Abstract

The dependence of fluorescence intensity distributions within droplets on added dye concentration has been calculated by extension of the geometrical-optics approximation and verified by experimental observations. With rising dye concentration, surface plots of the equatorial fluorescence pattern show decreasing relevance of intensity enhancement at focusing points of internal light rays and increasing effects of linear absorption on the characteristic features of the distribution. For comparison with experimentally obtained images of the fluorescence intensity distribution within droplets, a method for calculating volume-integrated intensity distributions was developed in which image distortion at the fluid–air interface is included. A comparison of the calculated and the experimentally determined fluorescence intensity distributions within a droplet confirmed the accuracy of the geometrical-optics approach at high dye concentrations. However, discrepancies from experimental results are visible at low dye concentrations owing to nonlinear optical effects.

© 2001 Optical Society of America

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References

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  1. W. D. Bachalo, J. Houser, “Phase Doppler analyzer for simultaneous measurements of drop size and velocity distributions,” Opt. Eng. 23, 583–590 (1984).
  2. Y. Hardalupas, J. H. Whitelaw, “The characteristics of sprays produced by coaxial airblast atomizers,” J. Propul. Power 10, 453–460 (1994).
    [CrossRef]
  3. G. Pitcher, G. Wigley, M. Saffman, “Velocity and drop size measurements in fuel sprays in a direct injection diesel engine,” Part. Part. Syst. Charact. 7, 160–168 (1990).
    [CrossRef]
  4. G. Wigley, G. K. Hargrave, J. Heath, “A high power, high resolution LDA PDA system applied to gasoline direct injection sprays,” Part. Part. Syst. Charact. 16, 11–19 (1999).
    [CrossRef]
  5. R. Bazile, D. Stepowski, “Measurements of vaporized and liquid fuel concentrations in a burning spray jet of acetone using planar laser-induced fluorescence,” Exp. Fluids 20, 1–9 (1995).
  6. A. Serpengüzel, J. C. Swindal, R. K. Chang, W. P. Acker, “Two-dimensional imaging of sprays with fluorescence, lasing and stimulated Raman scattering,” Appl. Opt. 31, 3543–3551 (1992).
    [CrossRef] [PubMed]
  7. N. Ladommatos, H. Zhao, “Optical diagnostics for in-cylinder mixture formation measurements in IC engines,” Prog. Energy Combust. Sci. 24, 297–336 (1998).
    [CrossRef]
  8. C.-N. Yeh, H. Kosaka, T. Kamimoto, “A fluorescence/scattering imaging technique for instantaneous 2-D measurement of particle size distribution in a transient spray,” presented at the 3rd congress on Optical Partical Sizing, Yokohama, Japan, 23–26 August 1993.
  9. S. V. Sankar, K. E. Mahler, D. M. Robart, “Rapid characterization of fuel atomizers using an optical patternator,” J. Eng. Gas Turbines Power 121, 409–414 (1999).
    [CrossRef]
  10. P. LeGal, N. Farrugia, D. A. Greenhalgh, “Laser sheet dropsizing of dense sprays,” Opt. Laser Technol. 31, 75–83 (1999).
    [CrossRef]
  11. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
  12. S. V. Sankar, W. D. Bachalo, “Response characteristics of the phase Doppler particle analyzer for sizing spherical particles larger than the light wavelength,” Appl. Opt. 30, 1487–1496 (1991).
    [CrossRef] [PubMed]
  13. Y. Hardalupas, C. H. Liu, “Backscatter phase-Doppler anemometry for transparent nonabsorbing spheres,” Exp. Fluids 14, 379–390 (1993).
  14. D. Q. Chowdhury, P. W. Barber, S. C. Hill, “Energy-density distribution inside large nonabsorbing spheres by using Mie theory and geometrical optics,” Appl. Opt. 31, 3518–3523 (1992).
    [CrossRef] [PubMed]
  15. N. Velesco, T. Kaiser, G. Schweiger, “Computation of the internal field of a large spherical particle by use of the geometrical-optics approximation,” Appl. Opt. 36, 8724–8728 (1997).
    [CrossRef]
  16. M. Kerker, S. D. Druger, “Raman fluorescent scattering by molecules embedded in spheres with radii up to several multiples of the wavelength (T),” Appl. Opt. 18, 1172–1179 (1979).
    [CrossRef] [PubMed]
  17. S. C. Hill, S. Arnold, J. M. Ramsey, M. D. Barnes, “Fluorescence image of a single molecule in a microsphere: model,” J. Opt. Soc. Am. B 16, 1868–1873 (1999).
    [CrossRef]
  18. C. G. Guilbault, Practical Fluorescence–Theory, Methods and Techniques (Marcel Dekker, New York, 1973).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  21. J. Zhang, L. A. Melton, “Numerical simulations and restorations of laser droplet-slicing images,” Appl. Opt. 33, 192–200 (1994).
    [CrossRef] [PubMed]
  22. G. H. McKinley, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Mass. 02139 (personal communication, 1998).
  23. Y. Hardalupas, A. M. K. Taylor, J. H. Wilkins, “Experimental investigation of sub-milimetre droplet impingement onto spherical surfaces,” Int. J. Heat Fluid Flow 20, 477–485 (1999).
    [CrossRef]
  24. J.-G. Xie, T. E. Ruekgauer, J. Gu, R. L. Armstrong, R. G. Pinnick, J. D. Pendelton, “Physical basis for Descartes ring scattering in laser-irradiated microdroplets,” Opt. Lett. 16, 1817–1819 (1991).
    [CrossRef] [PubMed]
  25. J. A. Lock, E. A. Hovenac, “Internal caustic structure of illuminated liquid droplets,” J. Opt. Soc. Am. A 8, 1541–1552 (1991).
    [CrossRef]
  26. R. Domann, Y. Hardalupas, “Evaluation of the planar droplet sizing (PDS) technique,” presented at the 8th. International Conference on Liquid Atomization and Spray Systems, Pasadena, Calif., 16–20 July 2000.
  27. R. Domann, Y. Hardalupas, “A study of parameters that influence the accuracy of the Planar Droplet Sizing (PDS) technique,” Part. Part. Syst. Charact. (to be published).

