Abstract

The sizing of droplets by optical imaging typically requires a small depth of field so that variations in the magnification ratio are minimized. However, if the location of the drop along the optical axis can be determined, a variable magnification ratio can be imposed on each imaged drop, and the depth of field can be increased. Previous research suggested that droplet location can be determined with a characteristic of droplet images that is obtained when the droplet is illuminated from behind. In this prior research, the method was demonstrated with spherical glass objects to simulate raindrops. Raindrops are known to deviate significantly from a spherical shape, especially when the drop size is large. We demonstrate the ability to locate the position of objects that deviate from sphericity. Deformed water drops and glass ellipsoids are tested, along with glass spheres. The role of refractive index is also discussed.

© 2003 Optical Society of America

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References

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  1. F. A. Jenkins, H. A. White, Fundamentals of Optics (McGraw-Hill, New York, 1957).
  2. J. R. Saylor, B. K. Jones, L. F. Bliven, “A method for increasing depth of field during droplet imaging,” Rev. Sci. Instrum. 73, 2422–2427 (2002).
    [CrossRef]
  3. T. Nousiainen, K. Muinonen, “Light scattering by Gaussian, randomly oscillating raindrops,” J. Quant. Spectrosc. Radiat. Transfer 63, 643–666 (1999).
    [CrossRef]
  4. K. V. Beard, H. T. Ochs, R. J. Kubesh, “Natural oscillations of small raindrops,” Nature (London) 342, 408–410 (1989).
    [CrossRef]
  5. K. V. Beard, C. Chuang, “A new model for the equilibrium shape of raindrops,” J. Atmos. Sci. 44, 1509–1524 (1987).
    [CrossRef]
  6. K. V. Beard, “Raindrop oscillations: evaluation of a potential flow model with gravity,” J. Atmos. Sci. 41, 1765–1774 (1984).
    [CrossRef]
  7. K. V. Beard, “Oscillation models for predicting raindrop axis and backscatter ratios,” Radio Sci. 19, 67–74 (1984).
    [CrossRef]
  8. K. V. Beard, R. J. Kubesh, “Laboratory measurements of small raindrop distortion. Part 2: Oscillation frequencies and modes,” J. Atmos. Sci. 48, 2245–2264 (1991).
    [CrossRef]
  9. K. V. Beard, A. Tokay, “A field study of raindrop oscillations: observations of size spectra and evaluation of oscillation causes,” Geophys. Res. Lett. 18, 2257–2260 (1991).
    [CrossRef]
  10. R. J. Kubesh, K. V. Beard, “Laboratory measurements of spontaneous oscillations for moderate-size raindrops,” J. Atmos. Sci. 50, 1089–1098 (1993).
    [CrossRef]
  11. A. Tokay, K. V. Beard, “A field study of raindrop oscillations. Part 1: Observation of size spectra and evaluation of oscillation modes,” J. Appl. Meteorol. 35, 1671–1687 (1996).
    [CrossRef]
  12. K. Andsager, K. V. Beard, N. F. Laird, “Laboratory measurements of axis ratios for large raindrops,” J. Atmos. Sci. 56, 2673–2683 (1999).
    [CrossRef]
  13. D. C. Blanchard, “The behavior of water drops at terminal velocity in air,” Eos Trans. Am. Geophys. Union 31, 836–842 (1950).
    [CrossRef]
  14. D. M. A. Jones, “The shape of raindrops,” J. Meteorol. 16, 504–510 (1959).
    [CrossRef]
  15. G. C. McCormick, A. Hendry, B. L. Barge, “The anisotropy of precipitation media,” Nature (London) 238, 214–216 (1972).
    [CrossRef]
  16. T. A. Seligia, V. N. Bringi, “Potential use of radar differential reflectivity measurements at orthogonal polarizations for measuring precipitation,” J. Appl. Meteorol. 5, 69–76 (1976).
    [CrossRef]
  17. C. W. Ulbrich, “A review of the differential reflectivity technique of measuring rainfall,” IEEE Trans. Geosci. Remote Sens. GE-24, 955–965 (1986).
    [CrossRef]
  18. T. Oguchi, “Scattering from hydrometeors: a survey,” Radio Sci. 16, 691–730 (1981).
    [CrossRef]
  19. R. N. Berglund, R. Y. H. Liu, “Generation of monodisperse aerosol standards,” Environ. Sci. Technol. 7, 147–153 (1973).
    [CrossRef]
  20. E. H. Trinh, “Compact acoustic levitation device for studies in fluid dynamics and material science in the laboratory and microgravity,” Rev. Sci. Instrum. 56, 2059–2065 (1985).
    [CrossRef]
  21. R. C. Weast, Handbook of Chemistry and Physics, 52nd ed., (Chemical Rubber Co., Cleveland, Ohio, 1972).

