Abstract

A technique is described and demonstrated to measure the size of spherical particles of known index of refraction by laser light scattering with an accuracy of better than 1%. This technique entails imaging the angular scattering intensity onto a photodiode array and applying a fast Fourier transform to the array output to obtain a frequency and phase corresponding to the number and angular position of the scattering lobes. Errors associated with particle trajectory effects and changes in the index of refraction are also considered. Results are not affected by the former, whereas variations of the refractive index by 2%, as may be typical, for example, of the transient heat up of a liquid hydrocarbon droplet, cause a deterioration of sizing accuracy to approximately 3%. The technique can in principle be applied in real time at data rates as high as 20–30 kHz with a modest equipment investment. Therefore, the measurement of droplet evaporation rates in dilute sprays with unprecedented accuracy appears to be feasible.

© 1996 Optical Society of America

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References

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    [CrossRef]
  2. W. D. Bachalo, M. J. Houser, “Phase-Doppler spray analyzer for simultaneous measurements of drop size and velocity distribution,” Opt. Eng. 23, 583–590 (1984).
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    [CrossRef] [PubMed]
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  10. G. Chen, M. M. Mazumder, Y. R. Chemla, A. Serpenguzel, R. K. Chang, “Wavelength variation of laser emission along the entire rim of slightly deformed microdroplets,” Opt. Lett. 18, 1993–1995 (1993).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  13. M. Saffman, T. H. Buchhave, “Simultaneous measurement of size, concentration and velocity of spherical particles by a laser Doppler method,” in Proceedings, Second International Symposium on Applications of Laser Anemometry to Fluid Mechanics, 2–4 July 1984, Lisbon, Portugal.
  14. G. König, K. Anders, A. Frohn, “A new light-scattering technique to measure the diameter of periodically generated moving droplets,” J. Aerosol Sci. 17, 157–167 (1986).
    [CrossRef]
  15. S. V. Sankar, D. H. Buermann, W. D. Bachalo, “Development of advanced diagnostics for characterization of burning droplets in microgravity,” in Proceedings of the Third International Microgravity Combustion Conference, NASA Conf. Publ. 10174 (NASA, Washington, D. C., 1995), pp. 269–273.
  16. G. Grehan, G. Gouesbet, A. Naqwi, F. Durst, “Particle trajectory effects in phase Doppler systems: computations and experiments,” Part. Part. Syst. Charact. 10, 332–338 (1993).
    [CrossRef]
  17. S. A. Schaub, D. R. Alexander, J. P. Barton, “Theoretical analysis of the effects of particle trajectory and structural resonances on the performance of a phase-Doppler particle analyzer,” Appl. Opt. 33, 473–483 (1994).
    [CrossRef] [PubMed]
  18. S. V. Sankar, B. J. Weber, D. Y. Kamemoto, W. D. Bachalo, “Sizing fine particles with the phase Doppler interferometric technique,” Appl. Opt. 30, 4914–4920 (1991).
    [CrossRef] [PubMed]

1994 (1)

1993 (2)

G. Chen, M. M. Mazumder, Y. R. Chemla, A. Serpenguzel, R. K. Chang, “Wavelength variation of laser emission along the entire rim of slightly deformed microdroplets,” Opt. Lett. 18, 1993–1995 (1993).
[CrossRef] [PubMed]

G. Grehan, G. Gouesbet, A. Naqwi, F. Durst, “Particle trajectory effects in phase Doppler systems: computations and experiments,” Part. Part. Syst. Charact. 10, 332–338 (1993).
[CrossRef]

1991 (2)

1986 (1)

G. König, K. Anders, A. Frohn, “A new light-scattering technique to measure the diameter of periodically generated moving droplets,” J. Aerosol Sci. 17, 157–167 (1986).
[CrossRef]

1984 (1)

W. D. Bachalo, M. J. Houser, “Phase-Doppler spray analyzer for simultaneous measurements of drop size and velocity distribution,” Opt. Eng. 23, 583–590 (1984).

