Abstract

Optical fiber sensors based on the total light transmittance are widely used to measure the volume fraction of particles in suspensions. However, the sensor response depends not only on the volume fraction but also on the particle size. The particle size effect is studied for a sensor configuration consisting of two linear arrays of fibers on each of two blocks: the emitting and receiving blocks. These two linear arrays are arranged with three adjacent fibers (one fiber on the first array, two fibers on the second array) forming a perfect triangle. The almost superimposition of the calculated sensor response versus the extinction factor for different particle sizes allows for the application of single- curve models. Two single-curve models that describe the sensor response for all particle sizes ranging from 36 to 200μm are proposed. The models are validated by Monte Carlo simulation for different particle sizes and are valid within a detectable volume fraction. The single-curve models proposed provide an easier approach to creating a database for sensor calibration for suspended sediment concentration measurements.

© 2006 Optical Society of America

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  1. M. E. Nelson and P. C. Benedict, "Measurement and analysis of suspended-sediment loads in streams," Trans. ASCE 116, 891-918 (1951).
  2. D. G. Wren, B. D. Barkdoll, R. A. Kuhnle, and R. W. Derrow, "Field techniques for suspended-sediment measurement," J. Hydraul. Eng. 126, 97-104 (2000).
    [CrossRef]
  3. D. W. Dockery, A. Pope III, X. Xu, J. D. Spengler, J. H. Ware, M. E. Fay, B. G. Ferris, Jr., and F. E. Speizer, "An association between air pollution and mortality in six U.S. cities," N. Engl. J. Med. 329, 1753-1759 (1993).
    [CrossRef] [PubMed]
  4. C. G. Campbell, D. T. Laycak, W. Hoppes, N. T. Tran, and F. G. Shi, "High concentration suspended sediment measurements using a continuous fiber optic in-stream transmissometer," J. Hydrol. 311, 244-253 (2005).
    [CrossRef]
  5. S. J. Riley, "The sediment concentration-turbidity relation: its value in monitoring at ranger uranium mine, Northern Territory, Australia," Cantena 32(1), 1-14 (1998).
    [CrossRef]
  6. N. J. Clifford, K. S. Richards, R. A. Brown, and S. N. Lane, "Laboratory and field assessment of an infrared turbidity probe and its response to particle size and variation in suspended sediment concentration," Hydrol. Sci. J. 40, 771-791 (1995).
    [CrossRef]
  7. R. J. Davies-Colley and D. G. Smith, "Turbidity, suspended sediment, and water clarity: a review," J. Am. Water Resour. Assoc. 37, 1085-1101 (2001).
    [CrossRef]
  8. L. Bergougnoux, J. Misguich-Ripault, J. L. Firpro, and J. Andre, "Monte Carlo calculation of backscattered light intensity by suspension: comparison with experimental data," Appl. Opt. 35, 1735-1741 (1996).
    [CrossRef] [PubMed]
  9. D. J. Lischer and M. Y. Louge, "Optical fiber measurements of particle concentration in dense suspensions: calibration and simulation," Appl. Opt. 31, 5106-5113 (1992).
    [CrossRef] [PubMed]
  10. J. Hong and Y. Tomita, "Measurement of distribution of solids concentration on high density gas-solids flow using an optical-fiber probe system," Powder Technol. 83, 85-91 (1995).
    [CrossRef]
  11. S. Ibrahim, R. G. Green, K. Dutton, K. Evan, R. A. Rahim, and A. Goude, "Optical sensor configurations for process tomography," Meas. Sci. Technol. 10, 1079-1086 (1999).
    [CrossRef]
  12. S. Ibrahim, R. G. Green, K. Dutton, and R. A. Rahim, "Application of optical tomography in industrial process control system," in 2000 TENCON Proceedings Intelligent Systems and Technologies for the New Millennium, (IEEE, 2000), Vol. 1, pp. 493-498.
    [CrossRef]
  13. S. Ibrahim, Y. M. Yunost, R. G. Green, and K. Dutton, "A tomography system using optical-fibre sensors for measuring concentration and velocity of bubbles," Meas. Control 34, 47-51 (2001).
  14. R. G. Green, R. A. Rahim, K. Evans, F. J. Dickin, B. D. Naylor, and T. P. Pridmore, "Concentration profiles in a gravity chute conveyor by optical tomography measurement," Powder Technol. 95, 49-54 (1998).
    [CrossRef]
  15. E. T. Baker and J. W. Lavelle, "The effect of particle size on the light attenuation coefficient of natural suspensions," J. Geophys. Res. 89, 8197-8203 (1984).
    [CrossRef]
  16. E. T. Baker, D. A. Tennant, R. A. Feely, G. T. Lebon, and S. L. Walker, "Field and laboratory studies on the effect of particle size and composition on optical backscattering measurements in hydrothermal plumes," Deep-Sea Res. 48, 593-604 (2001).
    [CrossRef]
  17. Y. Matsuno, H. Yamaguchi, T. Oka, H. Kage, and K. Higashitani, "The use of optic fiber probes for the measurement of dilute particle concentrations: calibration and application to gas-fluidized bad carryover," Powder Technol. 36, 215-221 (1983).
    [CrossRef]
  18. L. Wang, S. L. Jacques, and L. Zheng, "MCML-Monte Carlo modeling of light transport in multi-layered tissues," Comput. Methods Programs Biomed. 47, 131-146 (1995).
    [CrossRef] [PubMed]
  19. M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles (Academic, 2000), Chap. 10.
  20. M. H. Kalos and P. A. Whitlock, Monte Carlo Methods, I: Basics (Wiley, 1986).
  21. E. D. Cashwell and C. J. Everett, A Practical Manual on the Monte Carlo Method for Random Walk Problems (Pergamon, 1959).
  22. H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981), p. 129.
  23. A. A. Kokhanovsky, Optics of Light Scattering Media (Springer, 2001), p. 211.
  24. A. N. Witt, "Multiple scattering in reflection nebulae. 1. Monte Carlo approach," Astrophys. J., Suppl. Ser. 35, 1-6 (1977).
    [CrossRef]
  25. J. T. Verdeyen, Laser Electronics (Prentice Hall, 2000), p. 20.

