Abstract

We report the development of an interferometric laser imaging for droplet sizing (ILIDS) numerical simulator. It is based on the use of generalized Huygens–Fresnel integrals associated to transfer matrices that describe the whole imaging setup. This simulator allows easy simulation of any kind of ILIDS setup. Simulations are shown to be in good agreement with experimental results. This simulator offers important perspectives in the design, realization, and calibration of ILIDS instruments, as airborne instruments, or in situ measurements in flows.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. V. Dave, “Scattering of visible light by large water spheres,” Appl. Opt. 8, 155–164 (1969).
    [CrossRef]
  2. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, 1957).
  3. G. König, K. Anders, and A. Frohn, “A new light-scattering technique to measure the diameter of periodically generated moving droplets,” J. Aerosol Sci. 17, 157–167 (1986).
    [CrossRef]
  4. R. Ragucci, A. Cavaliere, and P. Massoli, “Drop sizing by laser light scattering exploiting intensity angular oscillation in the Mie regime,” Part. Part. Syst. Charact. 7, 221–225 (1990).
    [CrossRef]
  5. A. R. Glover, S. M. Skippon, and R. D. Boyle, “Interferometric laser imaging for droplet sizing: a method for droplet-size measurement in sparse spray systems,” Appl. Opt. 34, 8409–8421 (1995).
    [CrossRef]
  6. H. C. van de Hulst and R. T. Wang, “Glare points,” Appl. Opt. 30, 4755–4763 (1991).
    [CrossRef]
  7. S. M. Skippon, A. R. Glover, and P. J. Cooney, “Studies of mixture preparation in a spark ignition engine using interferometric laser imaging for droplet sizing (ILIDS),” in SAE Transactions (Society of Automotive Engineers, 1995), Vol. 104, pp. 876–889.
  8. S. M. Skippon and Y. Tagaki, “ILIDS measurements of the evaporation of fuel droplets during the intake and compression strokes in a firing lean burn engine,” SAE Transactions (Society of Automotive Engineers, 1996), Vol. 105, pp. 1111–1126.
  9. T. Kawaguchi, Y. Akasaka, and M. Maeda, “Size measurements of droplets and bubbles by advanced interferometric laser imaging technique,” Meas. Sci. Technol. 13, 308–316 (2002).
    [CrossRef]
  10. C. Mounaïm-Rousselle and O. Pajot, “Droplet sizing by Mie scattering interferometry in a spark ignition engine,” Part. Part. Syst. Charact. 16, 160–168 (1999).
    [CrossRef]
  11. O. Pajot and C. Mounaïs-Rousselle, “Droplet sizing by interferometric method based on Mie scattering in an I.C. engine,” presented at the 9th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 13–16 July1998.
  12. C. Mounaim-Rousselle and O. Pajot, “Droplet sizing by interferometric Mie scattering in engine environment,” Proc. SPIE 3172, 700–707 (1997).
    [CrossRef]
  13. K. H. Hesselbacher, K. Anders, and A. Frohn, “Experimental investigation of Gaussian beam effects on the accuracy of a droplet sizing method,” Appl. Opt. 30, 4930–4935 (1991).
    [CrossRef]
  14. W. J. Glantschnig and S. H. Chen, “Light scattering from water droplets in the geometrical optics approximation,” Appl. Opt. 20, 2499–2509 (1981).
    [CrossRef]
  15. H. C. van de Hulst, Light Scattering by Small Particles(Dover, 1981).
  16. A. Quérel, P. Lemaitre, M. Brunel, E. Porcheron, and G. Gréhan, “Real-time global interferometric laser imaging for the droplet sizing (ILIDS) algorithm for airborne research,” Meas. Sci. Technol. 21, 015306 (2010).
    [CrossRef]
  17. G. Mie, “Beitrage zer Optik truber Meiden speziell kolloidaler Metallosungen,” Ann. Phys. 25, 377–445 (1908).
    [CrossRef]
  18. H. Shen, M. Brunel, S. Coëtmellec, G. Gréhan, D. Lebrun, X. Wu, and K. Cen, “Glare point reconstruction in digital holographic microscopy for droplet characterization,” in Progress In Electromagnetics Research Symposium Proceedings(Electromagnetics Academy, 2011), pp. 171–174.
  19. X. Wu, S. Meunier-Guttin-Cluzel, Y. Wu, S. Saengkaew, D. Lebrun, M. Brunel, L. Chen, S. Coëtmellec, K. Cen, and G. Gréhan, “Holography and micro-holography of particle fields: a numerical standard,” Opt. Commun. 285, 3013–3020(2012).
    [CrossRef]
  20. C. Palma and V. Bagini, “Extension of the Fresnel transform to ABCD systems,” J. Opt. Soc. Am. A 14, 1774–1779 (1997).
    [CrossRef]
  21. A. J. Lambert and D. Fraser, “Linear systems approach to simulation of optical diffraction,” Appl. Opt. 37, 7933–7939 (1998).
    [CrossRef]
  22. H. T. Yura and S. G. Hanson, “Optical beam wave propagation through complex optical systems,” J. Opt. Soc. Am. A 4, 1931–1948 (1987).
    [CrossRef]
  23. N. Verrier, S. Coëtmellec, M. Brunel, and D. Lebrun, “Digital in-line holography in thick optical systems: application to visualization in pipes,” Appl. Opt. 47, 4147–4157 (2008).
    [CrossRef]
  24. M. Brunel, H. Shen, S. Coëtmellec, and D. Lebrun, “Extended ABCD matrix formalism for the description of femtosecond diffraction patterns; application to femtosecond digital in-line holography with anamorphic optical systems,” Appl. Opt. 51, 1137–1148 (2012).
    [CrossRef]
  25. P. Debye, “Das elektromagnetische Feld um einen Zylinder und die Theorie des Regenbonens,” Phys. Z. 9, 775–778(1908).
  26. H. M. Nussenzveig, “High-frequency scattering by a transparent sphere I: direct reflection and transmission,” J. Math. Phys. 10, 82–124 (1969).
    [CrossRef]
  27. J. J. Wen and M. Breazeale, “Gaussian beam functions as a base function set for acoustical field calculations,” in Proceedings of the IEEE Ultrasonics Symposium (IEEE, 1987), pp. 1137–1140.
  28. J. J. Wen and M. Breazeale, “A diffraction beam expressed as the superposition of Gaussian beams,” J. Acoust. Soc. Am. 83, 1752–1756 (1988).
    [CrossRef]
  29. T. Girasole, K. F. Ren, D. Lebrun, G. Gouesbet, and G. Grehan, “Particle imaging sizing: GLMT simulations,” J. Vis. 3, 195–202 (2000).
    [CrossRef]
  30. H. E. Albrecht, M. Borys, N. Damaschke, and C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques(Springer-Verlag, 2003).
  31. C. F. Hess and D. L’Esperance, “Droplet imaging velocimeter and sizer: a two-dimensional technique to measure droplet size,” Exp. Fluids 47, 171–182 (2009).
    [CrossRef]
  32. E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. 38, 6994–7001 (1999).
    [CrossRef]
  33. M. Brunel, S. Coëtmellec, D. Lebrun, and K. Aït Ameur, “Digital phase contrast with the fractional Fourier transform,” Appl. Opt. 48, 579–583 (2009).
    [CrossRef]
  34. S. Dehaeck and J. van Beeck, “Multifrequency interferometric particle imaging for gas bubble sizing,” Exp. Fluids 45, 823–831 (2008).
    [CrossRef]