1981 (1)

1980 (1)

1979 (1)

Alexander, D. R.

Allen, T. M.

Anders, K.

G. König, K. Anders, A. Frohn, “A new light-scattering technique to measure the diameter of periodically generated moving droplets,” J. Aerosol Sci. 17, 157–167 (1986).
[CrossRef]

Ashkin, A.

Bachalo, W. D.

S. V. Sankar, B. J. Weber, D. Y. Kamemoto, W. D. Bachalo, “Sizing fine particles with the phase Doppler interferometric technique,” Appl. Opt. 30, 4914–4920 (1991).
[CrossRef] [PubMed]

W. D. Bachalo, M. J. Houser, “Phase-Doppler spray analyzer for simultaneous measurements of drop size and velocity distribution,” Opt. Eng. 23, 583–590 (1984).

S. V. Sankar, D. H. Buermann, W. D. Bachalo, “Development of advanced diagnostics for characterization of burning droplets in microgravity,” in Proceedings of the Third International Microgravity Combustion Conference, NASA Conf. Publ. 10174 (NASA, Washington, D. C., 1995), pp. 269–273.

Bartholdi, M.

Barton, J. P.

Beretta, F.

A. D’Alessio, A. Di Lorenzo, F. Beretta, C. Venitozzi, “Optical and chemical investigations on fuel-rich methane-oxygen premixed flames at atmospheric pressure,” in Proceedings of the 14th Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1973), pp. 941–953.
[CrossRef]

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Buchhave, T. H.

M. Saffman, T. H. Buchhave, “Simultaneous measurement of size, concentration and velocity of spherical particles by a laser Doppler method,” in Proceedings, Second International Symposium on Applications of Laser Anemometry to Fluid Mechanics, 2–4 July 1984, Lisbon, Portugal.

Buermann, D. H.

S. V. Sankar, D. H. Buermann, W. D. Bachalo, “Development of advanced diagnostics for characterization of burning droplets in microgravity,” in Proceedings of the Third International Microgravity Combustion Conference, NASA Conf. Publ. 10174 (NASA, Washington, D. C., 1995), pp. 269–273.

Chang, R. K.

G. Chen, M. M. Mazumder, Y. R. Chemla, A. Serpenguzel, R. K. Chang, “Wavelength variation of laser emission along the entire rim of slightly deformed microdroplets,” Opt. Lett. 18, 1993–1995 (1993).
[CrossRef] [PubMed]

G. Chen, A. Serpenguzel, R. K. Chang, “Relative evaporation rates of droplets in a segmented stream determined by droplet cavity fluorescence peak shifts,” in Laser Applications in Combustion and Combustion Diagnostics, L. C. Liou, ed., Proc. SPIE1862, 200–208 (1993).

Chemla, Y. R.

Chen, G.

G. Chen, M. M. Mazumder, Y. R. Chemla, A. Serpenguzel, R. K. Chang, “Wavelength variation of laser emission along the entire rim of slightly deformed microdroplets,” Opt. Lett. 18, 1993–1995 (1993).
[CrossRef] [PubMed]

G. Chen, A. Serpenguzel, R. K. Chang, “Relative evaporation rates of droplets in a segmented stream determined by droplet cavity fluorescence peak shifts,” in Laser Applications in Combustion and Combustion Diagnostics, L. C. Liou, ed., Proc. SPIE1862, 200–208 (1993).

D’Alessio, A.

A. D’Alessio, A. Di Lorenzo, F. Beretta, C. Venitozzi, “Optical and chemical investigations on fuel-rich methane-oxygen premixed flames at atmospheric pressure,” in Proceedings of the 14th Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1973), pp. 941–953.
[CrossRef]

Davis, E. J.

Di Lorenzo, A.