2005 (1)

C. G. Campbell, D. T. Laycak, W. Hoppes, N. T. Tran, and F. G. Shi, "High concentration suspended sediment measurements using a continuous fiber optic in-stream transmissometer," J. Hydrol. 311, 244-253 (2005).
[CrossRef]

2001 (3)

R. J. Davies-Colley and D. G. Smith, "Turbidity, suspended sediment, and water clarity: a review," J. Am. Water Resour. Assoc. 37, 1085-1101 (2001).
[CrossRef]

S. Ibrahim, Y. M. Yunost, R. G. Green, and K. Dutton, "A tomography system using optical-fibre sensors for measuring concentration and velocity of bubbles," Meas. Control 34, 47-51 (2001).

E. T. Baker, D. A. Tennant, R. A. Feely, G. T. Lebon, and S. L. Walker, "Field and laboratory studies on the effect of particle size and composition on optical backscattering measurements in hydrothermal plumes," Deep-Sea Res. 48, 593-604 (2001).
[CrossRef]

2000 (1)

D. G. Wren, B. D. Barkdoll, R. A. Kuhnle, and R. W. Derrow, "Field techniques for suspended-sediment measurement," J. Hydraul. Eng. 126, 97-104 (2000).
[CrossRef]

1999 (1)

S. Ibrahim, R. G. Green, K. Dutton, K. Evan, R. A. Rahim, and A. Goude, "Optical sensor configurations for process tomography," Meas. Sci. Technol. 10, 1079-1086 (1999).
[CrossRef]

1998 (2)

S. J. Riley, "The sediment concentration-turbidity relation: its value in monitoring at ranger uranium mine, Northern Territory, Australia," Cantena 32(1), 1-14 (1998).
[CrossRef]

R. G. Green, R. A. Rahim, K. Evans, F. J. Dickin, B. D. Naylor, and T. P. Pridmore, "Concentration profiles in a gravity chute conveyor by optical tomography measurement," Powder Technol. 95, 49-54 (1998).
[CrossRef]

1996 (1)

1995 (3)

L. Wang, S. L. Jacques, and L. Zheng, "MCML-Monte Carlo modeling of light transport in multi-layered tissues," Comput. Methods Programs Biomed. 47, 131-146 (1995).
[CrossRef] [PubMed]

N. J. Clifford, K. S. Richards, R. A. Brown, and S. N. Lane, "Laboratory and field assessment of an infrared turbidity probe and its response to particle size and variation in suspended sediment concentration," Hydrol. Sci. J. 40, 771-791 (1995).
[CrossRef]

J. Hong and Y. Tomita, "Measurement of distribution of solids concentration on high density gas-solids flow using an optical-fiber probe system," Powder Technol. 83, 85-91 (1995).
[CrossRef]

1993 (1)

