 (1)

D. L. Donoho and I. M. Johnstone , “Ideal spatial adaptation by wavelet shrinkage,” Biometrika 81, 425–455(1994).
[CrossRef]

1993 (1)

D. A. Ross and N. Dimas, “Particle sizing by dynamic light scattering: Noise and distortion in correlation data,” Part. Part. Syst. Charact. 10, 62–69 (1993).
[CrossRef]

1992 (1)

R. Finsy, N. de Jaeger, R. Sneyers, and E. Geladé, “Particle sizing by photon correlation spectroscopy. part III: mono and bimodal distributions and data analysis,” Part. Part. Syst. Charact. 9, 125–137 (1992).
[CrossRef]

1988 (1)

W. Krahn, M. Luckas, and K. Lucas, “Determination of particle size distribution in fluids using photon correlation spectroscopy,” Part. Part. Syst. Charact. 5, 72–76 (1988).
[CrossRef]

Andreopoulos, Y.

Y. Andreopoulos and M. van der Schaar, “Generalized phase shifting for M-band discrete wavelet packet transforms,” IEEE Trans. Signal Process. 55, 742–747(2007).
[CrossRef]

Ao, Y.

Y. Ao and G. Qiao, “Prognostics for drilling process with wavelet packet decomposition,” Int. J. Adv. Manuf. Technol. 50, 47–52 (2010).
[CrossRef]

Barros, J.

J. Barros and R. I. Diego, “Analysis of harmonics in power systems using the wavelet-packet transform,” IEEE Trans. Instrum. Meas. 57, 63–69 (2008).
[CrossRef]

de Jaeger, N.

R. Finsy, N. de Jaeger, R. Sneyers, and E. Geladé, “Particle sizing by photon correlation spectroscopy. part III: mono and bimodal distributions and data analysis,” Part. Part. Syst. Charact. 9, 125–137 (1992).
[CrossRef]

Diego, R. I.

J. Barros and R. I. Diego, “Analysis of harmonics in power systems using the wavelet-packet transform,” IEEE Trans. Instrum. Meas. 57, 63–69 (2008).
[CrossRef]

Dimas, N.

D. A. Ross and N. Dimas, “Particle sizing by dynamic light scattering: Noise and distortion in correlation data,” Part. Part. Syst. Charact. 10, 62–69 (1993).
[CrossRef]

Donoho, D. L.

D. L. Donoho and I. M. Johnstone , “Ideal spatial adaptation by wavelet shrinkage,” Biometrika 81, 425–455(1994).
[CrossRef]

Fan, X.

X. Fan and M. J. Zuo, “Gearbox fault detection using Hilbert and wavelet packet transform,” Mech. Sys. Sig. Process. 20, 966–982 (2006).
[CrossRef]

Finsy, R.

R. Finsy, N. de Jaeger, R. Sneyers, and E. Geladé, “Particle sizing by photon correlation spectroscopy. part III: mono and bimodal distributions and data analysis,” Part. Part. Syst. Charact. 9, 125–137 (1992).
[CrossRef]

Geladé, E.

R. Finsy, N. de Jaeger, R. Sneyers, and E. Geladé, “Particle sizing by photon correlation spectroscopy. part III: mono and bimodal distributions and data analysis,” Part. Part. Syst. Charact. 9, 125–137 (1992).
[CrossRef]

Johnstone, I. M.

D. L. Donoho and I. M. Johnstone , “Ideal spatial adaptation by wavelet shrinkage,” Biometrika 81, 425–455(1994).
[CrossRef]

Krahn, W.

W. Krahn, M. Luckas, and K. Lucas, “Determination of particle size distribution in fluids using photon correlation spectroscopy,” Part. Part. Syst. Charact. 5, 72–76 (1988).
[CrossRef]

Li, M.-C.

H. Yang, G. Zheng, and M.-C. Li, “A discussion of noise in dynamic light scattering for particle sizing,” Part. Part. Syst. Charact. 25, 406–413 (2009).
[CrossRef]

Liu, W.