2002

J. R. Saylor, B. K. Jones, L. F. Bliven, “A method for increasing depth of field during droplet imaging,” Rev. Sci. Instrum. 73, 2422–2427 (2002).
[CrossRef]

1999

T. Nousiainen, K. Muinonen, “Light scattering by Gaussian, randomly oscillating raindrops,” J. Quant. Spectrosc. Radiat. Transfer 63, 643–666 (1999).
[CrossRef]

K. Andsager, K. V. Beard, N. F. Laird, “Laboratory measurements of axis ratios for large raindrops,” J. Atmos. Sci. 56, 2673–2683 (1999).
[CrossRef]

1996

A. Tokay, K. V. Beard, “A field study of raindrop oscillations. Part 1: Observation of size spectra and evaluation of oscillation modes,” J. Appl. Meteorol. 35, 1671–1687 (1996).
[CrossRef]

1993

R. J. Kubesh, K. V. Beard, “Laboratory measurements of spontaneous oscillations for moderate-size raindrops,” J. Atmos. Sci. 50, 1089–1098 (1993).
[CrossRef]

1991

K. V. Beard, R. J. Kubesh, “Laboratory measurements of small raindrop distortion. Part 2: Oscillation frequencies and modes,” J. Atmos. Sci. 48, 2245–2264 (1991).
[CrossRef]

K. V. Beard, A. Tokay, “A field study of raindrop oscillations: observations of size spectra and evaluation of oscillation causes,” Geophys. Res. Lett. 18, 2257–2260 (1991).
[CrossRef]

1989

K. V. Beard, H. T. Ochs, R. J. Kubesh, “Natural oscillations of small raindrops,” Nature (London) 342, 408–410 (1989).
[CrossRef]

1987

K. V. Beard, C. Chuang, “A new model for the equilibrium shape of raindrops,” J. Atmos. Sci. 44, 1509–1524 (1987).
[CrossRef]

1986

C. W. Ulbrich, “A review of the differential reflectivity technique of measuring rainfall,” IEEE Trans. Geosci. Remote Sens. GE-24, 955–965 (1986).
[CrossRef]

1985

E. H. Trinh, “Compact acoustic levitation device for studies in fluid dynamics and material science in the laboratory and microgravity,” Rev. Sci. Instrum. 56, 2059–2065 (1985).
[CrossRef]

1984

K. V. Beard, “Raindrop oscillations: evaluation of a potential flow model with gravity,” J. Atmos. Sci. 41, 1765–1774 (1984).
[CrossRef]

K. V. Beard, “Oscillation models for predicting raindrop axis and backscatter ratios,” Radio Sci. 19, 67–74 (1984).
[CrossRef]

1981

T. Oguchi, “Scattering from hydrometeors: a survey,” Radio Sci. 16, 691–730 (1981).
[CrossRef]

1976

T. A. Seligia, V. N. Bringi, “Potential use of radar differential reflectivity measurements at orthogonal polarizations for measuring precipitation,” J. Appl. Meteorol. 5, 69–76 (1976).
[CrossRef]

1973

R. N. Berglund, R. Y. H. Liu, “Generation of monodisperse aerosol standards,” Environ. Sci. Technol. 7, 147–153 (1973).
[CrossRef]

1972

G. C. McCormick, A. Hendry, B. L. Barge, “The anisotropy of precipitation media,” Nature (London) 238, 214–216 (1972).
[CrossRef]

1959

D. M. A. Jones, “The shape of raindrops,” J. Meteorol. 16, 504–510 (1959).
[CrossRef]

1950

D. C. Blanchard, “The behavior of water drops at terminal velocity in air,” Eos Trans. Am. Geophys. Union 31, 836–842 (1950).
[CrossRef]

Andsager, K.

K. Andsager, K. V. Beard, N. F. Laird, “Laboratory measurements of axis ratios for large raindrops,” J. Atmos. Sci. 56, 2673–2683 (1999).
[CrossRef]

Barge, B. L.

G. C. McCormick, A. Hendry, B. L. Barge, “The anisotropy of precipitation media,” Nature (London) 238, 214–216 (1972).
[CrossRef]

Beard, K. V.