1999 (5)

G. Wigley, G. K. Hargrave, J. Heath, “A high power, high resolution LDA PDA system applied to gasoline direct injection sprays,” Part. Part. Syst. Charact. 16, 11–19 (1999).
[CrossRef]

S. V. Sankar, K. E. Mahler, D. M. Robart, “Rapid characterization of fuel atomizers using an optical patternator,” J. Eng. Gas Turbines Power 121, 409–414 (1999).
[CrossRef]

P. LeGal, N. Farrugia, D. A. Greenhalgh, “Laser sheet dropsizing of dense sprays,” Opt. Laser Technol. 31, 75–83 (1999).
[CrossRef]

S. C. Hill, S. Arnold, J. M. Ramsey, M. D. Barnes, “Fluorescence image of a single molecule in a microsphere: model,” J. Opt. Soc. Am. B 16, 1868–1873 (1999).
[CrossRef]

Y. Hardalupas, A. M. K. Taylor, J. H. Wilkins, “Experimental investigation of sub-milimetre droplet impingement onto spherical surfaces,” Int. J. Heat Fluid Flow 20, 477–485 (1999).
[CrossRef]

1998 (1)

N. Ladommatos, H. Zhao, “Optical diagnostics for in-cylinder mixture formation measurements in IC engines,” Prog. Energy Combust. Sci. 24, 297–336 (1998).
[CrossRef]

1997 (1)

1995 (1)

R. Bazile, D. Stepowski, “Measurements of vaporized and liquid fuel concentrations in a burning spray jet of acetone using planar laser-induced fluorescence,” Exp. Fluids 20, 1–9 (1995).

1994 (2)

Y. Hardalupas, J. H. Whitelaw, “The characteristics of sprays produced by coaxial airblast atomizers,” J. Propul. Power 10, 453–460 (1994).
[CrossRef]

J. Zhang, L. A. Melton, “Numerical simulations and restorations of laser droplet-slicing images,” Appl. Opt. 33, 192–200 (1994).
[CrossRef] [PubMed]

1993 (1)

Y. Hardalupas, C. H. Liu, “Backscatter phase-Doppler anemometry for transparent nonabsorbing spheres,” Exp. Fluids 14, 379–390 (1993).

