## Wavelet denoising experiments in dynamic light scattering |

Optics Express, Vol. 19, Issue 13, pp. 12284-12290 (2011)

http://dx.doi.org/10.1364/OE.19.012284

Acrobat PDF (858 KB)

### Abstract

Dynamic light scattering (DLS) is widely used for particle size measurement. Recovering accurate particle sizes from noisy DLS measurements (short duration and/or low count rate) is problematic. We demonstrate that denoising of the light scattering signal using wavelet packet filtering is beneficial and leads to more accurate particle sizes being recovered.

© 2011 OSA

## 1. Introduction

1. R. Pecora, “Doppler shifts in light scattering from pure liquids and polymer solutions,” J. Chem. Phys. **40**(6), 1604–1614 (1964). [CrossRef]

3. N. C. Ford Jr and G. B. Benedek, “Observation of the spectrum of light scattered from a pure fluid near it’s critical point,” Phys. Rev. Lett. **15**(16), 649–653 (1965). [CrossRef]

## 2. Wavelet packet denoising method

*j*is the decomposition layer number,

*k*is the time series shift index,

*l*is the wavelet packet coefficient sequence index and

*n*is the wavelet packet node number.

*i*

^{th}sample of the signal with noise can be written aswhere

*δ*the noise intensity. Because the wavelet transform is linear, the wavelet transform of

## 3. Experiments and results

^{+}laser operating at a wavelength of 488nm. The time-history scattered light signals were captured with a DSO which had 500MHz bandwidth, 2.5 GS/s sample rate and a 10 megapoint record length (Tektronix MSO4054 Mixed Signal Oscilloscope).

16. D. E. Koppel, “Analysis of macromolecular polydispersity in intensity correlation spectroscopy: The method of cumulants,” J. Chem. Phys. **57**(11), 4814–4820 (1972). [CrossRef]

^{−1}), 1033µs (Г = 968s

^{−1}), 1739µs (Г = 575s

^{−1}), and 3564µs (Г = 281s

^{−1}) respectively. From these we can calculate the average number of photon counts detected in a coherence time,

## 4. Discussion and conclusions

17. J. N. Shaumeyer, M. E. Briggs, and R. W. Gammon, “Statistical fitting accuracy in photon correlation spectroscopy,” Appl. Opt. **32**(21), 3871–3879 (1993). [PubMed]

## Acknowledgments

## References and links

1. | R. Pecora, “Doppler shifts in light scattering from pure liquids and polymer solutions,” J. Chem. Phys. |

2. | H. Z. Cummins, N. Knable, and Y. Yeh, “Observation of diffusion broadening of Rayleigh scattered light,” Phys. Rev. Lett. |

3. | N. C. Ford Jr and G. B. Benedek, “Observation of the spectrum of light scattered from a pure fluid near it’s critical point,” Phys. Rev. Lett. |

4. | S. P. Lee, W. Tscharnuter, and B. Chu, “Calibration of an optical self-beating spectrometer by polystyrene latex spheres, and confirmation of the Stokes-Einstein formula,” Polym. Sci. |

5. | ISO 13321: Particle size analysis–Photon correlation spectroscopy (1996). |

6. | ISO 22412: Particle size analysis–Dynamic light scattering (DLS) (2008). |

7. | J. C. Thomas, “Photon correlation spectroscopy: technique and instrumentation,” Proc. SPIE |

8. | J. B. Lastovka, “Light mixing spectroscopy and the spectrum of light scattered by thermal fluctuations in liquids,” PhD Thesis, Massachusetts Institute of Technology, 1968. |

9. | V. Degiorgio and J. B. Lastovka, “Intensity correlation spectroscopy,” Phys. Rev. A |

10. | K. Schätzel, “Noise in photon correlation and photon structure functions,” Opt. Acta (Lond.) |

11. | D. A. Ross and N. Dimas, “Particle sizing by dynamic light scattering: noise and distortion in correlation data,” Part. Part. Syst. Charact. |

12. | W. Brown, |

13. | B. Lou, “The influence and corresponding solution of noise in DLS particle sizing experiment,” J. Light Scattering |

14. | H. Yang, G. Zheng, and M. Li, “A discussion of noise in dynamic light scattering for particle sizing,” Part. Part. Syst. Charact. |