K. Andsager, K. V. Beard, N. F. Laird, “Laboratory measurements of axis ratios for large raindrops,” J. Atmos. Sci. 56, 2673–2683 (1999).
[CrossRef]

A. Tokay, K. V. Beard, “A field study of raindrop oscillations. Part 1: Observation of size spectra and evaluation of oscillation modes,” J. Appl. Meteorol. 35, 1671–1687 (1996).
[CrossRef]

R. J. Kubesh, K. V. Beard, “Laboratory measurements of spontaneous oscillations for moderate-size raindrops,” J. Atmos. Sci. 50, 1089–1098 (1993).
[CrossRef]

K. V. Beard, A. Tokay, “A field study of raindrop oscillations: observations of size spectra and evaluation of oscillation causes,” Geophys. Res. Lett. 18, 2257–2260 (1991).
[CrossRef]

K. V. Beard, R. J. Kubesh, “Laboratory measurements of small raindrop distortion. Part 2: Oscillation frequencies and modes,” J. Atmos. Sci. 48, 2245–2264 (1991).
[CrossRef]

K. V. Beard, H. T. Ochs, R. J. Kubesh, “Natural oscillations of small raindrops,” Nature (London) 342, 408–410 (1989).
[CrossRef]

K. V. Beard, C. Chuang, “A new model for the equilibrium shape of raindrops,” J. Atmos. Sci. 44, 1509–1524 (1987).
[CrossRef]

K. V. Beard, “Oscillation models for predicting raindrop axis and backscatter ratios,” Radio Sci. 19, 67–74 (1984).
[CrossRef]

K. V. Beard, “Raindrop oscillations: evaluation of a potential flow model with gravity,” J. Atmos. Sci. 41, 1765–1774 (1984).
[CrossRef]

Berglund, R. N.

R. N. Berglund, R. Y. H. Liu, “Generation of monodisperse aerosol standards,” Environ. Sci. Technol. 7, 147–153 (1973).
[CrossRef]

Blanchard, D. C.

D. C. Blanchard, “The behavior of water drops at terminal velocity in air,” Eos Trans. Am. Geophys. Union 31, 836–842 (1950).
[CrossRef]

Bliven, L. F.

J. R. Saylor, B. K. Jones, L. F. Bliven, “A method for increasing depth of field during droplet imaging,” Rev. Sci. Instrum. 73, 2422–2427 (2002).
[CrossRef]

Bringi, V. N.

T. A. Seligia, V. N. Bringi, “Potential use of radar differential reflectivity measurements at orthogonal polarizations for measuring precipitation,” J. Appl. Meteorol. 5, 69–76 (1976).
[CrossRef]

Chuang, C.

K. V. Beard, C. Chuang, “A new model for the equilibrium shape of raindrops,” J. Atmos. Sci. 44, 1509–1524 (1987).
[CrossRef]

Hendry, A.

G. C. McCormick, A. Hendry, B. L. Barge, “The anisotropy of precipitation media,” Nature (London) 238, 214–216 (1972).
[CrossRef]

Jenkins, F. A.

F. A. Jenkins, H. A. White, Fundamentals of Optics (McGraw-Hill, New York, 1957).

Jones, B. K.

J. R. Saylor, B. K. Jones, L. F. Bliven, “A method for increasing depth of field during droplet imaging,” Rev. Sci. Instrum. 73, 2422–2427 (2002).
[CrossRef]

Jones, D. M. A.

D. M. A. Jones, “The shape of raindrops,” J. Meteorol. 16, 504–510 (1959).
[CrossRef]

Kubesh, R. J.

R. J. Kubesh, K. V. Beard, “Laboratory measurements of spontaneous oscillations for moderate-size raindrops,” J. Atmos. Sci. 50, 1089–1098 (1993).
[CrossRef]

K. V. Beard, R. J. Kubesh, “Laboratory measurements of small raindrop distortion. Part 2: Oscillation frequencies and modes,” J. Atmos. Sci. 48, 2245–2264 (1991).
[CrossRef]

K. V. Beard, H. T. Ochs, R. J. Kubesh, “Natural oscillations of small raindrops,” Nature (London) 342, 408–410 (1989).
[CrossRef]

Laird, N. F.

K. Andsager, K. V. Beard, N. F. Laird, “Laboratory measurements of axis ratios for large raindrops,” J. Atmos. Sci. 56, 2673–2683 (1999).
[CrossRef]

Liu, R. Y. H.

R. N. Berglund, R. Y. H. Liu, “Generation of monodisperse aerosol standards,” Environ. Sci. Technol. 7, 147–153 (1973).
[CrossRef]

McCormick, G. C.

