OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 41, Iss. 21 — Jul. 20, 2002
  • pp: 4421–4431

Least-mean-squares algorithm to determine submicrometer particle diameter, volume fraction, and size distribution width by elastic light scattering

R. Patrick Earhart and Terry E. Parker  »View Author Affiliations

Applied Optics, Vol. 41, Issue 21, pp. 4421-4431 (2002)

View Full Text Article

Enhanced HTML    Acrobat PDF (271 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A computationally fast method to determine values and their uncertainty for particulate system volume median diameter, volume fraction, and size distribution width is presented. These properties cannot be obtained for submicrometer particulate by diffraction-based methods. The technique relies on a least-mean-squares method applied over a prespecified size range and distribution width. Prespecifying the range significantly reduces the number of calculations required to determine the particulate parameters from experimental data, allowing the practical evaluation of large data sets. The solution method that was developed has significant advantages over ratio-style calculations that are more commonly performed, the primary of which is a simple method to determine errors in the measurement parameters. We evaluated the predicted performance for a specific experimental system for various levels of noise, with monodisperse and log-normal distributions, by analyzing synthetic data with the algorithm. Results were a quantitative statement of system accuracy. In addition, synthetic log-normal data evaluated with monodisperse models revealed significant and systematic errors in the predicted volume median diameter. These errors indicate that, in general, systems with a significant size distribution width must be analyzed with a model that includes this size distribution. Finally, calibrated polystyrene spheres were measured with an experimental system that used four simultaneous scattering measurements, and all diameters were within the reported uncertainty.

© 2002 Optical Society of America

OCIS Codes
(120.1740) Instrumentation, measurement, and metrology : Combustion diagnostics
(120.5820) Instrumentation, measurement, and metrology : Scattering measurements
(290.3200) Scattering : Inverse scattering
(290.4020) Scattering : Mie theory
(290.5820) Scattering : Scattering measurements
(290.5850) Scattering : Scattering, particles

Original Manuscript: December 13, 2001
Revised Manuscript: May 13, 2002
Published: July 20, 2002

R. Patrick Earhart and Terry E. Parker, "Least-mean-squares algorithm to determine submicrometer particle diameter, volume fraction, and size distribution width by elastic light scattering," Appl. Opt. 41, 4421-4431 (2002)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. C. S. Johnson, D. A. Gabriel, Laser Light Scattering (Dover, New York, 1981).
  2. M. R. Zachariah, D. Chin, H. G. Semerjian, J. L. Katz, “Dynamic light scattering and angular dissymmetry for the in situ measurements of silicon dioxide particle synthesis in flames,” Appl. Opt. 28, 530–536 (1989). [CrossRef] [PubMed]
  3. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  4. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1957).
  5. A. J. Rulison, P. F. Miquel, J. L. Katz, “Titania and silica powders produced in a counterflow diffusion flame,” J. Mater. Res. 11, 3083–3089 (1996). [CrossRef]
  6. P. F. Miquel, C. H. Hung, J. L. Katz, “Formation of V2O5-based mixed oxides in flames,” J. Mater. Res. 8, 2404–2413 (1993). [CrossRef]
  7. J. L. Katz, P. F. Miquel, “Synthesis and applications of oxides and mixed oxides produced by a flame process,” Nanostruct. Mater. 4, 551–557 (1994). [CrossRef]
  8. R. L. Axelbaum, C. R. Lottes, J. I. Huertas, L. J. Rosen, “Gas-phase combustion synthesis of aluminum nitride powder,” in the Twenty-Sixth Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1996), pp. 1891–1897. [CrossRef]
  9. Y. Xing, U. O. Koylu, D. E. Rosner, “Synthesis and restructing of inorganic nanoparticles in laminar counterflow diffusion flames,” Combust. Flame 107, 85–102 (1996). [CrossRef]
  10. K. Brezinsky, “The gas phase combustion synthesis of materials,” in the Twenty-Sixth Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1996), pp. 1805–1816. [CrossRef]
  11. S. E. Pratsinis, “Flame aerosol synthesis of ceramic powders,” Prog. Energy Combust. Sci. 24, 197–219 (1998). [CrossRef]
  12. M. S. Wooldridge, “Gas phase combustion synthesis of particles,” Prog. Energy Combust. Sci. 24, 63–87 (1998). [CrossRef]
  13. M. R. Zachariah, P. Dimitriou, “Controlled nucleation in aerosol reactors for suppression of agglomerate formation: a numerical study,” Aerosol Sci. Technol. 13, 413–425 (1990). [CrossRef]
  14. I. H. Malitson, “Interspecimen comparison of refractive index of fused silica,” J. Opt. Soc. Am. 55, 1205–1209 (1965). [CrossRef]
  15. A. H. Lefebvre, Atomization and Sprays (Hemisphere, Washington, D.C., 1989).
  16. M. R. Zachariah, H. G. Semerjian, “Simulation of ceramic particle formation: comparison with in-situ measurements,” AIChE J. 35, 2003–2012 (1989). [CrossRef]
  17. R. A. Dobbins, G. W. Mulholland, “Interpretation of optical measurements of flame generated particles,” Combust. Sci. Technol. 40, 175–191 (1984). [CrossRef]
  18. T. Parker, E. Jepsen, H. McCann, “Measurements and error analysis of droplet size in optically thick diesel sprays,” in the Twenty-Seventh Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1998), pp. 1881–1888. [CrossRef]
  19. C. Xiao-shu, W. Nai-ning, W. Jing-ming, Z. Gang, “Experimental investigation of the light extinction method for measuring aerosol size distributions,” J. Aerosol Sci. 23, 749–757 (1992). [CrossRef]
  20. T. Wriedt, “A review of elastic light scattering theories,” Part. Part. Syst. Charact. 15, 67–74 (1997). [CrossRef]
  21. R. A. Dobbins, M. Megaridis, “Absorption and scattering of light by polydisperse aggregates,” Appl. Opt. 30, 4747–4754 (1991). [CrossRef] [PubMed]
  22. N. G. Glumac, Y. J. Chen, G. Skandan, “Diagnostics and modeling of nanopowders synthesis in low pressure flames,” J. Mater. Res. 13, 2572–2579 (1998). [CrossRef]
  23. T. Hatch, S. P. Choate, “Statistical description of the size properties of non-uniform particulate substances,” J. Franklin Inst. 207, 369–387 (1929). [CrossRef]
  24. W. Hinds, Aerosol Technology (Wiley, New York, 1982).
  25. P. R. Bevington, D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences, 2nd ed. (McGraw-Hill, New York, 1992).
  26. W. H. Press, W. T. Vetterling, S. A. Teukolsky, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).
  27. A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species (Abacus, Cambridge, Mass., 1988).
  28. T. Inagaki, E. T. Arakawa, R. N. Hamm, M. W. Williams, “Optical properties of polystyrene from the near infrared to the x-ray region and convergence of optical sum rules,” Phys. Rev. B 15, 3243–3253 (1977). [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