Abstract

Three-dimensional position and velocity information can be extracted by direct analysis of the diffraction patterns of seeding particles in imaging velocimetry with real-time CCD cameras. The generalized Lorenz–Mie theory is shown to yield quantitatively accurate models of particle position, such that it can be deduced from typical experimental particle images with an accuracy of the order of 20 µm and an error of 11 gray levels rms, data obtained by comparison of theoretical and experimental images. Both the theory and an experimental verification of the problem presented here are discussed.

© 2000 Optical Society of America

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  2. J. Westerweel, F. T. M. Nieuwstadt, “Performance tests on 3-dimensional velocity measurements with a two-camera digital particle image velocimeter,” in Laser Anemometry: Advances and Applications, A. Dybbs, B. Ghorashi, eds. (American Society of Mechanical Engineers, New York, 1991), Vol. 1, pp. 349–355.
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    [CrossRef]
  4. H. Meng, F. Hussain, “Holographic particle velocimetry: a 3D measurement technique for vortex interactions, coherent structures and turbulence,” Fluid Dynam. Res. 8, 33–52 (1991).
    [CrossRef]
  5. C. Brucker, “Study of vortex breakdown by particle tracking velocimetry,” Exp. Fluids 13, 339–349 (1992).
    [CrossRef]
  6. P. J. Bryanston-Cross, M. Funes-Gallanzi, T. R. Quan, T. R. Judge, “Holographic particle image velocimetry (HPIV),” Opt. Laser Technol. 24, 251–256 (1992).
    [CrossRef]
  7. F. Dinkelaker, M. Schaffer, W. Ketterle, J. Wolfrum, “Determination of the third velocity component with PTA using an intensity graded light sheet,” Exp. Fluids 13, 357–359 (1992).
  8. C. E. Willert, M. Gharib, “Three-dimensional particle imaging with a single camera,” Exp. Fluids 12, 353–358 (1992).
    [CrossRef]
  9. B. Ovryn, E. A. Hovenac, “Coherent forward scattering particle image velocimetry: application of Poisson’s spot for velocity measurements in fluids,” in Optical Diagnostics in Fluid and Thermal Flow, S. S. Cha, J. D. Trolinger, eds., Proc. SPIE2005, 338–348 (1993).
    [CrossRef]
  10. A. K. Prasad, R. J. Adrian, “Stereoscopic particle image velocimetry applied to liquid flows,” Exp. Fluids 15, 49–60 (1993).
    [CrossRef]
  11. R. J. Adrian, C. D. Meinhart, D. H. Barnhart, G. C. Papen, “An HPIV system for turbulence research,” in Proceedings of Conference on Holographic Particle Velicometry (American Socieyt of Mechanical Engineers, New York, 1993), pp. 17–22.
  12. Y. G. Guezennec, Y. Zhao, T. J. Gieseke, “High-speed 3D scanning particle image velocimetry (3-D PIV) technique,” presented at the Seventh International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 11–14 July 1994.
  13. A. K. Prasad, K. Jensen, “Schiempflug stereocamera for particle image velocimetry in liquid flows,” Appl. Opt. 34, 7092–7099 (1995).
    [CrossRef] [PubMed]
  14. K. D. Hinsch, “Three-dimensional particle velocimetry,” Meas. Sci. Technol. 6, 742–753 (1995).
    [CrossRef]
  15. A. Lecerf, B. Renou, D. Allano, A. Boukhalfa, M. Trinité, “Stereoscopic PIV: validation and application to an isotropic turbulent flow,” Exp. Fluids 26, 107–115 (1999).
    [CrossRef]
  16. M. Funes-Gallanzi, “High accuracy measurement of unsteady flows using digital PIV,” Laser Opt. Technol. 30, 349–359 (1998).
    [CrossRef]
  17. P. Padilla Sosa, M. Funes-Gallanzi are preparing a manuscript to be called “High accuracy at low magnification 3D PIV measurement using the concept of locales.”
  18. G. Gouesbet, G. Gréhan, “Sur la généralisation de la théorie de Lorentz–Mie,” J. Opt. (Paris) 13, 97–103 (1982).
    [CrossRef]
  19. K. F. Ren, G. Gréhan, G. Gouesbet, “Electromagnetic field expression of a laser sheet and the order of approximation,” J. Opt. (Paris) 25, 165–176 (1994).