G. C. McCormick, A. Hendry, B. L. Barge, “The anisotropy of precipitation media,” Nature (London) 238, 214–216 (1972).
[CrossRef]

Muinonen, K.

T. Nousiainen, K. Muinonen, “Light scattering by Gaussian, randomly oscillating raindrops,” J. Quant. Spectrosc. Radiat. Transfer 63, 643–666 (1999).
[CrossRef]

Nousiainen, T.

T. Nousiainen, K. Muinonen, “Light scattering by Gaussian, randomly oscillating raindrops,” J. Quant. Spectrosc. Radiat. Transfer 63, 643–666 (1999).
[CrossRef]

Ochs, H. T.

K. V. Beard, H. T. Ochs, R. J. Kubesh, “Natural oscillations of small raindrops,” Nature (London) 342, 408–410 (1989).
[CrossRef]

Oguchi, T.

T. Oguchi, “Scattering from hydrometeors: a survey,” Radio Sci. 16, 691–730 (1981).
[CrossRef]

Saylor, J. R.

J. R. Saylor, B. K. Jones, L. F. Bliven, “A method for increasing depth of field during droplet imaging,” Rev. Sci. Instrum. 73, 2422–2427 (2002).
[CrossRef]

Seligia, T. A.

T. A. Seligia, V. N. Bringi, “Potential use of radar differential reflectivity measurements at orthogonal polarizations for measuring precipitation,” J. Appl. Meteorol. 5, 69–76 (1976).
[CrossRef]

Tokay, A.

A. Tokay, K. V. Beard, “A field study of raindrop oscillations. Part 1: Observation of size spectra and evaluation of oscillation modes,” J. Appl. Meteorol. 35, 1671–1687 (1996).
[CrossRef]

K. V. Beard, A. Tokay, “A field study of raindrop oscillations: observations of size spectra and evaluation of oscillation causes,” Geophys. Res. Lett. 18, 2257–2260 (1991).
[CrossRef]

Trinh, E. H.

E. H. Trinh, “Compact acoustic levitation device for studies in fluid dynamics and material science in the laboratory and microgravity,” Rev. Sci. Instrum. 56, 2059–2065 (1985).
[CrossRef]

Ulbrich, C. W.

C. W. Ulbrich, “A review of the differential reflectivity technique of measuring rainfall,” IEEE Trans. Geosci. Remote Sens. GE-24, 955–965 (1986).
[CrossRef]

Weast, R. C.

R. C. Weast, Handbook of Chemistry and Physics, 52nd ed., (Chemical Rubber Co., Cleveland, Ohio, 1972).

White, H. A.

F. A. Jenkins, H. A. White, Fundamentals of Optics (McGraw-Hill, New York, 1957).

Environ. Sci. Technol.

R. N. Berglund, R. Y. H. Liu, “Generation of monodisperse aerosol standards,” Environ. Sci. Technol. 7, 147–153 (1973).
[CrossRef]

Eos Trans. Am. Geophys. Union

D. C. Blanchard, “The behavior of water drops at terminal velocity in air,” Eos Trans. Am. Geophys. Union 31, 836–842 (1950).
[CrossRef]

Geophys. Res. Lett.

K. V. Beard, A. Tokay, “A field study of raindrop oscillations: observations of size spectra and evaluation of oscillation causes,” Geophys. Res. Lett. 18, 2257–2260 (1991).
[CrossRef]

IEEE Trans. Geosci. Remote Sens.

C. W. Ulbrich, “A review of the differential reflectivity technique of measuring rainfall,” IEEE Trans. Geosci. Remote Sens. GE-24, 955–965 (1986).
[CrossRef]

J. Appl. Meteorol.

T. A. Seligia, V. N. Bringi, “Potential use of radar differential reflectivity measurements at orthogonal polarizations for measuring precipitation,” J. Appl. Meteorol. 5, 69–76 (1976).
[CrossRef]

A. Tokay, K. V. Beard, “A field study of raindrop oscillations. Part 1: Observation of size spectra and evaluation of oscillation modes,” J. Appl. Meteorol. 35, 1671–1687 (1996).
[CrossRef]

J. Atmos. Sci.

K. Andsager, K. V. Beard, N. F. Laird, “Laboratory measurements of axis ratios for large raindrops,” J. Atmos. Sci. 56, 2673–2683 (1999).
[CrossRef]