D. W. Dockery, A. Pope III, X. Xu, J. D. Spengler, J. H. Ware, M. E. Fay, B. G. Ferris, Jr., and F. E. Speizer, "An association between air pollution and mortality in six U.S. cities," N. Engl. J. Med. 329, 1753-1759 (1993).
[CrossRef] [PubMed]

1992 (1)

1984 (1)

E. T. Baker and J. W. Lavelle, "The effect of particle size on the light attenuation coefficient of natural suspensions," J. Geophys. Res. 89, 8197-8203 (1984).
[CrossRef]

1983 (1)

Y. Matsuno, H. Yamaguchi, T. Oka, H. Kage, and K. Higashitani, "The use of optic fiber probes for the measurement of dilute particle concentrations: calibration and application to gas-fluidized bad carryover," Powder Technol. 36, 215-221 (1983).
[CrossRef]

1977 (1)

A. N. Witt, "Multiple scattering in reflection nebulae. 1. Monte Carlo approach," Astrophys. J., Suppl. Ser. 35, 1-6 (1977).
[CrossRef]

1951 (1)

M. E. Nelson and P. C. Benedict, "Measurement and analysis of suspended-sediment loads in streams," Trans. ASCE 116, 891-918 (1951).

Andre, J.

Baker, E. T.

E. T. Baker, D. A. Tennant, R. A. Feely, G. T. Lebon, and S. L. Walker, "Field and laboratory studies on the effect of particle size and composition on optical backscattering measurements in hydrothermal plumes," Deep-Sea Res. 48, 593-604 (2001).
[CrossRef]

E. T. Baker and J. W. Lavelle, "The effect of particle size on the light attenuation coefficient of natural suspensions," J. Geophys. Res. 89, 8197-8203 (1984).
[CrossRef]

Barkdoll, B. D.

D. G. Wren, B. D. Barkdoll, R. A. Kuhnle, and R. W. Derrow, "Field techniques for suspended-sediment measurement," J. Hydraul. Eng. 126, 97-104 (2000).
[CrossRef]

Benedict, P. C.

M. E. Nelson and P. C. Benedict, "Measurement and analysis of suspended-sediment loads in streams," Trans. ASCE 116, 891-918 (1951).

Bergougnoux, L.

Brown, R. A.

N. J. Clifford, K. S. Richards, R. A. Brown, and S. N. Lane, "Laboratory and field assessment of an infrared turbidity probe and its response to particle size and variation in suspended sediment concentration," Hydrol. Sci. J. 40, 771-791 (1995).
[CrossRef]

Campbell, C. G.

C. G. Campbell, D. T. Laycak, W. Hoppes, N. T. Tran, and F. G. Shi, "High concentration suspended sediment measurements using a continuous fiber optic in-stream transmissometer," J. Hydrol. 311, 244-253 (2005).
[CrossRef]

Cashwell, E. D.

E. D. Cashwell and C. J. Everett, A Practical Manual on the Monte Carlo Method for Random Walk Problems (Pergamon, 1959).

Clifford, N. J.

N. J. Clifford, K. S. Richards, R. A. Brown, and S. N. Lane, "Laboratory and field assessment of an infrared turbidity probe and its response to particle size and variation in suspended sediment concentration," Hydrol. Sci. J. 40, 771-791 (1995).
[CrossRef]

Davies-Colley, R. J.

R. J. Davies-Colley and D. G. Smith, "Turbidity, suspended sediment, and water clarity: a review," J. Am. Water Resour. Assoc. 37, 1085-1101 (2001).
[CrossRef]

Derrow, R. W.

D. G. Wren, B. D. Barkdoll, R. A. Kuhnle, and R. W. Derrow, "Field techniques for suspended-sediment measurement," J. Hydraul. Eng. 126, 97-104 (2000).
[CrossRef]

Dickin, F. J.

R. G. Green, R. A. Rahim, K. Evans, F. J. Dickin, B. D. Naylor, and T. P. Pridmore, "Concentration profiles in a gravity chute conveyor by optical tomography measurement," Powder Technol. 95, 49-54 (1998).
[CrossRef]

Dockery, D. W.

D. W. Dockery, A. Pope III, X. Xu, J. D. Spengler, J. H. Ware, M. E. Fay, B. G. Ferris, Jr., and F. E. Speizer, "An association between air pollution and mortality in six U.S. cities," N. Engl. J. Med. 329, 1753-1759 (1993).
[CrossRef] [PubMed]

Dutton, K.

S. Ibrahim, Y. M. Yunost, R. G. Green, and K. Dutton, "A tomography system using optical-fibre sensors for measuring concentration and velocity of bubbles," Meas. Control 34, 47-51 (2001).