1992 (3)

1991 (3)

1990 (1)

G. Pitcher, G. Wigley, M. Saffman, “Velocity and drop size measurements in fuel sprays in a direct injection diesel engine,” Part. Part. Syst. Charact. 7, 160–168 (1990).
[CrossRef]

1987 (1)

1984 (1)

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

1979 (1)

Acker, W. P.

Alexander, D. R.

Armstrong, R. L.

Arnold, S.

Bachalo, W. D.

S. V. Sankar, W. D. Bachalo, “Response characteristics of the phase Doppler particle analyzer for sizing spherical particles larger than the light wavelength,” Appl. Opt. 30, 1487–1496 (1991).
[CrossRef] [PubMed]

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

Barber, P. W.

Barnes, M. D.

Bazile, R.

R. Bazile, D. Stepowski, “Measurements of vaporized and liquid fuel concentrations in a burning spray jet of acetone using planar laser-induced fluorescence,” Exp. Fluids 20, 1–9 (1995).

Benincasa, D. S.

Chang, R. K.

Chowdhury, D. Q.

Domann, R.

R. Domann, Y. Hardalupas, “Evaluation of the planar droplet sizing (PDS) technique,” presented at the 8th. International Conference on Liquid Atomization and Spray Systems, Pasadena, Calif., 16–20 July 2000.

R. Domann, Y. Hardalupas, “A study of parameters that influence the accuracy of the Planar Droplet Sizing (PDS) technique,” Part. Part. Syst. Charact. (to be published).

Druger, S. D.

Farrugia, N.

P. LeGal, N. Farrugia, D. A. Greenhalgh, “Laser sheet dropsizing of dense sprays,” Opt. Laser Technol. 31, 75–83 (1999).
[CrossRef]

Greenhalgh, D. A.

P. LeGal, N. Farrugia, D. A. Greenhalgh, “Laser sheet dropsizing of dense sprays,” Opt. Laser Technol. 31, 75–83 (1999).
[CrossRef]

Gu, J.

Guilbault, C. G.

C. G. Guilbault, Practical Fluorescence–Theory, Methods and Techniques (Marcel Dekker, New York, 1973).

Hardalupas, Y.

Y. Hardalupas, A. M. K. Taylor, J. H. Wilkins, “Experimental investigation of sub-milimetre droplet impingement onto spherical surfaces,” Int. J. Heat Fluid Flow 20, 477–485 (1999).
[CrossRef]

Y. Hardalupas, J. H. Whitelaw, “The characteristics of sprays produced by coaxial airblast atomizers,” J. Propul. Power 10, 453–460 (1994).
[CrossRef]

Y. Hardalupas, C. H. Liu, “Backscatter phase-Doppler anemometry for transparent nonabsorbing spheres,” Exp. Fluids 14, 379–390 (1993).

R. Domann, Y. Hardalupas, “A study of parameters that influence the accuracy of the Planar Droplet Sizing (PDS) technique,” Part. Part. Syst. Charact. (to be published).

R. Domann, Y. Hardalupas, “Evaluation of the planar droplet sizing (PDS) technique,” presented at the 8th. International Conference on Liquid Atomization and Spray Systems, Pasadena, Calif., 16–20 July 2000.

Hargrave, G. K.

G. Wigley, G. K. Hargrave, J. Heath, “A high power, high resolution LDA PDA system applied to gasoline direct injection sprays,” Part. Part. Syst. Charact. 16, 11–19 (1999).
[CrossRef]

Heath, J.

G. Wigley, G. K. Hargrave, J. Heath, “A high power, high resolution LDA PDA system applied to gasoline direct injection sprays,” Part. Part. Syst. Charact. 16, 11–19 (1999).
[CrossRef]

Hill, S. C.

Houser, J.

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

Hovenac, E. A.

Hsieh, W.-F.

Kaiser, T.

Kamimoto, T.

C.-N. Yeh, H. Kosaka, T. Kamimoto, “A fluorescence/scattering imaging technique for instantaneous 2-D measurement of particle size distribution in a transient spray,” presented at the 3rd congress on Optical Partical Sizing, Yokohama, Japan, 23–26 August 1993.

Kerker, M.

Kosaka, H.

C.-N. Yeh, H. Kosaka, T. Kamimoto, “A fluorescence/scattering imaging technique for instantaneous 2-D measurement of particle size distribution in a transient spray,” presented at the 3rd congress on Optical Partical Sizing, Yokohama, Japan, 23–26 August 1993.