K. V. Beard, R. J. Kubesh, “Laboratory measurements of small raindrop distortion. Part 2: Oscillation frequencies and modes,” J. Atmos. Sci. 48, 2245–2264 (1991).
[CrossRef]

R. J. Kubesh, K. V. Beard, “Laboratory measurements of spontaneous oscillations for moderate-size raindrops,” J. Atmos. Sci. 50, 1089–1098 (1993).
[CrossRef]

K. V. Beard, C. Chuang, “A new model for the equilibrium shape of raindrops,” J. Atmos. Sci. 44, 1509–1524 (1987).
[CrossRef]

K. V. Beard, “Raindrop oscillations: evaluation of a potential flow model with gravity,” J. Atmos. Sci. 41, 1765–1774 (1984).
[CrossRef]

J. Meteorol.

D. M. A. Jones, “The shape of raindrops,” J. Meteorol. 16, 504–510 (1959).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer

T. Nousiainen, K. Muinonen, “Light scattering by Gaussian, randomly oscillating raindrops,” J. Quant. Spectrosc. Radiat. Transfer 63, 643–666 (1999).
[CrossRef]

Nature (London)

K. V. Beard, H. T. Ochs, R. J. Kubesh, “Natural oscillations of small raindrops,” Nature (London) 342, 408–410 (1989).
[CrossRef]

G. C. McCormick, A. Hendry, B. L. Barge, “The anisotropy of precipitation media,” Nature (London) 238, 214–216 (1972).
[CrossRef]

Radio Sci.

T. Oguchi, “Scattering from hydrometeors: a survey,” Radio Sci. 16, 691–730 (1981).
[CrossRef]

K. V. Beard, “Oscillation models for predicting raindrop axis and backscatter ratios,” Radio Sci. 19, 67–74 (1984).
[CrossRef]

Rev. Sci. Instrum.

J. R. Saylor, B. K. Jones, L. F. Bliven, “A method for increasing depth of field during droplet imaging,” Rev. Sci. Instrum. 73, 2422–2427 (2002).
[CrossRef]

E. H. Trinh, “Compact acoustic levitation device for studies in fluid dynamics and material science in the laboratory and microgravity,” Rev. Sci. Instrum. 56, 2059–2065 (1985).
[CrossRef]

Other

R. C. Weast, Handbook of Chemistry and Physics, 52nd ed., (Chemical Rubber Co., Cleveland, Ohio, 1972).

F. A. Jenkins, H. A. White, Fundamentals of Optics (McGraw-Hill, New York, 1957).

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Figures (10)

Fig. 1
Fig. 1

Sample image of a falling water drop illuminated from behind. The bright spot in the center of the drop is an image of the illumination source, obtained through the drop.

Fig. 2
Fig. 2

Experimental setup used to investigate glass spheres and ellipsoids.

Fig. 3
Fig. 3

Sample images of (a) glass sphere, (b) falling water drop, (c) glass ellipsoid. The horizontal dimension of these three are 4.0, 4.2, and 10 mm, respectively. The glass objects presented in images (a) and (c) are supported on a small set screw that can be seen protruding from the bottom of the image. Also visible in (a) and (c) is a curved piece of double-sided tape that was used to attach the glass to the set screw.

Fig. 4
Fig. 4

Experimental setup used to image falling water drops.

Fig. 5
Fig. 5

Plot of α versus z d for glass spheres of diameter d = 4, 6, 8, and 10 mm.

Fig. 6
Fig. 6

Plot of α versus z d for glass ellipsoids with a/ b = 0.55, 0.70, 0.78, 1.29, 1.42.

Fig. 7
Fig. 7

Plot of α versus z d for glass spheres and glass ellipsoids. The numbers listed in the legend correspond to the diameter in millimeters for the glass spheres and the value of a/ b for the glass ellipsoids.

Fig. 8
Fig. 8

Plot of α versus z d for falling water drops. d ∼ 4 mm.

Fig. 9
Fig. 9

Plot of α versus z d for falling water drops, a glass ellipsoid, and a glass sphere. For the glass sphere the diameter is 8 mm, and for the glass ellipsoid the value of a/ b is 1.42.

Fig. 10
Fig. 10

Plot of α versus z d for two 8-mm spheres with different indices of refraction.

Tables (2)

Tables Icon

Table 1 Dimensions of the Three Ellipsoids Used in This Study

Tables Icon

Table 2 Values of a/ b for Each of the Three Ellipsoids Investigateda

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

M=dd,
α=dsd,
α=a3zd3+a2zd2+a1zd+a0,

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