Y.-J. Wang, G. Zheng, J. Shen, W. Liu, and X.-J. Zhu, “Simulation of dynamic light scattering signal for ultrafine particles based on the exponential model,” Optoelectron. Lett. l6, 302–305 (2010).
[CrossRef]

Lucas, K.

W. Krahn, M. Luckas, and K. Lucas, “Determination of particle size distribution in fluids using photon correlation spectroscopy,” Part. Part. Syst. Charact. 5, 72–76 (1988).
[CrossRef]

Luckas, M.

W. Krahn, M. Luckas, and K. Lucas, “Determination of particle size distribution in fluids using photon correlation spectroscopy,” Part. Part. Syst. Charact. 5, 72–76 (1988).
[CrossRef]

Pecora, R.

R. Pecora, Dynamic Light Scattering: Applications of Photon Correlation Spectroscopy (Plenum, 1985), pp. 45–50.

Qiao, G.

Y. Ao and G. Qiao, “Prognostics for drilling process with wavelet packet decomposition,” Int. J. Adv. Manuf. Technol. 50, 47–52 (2010).
[CrossRef]

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. 10, 62–69 (1993).
[CrossRef]

Shen, J.

Y.-J. Wang, G. Zheng, J. Shen, W. Liu, and X.-J. Zhu, “Simulation of dynamic light scattering signal for ultrafine particles based on the exponential model,” Optoelectron. Lett. l6, 302–305 (2010).
[CrossRef]

Sneyers, R.

R. Finsy, N. de Jaeger, R. Sneyers, and E. Geladé, “Particle sizing by photon correlation spectroscopy. part III: mono and bimodal distributions and data analysis,” Part. Part. Syst. Charact. 9, 125–137 (1992).
[CrossRef]

van der Schaar, M.

Y. Andreopoulos and M. van der Schaar, “Generalized phase shifting for M-band discrete wavelet packet transforms,” IEEE Trans. Signal Process. 55, 742–747(2007).
[CrossRef]

Wang, Y.-J.

Y.-J. Wang, G. Zheng, J. Shen, W. Liu, and X.-J. Zhu, “Simulation of dynamic light scattering signal for ultrafine particles based on the exponential model,” Optoelectron. Lett. l6, 302–305 (2010).
[CrossRef]

Yang, H.

H. Yang, G. Zheng, and M.-C. Li, “A discussion of noise in dynamic light scattering for particle sizing,” Part. Part. Syst. Charact. 25, 406–413 (2009).
[CrossRef]

Zheng, G.

Y.-J. Wang, G. Zheng, J. Shen, W. Liu, and X.-J. Zhu, “Simulation of dynamic light scattering signal for ultrafine particles based on the exponential model,” Optoelectron. Lett. l6, 302–305 (2010).
[CrossRef]

H. Yang, G. Zheng, and M.-C. Li, “A discussion of noise in dynamic light scattering for particle sizing,” Part. Part. Syst. Charact. 25, 406–413 (2009).
[CrossRef]

Zhu, X.-J.

Y.-J. Wang, G. Zheng, J. Shen, W. Liu, and X.-J. Zhu, “Simulation of dynamic light scattering signal for ultrafine particles based on the exponential model,” Optoelectron. Lett. l6, 302–305 (2010).
[CrossRef]

Zuo, M. J.

X. Fan and M. J. Zuo, “Gearbox fault detection using Hilbert and wavelet packet transform,” Mech. Sys. Sig. Process. 20, 966–982 (2006).
[CrossRef]

Biometrika (1)

D. L. Donoho and I. M. Johnstone , “Ideal spatial adaptation by wavelet shrinkage,” Biometrika 81, 425–455(1994).
[CrossRef]

IEEE Trans. Instrum. Meas. (1)

J. Barros and R. I. Diego, “Analysis of harmonics in power systems using the wavelet-packet transform,” IEEE Trans. Instrum. Meas. 57, 63–69 (2008).
[CrossRef]

IEEE Trans. Signal Process. (1)

Y. Andreopoulos and M. van der Schaar, “Generalized phase shifting for M-band discrete wavelet packet transforms,” IEEE Trans. Signal Process. 55, 742–747(2007).
[CrossRef]