2012

X. Wu, S. Meunier-Guttin-Cluzel, Y. Wu, S. Saengkaew, D. Lebrun, M. Brunel, L. Chen, S. Coëtmellec, K. Cen, and G. Gréhan, “Holography and micro-holography of particle fields: a numerical standard,” Opt. Commun. 285, 3013–3020(2012).
[CrossRef]

M. Brunel, H. Shen, S. Coëtmellec, and D. Lebrun, “Extended ABCD matrix formalism for the description of femtosecond diffraction patterns; application to femtosecond digital in-line holography with anamorphic optical systems,” Appl. Opt. 51, 1137–1148 (2012).
[CrossRef]

2010

A. Quérel, P. Lemaitre, M. Brunel, E. Porcheron, and G. Gréhan, “Real-time global interferometric laser imaging for the droplet sizing (ILIDS) algorithm for airborne research,” Meas. Sci. Technol. 21, 015306 (2010).
[CrossRef]

2009

C. F. Hess and D. L’Esperance, “Droplet imaging velocimeter and sizer: a two-dimensional technique to measure droplet size,” Exp. Fluids 47, 171–182 (2009).
[CrossRef]

M. Brunel, S. Coëtmellec, D. Lebrun, and K. Aït Ameur, “Digital phase contrast with the fractional Fourier transform,” Appl. Opt. 48, 579–583 (2009).
[CrossRef]

2008

N. Verrier, S. Coëtmellec, M. Brunel, and D. Lebrun, “Digital in-line holography in thick optical systems: application to visualization in pipes,” Appl. Opt. 47, 4147–4157 (2008).
[CrossRef]

S. Dehaeck and J. van Beeck, “Multifrequency interferometric particle imaging for gas bubble sizing,” Exp. Fluids 45, 823–831 (2008).
[CrossRef]

2002

T. Kawaguchi, Y. Akasaka, and M. Maeda, “Size measurements of droplets and bubbles by advanced interferometric laser imaging technique,” Meas. Sci. Technol. 13, 308–316 (2002).
[CrossRef]

2000

T. Girasole, K. F. Ren, D. Lebrun, G. Gouesbet, and G. Grehan, “Particle imaging sizing: GLMT simulations,” J. Vis. 3, 195–202 (2000).
[CrossRef]

1999

C. Mounaïm-Rousselle and O. Pajot, “Droplet sizing by Mie scattering interferometry in a spark ignition engine,” Part. Part. Syst. Charact. 16, 160–168 (1999).
[CrossRef]

E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. 38, 6994–7001 (1999).
[CrossRef]

1998

1997

C. Mounaim-Rousselle and O. Pajot, “Droplet sizing by interferometric Mie scattering in engine environment,” Proc. SPIE 3172, 700–707 (1997).
[CrossRef]

C. Palma and V. Bagini, “Extension of the Fresnel transform to ABCD systems,” J. Opt. Soc. Am. A 14, 1774–1779 (1997).
[CrossRef]

1995

1991

1990

R. Ragucci, A. Cavaliere, and P. Massoli, “Drop sizing by laser light scattering exploiting intensity angular oscillation in the Mie regime,” Part. Part. Syst. Charact. 7, 221–225 (1990).
[CrossRef]

1988

J. J. Wen and M. Breazeale, “A diffraction beam expressed as the superposition of Gaussian beams,” J. Acoust. Soc. Am. 83, 1752–1756 (1988).
[CrossRef]

1987

1986

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

1981

1969

H. M. Nussenzveig, “High-frequency scattering by a transparent sphere I: direct reflection and transmission,” J. Math. Phys. 10, 82–124 (1969).
[CrossRef]

J. V. Dave, “Scattering of visible light by large water spheres,” Appl. Opt. 8, 155–164 (1969).
[CrossRef]

1908

G. Mie, “Beitrage zer Optik truber Meiden speziell kolloidaler Metallosungen,” Ann. Phys. 25, 377–445 (1908).
[CrossRef]

P. Debye, “Das elektromagnetische Feld um einen Zylinder und die Theorie des Regenbonens,” Phys. Z. 9, 775–778(1908).

Aït Ameur, K.