Ladommatos, N.

N. Ladommatos, H. Zhao, “Optical diagnostics for in-cylinder mixture formation measurements in IC engines,” Prog. Energy Combust. Sci. 24, 297–336 (1998).
[CrossRef]

LeGal, P.

P. LeGal, N. Farrugia, D. A. Greenhalgh, “Laser sheet dropsizing of dense sprays,” Opt. Laser Technol. 31, 75–83 (1999).
[CrossRef]

Liu, C. H.

Y. Hardalupas, C. H. Liu, “Backscatter phase-Doppler anemometry for transparent nonabsorbing spheres,” Exp. Fluids 14, 379–390 (1993).

Lock, J. A.

Mahler, K. E.

S. V. Sankar, K. E. Mahler, D. M. Robart, “Rapid characterization of fuel atomizers using an optical patternator,” J. Eng. Gas Turbines Power 121, 409–414 (1999).
[CrossRef]

McKinley, G. H.

G. H. McKinley, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Mass. 02139 (personal communication, 1998).

Melton, L. A.

Pendelton, J. D.

Pinnick, R. G.

Pitcher, G.

G. Pitcher, G. Wigley, M. Saffman, “Velocity and drop size measurements in fuel sprays in a direct injection diesel engine,” Part. Part. Syst. Charact. 7, 160–168 (1990).
[CrossRef]

Ramsey, J. M.

Robart, D. M.

S. V. Sankar, K. E. Mahler, D. M. Robart, “Rapid characterization of fuel atomizers using an optical patternator,” J. Eng. Gas Turbines Power 121, 409–414 (1999).
[CrossRef]

Ruekgauer, T. E.

Saffman, M.

G. Pitcher, G. Wigley, M. Saffman, “Velocity and drop size measurements in fuel sprays in a direct injection diesel engine,” Part. Part. Syst. Charact. 7, 160–168 (1990).
[CrossRef]

Sankar, S. V.

S. V. Sankar, K. E. Mahler, D. M. Robart, “Rapid characterization of fuel atomizers using an optical patternator,” J. Eng. Gas Turbines Power 121, 409–414 (1999).
[CrossRef]

S. V. Sankar, W. D. Bachalo, “Response characteristics of the phase Doppler particle analyzer for sizing spherical particles larger than the light wavelength,” Appl. Opt. 30, 1487–1496 (1991).
[CrossRef] [PubMed]

Schweiger, G.

Serpengüzel, A.

Stepowski, D.

R. Bazile, D. Stepowski, “Measurements of vaporized and liquid fuel concentrations in a burning spray jet of acetone using planar laser-induced fluorescence,” Exp. Fluids 20, 1–9 (1995).

Swindal, J. C.

Taylor, A. M. K.

Y. Hardalupas, A. M. K. Taylor, J. H. Wilkins, “Experimental investigation of sub-milimetre droplet impingement onto spherical surfaces,” Int. J. Heat Fluid Flow 20, 477–485 (1999).
[CrossRef]

van de Hulst, H. C.

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

Velesco, N.

Whitelaw, J. H.

Y. Hardalupas, J. H. Whitelaw, “The characteristics of sprays produced by coaxial airblast atomizers,” J. Propul. Power 10, 453–460 (1994).
[CrossRef]

Wigley, G.

G. Wigley, G. K. Hargrave, J. Heath, “A high power, high resolution LDA PDA system applied to gasoline direct injection sprays,” Part. Part. Syst. Charact. 16, 11–19 (1999).
[CrossRef]

G. Pitcher, G. Wigley, M. Saffman, “Velocity and drop size measurements in fuel sprays in a direct injection diesel engine,” Part. Part. Syst. Charact. 7, 160–168 (1990).
[CrossRef]

Wilkins, J. H.

Y. Hardalupas, A. M. K. Taylor, J. H. Wilkins, “Experimental investigation of sub-milimetre droplet impingement onto spherical surfaces,” Int. J. Heat Fluid Flow 20, 477–485 (1999).
[CrossRef]

Xie, J.-G.

Yeh, C.-N.

