OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 15, Iss. 6 — Jun. 1, 1998
  • pp: 1689–1697

Fluctuations in the regular transmittance of dispersions of straight circular cylinders with a diameter much larger than the wavelength of the radiation

Staffan Rydefalk  »View Author Affiliations

JOSA A, Vol. 15, Issue 6, pp. 1689-1697 (1998)

View Full Text Article

Enhanced HTML    Acrobat PDF (249 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The expected value and the variance of the regular transmittance of a dilute dispersion of slender straight circular cylinders with a diameter much larger than the wavelength of the radiation are studied theoretically in relation to the dimensions of the cylinders and the diameter of the radiation beam used. Both monodisperse and heterodisperse dispersions are considered. The study is limited to two particle categories: (i) particles that are short and (ii) particles that are long but thin compared with the diameter of the radiation beam. The expected value is a function of concentration and particle diameter. The variance is proportional to the concentration. The variance is also proportional to particle length in the case of short particles but not in the case of long particles. The results explain interesting possibilities for the characterization of dispersions of large cylindrical particles shown earlier in industrial on-line applications.

© 1998 Optical Society of America

OCIS Codes
(120.7000) Instrumentation, measurement, and metrology : Transmission
(290.7050) Scattering : Turbid media

Original Manuscript: September 19, 1997
Revised Manuscript: January 15, 1998
Manuscript Accepted: February 10, 1998
Published: June 1, 1998

Staffan Rydefalk, "Fluctuations in the regular transmittance of dispersions of straight circular cylinders with a diameter much larger than the wavelength of the radiation," J. Opt. Soc. Am. A 15, 1689-1697 (1998)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. T. Pettersson, G. Fladda, L. Eriksson, “Förfarande för koncentrationsbestämning,” Swedish patent75 135 24–4 (September29, 1977) and “Method for determination of concentration,” U.S. patent4,110,044 (August29, 1978).
  2. T. Pettersson, H. Karlsson, “Förfarande för att bestämma medelpartikelradie och/eller medelpartikellängd,” Swedish patent81 058 02–6 (April21, 1988), and “Method for determining the average radius and/or the average length of particles carried by a flowing medium,” U.S. patent4,529,309 (July16, 1985).
  3. I. Lundqvist, T. Pettersson, G. Fladda, “Förfarande för att indikera fraktionsfördelningen hos suspenderade ämnen i ett strömmande medium,” Swedish patent77 063 20–4 (March1, 1979), and “Method and apparatus for indicating the size distribution of particles in a flowing medium,” U.S. patent4,318,180 (March2, 1982).
  4. S. Rydefalk, J. Einarsson, “Anordning för att i en suspension med åtminstone två typer av suspenderade ämnen var för sig mäta halten av varje ämnestyp,” Swedish patent84 007 84–8 (March3, 1986), and “Device for separately measuring particles in a suspension,” U.S. patent4,689,988 (September1, 1987).
  5. J. Hill, T. Pettersson, S. Rydefalk, “The STFI long-fibre content meter in process control applications,” Sven. Papperstidn. 80, 579–586 (1977).
  6. G. Fladda, T. Pettersson, L. Eriksson, G. Tidstam, “A new optical method for measuring suspended solids in pulp and paper effluents,” in Instrumentation and Automation in the Paper, Rubber, Plastics and Polymerisation Industries—Proceedings of the 4th IFAC Conference (International Federation of Automatic Control, Ghent, Belgium, 1980), pp. 9–22.
  7. S. Rydefalk, T. Pettersson, E. Jung, I. Lundqvist, “The STFI optical fibre classifier,” in International Mechanical Pulping Conference (Comité Européen de Liaison pour laCellulose et le Papier—EUCEPA, Olso, Norway, 1981), Session III, No. 4.
  8. T. Lindström, S. Rydefalk, L. Wågberg, “The development of an integrated retention Control System,” in SPCI 84—The World Pulp and Paper Week. New Available Techniques (The Swedish Association of Pulp and Paper Engineers, Stockholm, Sweden, 1984), pp. 492–496.
  9. C. E. Hubley, A. A. Robertson, S. G. Mason, “Flocculation in suspensions of large particles,” Can. J. Res. 28, 770–787 (1950).
  10. A. A. Robertson, S. G. Mason, “Flocculation in flowing pulp suspensions,” Pulp & Pap. Mag. Can. 55, 263–269 (1954).
  11. B. G. Norman, K. Möller, R. Ek, G. G. Duffy, “Hydrodynamics of papermaking fibres in water suspensions,” in Transactions of Fibre–Water Interactions in Paper-Making (The British Paper and Board Industry Federation, Oxford, 1977), pp. 195–249.
  12. J. Eisenlauer, D. Horn, F. Linhart, R. Hemel, “Fiber-optic flocculation sensor for on-line control of retention and drainage aids efficiency,” Nord. Pulp Paper Res. J. 2, 132–138 (1987). [CrossRef]
  13. J. Gregory, D. W. Nelson, “A new optical method for flocculation monitoring,” in Solid-Liquid Separation, J. Gregory, ed. (Ellis Horwood, Chichester, UK, 1984), pp. 172–182.
  14. J. Gregory, “Turbidity fluctuations in flowing suspensions,” J. Colloid Interface Sci. 105, 357–371 (1985). [CrossRef]
  15. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
  16. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  17. P. Latimer, “Dependence of extinction efficiency of spherical scatterers on photometer geometry,” J. Opt. Soc. Am. 62, 208–211 (1972). [CrossRef]
  18. B. W. Lindgren, Statistical Theory (Macmillan, New York, 1976).

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