S. Ibrahim, R. G. Green, K. Dutton, K. Evan, R. A. Rahim, and A. Goude, "Optical sensor configurations for process tomography," Meas. Sci. Technol. 10, 1079-1086 (1999).
[CrossRef]

S. Ibrahim, R. G. Green, K. Dutton, and R. A. Rahim, "Application of optical tomography in industrial process control system," in 2000 TENCON Proceedings Intelligent Systems and Technologies for the New Millennium, (IEEE, 2000), Vol. 1, pp. 493-498.
[CrossRef]

Evan, K.

S. Ibrahim, R. G. Green, K. Dutton, K. Evan, R. A. Rahim, and A. Goude, "Optical sensor configurations for process tomography," Meas. Sci. Technol. 10, 1079-1086 (1999).
[CrossRef]

Evans, K.

R. G. Green, R. A. Rahim, K. Evans, F. J. Dickin, B. D. Naylor, and T. P. Pridmore, "Concentration profiles in a gravity chute conveyor by optical tomography measurement," Powder Technol. 95, 49-54 (1998).
[CrossRef]

Everett, C. J.

E. D. Cashwell and C. J. Everett, A Practical Manual on the Monte Carlo Method for Random Walk Problems (Pergamon, 1959).

Fay, M. E.

D. W. Dockery, A. Pope III, X. Xu, J. D. Spengler, J. H. Ware, M. E. Fay, B. G. Ferris, Jr., and F. E. Speizer, "An association between air pollution and mortality in six U.S. cities," N. Engl. J. Med. 329, 1753-1759 (1993).
[CrossRef] [PubMed]

Feely, R. A.

E. T. Baker, D. A. Tennant, R. A. Feely, G. T. Lebon, and S. L. Walker, "Field and laboratory studies on the effect of particle size and composition on optical backscattering measurements in hydrothermal plumes," Deep-Sea Res. 48, 593-604 (2001).
[CrossRef]

Ferris, B. G.

D. W. Dockery, A. Pope III, X. Xu, J. D. Spengler, J. H. Ware, M. E. Fay, B. G. Ferris, Jr., and F. E. Speizer, "An association between air pollution and mortality in six U.S. cities," N. Engl. J. Med. 329, 1753-1759 (1993).
[CrossRef] [PubMed]

Firpro, J. L.

Goude, A.

S. Ibrahim, R. G. Green, K. Dutton, K. Evan, R. A. Rahim, and A. Goude, "Optical sensor configurations for process tomography," Meas. Sci. Technol. 10, 1079-1086 (1999).
[CrossRef]

Green, R. G.

S. Ibrahim, Y. M. Yunost, R. G. Green, and K. Dutton, "A tomography system using optical-fibre sensors for measuring concentration and velocity of bubbles," Meas. Control 34, 47-51 (2001).

S. Ibrahim, R. G. Green, K. Dutton, K. Evan, R. A. Rahim, and A. Goude, "Optical sensor configurations for process tomography," Meas. Sci. Technol. 10, 1079-1086 (1999).
[CrossRef]

R. G. Green, R. A. Rahim, K. Evans, F. J. Dickin, B. D. Naylor, and T. P. Pridmore, "Concentration profiles in a gravity chute conveyor by optical tomography measurement," Powder Technol. 95, 49-54 (1998).
[CrossRef]

S. Ibrahim, R. G. Green, K. Dutton, and R. A. Rahim, "Application of optical tomography in industrial process control system," in 2000 TENCON Proceedings Intelligent Systems and Technologies for the New Millennium, (IEEE, 2000), Vol. 1, pp. 493-498.
[CrossRef]

Higashitani, K.

Y. Matsuno, H. Yamaguchi, T. Oka, H. Kage, and K. Higashitani, "The use of optic fiber probes for the measurement of dilute particle concentrations: calibration and application to gas-fluidized bad carryover," Powder Technol. 36, 215-221 (1983).
[CrossRef]

Hong, J.

J. Hong and Y. Tomita, "Measurement of distribution of solids concentration on high density gas-solids flow using an optical-fiber probe system," Powder Technol. 83, 85-91 (1995).
[CrossRef]

Hoppes, W.

C. G. Campbell, D. T. Laycak, W. Hoppes, N. T. Tran, and F. G. Shi, "High concentration suspended sediment measurements using a continuous fiber optic in-stream transmissometer," J. Hydrol. 311, 244-253 (2005).
[CrossRef]

Hovenier, J. W.

