OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: James C. Wyant
  • Vol. 45, Iss. 28 — Oct. 1, 2006
  • pp: 7456–7467

Regularized inversion method for retrieval of aerosol particle size distribution function in W 1,2 space

Yanfei Wang, Shufang Fan, Xue Feng, Guangjian Yan, and Yanning Guan  »View Author Affiliations


Applied Optics, Vol. 45, Issue 28, pp. 7456-7467 (2006)
http://dx.doi.org/10.1364/AO.45.007456


View Full Text Article

Enhanced HTML    Acrobat PDF (668 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A determination of the aerosol particle size distribution function by using the particle spectrum extinction equation is an ill-posed integral equation of the first kind. To overcome this, we must incorporate regularization techniques. Most of the literature focuses on the Phillips–Twomey regularization or its variations. However, there are drawbacks for some applications in which the real aerosol distributions have large oscillations in a Junge-type distribution. The reason for this is that the scale matrix based on the norm of the second differences in the Phillips–Twomey regularization is too ill- conditioned to filter the large perturbations induced by the small algebraic spectrum of the kernel matrix and the additive noise. Therefore we reexamine the aerosol particle size distribution function retrieval problem and solve it in W1,2 space. This setting is based on Sobolev's embedding theorem in which the approximate solution best simulates the true particle size distribution functions. For choosing the regularization parameters, we also develop an a posteriori parameter choice method, which is based on the discrepancy principle. Our numerical results are based on the remote sensing data measured by the CE318 sunphotometer in Jia Xiang County, Shan Dong Province, China, and are performed to show the feasibility of the proposed algorithms.

© 2006 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(010.1100) Atmospheric and oceanic optics : Aerosol detection
(010.1110) Atmospheric and oceanic optics : Aerosols
(100.0100) Image processing : Image processing
(100.3190) Image processing : Inverse problems
(280.1100) Remote sensing and sensors : Aerosol detection

ToC Category:
Atmospheric and Oceanic Optics

History
Original Manuscript: January 10, 2006
Revised Manuscript: May 7, 2006
Manuscript Accepted: May 8, 2006

Citation
Yanfei Wang, Shufang Fan, Xue Feng, Guangjian Yan, and Yanning Guan, "Regularized inversion method for retrieval of aerosol particle size distribution function in W<sup>1,2</sup> space," Appl. Opt. 45, 7456-7467 (2006)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-45-28-7456