A. D’Alessio, A. Di Lorenzo, F. Beretta, C. Venitozzi, “Optical and chemical investigations on fuel-rich methane-oxygen premixed flames at atmospheric pressure,” in Proceedings of the 14th Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1973), pp. 941–953.
[CrossRef]

Durst, F.

G. Grehan, G. Gouesbet, A. Naqwi, F. Durst, “Particle trajectory effects in phase Doppler systems: computations and experiments,” Part. Part. Syst. Charact. 10, 332–338 (1993).
[CrossRef]

F. Durst, M. Zare, “Laser Doppler measurements in two-phase flows,” presented at the Laser Doppler Anemometry Symposium, Copenhagen, 1975.

Dziedzic, J. M.

Frohn, A.

G. König, K. Anders, A. Frohn, “A new light-scattering technique to measure the diameter of periodically generated moving droplets,” J. Aerosol Sci. 17, 157–167 (1986).
[CrossRef]

Gouesbet, G.

G. Grehan, G. Gouesbet, A. Naqwi, F. Durst, “Particle trajectory effects in phase Doppler systems: computations and experiments,” Part. Part. Syst. Charact. 10, 332–338 (1993).
[CrossRef]

Grehan, G.

G. Grehan, G. Gouesbet, A. Naqwi, F. Durst, “Particle trajectory effects in phase Doppler systems: computations and experiments,” Part. Part. Syst. Charact. 10, 332–338 (1993).
[CrossRef]

Hiebert, R. D.

Holve, D.

Houser, M. J.

W. D. Bachalo, M. J. Houser, “Phase-Doppler spray analyzer for simultaneous measurements of drop size and velocity distribution,” Opt. Eng. 23, 583–590 (1984).

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Kamemoto, D. Y.

Kerker, M.

König, G.

G. König, K. Anders, A. Frohn, “A new light-scattering technique to measure the diameter of periodically generated moving droplets,” J. Aerosol Sci. 17, 157–167 (1986).
[CrossRef]

Mazumder, M. M.

Naqwi, A.

G. Grehan, G. Gouesbet, A. Naqwi, F. Durst, “Particle trajectory effects in phase Doppler systems: computations and experiments,” Part. Part. Syst. Charact. 10, 332–338 (1993).
[CrossRef]

Ray, A. K.

Saffman, M.

M. Saffman, T. H. Buchhave, “Simultaneous measurement of size, concentration and velocity of spherical particles by a laser Doppler method,” in Proceedings, Second International Symposium on Applications of Laser Anemometry to Fluid Mechanics, 2–4 July 1984, Lisbon, Portugal.

Salzman, G. C.

Sankar, S. V.

S. V. Sankar, B. J. Weber, D. Y. Kamemoto, W. D. Bachalo, “Sizing fine particles with the phase Doppler interferometric technique,” Appl. Opt. 30, 4914–4920 (1991).
[CrossRef] [PubMed]

S. V. Sankar, D. H. Buermann, W. D. Bachalo, “Development of advanced diagnostics for characterization of burning droplets in microgravity,” in Proceedings of the Third International Microgravity Combustion Conference, NASA Conf. Publ. 10174 (NASA, Washington, D. C., 1995), pp. 269–273.

Schaub, S. A.

Self, S. A.

Serpenguzel, A.

G. Chen, M. M. Mazumder, Y. R. Chemla, A. Serpenguzel, R. K. Chang, “Wavelength variation of laser emission along the entire rim of slightly deformed microdroplets,” Opt. Lett. 18, 1993–1995 (1993).
[CrossRef] [PubMed]

G. Chen, A. Serpenguzel, R. K. Chang, “Relative evaporation rates of droplets in a segmented stream determined by droplet cavity fluorescence peak shifts,” in Laser Applications in Combustion and Combustion Diagnostics, L. C. Liou, ed., Proc. SPIE1862, 200–208 (1993).

Souyri, A.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

Venitozzi, C.

