Abstract

In the shadow image of a spherical gas bubble, high intensity rings are visible, i.e., glare circles. These can be used to obtain a more precise estimate of the bubble diameter than can be obtained from the shadow contour. The glare circle diameter can also be used to determine the relative refractive index by comparing it with the shadow diameter. The precision of this refractive index measurement reaches the third decimal, which is demonstrated experimentally. Thus, one can simultaneously determine the bubble diameter (from the shadow contour) and the relative refractive index (from the glare circle).

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. H. van de Hulst and R. Wang, "Glare points," Appl. Opt. 30, 4755-4763 (1991).
    [CrossRef] [PubMed]
  2. C. Hess, "Planar particle image analyzer," in Laser Techniques Applied to Fluid Mechanics (Springer, 2000).
  3. S. Dehaeck, J. P. A. J. van Beeck, and M. L. Riethmuller, "Extended glare point velocimetry and sizing for bubbly flows," Exp. Fluids 39, 407-419 (2005).
    [CrossRef]
  4. C. Bongiovanni, J. P. Chevaillier, and J. Fabre, "Sizing of bubbles by incoherent imaging: defocus bias," Exp. Fluids 23, 209-216 (1997).
    [CrossRef]
  5. D. S. Langley and P. L. Marston, "Forward glory scattering from bubbles," Appl. Opt. 30, 3452-3458 (1991).
    [CrossRef] [PubMed]
  6. M. Marxen, P. E. Sullivan, M. R. Loewen, and B. Jaehne, "Comparison of Gaussian particle center estimators and the achievable measurement density for particle tracking velocimetry," Exp. Fluids 29, 145-153 (2000).
    [CrossRef]
  7. E. Hecht, Optics (Addison-Wesley, 1990).
  8. K. Ren, D. Lebrun, C. Ozkul, A. Kleitz, G. Gouesbet, and G. Grehan, "On the measurements of particles by imaging methods: theoretical and experimental aspects," Part. Part. Syst. Charact. 13, 156-164 (1996).
    [CrossRef]
  9. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

2005 (1)

S. Dehaeck, J. P. A. J. van Beeck, and M. L. Riethmuller, "Extended glare point velocimetry and sizing for bubbly flows," Exp. Fluids 39, 407-419 (2005).
[CrossRef]

2000 (1)

M. Marxen, P. E. Sullivan, M. R. Loewen, and B. Jaehne, "Comparison of Gaussian particle center estimators and the achievable measurement density for particle tracking velocimetry," Exp. Fluids 29, 145-153 (2000).
[CrossRef]

1997 (1)

C. Bongiovanni, J. P. Chevaillier, and J. Fabre, "Sizing of bubbles by incoherent imaging: defocus bias," Exp. Fluids 23, 209-216 (1997).
[CrossRef]

1996 (1)

K. Ren, D. Lebrun, C. Ozkul, A. Kleitz, G. Gouesbet, and G. Grehan, "On the measurements of particles by imaging methods: theoretical and experimental aspects," Part. Part. Syst. Charact. 13, 156-164 (1996).
[CrossRef]

1991 (2)

Appl. Opt. (2)

Exp. Fluids (3)

M. Marxen, P. E. Sullivan, M. R. Loewen, and B. Jaehne, "Comparison of Gaussian particle center estimators and the achievable measurement density for particle tracking velocimetry," Exp. Fluids 29, 145-153 (2000).
[CrossRef]

S. Dehaeck, J. P. A. J. van Beeck, and M. L. Riethmuller, "Extended glare point velocimetry and sizing for bubbly flows," Exp. Fluids 39, 407-419 (2005).
[CrossRef]

C. Bongiovanni, J. P. Chevaillier, and J. Fabre, "Sizing of bubbles by incoherent imaging: defocus bias," Exp. Fluids 23, 209-216 (1997).
[CrossRef]

Part. Part. Syst. Charact. (1)

K. Ren, D. Lebrun, C. Ozkul, A. Kleitz, G. Gouesbet, and G. Grehan, "On the measurements of particles by imaging methods: theoretical and experimental aspects," Part. Part. Syst. Charact. 13, 156-164 (1996).
[CrossRef]

Other (3)

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).

E. Hecht, Optics (Addison-Wesley, 1990).

C. Hess, "Planar particle image analyzer," in Laser Techniques Applied to Fluid Mechanics (Springer, 2000).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

(Color online) (a) Backlighting image showing a bubble ( ± 1   mm ) with glare circles. (b) Geometrical location of the glare circle corresponding to N = 3 .

Fig. 2
Fig. 2

(a) Diameter ratio versus refractive index of the liquid. (b) Sensitivity of the diameter ratio versus the refractive index.

Fig. 3
Fig. 3

Intensity profile with dashed lines representing the glare circle locations and dash-dot lines for the bubble edge calculated from glare circle N = 3 .

Fig. 4
Fig. 4

(a) Picture of a bubble ( ± 1   mm ) with a glare circle in silicone oil. (b) Picture of a bubble ( ± 250   μm ) with a glare circle in water.

Fig. 5
Fig. 5

(Color online) Uncertainty in the glare circle diameter introduced by using a finite size, diffuse light source.

Equations (3)

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

D 3 = 1 + 1 + 8 n liq 2 4 n liq 2 D b ,
D b = 4 n liq 2 1 + 1 + 8 n liq 2 D 3 C ,
n liq = 1 + η 2 η 2 .

Metrics