M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles (Academic, 2000), Chap. 10.

Ibrahim, S.

S. Ibrahim, Y. M. Yunost, R. G. Green, and K. Dutton, "A tomography system using optical-fibre sensors for measuring concentration and velocity of bubbles," Meas. Control 34, 47-51 (2001).

S. Ibrahim, R. G. Green, K. Dutton, K. Evan, R. A. Rahim, and A. Goude, "Optical sensor configurations for process tomography," Meas. Sci. Technol. 10, 1079-1086 (1999).
[CrossRef]

S. Ibrahim, R. G. Green, K. Dutton, and R. A. Rahim, "Application of optical tomography in industrial process control system," in 2000 TENCON Proceedings Intelligent Systems and Technologies for the New Millennium, (IEEE, 2000), Vol. 1, pp. 493-498.
[CrossRef]

Jacques, S. L.

L. Wang, S. L. Jacques, and L. Zheng, "MCML-Monte Carlo modeling of light transport in multi-layered tissues," Comput. Methods Programs Biomed. 47, 131-146 (1995).
[CrossRef] [PubMed]

Kage, H.

Y. Matsuno, H. Yamaguchi, T. Oka, H. Kage, and K. Higashitani, "The use of optic fiber probes for the measurement of dilute particle concentrations: calibration and application to gas-fluidized bad carryover," Powder Technol. 36, 215-221 (1983).
[CrossRef]

Kalos, M. H.

M. H. Kalos and P. A. Whitlock, Monte Carlo Methods, I: Basics (Wiley, 1986).

Kokhanovsky, A. A.

A. A. Kokhanovsky, Optics of Light Scattering Media (Springer, 2001), p. 211.

Kuhnle, R. A.

D. G. Wren, B. D. Barkdoll, R. A. Kuhnle, and R. W. Derrow, "Field techniques for suspended-sediment measurement," J. Hydraul. Eng. 126, 97-104 (2000).
[CrossRef]

Lane, S. N.

N. J. Clifford, K. S. Richards, R. A. Brown, and S. N. Lane, "Laboratory and field assessment of an infrared turbidity probe and its response to particle size and variation in suspended sediment concentration," Hydrol. Sci. J. 40, 771-791 (1995).
[CrossRef]

Lavelle, J. W.

E. T. Baker and J. W. Lavelle, "The effect of particle size on the light attenuation coefficient of natural suspensions," J. Geophys. Res. 89, 8197-8203 (1984).
[CrossRef]

Laycak, D. T.

C. G. Campbell, D. T. Laycak, W. Hoppes, N. T. Tran, and F. G. Shi, "High concentration suspended sediment measurements using a continuous fiber optic in-stream transmissometer," J. Hydrol. 311, 244-253 (2005).
[CrossRef]

Lebon, G. T.

E. T. Baker, D. A. Tennant, R. A. Feely, G. T. Lebon, and S. L. Walker, "Field and laboratory studies on the effect of particle size and composition on optical backscattering measurements in hydrothermal plumes," Deep-Sea Res. 48, 593-604 (2001).
[CrossRef]

Lischer, D. J.

Louge, M. Y.

Matsuno, Y.

Y. Matsuno, H. Yamaguchi, T. Oka, H. Kage, and K. Higashitani, "The use of optic fiber probes for the measurement of dilute particle concentrations: calibration and application to gas-fluidized bad carryover," Powder Technol. 36, 215-221 (1983).
[CrossRef]

Misguich-Ripault, J.

Mishchenko, M. I.

M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles (Academic, 2000), Chap. 10.

Naylor, B. D.

R. G. Green, R. A. Rahim, K. Evans, F. J. Dickin, B. D. Naylor, and T. P. Pridmore, "Concentration profiles in a gravity chute conveyor by optical tomography measurement," Powder Technol. 95, 49-54 (1998).
[CrossRef]

Nelson, M. E.

M. E. Nelson and P. C. Benedict, "Measurement and analysis of suspended-sediment loads in streams," Trans. ASCE 116, 891-918 (1951).

Oka, T.

Y. Matsuno, H. Yamaguchi, T. Oka, H. Kage, and K. Higashitani, "The use of optic fiber probes for the measurement of dilute particle concentrations: calibration and application to gas-fluidized bad carryover," Powder Technol. 36, 215-221 (1983).
[CrossRef]

Pope, A.