Akasaka, Y.

T. Kawaguchi, Y. Akasaka, and M. Maeda, “Size measurements of droplets and bubbles by advanced interferometric laser imaging technique,” Meas. Sci. Technol. 13, 308–316 (2002).
[CrossRef]

Albrecht, H. E.

H. E. Albrecht, M. Borys, N. Damaschke, and C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques(Springer-Verlag, 2003).

Anders, K.

K. H. Hesselbacher, K. Anders, and A. Frohn, “Experimental investigation of Gaussian beam effects on the accuracy of a droplet sizing method,” Appl. Opt. 30, 4930–4935 (1991).
[CrossRef]

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

Bagini, V.

Borys, M.

H. E. Albrecht, M. Borys, N. Damaschke, and C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques(Springer-Verlag, 2003).

Boyle, R. D.

Breazeale, M.

J. J. Wen and M. Breazeale, “A diffraction beam expressed as the superposition of Gaussian beams,” J. Acoust. Soc. Am. 83, 1752–1756 (1988).
[CrossRef]

J. J. Wen and M. Breazeale, “Gaussian beam functions as a base function set for acoustical field calculations,” in Proceedings of the IEEE Ultrasonics Symposium (IEEE, 1987), pp. 1137–1140.

Brunel, M.

M. Brunel, H. Shen, S. Coëtmellec, and D. Lebrun, “Extended ABCD matrix formalism for the description of femtosecond diffraction patterns; application to femtosecond digital in-line holography with anamorphic optical systems,” Appl. Opt. 51, 1137–1148 (2012).
[CrossRef]

X. Wu, S. Meunier-Guttin-Cluzel, Y. Wu, S. Saengkaew, D. Lebrun, M. Brunel, L. Chen, S. Coëtmellec, K. Cen, and G. Gréhan, “Holography and micro-holography of particle fields: a numerical standard,” Opt. Commun. 285, 3013–3020(2012).
[CrossRef]

A. Quérel, P. Lemaitre, M. Brunel, E. Porcheron, and G. Gréhan, “Real-time global interferometric laser imaging for the droplet sizing (ILIDS) algorithm for airborne research,” Meas. Sci. Technol. 21, 015306 (2010).
[CrossRef]

M. Brunel, S. Coëtmellec, D. Lebrun, and K. Aït Ameur, “Digital phase contrast with the fractional Fourier transform,” Appl. Opt. 48, 579–583 (2009).
[CrossRef]

N. Verrier, S. Coëtmellec, M. Brunel, and D. Lebrun, “Digital in-line holography in thick optical systems: application to visualization in pipes,” Appl. Opt. 47, 4147–4157 (2008).
[CrossRef]

H. Shen, M. Brunel, S. Coëtmellec, G. Gréhan, D. Lebrun, X. Wu, and K. Cen, “Glare point reconstruction in digital holographic microscopy for droplet characterization,” in Progress In Electromagnetics Research Symposium Proceedings(Electromagnetics Academy, 2011), pp. 171–174.

Cavaliere, A.

R. Ragucci, A. Cavaliere, and P. Massoli, “Drop sizing by laser light scattering exploiting intensity angular oscillation in the Mie regime,” Part. Part. Syst. Charact. 7, 221–225 (1990).
[CrossRef]

Cen, K.

X. Wu, S. Meunier-Guttin-Cluzel, Y. Wu, S. Saengkaew, D. Lebrun, M. Brunel, L. Chen, S. Coëtmellec, K. Cen, and G. Gréhan, “Holography and micro-holography of particle fields: a numerical standard,” Opt. Commun. 285, 3013–3020(2012).
[CrossRef]

H. Shen, M. Brunel, S. Coëtmellec, G. Gréhan, D. Lebrun, X. Wu, and K. Cen, “Glare point reconstruction in digital holographic microscopy for droplet characterization,” in Progress In Electromagnetics Research Symposium Proceedings(Electromagnetics Academy, 2011), pp. 171–174.

Chen, L.

X. Wu, S. Meunier-Guttin-Cluzel, Y. Wu, S. Saengkaew, D. Lebrun, M. Brunel, L. Chen, S. Coëtmellec, K. Cen, and G. Gréhan, “Holography and micro-holography of particle fields: a numerical standard,” Opt. Commun. 285, 3013–3020(2012).
[CrossRef]

Chen, S. H.

Coëtmellec, S.