C.-N. Yeh, H. Kosaka, T. Kamimoto, “A fluorescence/scattering imaging technique for instantaneous 2-D measurement of particle size distribution in a transient spray,” presented at the 3rd congress on Optical Partical Sizing, Yokohama, Japan, 23–26 August 1993.

Zhang, J.

Zhang, J.-Z.

Zhao, H.

N. Ladommatos, H. Zhao, “Optical diagnostics for in-cylinder mixture formation measurements in IC engines,” Prog. Energy Combust. Sci. 24, 297–336 (1998).
[CrossRef]

Appl. Opt. (8)

A. Serpengüzel, J. C. Swindal, R. K. Chang, W. P. Acker, “Two-dimensional imaging of sprays with fluorescence, lasing and stimulated Raman scattering,” Appl. Opt. 31, 3543–3551 (1992).
[CrossRef] [PubMed]

D. Q. Chowdhury, P. W. Barber, S. C. Hill, “Energy-density distribution inside large nonabsorbing spheres by using Mie theory and geometrical optics,” Appl. Opt. 31, 3518–3523 (1992).
[CrossRef] [PubMed]

N. Velesco, T. Kaiser, G. Schweiger, “Computation of the internal field of a large spherical particle by use of the geometrical-optics approximation,” Appl. Opt. 36, 8724–8728 (1997).
[CrossRef]

M. Kerker, S. D. Druger, “Raman fluorescent scattering by molecules embedded in spheres with radii up to several multiples of the wavelength (T),” Appl. Opt. 18, 1172–1179 (1979).
[CrossRef] [PubMed]

J. Zhang, D. R. Alexander, “Hybrid inelastic-scattering models for particle thermometry: unpolarized emissions,” Appl. Opt. 31, 7132–7139 (1992).
[CrossRef] [PubMed]

D. S. Benincasa, P. W. Barber, J.-Z. Zhang, W.-F. Hsieh, R. K. Chang, “Spatial distribution of the internal and near-field intensities of large cylindrical and spherical scatterers,” Appl. Opt. 26, 1348–1356 (1987).
[CrossRef] [PubMed]

J. Zhang, L. A. Melton, “Numerical simulations and restorations of laser droplet-slicing images,” Appl. Opt. 33, 192–200 (1994).
[CrossRef] [PubMed]

S. V. Sankar, W. D. Bachalo, “Response characteristics of the phase Doppler particle analyzer for sizing spherical particles larger than the light wavelength,” Appl. Opt. 30, 1487–1496 (1991).
[CrossRef] [PubMed]

Exp. Fluids (2)

Y. Hardalupas, C. H. Liu, “Backscatter phase-Doppler anemometry for transparent nonabsorbing spheres,” Exp. Fluids 14, 379–390 (1993).

R. Bazile, D. Stepowski, “Measurements of vaporized and liquid fuel concentrations in a burning spray jet of acetone using planar laser-induced fluorescence,” Exp. Fluids 20, 1–9 (1995).

Int. J. Heat Fluid Flow (1)

Y. Hardalupas, A. M. K. Taylor, J. H. Wilkins, “Experimental investigation of sub-milimetre droplet impingement onto spherical surfaces,” Int. J. Heat Fluid Flow 20, 477–485 (1999).
[CrossRef]

J. Eng. Gas Turbines Power (1)

S. V. Sankar, K. E. Mahler, D. M. Robart, “Rapid characterization of fuel atomizers using an optical patternator,” J. Eng. Gas Turbines Power 121, 409–414 (1999).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

J. Propul. Power (1)

Y. Hardalupas, J. H. Whitelaw, “The characteristics of sprays produced by coaxial airblast atomizers,” J. Propul. Power 10, 453–460 (1994).
[CrossRef]

Opt. Eng. (1)

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

Opt. Laser Technol. (1)

P. LeGal, N. Farrugia, D. A. Greenhalgh, “Laser sheet dropsizing of dense sprays,” Opt. Laser Technol. 31, 75–83 (1999).
[CrossRef]

Opt. Lett. (1)

Part. Part. Syst. Charact. (2)

G. Pitcher, G. Wigley, M. Saffman, “Velocity and drop size measurements in fuel sprays in a direct injection diesel engine,” Part. Part. Syst. Charact. 7, 160–168 (1990).
[CrossRef]