D. W. Dockery, A. Pope III, X. Xu, J. D. Spengler, J. H. Ware, M. E. Fay, B. G. Ferris, Jr., and F. E. Speizer, "An association between air pollution and mortality in six U.S. cities," N. Engl. J. Med. 329, 1753-1759 (1993).
[CrossRef] [PubMed]

Pridmore, T. P.

R. G. Green, R. A. Rahim, K. Evans, F. J. Dickin, B. D. Naylor, and T. P. Pridmore, "Concentration profiles in a gravity chute conveyor by optical tomography measurement," Powder Technol. 95, 49-54 (1998).
[CrossRef]

Rahim, R. A.

S. Ibrahim, R. G. Green, K. Dutton, K. Evan, R. A. Rahim, and A. Goude, "Optical sensor configurations for process tomography," Meas. Sci. Technol. 10, 1079-1086 (1999).
[CrossRef]

R. G. Green, R. A. Rahim, K. Evans, F. J. Dickin, B. D. Naylor, and T. P. Pridmore, "Concentration profiles in a gravity chute conveyor by optical tomography measurement," Powder Technol. 95, 49-54 (1998).
[CrossRef]

S. Ibrahim, R. G. Green, K. Dutton, and R. A. Rahim, "Application of optical tomography in industrial process control system," in 2000 TENCON Proceedings Intelligent Systems and Technologies for the New Millennium, (IEEE, 2000), Vol. 1, pp. 493-498.
[CrossRef]

Richards, K. S.

N. J. Clifford, K. S. Richards, R. A. Brown, and S. N. Lane, "Laboratory and field assessment of an infrared turbidity probe and its response to particle size and variation in suspended sediment concentration," Hydrol. Sci. J. 40, 771-791 (1995).
[CrossRef]

Riley, S. J.

S. J. Riley, "The sediment concentration-turbidity relation: its value in monitoring at ranger uranium mine, Northern Territory, Australia," Cantena 32(1), 1-14 (1998).
[CrossRef]

Shi, F. G.

C. G. Campbell, D. T. Laycak, W. Hoppes, N. T. Tran, and F. G. Shi, "High concentration suspended sediment measurements using a continuous fiber optic in-stream transmissometer," J. Hydrol. 311, 244-253 (2005).
[CrossRef]

Smith, D. G.

R. J. Davies-Colley and D. G. Smith, "Turbidity, suspended sediment, and water clarity: a review," J. Am. Water Resour. Assoc. 37, 1085-1101 (2001).
[CrossRef]

Speizer, F. E.

D. W. Dockery, A. Pope III, X. Xu, J. D. Spengler, J. H. Ware, M. E. Fay, B. G. Ferris, Jr., and F. E. Speizer, "An association between air pollution and mortality in six U.S. cities," N. Engl. J. Med. 329, 1753-1759 (1993).
[CrossRef] [PubMed]

Spengler, J. D.

D. W. Dockery, A. Pope III, X. Xu, J. D. Spengler, J. H. Ware, M. E. Fay, B. G. Ferris, Jr., and F. E. Speizer, "An association between air pollution and mortality in six U.S. cities," N. Engl. J. Med. 329, 1753-1759 (1993).
[CrossRef] [PubMed]

Tennant, D. A.

E. T. Baker, D. A. Tennant, R. A. Feely, G. T. Lebon, and S. L. Walker, "Field and laboratory studies on the effect of particle size and composition on optical backscattering measurements in hydrothermal plumes," Deep-Sea Res. 48, 593-604 (2001).
[CrossRef]

Tomita, Y.

J. Hong and Y. Tomita, "Measurement of distribution of solids concentration on high density gas-solids flow using an optical-fiber probe system," Powder Technol. 83, 85-91 (1995).
[CrossRef]

Tran, N. T.

C. G. Campbell, D. T. Laycak, W. Hoppes, N. T. Tran, and F. G. Shi, "High concentration suspended sediment measurements using a continuous fiber optic in-stream transmissometer," J. Hydrol. 311, 244-253 (2005).
[CrossRef]

Travis, L. D.

M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Light Scattering by Nonspherical Particles (Academic, 2000), Chap. 10.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981), p. 129.

Verdeyen, J. T.

J. T. Verdeyen, Laser Electronics (Prentice Hall, 2000), p. 20.

Walker, S. L.

E. T. Baker, D. A. Tennant, R. A. Feely, G. T. Lebon, and S. L. Walker, "Field and laboratory studies on the effect of particle size and composition on optical backscattering measurements in hydrothermal plumes," Deep-Sea Res. 48, 593-604 (2001).
[CrossRef]

Wang, L.