M. Brunel, H. Shen, S. Coëtmellec, and D. Lebrun, “Extended ABCD matrix formalism for the description of femtosecond diffraction patterns; application to femtosecond digital in-line holography with anamorphic optical systems,” Appl. Opt. 51, 1137–1148 (2012).
[CrossRef]

X. Wu, S. Meunier-Guttin-Cluzel, Y. Wu, S. Saengkaew, D. Lebrun, M. Brunel, L. Chen, S. Coëtmellec, K. Cen, and G. Gréhan, “Holography and micro-holography of particle fields: a numerical standard,” Opt. Commun. 285, 3013–3020(2012).
[CrossRef]

M. Brunel, S. Coëtmellec, D. Lebrun, and K. Aït Ameur, “Digital phase contrast with the fractional Fourier transform,” Appl. Opt. 48, 579–583 (2009).
[CrossRef]

N. Verrier, S. Coëtmellec, M. Brunel, and D. Lebrun, “Digital in-line holography in thick optical systems: application to visualization in pipes,” Appl. Opt. 47, 4147–4157 (2008).
[CrossRef]

H. Shen, M. Brunel, S. Coëtmellec, G. Gréhan, D. Lebrun, X. Wu, and K. Cen, “Glare point reconstruction in digital holographic microscopy for droplet characterization,” in Progress In Electromagnetics Research Symposium Proceedings(Electromagnetics Academy, 2011), pp. 171–174.

Cooney, P. J.

S. M. Skippon, A. R. Glover, and P. J. Cooney, “Studies of mixture preparation in a spark ignition engine using interferometric laser imaging for droplet sizing (ILIDS),” in SAE Transactions (Society of Automotive Engineers, 1995), Vol. 104, pp. 876–889.

Cuche, E.

Damaschke, N.

H. E. Albrecht, M. Borys, N. Damaschke, and C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques(Springer-Verlag, 2003).

Dave, J. V.

Debye, P.

P. Debye, “Das elektromagnetische Feld um einen Zylinder und die Theorie des Regenbonens,” Phys. Z. 9, 775–778(1908).

Dehaeck, S.

S. Dehaeck and J. van Beeck, “Multifrequency interferometric particle imaging for gas bubble sizing,” Exp. Fluids 45, 823–831 (2008).
[CrossRef]

Depeursinge, C.

Fraser, D.

Frohn, A.

K. H. Hesselbacher, K. Anders, and A. Frohn, “Experimental investigation of Gaussian beam effects on the accuracy of a droplet sizing method,” Appl. Opt. 30, 4930–4935 (1991).
[CrossRef]

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

Girasole, T.

T. Girasole, K. F. Ren, D. Lebrun, G. Gouesbet, and G. Grehan, “Particle imaging sizing: GLMT simulations,” J. Vis. 3, 195–202 (2000).
[CrossRef]

Glantschnig, W. J.

Glover, A. R.

A. R. Glover, S. M. Skippon, and R. D. Boyle, “Interferometric laser imaging for droplet sizing: a method for droplet-size measurement in sparse spray systems,” Appl. Opt. 34, 8409–8421 (1995).
[CrossRef]

S. M. Skippon, A. R. Glover, and P. J. Cooney, “Studies of mixture preparation in a spark ignition engine using interferometric laser imaging for droplet sizing (ILIDS),” in SAE Transactions (Society of Automotive Engineers, 1995), Vol. 104, pp. 876–889.

Gouesbet, G.

T. Girasole, K. F. Ren, D. Lebrun, G. Gouesbet, and G. Grehan, “Particle imaging sizing: GLMT simulations,” J. Vis. 3, 195–202 (2000).
[CrossRef]

Grehan, G.

T. Girasole, K. F. Ren, D. Lebrun, G. Gouesbet, and G. Grehan, “Particle imaging sizing: GLMT simulations,” J. Vis. 3, 195–202 (2000).
[CrossRef]

Gréhan, G.

X. Wu, S. Meunier-Guttin-Cluzel, Y. Wu, S. Saengkaew, D. Lebrun, M. Brunel, L. Chen, S. Coëtmellec, K. Cen, and G. Gréhan, “Holography and micro-holography of particle fields: a numerical standard,” Opt. Commun. 285, 3013–3020(2012).
[CrossRef]

A. Quérel, P. Lemaitre, M. Brunel, E. Porcheron, and G. Gréhan, “Real-time global interferometric laser imaging for the droplet sizing (ILIDS) algorithm for airborne research,” Meas. Sci. Technol. 21, 015306 (2010).
[CrossRef]

H. Shen, M. Brunel, S. Coëtmellec, G. Gréhan, D. Lebrun, X. Wu, and K. Cen, “Glare point reconstruction in digital holographic microscopy for droplet characterization,” in Progress In Electromagnetics Research Symposium Proceedings(Electromagnetics Academy, 2011), pp. 171–174.

Hanson, S. G.

Hess, C. F.

C. F. Hess and D. L’Esperance, “Droplet imaging velocimeter and sizer: a two-dimensional technique to measure droplet size,” Exp. Fluids 47, 171–182 (2009).
[CrossRef]

Hesselbacher, K. H.

Kawaguchi, T.

T. Kawaguchi, Y. Akasaka, and M. Maeda, “Size measurements of droplets and bubbles by advanced interferometric laser imaging technique,” Meas. Sci. Technol. 13, 308–316 (2002).
[CrossRef]

König, G.

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

L’Esperance, D.

C. F. Hess and D. L’Esperance, “Droplet imaging velocimeter and sizer: a two-dimensional technique to measure droplet size,” Exp. Fluids 47, 171–182 (2009).
[CrossRef]

Lambert, A. J.

Lebrun, D.

