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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: James C. Wyant
  • Vol. 47, Iss. 7 — Mar. 1, 2008
  • pp: 993–1001

Assessment of the mean and variance of the random regular transmittance through a dispersion of large cylinders using numerical simulations

Staffan Rydefalk  »View Author Affiliations


Applied Optics, Vol. 47, Issue 7, pp. 993-1001 (2008)
http://dx.doi.org/10.1364/AO.47.000993


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Abstract

In two previous papers [ J. Opt. Soc. Am. A 15, 1698 (1998); J. Opt. Soc. Am. A 16, 2737 (1999)] the theory of fluctuations in the regular transmittance Τ through a flowing dispersion of large slender cylindrical particles was presented. The theory covers, among other things, expressions for the expected value μ Τ and the variance σ Τ 2 of Τ in the two extreme cases when the cylinders are much shorter or much longer than the diameter of the optical beam used. Intermediate lengths were not treated. Numerical simulation is used to demonstrate the random behavior of Τ for intermediate cylinder lengths. The simulation results are consistent with the theory and provide a reliable estimate of the measurements produced by this analysis process. The result of the simulation is summarized as a fitted Bézier function model. The advantage of the simulation lies primarily in estimating measurement errors caused by the presence of intermediate length particles in measurement applications.

© 2008 Optical Society of America

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

ToC Category:
Scattering

History
Original Manuscript: November 21, 2007
Manuscript Accepted: December 14, 2007
Published: February 29, 2008

Virtual Issues
Vol. 3, Iss. 4 Virtual Journal for Biomedical Optics

Citation
Staffan Rydefalk, "Assessment of the mean and variance of the random regular transmittance through a dispersion of large cylinders using numerical simulations," Appl. Opt. 47, 993-1001 (2008)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-47-7-993


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References

  1. S. 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). [CrossRef]
  2. S. Rydefalk, “Theory of fluctuations in the regular transmittance through a dispersion of large cylindrical particles: extension to higher concentrations,” J. Opt. Soc. Am. A 16, 2737-2745 (1999). [CrossRef]
  3. T. Pettersson, G. Fladda, and L. Eriksson, “Förfarande för koncentrationsbestämning,” Swedish patent 7513524-4 (29 September 1977).
  4. T. Pettersson, G. Fladda, and L. Eriksson, “Method for determination of concentration,” U.S. patent 4,110,044 (29 August 1978).
  5. T. Pettersson and H. Karlsson, “Förfarande för att bestämma medelpartikelradie och/eller medelpartikellängd,” Swedish patent 8105802-6 (21 April 1988).
  6. T. Pettersson and H. Karlsson, “Method for determining the average radius and/or the average length of particles carried by a flowing medium,” U.S. patent 4,529,309 (16 July 1985).
  7. I. Lundqvist, T. Pettersson, and G. Fladda, “Förfarande för att indikera fraktionsfördelningen hos suspenderade ämnen i ett strömmande medium,” Swedish patent 7706320-4 (1 March 1979).
  8. I. Lundqvist, T. Pettersson, and G. Fladda, “Method and apparatus for indicating the size distribution of particles in a flowing medium,” U.S. patent 4,318,180 (2 March 1982).
  9. S. Rydefalk and J. Einarsson, “Anordning för att i en suspension med åtminstone två typer av suspenderade ämnen var för sig mäta halten av varje ämnestyp,” Swedish patent 8400784-8 (3 March 1986).
  10. S. Rydefalk and J. Einarsson, “Device for separately measuring particles in a suspension,” U.S. patent 4,689,988 (1 September 1987).
  11. J. Hill, T. Pettersson, and S. Rydefalk, “The STFI long-fibre content meter in process control applications,” Svensk Papperstidn. 80, 579-586 (1977).
  12. G. Fladda, T. Pettersson, L. Eriksson, and G. Tidstam, “A new optical method for measuring suspended solids in pulp and paper effluents,” in Proceedings of the 4th International Federation of Automatic Control Conference--Instrumentation and Automation in the Paper, Rubber, Plastics and Polymerisation Industries (International Federation of Automatic Control, Belgium, 1980), pp. 9-22.
  13. S. Rydefalk, T. Pettersson, E. Jung, and I. Lundqvist, “The STFI optical fibre classifier,” in Proceedings of the International Mechanical Pulping Conference (Comité Européen de Liaison pour la Cellulose et de le Papier--European Liaison Committee for Pulp and Paper, Oslo, 1981), Session III, no. 4, p. 16.
  14. T. Lindström, S. Rydefalk, and L. Wågberg, “The development of an integrated retention control system,” in Swedish Association of Pulp and Paper Engineers 84--The World Pulp and Paper Week. New Available Techniques (The Swedish Association of Pulp and Paper Engineers, 1984), pp. 492-496.

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