Int. J. Adv. Manuf. Technol. (1)

Y. Ao and G. Qiao, “Prognostics for drilling process with wavelet packet decomposition,” Int. J. Adv. Manuf. Technol. 50, 47–52 (2010).
[CrossRef]

Mech. Sys. Sig. Process. (1)

X. Fan and M. J. Zuo, “Gearbox fault detection using Hilbert and wavelet packet transform,” Mech. Sys. Sig. Process. 20, 966–982 (2006).
[CrossRef]

Optoelectron. Lett. (1)

Y.-J. Wang, G. Zheng, J. Shen, W. Liu, and X.-J. Zhu, “Simulation of dynamic light scattering signal for ultrafine particles based on the exponential model,” Optoelectron. Lett. l6, 302–305 (2010).
[CrossRef]

Part. Part. Syst. Charact. (4)

R. Finsy, N. de Jaeger, R. Sneyers, and E. Geladé, “Particle sizing by photon correlation spectroscopy. part III: mono and bimodal distributions and data analysis,” Part. Part. Syst. Charact. 9, 125–137 (1992).
[CrossRef]

W. Krahn, M. Luckas, and K. Lucas, “Determination of particle size distribution in fluids using photon correlation spectroscopy,” Part. Part. Syst. Charact. 5, 72–76 (1988).
[CrossRef]

H. Yang, G. Zheng, and M.-C. Li, “A discussion of noise in dynamic light scattering for particle sizing,” Part. Part. Syst. Charact. 25, 406–413 (2009).
[CrossRef]

D. A. Ross and N. Dimas, “Particle sizing by dynamic light scattering: Noise and distortion in correlation data,” Part. Part. Syst. Charact. 10, 62–69 (1993).
[CrossRef]

Other (1)

R. Pecora, Dynamic Light Scattering: Applications of Photon Correlation Spectroscopy (Plenum, 1985), pp. 45–50.

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Figures (4)

Fig. 1
Fig. 1

Arithmetic model of measurement of ultrafine particle DLS.

Fig. 2
Fig. 2

Frequency band division: (a) confusing frequency bands, (b) adjusted frequency.

Fig. 3
Fig. 3

ACFs for DLSs of 100 nm particles in different data lengths. (a)  N = 8192 , (b)  N = 65 , 536 , (c)  N = 524 , 288 , (d)  N = 1 , 048 , 576 .

Fig. 4
Fig. 4

Power spectrums of the noise-removed wavelet coefficients in different data lengths. (a)  N = 8192 , (b)  N = 65 , 536 , (c)  N = 524 , 288 , (d)  N = 1 , 048 , 576 .

Tables (3)

Tables Icon

Table 1 Relationship of Theoretical and Actual Node Sequence

Tables Icon

Table 2 Inversion Results of ACF of Noisy Signals in Different Data Lengths

Tables Icon

Table 3 Inversion Results of Noisy Signals Using the Wavelet Package Method in Different Data Lengths

Equations (15)

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

ϕ ( t ) = 2 k h ( k ) ϕ ( 2 t k ) ,
ψ ( t ) = 2 k g ( k ) ϕ ( 2 t k ) ,
w 2 n ( t ) = 2 k Z h ( k ) w n ( 2 t k ) ,
w 2 n + 1 ( t ) = 2 k z g ( k ) w n ( 2 t k ) ,
g j n ( t ) = k d k j , n w n ( 2 j t k ) ,
I ( k ) = s ( k ) + e ( k ) k = 0 , 1 , , n 1 ,
G i = B i + 1 B i ,
u k j , n = { sign ( d k j , n ) ( | d k j , n | λ ) | d k j , n | λ 0 | d k j , n | λ ,
λ = σ 2 log ( N ) .
σ = MAD 0.6745 ,
P j , n = 1 M k = 1 M | u k j , n | 2 k = 1 , 2 , , M ,
P ( ω ) = 2 Γ / π ω 2 + ( 2 Γ ) 2 .
Γ = D q 2 ,
q = 4 π n λ sin ( θ 2 ) ,
D = K B T 3 π η d ,

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