X. Wu, S. Meunier-Guttin-Cluzel, Y. Wu, S. Saengkaew, D. Lebrun, M. Brunel, L. Chen, S. Coëtmellec, K. Cen, and G. Gréhan, “Holography and micro-holography of particle fields: a numerical standard,” Opt. Commun. 285, 3013–3020(2012).
[CrossRef]

M. Brunel, H. Shen, S. Coëtmellec, and D. Lebrun, “Extended ABCD matrix formalism for the description of femtosecond diffraction patterns; application to femtosecond digital in-line holography with anamorphic optical systems,” Appl. Opt. 51, 1137–1148 (2012).
[CrossRef]

M. Brunel, S. Coëtmellec, D. Lebrun, and K. Aït Ameur, “Digital phase contrast with the fractional Fourier transform,” Appl. Opt. 48, 579–583 (2009).
[CrossRef]

N. Verrier, S. Coëtmellec, M. Brunel, and D. Lebrun, “Digital in-line holography in thick optical systems: application to visualization in pipes,” Appl. Opt. 47, 4147–4157 (2008).
[CrossRef]

T. Girasole, K. F. Ren, D. Lebrun, G. Gouesbet, and G. Grehan, “Particle imaging sizing: GLMT simulations,” J. Vis. 3, 195–202 (2000).
[CrossRef]

H. Shen, M. Brunel, S. Coëtmellec, G. Gréhan, D. Lebrun, X. Wu, and K. Cen, “Glare point reconstruction in digital holographic microscopy for droplet characterization,” in Progress In Electromagnetics Research Symposium Proceedings(Electromagnetics Academy, 2011), pp. 171–174.

Lemaitre, P.

A. Quérel, P. Lemaitre, M. Brunel, E. Porcheron, and G. Gréhan, “Real-time global interferometric laser imaging for the droplet sizing (ILIDS) algorithm for airborne research,” Meas. Sci. Technol. 21, 015306 (2010).
[CrossRef]

Maeda, M.

T. Kawaguchi, Y. Akasaka, and M. Maeda, “Size measurements of droplets and bubbles by advanced interferometric laser imaging technique,” Meas. Sci. Technol. 13, 308–316 (2002).
[CrossRef]

Marquet, P.

Massoli, P.

R. Ragucci, A. Cavaliere, and P. Massoli, “Drop sizing by laser light scattering exploiting intensity angular oscillation in the Mie regime,” Part. Part. Syst. Charact. 7, 221–225 (1990).
[CrossRef]

Meunier-Guttin-Cluzel, S.

X. Wu, S. Meunier-Guttin-Cluzel, Y. Wu, S. Saengkaew, D. Lebrun, M. Brunel, L. Chen, S. Coëtmellec, K. Cen, and G. Gréhan, “Holography and micro-holography of particle fields: a numerical standard,” Opt. Commun. 285, 3013–3020(2012).
[CrossRef]

Mie, G.

G. Mie, “Beitrage zer Optik truber Meiden speziell kolloidaler Metallosungen,” Ann. Phys. 25, 377–445 (1908).
[CrossRef]

Mounaim-Rousselle, C.

C. Mounaim-Rousselle and O. Pajot, “Droplet sizing by interferometric Mie scattering in engine environment,” Proc. SPIE 3172, 700–707 (1997).
[CrossRef]

Mounaïm-Rousselle, C.

C. Mounaïm-Rousselle and O. Pajot, “Droplet sizing by Mie scattering interferometry in a spark ignition engine,” Part. Part. Syst. Charact. 16, 160–168 (1999).
[CrossRef]

Mounaïs-Rousselle, C.

O. Pajot and C. Mounaïs-Rousselle, “Droplet sizing by interferometric method based on Mie scattering in an I.C. engine,” presented at the 9th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 13–16 July1998.

Nussenzveig, H. M.

H. M. Nussenzveig, “High-frequency scattering by a transparent sphere I: direct reflection and transmission,” J. Math. Phys. 10, 82–124 (1969).
[CrossRef]

Pajot, O.

C. Mounaïm-Rousselle and O. Pajot, “Droplet sizing by Mie scattering interferometry in a spark ignition engine,” Part. Part. Syst. Charact. 16, 160–168 (1999).
[CrossRef]

C. Mounaim-Rousselle and O. Pajot, “Droplet sizing by interferometric Mie scattering in engine environment,” Proc. SPIE 3172, 700–707 (1997).
[CrossRef]

O. Pajot and C. Mounaïs-Rousselle, “Droplet sizing by interferometric method based on Mie scattering in an I.C. engine,” presented at the 9th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 13–16 July1998.

Palma, C.

Porcheron, E.

A. Quérel, P. Lemaitre, M. Brunel, E. Porcheron, and G. Gréhan, “Real-time global interferometric laser imaging for the droplet sizing (ILIDS) algorithm for airborne research,” Meas. Sci. Technol. 21, 015306 (2010).
[CrossRef]

Quérel, A.

A. Quérel, P. Lemaitre, M. Brunel, E. Porcheron, and G. Gréhan, “Real-time global interferometric laser imaging for the droplet sizing (ILIDS) algorithm for airborne research,” Meas. Sci. Technol. 21, 015306 (2010).
[CrossRef]

Ragucci, R.

R. Ragucci, A. Cavaliere, and P. Massoli, “Drop sizing by laser light scattering exploiting intensity angular oscillation in the Mie regime,” Part. Part. Syst. Charact. 7, 221–225 (1990).
[CrossRef]

Ren, K. F.

T. Girasole, K. F. Ren, D. Lebrun, G. Gouesbet, and G. Grehan, “Particle imaging sizing: GLMT simulations,” J. Vis. 3, 195–202 (2000).
[CrossRef]

Saengkaew, S.

X. Wu, S. Meunier-Guttin-Cluzel, Y. Wu, S. Saengkaew, D. Lebrun, M. Brunel, L. Chen, S. Coëtmellec, K. Cen, and G. Gréhan, “Holography and micro-holography of particle fields: a numerical standard,” Opt. Commun. 285, 3013–3020(2012).
[CrossRef]

Shen, H.