15. | J. Shen, J. C. Thomas, X. Zhu, and Y. Wang, “Wavelet noise reduction in dynamic light scattering,” The International Conference on Information Science and Technology (CSIE 2011), 2011 (to be published). |

16. | D. E. Koppel, “Analysis of macromolecular polydispersity in intensity correlation spectroscopy: The method of cumulants,” J. Chem. Phys. |

17. | J. N. Shaumeyer, M. E. Briggs, and R. W. Gammon, “Statistical fitting accuracy in photon correlation spectroscopy,” Appl. Opt. |

**OCIS Codes**

(290.5850) Scattering : Scattering, particles

(110.7410) Imaging systems : Wavelets

**ToC Category:**

Scattering

**History**

Original Manuscript: March 25, 2011

Revised Manuscript: June 2, 2011

Manuscript Accepted: June 6, 2011

Published: June 9, 2011

**Citation**

Jin Shen, John C. Thomas, Xinjun Zhu, and Yajing Wang, "Wavelet denoising experiments in dynamic light scattering," Opt. Express **19**, 12284-12290 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-13-12284

Sort: Year | Journal | Reset

### References

- R. Pecora, “Doppler shifts in light scattering from pure liquids and polymer solutions,” J. Chem. Phys. 40(6), 1604–1614 (1964). [CrossRef]
- H. Z. Cummins, N. Knable, and Y. Yeh, “Observation of diffusion broadening of Rayleigh scattered light,” Phys. Rev. Lett. 12(6), 150–153 (1964). [CrossRef]
- N. C. Ford and G. B. Benedek, “Observation of the spectrum of light scattered from a pure fluid near it’s critical point,” Phys. Rev. Lett. 15(16), 649–653 (1965). [CrossRef]
- S. P. Lee, W. Tscharnuter, and B. Chu, “Calibration of an optical self-beating spectrometer by polystyrene latex spheres, and confirmation of the Stokes-Einstein formula,” Polym. Sci. 10, 2453–2459 (1972).
- ISO 13321: Particle size analysis–Photon correlation spectroscopy (1996).
- ISO 22412: Particle size analysis–Dynamic light scattering (DLS) (2008).
- J. C. Thomas, “Photon correlation spectroscopy: technique and instrumentation,” Proc. SPIE 1430, 2–18 (1991). [CrossRef]
- J. B. Lastovka, “Light mixing spectroscopy and the spectrum of light scattered by thermal fluctuations in liquids,” PhD Thesis, Massachusetts Institute of Technology, 1968.
- V. Degiorgio and J. B. Lastovka, “Intensity correlation spectroscopy,” Phys. Rev. A 4(5), 2033–2050 (1971). [CrossRef]
- K. Schätzel, “Noise in photon correlation and photon structure functions,” Opt. Acta (Lond.) 30, 155–166 (1983). [CrossRef]
- D. A. Ross and N. Dimas, “Particle sizing by dynamic light scattering: noise and distortion in correlation data,” Part. Part. Syst. Charact. 10(2), 62–69 (1993). [CrossRef]
- W. Brown, Dynamic Light Scattering: The Method and Some Applications (Oxford Science Publications, 1993), p.149.
- B. Lou, “The influence and corresponding solution of noise in DLS particle sizing experiment,” J. Light Scattering 20(4), 310–313 (2008).
- H. Yang, G. Zheng, and M. Li, “A discussion of noise in dynamic light scattering for particle sizing,” Part. Part. Syst. Charact. 25(5-6), 406–413 (2008). [CrossRef]
- J. Shen, J. C. Thomas, X. Zhu, and Y. Wang, “Wavelet noise reduction in dynamic light scattering,” The International Conference on Information Science and Technology (CSIE 2011), 2011 (to be published).
- D. E. Koppel, “Analysis of macromolecular polydispersity in intensity correlation spectroscopy: The method of cumulants,” J. Chem. Phys. 57(11), 4814–4820 (1972). [CrossRef]
- J. N. Shaumeyer, M. E. Briggs, and R. W. Gammon, “Statistical fitting accuracy in photon correlation spectroscopy,” Appl. Opt. 32(21), 3871–3879 (1993). [PubMed]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.