G. Wigley, G. K. Hargrave, J. Heath, “A high power, high resolution LDA PDA system applied to gasoline direct injection sprays,” Part. Part. Syst. Charact. 16, 11–19 (1999).
[CrossRef]

Prog. Energy Combust. Sci. (1)

N. Ladommatos, H. Zhao, “Optical diagnostics for in-cylinder mixture formation measurements in IC engines,” Prog. Energy Combust. Sci. 24, 297–336 (1998).
[CrossRef]

Other (6)

C.-N. Yeh, H. Kosaka, T. Kamimoto, “A fluorescence/scattering imaging technique for instantaneous 2-D measurement of particle size distribution in a transient spray,” presented at the 3rd congress on Optical Partical Sizing, Yokohama, Japan, 23–26 August 1993.

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

C. G. Guilbault, Practical Fluorescence–Theory, Methods and Techniques (Marcel Dekker, New York, 1973).

G. H. McKinley, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Mass. 02139 (personal communication, 1998).

R. Domann, Y. Hardalupas, “Evaluation of the planar droplet sizing (PDS) technique,” presented at the 8th. International Conference on Liquid Atomization and Spray Systems, Pasadena, Calif., 16–20 July 2000.

R. Domann, Y. Hardalupas, “A study of parameters that influence the accuracy of the Planar Droplet Sizing (PDS) technique,” Part. Part. Syst. Charact. (to be published).

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Figures (15)

Fig. 1
Fig. 1

Geometry of the droplet illuminated by a plane wave in the +z direction.

Fig. 2
Fig. 2

Schematic view of ray tracing within an illuminated plane of the droplet: refr., refracted; int. refl., internally reflected.

Fig. 3
Fig. 3

Light absorption versus path distance profiles, confirming the equivalence of geometric optics results and the Lambert–Beer relation.

Fig. 4
Fig. 4

Schematic of the experimental illumination and imaging setup. Comparison with calculated results requires volume integration of the equatorial fluorescence distribution and image distortion that are due to the fluid–air interface.

Fig. 5
Fig. 5

Schematic description of the image-processing method that provides droplet-slicing images at 0 < n < 1 positions for a 90° observation angle.

Fig. 6
Fig. 6

Examples of droplet-slicing intensity patterns at equidistant y-axis intervals of Δn = 0.06 for an α = 1500 water droplet, 10-3 M Rhodamine 6G. E indicates the direction of incident light.

Fig. 7
Fig. 7

Schematic description of the ray-tracing algorithm that provides correct distortion of droplet-slicing images at -1 < n < 1 positions.

Fig. 8
Fig. 8

Examples of image distortion. The shape of the fluid–air interface, determined by the n position, is decisive for the applied lens effect.

Fig. 9
Fig. 9

Experimental setup used for high-magnification imaging of fluorescence intensity distributions consisting of a droplet generator, an electrostatic deflector, a laser sheet, and a CCD camera.

Fig. 10
Fig. 10

Surface plot of the fluorescence intensity in the x, z plane, for a plane wave incident upon an absorbing sphere in the +z-axis direction with m = 1.333 and α = 1500. Rhodamine 6G concentrations: (a) 2 × 10-5 M and (b) 10-3 M.

Fig. 11
Fig. 11

Fluorescence intensity profiles on the z axis of the equatorial plane for droplets of 2 × 10-5 and 10-3 Rhodamine 6G solutions.

Fig. 12
Fig. 12

Fluorescence intensity profiles on the surface of a droplet shown as a function of angle θ for 2 × 10-5 and 10-3 M Rhodamine 6G solutions.

Fig. 13
Fig. 13

Comparison of intensity patterns in absorbing droplets from experimental imaging and calculations at (a) 2 × 10-5 M low Rhodamine 6G concentration and (b) 10-3 M high dye concentration and light absorption.

Fig. 14
Fig. 14

Experimental and calculated profiles superimposed upon the z-axis centerline of 2 × 10-5 M Rhodamine 6G droplets, showing good agreement on the shadow side and discrepancies on the illuminated side that are caused by nonlinear optical effects.

Fig. 15
Fig. 15

Experimental and calculated profiles superimposed upon the z-axis centerline of 10-3 M Rhodamine 6G droplets, showing good agreement for all features of the intensity pattern.

Equations (2)

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iflu=ϕi01-exp-εbc.
iabs=i01-exp-εΔbpc.

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