M. Brunel, H. Shen, S. Coëtmellec, and D. Lebrun, “Extended ABCD matrix formalism for the description of femtosecond diffraction patterns; application to femtosecond digital in-line holography with anamorphic optical systems,” Appl. Opt. 51, 1137–1148 (2012).
[CrossRef]

H. Shen, M. Brunel, S. Coëtmellec, G. Gréhan, D. Lebrun, X. Wu, and K. Cen, “Glare point reconstruction in digital holographic microscopy for droplet characterization,” in Progress In Electromagnetics Research Symposium Proceedings(Electromagnetics Academy, 2011), pp. 171–174.

Skippon, S. M.

A. R. Glover, S. M. Skippon, and R. D. Boyle, “Interferometric laser imaging for droplet sizing: a method for droplet-size measurement in sparse spray systems,” Appl. Opt. 34, 8409–8421 (1995).
[CrossRef]

S. M. Skippon, A. R. Glover, and P. J. Cooney, “Studies of mixture preparation in a spark ignition engine using interferometric laser imaging for droplet sizing (ILIDS),” in SAE Transactions (Society of Automotive Engineers, 1995), Vol. 104, pp. 876–889.

S. M. Skippon and Y. Tagaki, “ILIDS measurements of the evaporation of fuel droplets during the intake and compression strokes in a firing lean burn engine,” SAE Transactions (Society of Automotive Engineers, 1996), Vol. 105, pp. 1111–1126.

Tagaki, Y.

S. M. Skippon and Y. Tagaki, “ILIDS measurements of the evaporation of fuel droplets during the intake and compression strokes in a firing lean burn engine,” SAE Transactions (Society of Automotive Engineers, 1996), Vol. 105, pp. 1111–1126.

Tropea, C.

H. E. Albrecht, M. Borys, N. Damaschke, and C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques(Springer-Verlag, 2003).

van Beeck, J.

S. Dehaeck and J. van Beeck, “Multifrequency interferometric particle imaging for gas bubble sizing,” Exp. Fluids 45, 823–831 (2008).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst and R. T. Wang, “Glare points,” Appl. Opt. 30, 4755–4763 (1991).
[CrossRef]

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

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

Verrier, N.

Wang, R. T.

Wen, J. J.

J. J. Wen and M. Breazeale, “A diffraction beam expressed as the superposition of Gaussian beams,” J. Acoust. Soc. Am. 83, 1752–1756 (1988).
[CrossRef]

J. J. Wen and M. Breazeale, “Gaussian beam functions as a base function set for acoustical field calculations,” in Proceedings of the IEEE Ultrasonics Symposium (IEEE, 1987), pp. 1137–1140.

Wu, X.

X. Wu, S. Meunier-Guttin-Cluzel, Y. Wu, S. Saengkaew, D. Lebrun, M. Brunel, L. Chen, S. Coëtmellec, K. Cen, and G. Gréhan, “Holography and micro-holography of particle fields: a numerical standard,” Opt. Commun. 285, 3013–3020(2012).
[CrossRef]

H. Shen, M. Brunel, S. Coëtmellec, G. Gréhan, D. Lebrun, X. Wu, and K. Cen, “Glare point reconstruction in digital holographic microscopy for droplet characterization,” in Progress In Electromagnetics Research Symposium Proceedings(Electromagnetics Academy, 2011), pp. 171–174.

Wu, Y.

X. Wu, S. Meunier-Guttin-Cluzel, Y. Wu, S. Saengkaew, D. Lebrun, M. Brunel, L. Chen, S. Coëtmellec, K. Cen, and G. Gréhan, “Holography and micro-holography of particle fields: a numerical standard,” Opt. Commun. 285, 3013–3020(2012).
[CrossRef]

Yura, H. T.

Ann. Phys.

G. Mie, “Beitrage zer Optik truber Meiden speziell kolloidaler Metallosungen,” Ann. Phys. 25, 377–445 (1908).
[CrossRef]

Appl. Opt.

J. V. Dave, “Scattering of visible light by large water spheres,” Appl. Opt. 8, 155–164 (1969).
[CrossRef]

W. J. Glantschnig and S. H. Chen, “Light scattering from water droplets in the geometrical optics approximation,” Appl. Opt. 20, 2499–2509 (1981).
[CrossRef]

H. C. van de Hulst and R. T. Wang, “Glare points,” Appl. Opt. 30, 4755–4763 (1991).
[CrossRef]

K. H. Hesselbacher, K. Anders, and A. Frohn, “Experimental investigation of Gaussian beam effects on the accuracy of a droplet sizing method,” Appl. Opt. 30, 4930–4935 (1991).
[CrossRef]

A. J. Lambert and D. Fraser, “Linear systems approach to simulation of optical diffraction,” Appl. Opt. 37, 7933–7939 (1998).
[CrossRef]

A. R. Glover, S. M. Skippon, and R. D. Boyle, “Interferometric laser imaging for droplet sizing: a method for droplet-size measurement in sparse spray systems,” Appl. Opt. 34, 8409–8421 (1995).
[CrossRef]

E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. 38, 6994–7001 (1999).
[CrossRef]

N. Verrier, S. Coëtmellec, M. Brunel, and D. Lebrun, “Digital in-line holography in thick optical systems: application to visualization in pipes,” Appl. Opt. 47, 4147–4157 (2008).
[CrossRef]