    [CrossRef]
  20. G. Gouesbet, B. Maheu, G. Gréhan, “Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation,” J. Opt. Soc. Am. A 5, 1427–1443 (1988).
    [CrossRef]
  21. G. Gouesbet, C. Letellier, K. F. Ren, G. Gréhan, “Discussion of two quadrature methods of evaluating beam shape coefficients in generalized Lorenz–Mie theory,” Appl. Opt. 35, 1537–1542 (1996).
    [CrossRef] [PubMed]
  22. G. Gouesbet, G. Gréhan, B. Maheu, “Expressions to compute the coefficients gnm in the generalized Lorenz–Mie theory, using finite series,” J. Opt. (Paris) 19, 35–48 (1998).
    [CrossRef]
  23. G. Gréhan, B. Maheu, G. Gouesbet, “Scattering of laser beams by Mie scatters centers: numerical results using a localized approximation,” Appl. Opt. 25, 3539–3548 (1986).
    [CrossRef]
  24. G. Gouesbet, G. Gréhan, B. Maheu, “Localized interpretation to compute all the coefficients gnm in the generalized Lorenz–Mie theory,” J. Opt. Soc. Am. A 7, 998–1007 (1990).
    [CrossRef]
  25. J. A. Lock, G. Gouesbet, “Rigorous justification of the localized approximation to the beam shape coefficients in generalized Lorenz–Mie theory. I. On-axis beam,” J. Opt. Soc. Am. A 11, 2503–2515 (1994).
    [CrossRef]
  26. G. Gouesbet, J. A. Lock, “Rigorous justification of the localized approximation to the beam shape coefficients in generalized Lorenz–Mie theory. II. Off-axis beam,” J. Opt. Soc. Am. A 11, 2516–2525 (1994).
    [CrossRef]
  27. K. F. Ren, G. Gréhan, G. Gouesbet, “Evaluation of laser laser-sheet beam shape coefficients in generalized Lorenz–Mie theory by use of a localized approximation,” J. Opt. Soc. Am. A 11, 2072–2079 (1994).
    [CrossRef]
  28. G. Gouesbet, J. A. Lock, G. Gréhan, “Partial wave representation of laser beams for use in light scattering calculation,” Appl. Opt. 34, 2113–2143 (1995).
    [CrossRef]
  29. K. F. Ren, G. Gouesbet, G. Gréhan, “The integral localized approximation in generalized Lorenz–Mie theory,” Appl. Opt. 37, 4218–4225 (1998).
    [CrossRef]
  30. G. Gouesbet, “Validity of the localized approximation for arbitrary shaped beams in the generalized Lorenz–Mie theory for spheres,” J. Opt. Soc. Am. A 7, 1641–1650 (1999).
    [CrossRef]
  31. J. V. Dave, “Scattering of electromagnetic radiation by a large, absorbing sphere,” IBM J. Res. Dev. 13, 302–313 (1969).
    [CrossRef]
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  33. R. J. Adrian, C. S. Yao, “Development of pulsed laser velocimetry for measurement of fluid flow,” in Proceedings, Eighth biennial Symposium on Turbulence, G. Patterson, J. L. Zakin, eds. (University of Missouri, Rolla, Mo., 1983).
  34. K. J. Wiles, “Development of a system for secondary liquid injection into a Mach 2 supersonic flow to study drop size and distribution by video imaging techniques,” master’s degree thesis (University of Nebraska, Lincoln, Neb., 1985).
  35. S. A. Schaub, D. R. Alexander, J. P. Barton, “Theoretical model for the image formed by a spherical particle in a coherent imaging system: comparison to experiment,” Opt. Eng. 23, 565–571 (1989).
  36. P. Debye, “Der Lichtdruck auf Kugeln von beliebigem Material,” Ann. Phys. (Leipzig) 30, 57–136 (1909).
    [CrossRef]
  37. G. Mie, “Bietrage zur Optik trüber Medien, speziell kolloidaler Metallosungen,” Ann. Phys. (Leipzig) 25, 377–445 (1908).
    [CrossRef]
  38. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  39. J. A. Guerrero, F. Mendoza Santoyo, D. Moreno, M. Funes-Gallanzi, “Particle positioning from CCD images: experiments and comparison to the generalized Lorenz–Mie theory,” Meas. Sci. Technol. 11, 568–575 (2000).
    [CrossRef]

2000

J. A. Guerrero, F. Mendoza Santoyo, D. Moreno, M. Funes-Gallanzi, “Particle positioning from CCD images: experiments and comparison to the generalized Lorenz–Mie theory,” Meas. Sci. Technol. 11, 568–575 (2000).
[CrossRef]