L. Wang, S. L. Jacques, and L. Zheng, "MCML-Monte Carlo modeling of light transport in multi-layered tissues," Comput. Methods Programs Biomed. 47, 131-146 (1995).
[CrossRef] [PubMed]

Ware, J. H.

D. W. Dockery, A. Pope III, X. Xu, J. D. Spengler, J. H. Ware, M. E. Fay, B. G. Ferris, Jr., and F. E. Speizer, "An association between air pollution and mortality in six U.S. cities," N. Engl. J. Med. 329, 1753-1759 (1993).
[CrossRef] [PubMed]

Whitlock, P. A.

M. H. Kalos and P. A. Whitlock, Monte Carlo Methods, I: Basics (Wiley, 1986).

Witt, A. N.

A. N. Witt, "Multiple scattering in reflection nebulae. 1. Monte Carlo approach," Astrophys. J., Suppl. Ser. 35, 1-6 (1977).
[CrossRef]

Wren, D. G.

D. G. Wren, B. D. Barkdoll, R. A. Kuhnle, and R. W. Derrow, "Field techniques for suspended-sediment measurement," J. Hydraul. Eng. 126, 97-104 (2000).
[CrossRef]

Xu, X.

D. W. Dockery, A. Pope III, X. Xu, J. D. Spengler, J. H. Ware, M. E. Fay, B. G. Ferris, Jr., and F. E. Speizer, "An association between air pollution and mortality in six U.S. cities," N. Engl. J. Med. 329, 1753-1759 (1993).
[CrossRef] [PubMed]

Yamaguchi, H.

Y. Matsuno, H. Yamaguchi, T. Oka, H. Kage, and K. Higashitani, "The use of optic fiber probes for the measurement of dilute particle concentrations: calibration and application to gas-fluidized bad carryover," Powder Technol. 36, 215-221 (1983).
[CrossRef]

Yunost, Y. M.

S. Ibrahim, Y. M. Yunost, R. G. Green, and K. Dutton, "A tomography system using optical-fibre sensors for measuring concentration and velocity of bubbles," Meas. Control 34, 47-51 (2001).

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Appl. Opt. (2)

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S. J. Riley, "The sediment concentration-turbidity relation: its value in monitoring at ranger uranium mine, Northern Territory, Australia," Cantena 32(1), 1-14 (1998).
[CrossRef]

Comput. Methods Programs Biomed. (1)

L. Wang, S. L. Jacques, and L. Zheng, "MCML-Monte Carlo modeling of light transport in multi-layered tissues," Comput. Methods Programs Biomed. 47, 131-146 (1995).
[CrossRef] [PubMed]

Deep-Sea Res. (1)

E. T. Baker, D. A. Tennant, R. A. Feely, G. T. Lebon, and S. L. Walker, "Field and laboratory studies on the effect of particle size and composition on optical backscattering measurements in hydrothermal plumes," Deep-Sea Res. 48, 593-604 (2001).
[CrossRef]

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J. Am. Water Resour. Assoc. (1)

R. J. Davies-Colley and D. G. Smith, "Turbidity, suspended sediment, and water clarity: a review," J. Am. Water Resour. Assoc. 37, 1085-1101 (2001).
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D. G. Wren, B. D. Barkdoll, R. A. Kuhnle, and R. W. Derrow, "Field techniques for suspended-sediment measurement," J. Hydraul. Eng. 126, 97-104 (2000).
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C. G. Campbell, D. T. Laycak, W. Hoppes, N. T. Tran, and F. G. Shi, "High concentration suspended sediment measurements using a continuous fiber optic in-stream transmissometer," J. Hydrol. 311, 244-253 (2005).
[CrossRef]

Meas. Control (1)

S. Ibrahim, Y. M. Yunost, R. G. Green, and K. Dutton, "A tomography system using optical-fibre sensors for measuring concentration and velocity of bubbles," Meas. Control 34, 47-51 (2001).

Meas. Sci. Technol. (1)

S. Ibrahim, R. G. Green, K. Dutton, K. Evan, R. A. Rahim, and A. Goude, "Optical sensor configurations for process tomography," Meas. Sci. Technol. 10, 1079-1086 (1999).
[CrossRef]

N. Engl. J. Med. (1)

D. W. Dockery, A. Pope III, X. Xu, J. D. Spengler, J. H. Ware, M. E. Fay, B. G. Ferris, Jr., and F. E. Speizer, "An association between air pollution and mortality in six U.S. cities," N. Engl. J. Med. 329, 1753-1759 (1993).
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S. Ibrahim, R. G. Green, K. Dutton, and R. A. Rahim, "Application of optical tomography in industrial process control system," in 2000 TENCON Proceedings Intelligent Systems and Technologies for the New Millennium, (IEEE, 2000), Vol. 1, pp. 493-498.
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Figures (9)

Fig. 1
Fig. 1

Principle of the optical fiber sensor and projection of the sensor head on the plane perpendicular to the flow direction.