M. Brunel, S. Coëtmellec, D. Lebrun, and K. Aït Ameur, “Digital phase contrast with the fractional Fourier transform,” Appl. Opt. 48, 579–583 (2009).
[CrossRef]

M. Brunel, H. Shen, S. Coëtmellec, and D. Lebrun, “Extended ABCD matrix formalism for the description of femtosecond diffraction patterns; application to femtosecond digital in-line holography with anamorphic optical systems,” Appl. Opt. 51, 1137–1148 (2012).
[CrossRef]

Exp. Fluids

C. F. Hess and D. L’Esperance, “Droplet imaging velocimeter and sizer: a two-dimensional technique to measure droplet size,” Exp. Fluids 47, 171–182 (2009).
[CrossRef]

S. Dehaeck and J. van Beeck, “Multifrequency interferometric particle imaging for gas bubble sizing,” Exp. Fluids 45, 823–831 (2008).
[CrossRef]

J. Acoust. Soc. Am.

J. J. Wen and M. Breazeale, “A diffraction beam expressed as the superposition of Gaussian beams,” J. Acoust. Soc. Am. 83, 1752–1756 (1988).
[CrossRef]

J. Aerosol Sci.

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

J. Math. Phys.

H. M. Nussenzveig, “High-frequency scattering by a transparent sphere I: direct reflection and transmission,” J. Math. Phys. 10, 82–124 (1969).
[CrossRef]

J. Opt. Soc. Am. A

J. Vis.

T. Girasole, K. F. Ren, D. Lebrun, G. Gouesbet, and G. Grehan, “Particle imaging sizing: GLMT simulations,” J. Vis. 3, 195–202 (2000).
[CrossRef]

Meas. Sci. Technol.

A. Quérel, P. Lemaitre, M. Brunel, E. Porcheron, and G. Gréhan, “Real-time global interferometric laser imaging for the droplet sizing (ILIDS) algorithm for airborne research,” Meas. Sci. Technol. 21, 015306 (2010).
[CrossRef]

T. Kawaguchi, Y. Akasaka, and M. Maeda, “Size measurements of droplets and bubbles by advanced interferometric laser imaging technique,” Meas. Sci. Technol. 13, 308–316 (2002).
[CrossRef]

Opt. Commun.

X. Wu, S. Meunier-Guttin-Cluzel, Y. Wu, S. Saengkaew, D. Lebrun, M. Brunel, L. Chen, S. Coëtmellec, K. Cen, and G. Gréhan, “Holography and micro-holography of particle fields: a numerical standard,” Opt. Commun. 285, 3013–3020(2012).
[CrossRef]

Part. Part. Syst. Charact.

C. Mounaïm-Rousselle and O. Pajot, “Droplet sizing by Mie scattering interferometry in a spark ignition engine,” Part. Part. Syst. Charact. 16, 160–168 (1999).
[CrossRef]

R. Ragucci, A. Cavaliere, and P. Massoli, “Drop sizing by laser light scattering exploiting intensity angular oscillation in the Mie regime,” Part. Part. Syst. Charact. 7, 221–225 (1990).
[CrossRef]

Phys. Z.

P. Debye, “Das elektromagnetische Feld um einen Zylinder und die Theorie des Regenbonens,” Phys. Z. 9, 775–778(1908).

Proc. SPIE

C. Mounaim-Rousselle and O. Pajot, “Droplet sizing by interferometric Mie scattering in engine environment,” Proc. SPIE 3172, 700–707 (1997).
[CrossRef]

Other

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

O. Pajot and C. Mounaïs-Rousselle, “Droplet sizing by interferometric method based on Mie scattering in an I.C. engine,” presented at the 9th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 13–16 July1998.

S. M. Skippon, A. R. Glover, and P. J. Cooney, “Studies of mixture preparation in a spark ignition engine using interferometric laser imaging for droplet sizing (ILIDS),” in SAE Transactions (Society of Automotive Engineers, 1995), Vol. 104, pp. 876–889.

S. M. Skippon and Y. Tagaki, “ILIDS measurements of the evaporation of fuel droplets during the intake and compression strokes in a firing lean burn engine,” SAE Transactions (Society of Automotive Engineers, 1996), Vol. 105, pp. 1111–1126.

J. J. Wen and M. Breazeale, “Gaussian beam functions as a base function set for acoustical field calculations,” in Proceedings of the IEEE Ultrasonics Symposium (IEEE, 1987), pp. 1137–1140.

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

H. Shen, M. Brunel, S. Coëtmellec, G. Gréhan, D. Lebrun, X. Wu, and K. Cen, “Glare point reconstruction in digital holographic microscopy for droplet characterization,” in Progress In Electromagnetics Research Symposium Proceedings(Electromagnetics Academy, 2011), pp. 171–174.

H. E. Albrecht, M. Borys, N. Damaschke, and C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques(Springer-Verlag, 2003).

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 (12)

Fig. 1.
Fig. 1.

Typical configuration of ILIDS (top view).

Fig. 2.
Fig. 2.

Geometrical positions of the two glare points for a water droplet.

Fig. 3.
Fig. 3.

Comparison between Lorenz–Mie and geometrical optics of the inter-glare-points distance.

Fig. 4.
Fig. 4.

(a) Experimental and (b) simulated ILIDS interferograms using Eqs. (15)–(21) (4.4 μm per pixel).

Fig. 5.
Fig. 5.

Normalized profiles of experimental and theoretical (dotted curve) ILIDS interferograms using Eqs. (15)–(21) (4.4 μm per pixel).

Fig. 6.
Fig. 6.

Interference fringes for different out-of-focus positions using Eqs. (15)–(21).

