OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 48, Iss. 25 — Sep. 1, 2009
  • pp: 4842–4850

Integral inversion to Fraunhofer diffraction for particle sizing

Zhang Cao, Lijun Xu, and Jie Ding  »View Author Affiliations

Applied Optics, Vol. 48, Issue 25, pp. 4842-4850 (2009)

View Full Text Article

Enhanced HTML    Acrobat PDF (1075 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A new solution to the inversion of Fraunhofer diffraction for particle sizing was introduced. Com pared with the well-known Chin–Shifrin inversion, it is an inversion of the form of integral transform and less sensitive to noise. Simulation results with noise-contaminated data were obtained and showed that the new inversion is better than the Chin–Shifrin inversion. Especially when the particle diameter was small, the new inversion still performed well, whereas the Chin–Shifrin inversion did not converge.

© 2009 Optical Society of America

OCIS Codes
(290.0290) Scattering : Scattering
(290.3200) Scattering : Inverse scattering
(290.5850) Scattering : Scattering, particles
(290.2558) Scattering : Forward scattering

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: April 21, 2009
Revised Manuscript: August 5, 2009
Manuscript Accepted: August 7, 2009
Published: August 21, 2009

Zhang Cao, Lijun Xu, and Jie Ding, "Integral inversion to Fraunhofer diffraction for particle sizing," Appl. Opt. 48, 4842-4850 (2009)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. A. P. Weber, L. J. Xu, and G. Kasper, “Simultaneous in situ measurement of size, charge and velocity of single aerosol particles,” J. Aerosol Sci. 31, 1015-1016 (2000). [CrossRef]
  2. D. Greaves, J. Boxall, J. Mulligan, A. Montesi, J. Creek, E. Dendy Sloan, and C. A. Koh, “Measuring the particle size of a known distribution using the focused beam reflectance measurement technique,” Chem. Eng. Sci. 63, 5410-5419(2008). [CrossRef]
  3. D. B. Curtis, M. Aycibin, M. A. Young, V. H. Grassian, and P. D. Kleiber, “Simultaneous measurement of light-scattering properties and particle size distribution for aerosols: application to ammonium sulfate and quartz aerosol particles,” Atmos. Environ. 41, 4748-4758 (2007). [CrossRef]
  4. B. Zhao, Z. Yang, M. V. Johnston, H. Wang, A. S. Wexler, M. Balthasar, and M. Kraft, “Measurement and numerical simulation of soot particle size distribution functions in a laminar premixed ethylene-oxygen-argon flame,” Combust. Flame 133, 173-188 (2003). [CrossRef]
  5. A. K. Jagodnicka, T. Stacewicz, G. Karasiński, M. L. Posyniak, and S. P. Malinowski, “Particle size distribution retrieval from multiwavelength lidar signals for droplet aerosol,” Appl. Opt. 48, B8-B16 (2009). [CrossRef] [PubMed]
  6. A. Garcia-Valenzuela, R. G. Barrera, and E. Gutierrez-Reyes, “Rigorous theoretical framework for particle sizing in turbid colloids using light refraction,” Opt. Express 16, 19741-19756(2008). [CrossRef] [PubMed]
  7. J. R. Hodkinson, “Particle sizing by means of the forward scattering lobe,” Appl. Opt. 5, 839-844 (1966). [CrossRef] [PubMed]
  8. J. V. Ubera, J. F. Aguilar, and D. M. Gale, “Reconstruction of particle-size distributions from light-scattering patterns using three inversion methods,” Appl. Opt. 46, 124-132(2007). [CrossRef]
  9. N. Riefler and T. Wriedt, “Intercomparison of inversion algorithms for particle-sizing using Mie scattering,” Part. Part. Syst. Charact. 25, 216-230 (2008). [CrossRef]
  10. H.G.Barth, Modern Methods of Particle Size Analysis (Wiley-Interscience, 1984).
  11. S. Nakadate and H. Saito, “Particle-size-distribution measurement using a Hankel transform of a Fraunhofer diffraction spectrum,” Opt. Lett. 8, 578-580 (1983). [CrossRef] [PubMed]
  12. J. J. Liu, “Essential parameters in particle sizing by integral transform inversions,” Appl. Opt. 36, 5535-5545 (1997). [CrossRef] [PubMed]
  13. K. S. Shifrin and I. G. Zolotov, “Determination of the aerosol particle-size distribution from simultaneous data on spectral attenuation and the small-angle phase function,” Appl. Opt. 36, 6047-6056 (1997). [CrossRef] [PubMed]
  14. J. R. Hatcher, “A method for solving Schlomilch's integral equation,” Am. Math. Mon. 63, 487-488 (1956). [CrossRef]
  15. S. D. Coston and N. George, “Recovery of particle size distributions by inversion of the optical transform intensity,” Opt. Lett. 16, 1918-1920 (1991). [CrossRef] [PubMed]
  16. B. Ge, Z. Luan, and Q. Lu, “Solution of the particle size distribution with improved Newton algorithm,” Opt. Eng. 44, 058003 (2005). [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