1999

G. Gouesbet, “Validity of the localized approximation for arbitrary shaped beams in the generalized Lorenz–Mie theory for spheres,” J. Opt. Soc. Am. A 7, 1641–1650 (1999).
[CrossRef]

A. Lecerf, B. Renou, D. Allano, A. Boukhalfa, M. Trinité, “Stereoscopic PIV: validation and application to an isotropic turbulent flow,” Exp. Fluids 26, 107–115 (1999).
[CrossRef]

1998

M. Funes-Gallanzi, “High accuracy measurement of unsteady flows using digital PIV,” Laser Opt. Technol. 30, 349–359 (1998).
[CrossRef]

G. Gouesbet, G. Gréhan, B. Maheu, “Expressions to compute the coefficients gnm in the generalized Lorenz–Mie theory, using finite series,” J. Opt. (Paris) 19, 35–48 (1998).
[CrossRef]

K. F. Ren, G. Gouesbet, G. Gréhan, “The integral localized approximation in generalized Lorenz–Mie theory,” Appl. Opt. 37, 4218–4225 (1998).
[CrossRef]

1996

1995

A. K. Prasad, K. Jensen, “Schiempflug stereocamera for particle image velocimetry in liquid flows,” Appl. Opt. 34, 7092–7099 (1995).
[CrossRef] [PubMed]

K. D. Hinsch, “Three-dimensional particle velocimetry,” Meas. Sci. Technol. 6, 742–753 (1995).
[CrossRef]

G. Gouesbet, J. A. Lock, G. Gréhan, “Partial wave representation of laser beams for use in light scattering calculation,” Appl. Opt. 34, 2113–2143 (1995).
[CrossRef]

1994

1993

A. K. Prasad, R. J. Adrian, “Stereoscopic particle image velocimetry applied to liquid flows,” Exp. Fluids 15, 49–60 (1993).
[CrossRef]

1992

C. Brucker, “Study of vortex breakdown by particle tracking velocimetry,” Exp. Fluids 13, 339–349 (1992).
[CrossRef]

P. J. Bryanston-Cross, M. Funes-Gallanzi, T. R. Quan, T. R. Judge, “Holographic particle image velocimetry (HPIV),” Opt. Laser Technol. 24, 251–256 (1992).
[CrossRef]

F. Dinkelaker, M. Schaffer, W. Ketterle, J. Wolfrum, “Determination of the third velocity component with PTA using an intensity graded light sheet,” Exp. Fluids 13, 357–359 (1992).

C. E. Willert, M. Gharib, “Three-dimensional particle imaging with a single camera,” Exp. Fluids 12, 353–358 (1992).
[CrossRef]

1991

C. Gray, C. A. Greated, D. R. McCluskey, W. J. Easson, “An analysis of the scanning beam PIV illumination system,” Meas. Sci. Technol. 2, 717–724 (1991).
[CrossRef]

H. Meng, F. Hussain, “Holographic particle velocimetry: a 3D measurement technique for vortex interactions, coherent structures and turbulence,” Fluid Dynam. Res. 8, 33–52 (1991).
[CrossRef]

1990

1989

S. A. Schaub, D. R. Alexander, J. P. Barton, “Theoretical model for the image formed by a spherical particle in a coherent imaging system: comparison to experiment,” Opt. Eng. 23, 565–571 (1989).

1988

1986

1982

G. Gouesbet, G. Gréhan, “Sur la généralisation de la théorie de Lorentz–Mie,” J. Opt. (Paris) 13, 97–103 (1982).
[CrossRef]

1969

J. V. Dave, “Scattering of electromagnetic radiation by a large, absorbing sphere,” IBM J. Res. Dev. 13, 302–313 (1969).
[CrossRef]

1909

P. Debye, “Der Lichtdruck auf Kugeln von beliebigem Material,” Ann. Phys. (Leipzig) 30, 57–136 (1909).
[CrossRef]

1908

G. Mie, “Bietrage zur Optik trüber Medien, speziell kolloidaler Metallosungen,” Ann. Phys. (Leipzig) 25, 377–445 (1908).
[CrossRef]

Adrian, R. J.

A. K. Prasad, R. J. Adrian, “Stereoscopic particle image velocimetry applied to liquid flows,” Exp. Fluids 15, 49–60 (1993).
[CrossRef]

R. J. Adrian, C. D. Meinhart, D. H. Barnhart, G. C. Papen, “An HPIV system for turbulence research,” in Proceedings of Conference on Holographic Particle Velicometry (American Socieyt of Mechanical Engineers, New York, 1993), pp. 17–22.