A. D’Alessio, A. Di Lorenzo, F. Beretta, C. Venitozzi, “Optical and chemical investigations on fuel-rich methane-oxygen premixed flames at atmospheric pressure,” in Proceedings of the 14th Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1973), pp. 941–953.
[CrossRef]

Weber, B. J.

Zare, M.

F. Durst, M. Zare, “Laser Doppler measurements in two-phase flows,” presented at the Laser Doppler Anemometry Symposium, Copenhagen, 1975.

Appl. Opt. (6)

J. Aerosol Sci. (1)

G. König, K. Anders, A. Frohn, “A new light-scattering technique to measure the diameter of periodically generated moving droplets,” J. Aerosol Sci. 17, 157–167 (1986).
[CrossRef]

Opt. Eng. (1)

W. D. Bachalo, M. J. Houser, “Phase-Doppler spray analyzer for simultaneous measurements of drop size and velocity distribution,” Opt. Eng. 23, 583–590 (1984).

Opt. Lett. (1)

Part. Part. Syst. Charact. (1)

G. Grehan, G. Gouesbet, A. Naqwi, F. Durst, “Particle trajectory effects in phase Doppler systems: computations and experiments,” Part. Part. Syst. Charact. 10, 332–338 (1993).
[CrossRef]

Other (8)

A. D’Alessio, A. Di Lorenzo, F. Beretta, C. Venitozzi, “Optical and chemical investigations on fuel-rich methane-oxygen premixed flames at atmospheric pressure,” in Proceedings of the 14th Symposium (International) on Combustion (Combustion Institute, Pittsburgh, Pa., 1973), pp. 941–953.
[CrossRef]

S. V. Sankar, D. H. Buermann, W. D. Bachalo, “Development of advanced diagnostics for characterization of burning droplets in microgravity,” in Proceedings of the Third International Microgravity Combustion Conference, NASA Conf. Publ. 10174 (NASA, Washington, D. C., 1995), pp. 269–273.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

G. Chen, A. Serpenguzel, R. K. Chang, “Relative evaporation rates of droplets in a segmented stream determined by droplet cavity fluorescence peak shifts,” in Laser Applications in Combustion and Combustion Diagnostics, L. C. Liou, ed., Proc. SPIE1862, 200–208 (1993).

F. Durst, M. Zare, “Laser Doppler measurements in two-phase flows,” presented at the Laser Doppler Anemometry Symposium, Copenhagen, 1975.

M. Saffman, T. H. Buchhave, “Simultaneous measurement of size, concentration and velocity of spherical particles by a laser Doppler method,” in Proceedings, Second International Symposium on Applications of Laser Anemometry to Fluid Mechanics, 2–4 July 1984, Lisbon, Portugal.

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Figures (8)

Fig. 1
Fig. 1

Calculated angular scattering profiles for three spherical particles. Optical parameters: 488-nm illumination wavelength; index of refraction of heptane at 298 K, 1.385; 13.65° scattering angle; 8.2° collection angle.

Fig. 2
Fig. 2

Index of the dominant spatial frequency component of the intensity phase functions as computed by the FFT versus particle diameter for the same optical parameters as in Fig. 1.

Fig. 3
Fig. 3

Sensitivity of the PFI and of the corresponding phase angle to the particle diameter.

Fig. 4
Fig. 4

Schematic of the experimental setup. CW, continuous wave.

Fig. 5
Fig. 5

Measured intensity profile for a 74.9-μm heptane droplet.

Fig. 6
Fig. 6

Size histogram of 5000 particles measured by a Dantec particle dynamic analyzer. The monodisperse droplets were produced by a vibrating orifice droplet generator.

Fig. 7
Fig. 7

Size histogram of 1000 particles measured by using the frequency phase technique.

Fig. 8
Fig. 8

Computed phase functions of a 60-μm heptane particle placed at the center and at the edge of a 488-nm illumination beam with a beam waist of 120 μm.

Equations (2)

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Δ α = β L ( 1 + S ) δ ,
S = L 4 f tan ( β / 2 )

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