Fig. 7.
Fig. 7.

Number of fringes predicted versus droplet diameter using our simulator (squares) and Lorenz-Mie codes of reference [29] (crosses).

Fig. 8.
Fig. 8.

Simulated ILIDS interferograms using (a) the exact model of Eqs. (15)–(21) or (b) the approached expression of Eq. (25) (4.4 μm per pixel).

Fig. 9.
Fig. 9.

Simulated ILIDS interferogram with six droplets randomly located using Eqs. (15)–(21). All droplets have the same diameter: 40 μm.

Fig. 10.
Fig. 10.

Geometrical position of three glare points for a water droplet.

Fig. 11.
Fig. 11.

Configuration of ILIDS with droplets in a pipe.

Fig. 12.
Fig. 12.

(a) Experimental out-of-focus image, (b) simulated image using the exact description of Eqs. (36)–(43), and (c) an approached model derived like Eq. (25) (in pixels, 4.4 μm per pixel).

Equations (47)

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

d=2λ1ΔΘ(cos(Θ/2)+msin(Θ/2)m2+12mcos(Θ/2))1,
a=d2sin(t),
b=d2cos(Θ/2).
sin(t)=msin(tΘ/2),
t=arctan(msin(Θ/2)mcos(Θ/2)1).
ab=d2(cos(Θ/2)+msin(Θ/2)m2+12mcos(Θ/2)).
φ=2π/λ*(d/2)*[2*sin(Θ/2)2*cos(t)+2*m*cos(tΘ/2)]π,
G1(ξ,η,z1+z2)=exp(i2πλE1)iλBtotR2G0(x,y,0)exp[iπλBtot(Atotx22ξx+Dtotξ2)]×exp[iπλBtot(Atoty22ηy+Dtotη2)]dxdy,
Mtot=(AtotBtotCtotDtot)=Mz2×MLens×Mz1.
G1(ξ,η,z1+z2)=ei2πλ(z1+z2)iλBtote[iπDtotη2λBtot](a1eiθ1+a2eiθ2+iφ),
θ1=πλBtot(Atota22aξ+Dtotξ2),
θ2=πλBtot(Atotb22bξ+Dtotξ2).
G2(x,y,z1+z2)=ei2πλz2iλB2R2T(ξ,η)G1(ξ,η,z1)exp[iπλB2(A2ξ22xξ+D2x2)]×exp[iπλB2(A2η22yη+D2y2)]dξdη,
T(ξ,η)=k=1NPkexp[QkR02(ξ2+η2)],
G2(x,y,z1+z2)=ei2πλ(z1+z2)eiπD2(x2+y2)λB2(iλ)2B1B2k=1NPkπγ(k)[a1eβ1(k)+a2eiφeβ2(k)],
β1(k)=iπA1a2λB1ϕ1x2+ϕ1y24γ(k),
β2(k)=iπA1b2λB1ϕ2x2+ϕ2y24γ(k),
γ(k)=QkR02iπλ(D1B1+A2B2),
ϕ1x=2πλ(aB1+xB2),
ϕ2x=2πλ(bB1+xB2),
ϕ1y=ϕ2y=2πyλB2,
Mtot=(1z2/fz1+z2z1z2/f1/f1z1/f).
z1+z2,focusz1z2,focus/f=0,
ϕd=D0|z2,focusz2z2,focus|.
G2(ξ,η,z1+z2)=e(i2πλE1)iλBtote[iπDtotη2λBtot](a1e[iπλBtot(Atota22aξ+Dtotξ2)]·circϕd(ξgxa,η)+a2e[iπλBtot(Atotb22bξ+Dtotξ2)]circϕd(ξgxb,η)),
1ΔΘ=Nα=S*F2arctan(G2NA(G+1)).
I1(ξ,η,z1+z2)=1λ2Btot2(a12+a22+2a1a2cos(θ1θ2)).
F=|abλBtot|.
F=|d2λBtot(cos(Θ/2)+msin(Θ/2)m2+12mcos(Θ/2))|,
d=2λ|Btot|F(cos(Θ/2)+msin(Θ/2)m2+12mcos(Θ/2))1.
1ΔΘ=|Btot|F.
c=d2sin(i1),
F=|bcλBtot|.
G1(ξ,η,z1+z2)=exp(i2πλE1)iλB1xB1yR2G0(x,y,0)exp[iπλB1x(A1xx22ξx+D1xξ2)]×exp[iπλB1y(A1yy22ηy+D1yη2)]dxdy,
M1x,y=(A1x,yB1x,yC1x,yD1x,y)=MLens×Mz2×MPipex,y×Mz1.
G2(x,y,z1+z2)=ei2πλ(z1+nqe+z2+z3)eiπλ(D2xx2B2x+D2yy2B2y)(iλ)2B1xB1yB2xB2yk=1NPkπγx(k)γy(k)[a1eβ1(k)+a2eiφeβ2(k)],
β1(k)=iπA1xa2λB1xϕ1x24γx(k)ϕ1y24γy(k),
β2(k)=iπA1xb2λB1xϕ2x24γx(k)ϕ2y24γy(k),
γx(k)=QkR02iπλ(D1xB1x+A2xB2x),
γy(k)=QkR02iπλ(D1yB1y+A2yB2y),
ϕ1x=2πλ(aB1x+xB2x),
ϕ2x=2πλ(bB1x+xB2x),
ϕ1y=ϕ2y=2πyλB2y.
Mz1=(1z101).
MLens=(101f1),
Mz2=(1z201).
Mtot=Mz2×MLens×Mz1.

Metrics