R. J. Adrian, C. S. Yao, “Development of pulsed laser velocimetry for measurement of fluid flow,” in Proceedings, Eighth biennial Symposium on Turbulence, G. Patterson, J. L. Zakin, eds. (University of Missouri, Rolla, Mo., 1983).

Alexander, D. R.

S. A. Schaub, D. R. Alexander, J. P. Barton, “Theoretical model for the image formed by a spherical particle in a coherent imaging system: comparison to experiment,” Opt. Eng. 23, 565–571 (1989).

Allano, D.

A. Lecerf, B. Renou, D. Allano, A. Boukhalfa, M. Trinité, “Stereoscopic PIV: validation and application to an isotropic turbulent flow,” Exp. Fluids 26, 107–115 (1999).
[CrossRef]

Barnhart, D. H.

R. J. Adrian, C. D. Meinhart, D. H. Barnhart, G. C. Papen, “An HPIV system for turbulence research,” in Proceedings of Conference on Holographic Particle Velicometry (American Socieyt of Mechanical Engineers, New York, 1993), pp. 17–22.

Barton, J. P.

S. A. Schaub, D. R. Alexander, J. P. Barton, “Theoretical model for the image formed by a spherical particle in a coherent imaging system: comparison to experiment,” Opt. Eng. 23, 565–571 (1989).

Boukhalfa, A.

A. Lecerf, B. Renou, D. Allano, A. Boukhalfa, M. Trinité, “Stereoscopic PIV: validation and application to an isotropic turbulent flow,” Exp. Fluids 26, 107–115 (1999).
[CrossRef]

Brucker, C.

C. Brucker, “Study of vortex breakdown by particle tracking velocimetry,” Exp. Fluids 13, 339–349 (1992).
[CrossRef]

Bryanston-Cross, P. J.

P. J. Bryanston-Cross, M. Funes-Gallanzi, T. R. Quan, T. R. Judge, “Holographic particle image velocimetry (HPIV),” Opt. Laser Technol. 24, 251–256 (1992).
[CrossRef]

Dave, J. V.

J. V. Dave, “Scattering of electromagnetic radiation by a large, absorbing sphere,” IBM J. Res. Dev. 13, 302–313 (1969).
[CrossRef]

Debye, P.

P. Debye, “Der Lichtdruck auf Kugeln von beliebigem Material,” Ann. Phys. (Leipzig) 30, 57–136 (1909).
[CrossRef]

Dinkelaker, F.

F. Dinkelaker, M. Schaffer, W. Ketterle, J. Wolfrum, “Determination of the third velocity component with PTA using an intensity graded light sheet,” Exp. Fluids 13, 357–359 (1992).

Easson, W. J.

C. Gray, C. A. Greated, D. R. McCluskey, W. J. Easson, “An analysis of the scanning beam PIV illumination system,” Meas. Sci. Technol. 2, 717–724 (1991).
[CrossRef]

Funes-Gallanzi, M.

J. A. Guerrero, F. Mendoza Santoyo, D. Moreno, M. Funes-Gallanzi, “Particle positioning from CCD images: experiments and comparison to the generalized Lorenz–Mie theory,” Meas. Sci. Technol. 11, 568–575 (2000).
[CrossRef]

M. Funes-Gallanzi, “High accuracy measurement of unsteady flows using digital PIV,” Laser Opt. Technol. 30, 349–359 (1998).
[CrossRef]

P. J. Bryanston-Cross, M. Funes-Gallanzi, T. R. Quan, T. R. Judge, “Holographic particle image velocimetry (HPIV),” Opt. Laser Technol. 24, 251–256 (1992).
[CrossRef]

P. Padilla Sosa, M. Funes-Gallanzi are preparing a manuscript to be called “High accuracy at low magnification 3D PIV measurement using the concept of locales.”

Gauthier, V.

V. Gauthier, M. L. Riethmuller, “Application of PIDV to complex flows: measurements of third component,” von Karman Institute for Fluid Dynamics, Vol. 1988-06 of Lecture Series on Particle Image Displacement Velicometry (Rhode Saint Genese, Belgium, 1988).

Gharib, M.

C. E. Willert, M. Gharib, “Three-dimensional particle imaging with a single camera,” Exp. Fluids 12, 353–358 (1992).
[CrossRef]

Gieseke, T. J.