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. G. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  2. C. N. Davies, "Size distribution of atmospheric aerosol," J. Aerosol Sci. 5, 293-300 (1974). [CrossRef]
  3. S. Twomey, Atmospheric Aerosols (Elsevier, 1977).
  4. G. J. McCartney, Optics of the Atmosphere (Wiley, 1976).
  5. A. J. Reagan, D. M. Byrne, D. M. King, J. D. Spinhirne, and B. M. Herman, "Determination of complex refractive index and size distribution of atmospheric particles from bistatic-monostatic Lidar and solar radiometer measurements," J. Geophys. Res. 85, 1591-1599 (1980). [CrossRef]
  6. M. Weindisch and W. von Hoyningen-Huen, "Possibility of refractive index determination of atmospheric aerosol particles by ground-based solar extinction and scattering measurements," Atmos. Environ. 28, 785-792 (1994). [CrossRef]
  7. D. L. Phillips, "A technique for the numerical solution of certain integral equations of the first kind," J. Assoc. Comput. Mach. 9, 84-97 (1962). [CrossRef]
  8. S. Twomey, "On the numerical solution of Fredholm integral equations of the first kind by the inversion of the linear system produced by quadrature," J. Assoc. Comput. Mach. 1097-101 (1963). [CrossRef]
  9. G. Yamamoto and M. Tanaka, "Determination of aerosol size distribution function from spectral attenuation measurements," Appl. Opt. 8, 447-453 (1969). [CrossRef] [PubMed]
  10. H. Grassl, "Determinzation of aerosol size distributions from spectral attenuation measurements," Appl. Opt. 10, 2534-2538 (1971). [CrossRef] [PubMed]
  11. S. Twomey, "Comparison of constrained linear inversion and an iterative nonlinear algorithm applied to the indirect estimation of particle size distributions," J. Comput. Phys. 18, 188-200 (1975). [CrossRef]
  12. M. D. King, D. M. Byrne, B. M. Herman, and J. A. Reagan, "Aerosol size distributions obtained by inversion of spectral optical depth measurements," J. Atmos. Sci. 35, 2153-2167 (1978). [CrossRef]
  13. J. A. Curcio, "Evaluation of atmospheric aerosol particle size distribution from scattering measurements in the visible and infrared," J. Opt. Soc. Am. 51, 548-551 (1961). [CrossRef]
  14. G. E. Shaw, "Inversion of optical scattering and spectral extinction measurements to receover aerosol size spectra," Appl. Opt. 18, 988-993 (1979). [CrossRef] [PubMed]
  15. T. Nguyen and K. Cox, "A method for the determination of aerosol particle distributions from light extinction data," in Abstracts of the American Association for Aerosol Research Annual Meeting (American Association of Aerosol Research, 1989), pp. 330-330.
  16. G. Ramachandran and D. Leith, "Extraction of aerosol-size distribution from multispectral light extinction data," Aerosol Sci. Technol. 17, 303-325 (1992). [CrossRef]
  17. G. Ramachandran, D. Leith, and L. Todd, "Extraction of spatial aerosol distribution from multispectral light extinction measurements with computed tomography," J. Opt. Soc. Am. A 11, 144-154 (1994). [CrossRef]
  18. K. Lumme and J. Rahola, "Light scattering by porous dust particles in the discrete-dipole approximation," Astrophys. J. 425, 653-667 (1994). [CrossRef]
  19. J. Heintzenberg, "Properties of lognormal particle size distributions," Aerosol Sci. Technol. 21, 46-48 (1994). [CrossRef]
  20. K. S. Shifrin and L. G. Zolotov, "Spectral attenuation and aerosol particle size distribution," Appl. Opt. 35, 2114-2124 (1996). [CrossRef] [PubMed]
  21. M. Ye, S. Wang, Y. Lu, T. Hu, Z. Zhu, and Y. Xu, "Inversion of particle-size distribution from angular light-scattering data with genetic algorithms," Appl. Opt. 38, 2677-2685 (1999). [CrossRef]
  22. C. Bockmann, "Hybrid regularization method for the ill-posed inversion of multiwave-length lidar data in the retrieval of aerosol size distributions," Appl. Opt. 40, 1329-1342 (2001). [CrossRef]
  23. J. T. Mao, C. C. Li, J. H. Zhang, X. Y. Liu, and K. H. L. Alexis, "The comparison of remote sensing aerosol optical depth from MODIS data and ground Sun-photometer observations," J. Appl. Meteorol. Sci. 13, 127-135 (2002), in Chinese.
  24. S. Platnick, M. D. King, S. A. Ackerman, W. P. Menzel, B. A. Baum, J. C. Riédi, and R. A. Frey, "The MODIS cloud products: algorithms and examples from Terra," IEEE Trans. Geosci. Remote Sens. 41, 459-473 (2003). [CrossRef]
  25. P. Demokritou, S. J. Lee, S. T. Ferguson, and P. Koutrakis, "A compact multistage (cascade) impactor for the characterization of atmospheric aerosols," J. Aerosol Sci. 35, 281-299 (2004). [CrossRef]
  26. J. Liu and C. H. Chen, "A study on remote-sensing inversion of atmospheric aerosol particle size distributions of Lanzhou City in winter," Plateau Meteorol. 23, 103-109 (2004), in Chinese.
  27. B. L. Preidecker, "Bacterial mutagenicity of particulates from Houston air," Environ. Mutagen. 2, 75-83 (1980). [CrossRef] [PubMed]
  28. Y. S. Cheng, "Condensation detection and diffusion size separation techniques," in Aerosol Measurement: Principles, Techniques and Applications, K.Willeke and P.A.Baron, eds. (Van Nostrand Reinhold, 1993), pp. 427-451.
  29. D. Sinclair and G. S. Hoopes, "A novel form of diffusion battery," Am. Ind. Hyg. Assoc. J. 36, 39-42 (1975). [CrossRef] [PubMed]
  30. E. O. Knutson and K. T. Whitby, "Aerosol classification by electrical mobility: apparatus, thoery and applications," J. Aerosol Sci. 6, 453-460 (1975). [CrossRef]
  31. J. Gebhart, "Optical direct-reading techniques: light intensity systems," in Aerosol Measurement: Principles, Techniques and Applications, K.Willeke and P.A.Baron, eds. (Van Nostrand Reinhold, 1993), pp. 313-344.
  32. F. Q. Yan, H. L. Hu, and J. Zhou, "Measurements of number density distribution and imaginary part of refractive index of aerosol particles," Acta Opt. Sin. 23, 854-859 (2003).
  33. D. K. Killinger and N. Menyuk, "Laser remote sensing of the atmosphere," Science 235, 37-45 (1987). [CrossRef] [PubMed]
  34. G. E. Shaw, "Sun photometry," Bull. Am. Meteorol. Soc. 64, 4-10 (1983). [CrossRef]
  35. W. C. Hinds, Aerosol Technology. Properties Behavior and Measurement of Airborne Particles (Wiley, 1982).
  36. K. Willeke and P. A. Baron eds., Aerosol Measurement: Principles, Techniques and Applications (Van Nostrand Reinhold, 1993).
  37. P. H. McMurry, "A review of atmospheric aerosol measurements," Atmos. Environ. 34, 1959-1999 (2000). [CrossRef]
  38. A. Voutilainenand and J. P. Kaipio, "Statistical inversion of aerosol size distribution data," J. Aerosol Sci. 31 (Suppl. 1), 767-768 (2000). [CrossRef]
  39. Y. F. Wang, Computational Methods and Applications for Inverse Problems (Higher Educational Press, 2006).
  40. A. N. Tikhonov and V. Y. Arsenin, Solutions of III-Posed Problems (Wiley, 1977).
  41. T. Y. Xiao, Sh. G. Yu, and Y. F. Wang, Numerical Methods for the Solution of Inverse Problems (Science Press, 2003).
  42. Y. F. Wang and T. Y. Xiao, "Fast realization algorithms for determining regularization parameters in linear inverse problems," Inverse Probl. 17, 281-291 (2001). [CrossRef]

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.

CrossCheck Deposited