Fig. 2
Fig. 2

(Color online) Layout of fibers in the receiving plane. Design and fiber parameters are shown in Table 1.

Fig. 3
Fig. 3

Flow chart for photon tracing in a suspended medium with the MC process.

Fig. 4
Fig. 4

Testing MC simulation code by comparing the simulation result (solid curve) with data from Bergougnoux et al.[8] (filled triangles). The setup is shown in this figure with d = 760 μm and a fiber diameter of 760 μm.

Fig. 5
Fig. 5

Simulation results of the spatiotemporal average signal as a function of the volume fraction for different particle sizes are obtained with fibers with a core radius of 100 μm and an optical path length L of 2000 μm. There are 2 rows with 10 fibers in each row. The fiber center-to-center distance is 210 μm.

Fig. 6
Fig. 6

Single curve expression for the sensor response to different particle sizes.

Fig. 7
Fig. 7

Comparison of a PCOS design of different optical path lengths (L = 2, 3, 4, 5, and 7 mm) for particle sizes of (a) 200 and (b) 150 μm and for L = 2, 3, 4, and 5 mm for particle sizes of (c) 50 and (d) 36 μm.

Fig. 8
Fig. 8

Comparison of the model, Eq. (3), with the simulation results for (a) the sensor geometry that is shown in Fig. 2 and (b) the sensor with only a pair of emitting–receiving fibers instead of linear arrays as shown in Fig. 2.

Fig. 9
Fig. 9

Single-curve fit of the sensor response and the simulation results versus X = NC ext(1 − g)L for different particle sizes at L = 2000 μm.

Tables (1)

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Table 1 Parameters Used a

Equations (25)

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I = I L ,max   exp ( K ) ,
I = I L ,max   exp ( N C ext L ) = I L ,max   exp ( 3 4 π C v a 3 C ext L ) ,
I I L ,max = exp [ κ N C ext ( 1 g ) L ] = exp [ 3 κ C v 4 π a 3 C ext ( 1 g ) L ] .
a b p d ( l ) d l = 1 .
l ¯ = 1 N C ext ,
p d ( l ) = 1 l ¯ exp ( - 1 l ¯ ) .
0 l 1 l ¯ exp ( - 1 l ¯ ) d l = ξ ,
l = ln ( 1 - ξ ) N C ext .
C sca = 2 π a 2 x 2 n = 1 ( 2 n + 1 ) ( | a n | 2 + | b n | 2 ) ,
C ext = 2 π a 2 x 2 n = 1 ( 2 n + 1 ) Re ( a n + b n ) ,
a n = ψ n ( y ) ψ n ( x ) m ψ n ( y ) ψ n ( x ) ψ n ( y ) ξ n ( x ) m ψ n ( y ) ξ n ( x ) ,
b n = m ψ n ( y ) ψ n ( x ) ψ n ( y ) ψ n ( x ) m ψ n ( y ) ξ n ( x ) ψ n ( y ) ξ n ( x ) ,
ω = C sca C ext ,
φ local = 2 π ξ 1 .
p ( χ ) = 1 g 2 4 π ( 1 + g 2 2 g χ ) 3 / 2 .
1 2 1 1 p ( χ ) d χ = 1.
1 2 1 χ p ( χ ) d χ = ξ 2 ,
θ local = arccos { 1 2 g [ 1 + g 2 ( 1 g 2 1 g + 2 g ξ 2 ) 2 ] } .
{ x y z } { x y z } + [ cos   φ   cos   θ sin   φ   cos   θ - sin   θ - sin   φ cos   φ 0 cos   φ   sin   θ sin   φ   sin   θ cos   θ ] × { x local y local z local } .
R S = | n 1   cos   θ i n 2   cos   θ t n 1   cos   θ i + n 2   cos   θ t | 2 ,
R P = | n 2   cos   θ i n 1   cos   θ t n 2   cos   θ i + n 1   cos   θ t | 2 ,
R = 1 2 ( R S + R P ) ,
T = 1 R ,
n 1   sin   θ i = n 2   sin   θ t .
    I I L ,max = b 1 X 5 + b 2 X 4 + b 3 X 3 + b 4 X 2 + b 5 X + 1 ,

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