Y. G. Guezennec, Y. Zhao, T. J. Gieseke, “High-speed 3D scanning particle image velocimetry (3-D PIV) technique,” presented at the Seventh International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 11–14 July 1994.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Gouesbet, G.

G. Gouesbet, “Validity of the localized approximation for arbitrary shaped beams in the generalized Lorenz–Mie theory for spheres,” J. Opt. Soc. Am. A 7, 1641–1650 (1999).
[CrossRef]

K. F. Ren, G. Gouesbet, G. Gréhan, “The integral localized approximation in generalized Lorenz–Mie theory,” Appl. Opt. 37, 4218–4225 (1998).
[CrossRef]

G. Gouesbet, G. Gréhan, B. Maheu, “Expressions to compute the coefficients gnm in the generalized Lorenz–Mie theory, using finite series,” J. Opt. (Paris) 19, 35–48 (1998).
[CrossRef]

G. Gouesbet, C. Letellier, K. F. Ren, G. Gréhan, “Discussion of two quadrature methods of evaluating beam shape coefficients in generalized Lorenz–Mie theory,” Appl. Opt. 35, 1537–1542 (1996).
[CrossRef] [PubMed]

G. Gouesbet, J. A. Lock, G. Gréhan, “Partial wave representation of laser beams for use in light scattering calculation,” Appl. Opt. 34, 2113–2143 (1995).
[CrossRef]

K. F. Ren, G. Gréhan, G. Gouesbet, “Evaluation of laser laser-sheet beam shape coefficients in generalized Lorenz–Mie theory by use of a localized approximation,” J. Opt. Soc. Am. A 11, 2072–2079 (1994).
[CrossRef]

J. A. Lock, G. Gouesbet, “Rigorous justification of the localized approximation to the beam shape coefficients in generalized Lorenz–Mie theory. I. On-axis beam,” J. Opt. Soc. Am. A 11, 2503–2515 (1994).
[CrossRef]

G. Gouesbet, J. A. Lock, “Rigorous justification of the localized approximation to the beam shape coefficients in generalized Lorenz–Mie theory. II. Off-axis beam,” J. Opt. Soc. Am. A 11, 2516–2525 (1994).
[CrossRef]

K. F. Ren, G. Gréhan, G. Gouesbet, “Electromagnetic field expression of a laser sheet and the order of approximation,” J. Opt. (Paris) 25, 165–176 (1994).
[CrossRef]

G. Gouesbet, G. Gréhan, B. Maheu, “Localized interpretation to compute all the coefficients gnm in the generalized Lorenz–Mie theory,” J. Opt. Soc. Am. A 7, 998–1007 (1990).
[CrossRef]

G. Gouesbet, B. Maheu, G. Gréhan, “Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation,” J. Opt. Soc. Am. A 5, 1427–1443 (1988).
[CrossRef]

G. Gréhan, B. Maheu, G. Gouesbet, “Scattering of laser beams by Mie scatters centers: numerical results using a localized approximation,” Appl. Opt. 25, 3539–3548 (1986).
[CrossRef]

G. Gouesbet, G. Gréhan, “Sur la généralisation de la théorie de Lorentz–Mie,” J. Opt. (Paris) 13, 97–103 (1982).
[CrossRef]

Gray, C.

C. Gray, C. A. Greated, D. R. McCluskey, W. J. Easson, “An analysis of the scanning beam PIV illumination system,” Meas. Sci. Technol. 2, 717–724 (1991).
[CrossRef]

Greated, C. A.

C. Gray, C. A. Greated, D. R. McCluskey, W. J. Easson, “An analysis of the scanning beam PIV illumination system,” Meas. Sci. Technol. 2, 717–724 (1991).
[CrossRef]

Gréhan, G.

G. Gouesbet, G. Gréhan, B. Maheu, “Expressions to compute the coefficients gnm in the generalized Lorenz–Mie theory, using finite series,” J. Opt. (Paris) 19, 35–48 (1998).
[CrossRef]

K. F. Ren, G. Gouesbet, G. Gréhan, “The integral localized approximation in generalized Lorenz–Mie theory,” Appl. Opt. 37, 4218–4225 (1998).
[CrossRef]

G. Gouesbet, C. Letellier, K. F. Ren, G. Gréhan, “Discussion of two quadrature methods of evaluating beam shape coefficients in generalized Lorenz–Mie theory,” Appl. Opt. 35, 1537–1542 (1996).
[CrossRef] [PubMed]

G. Gouesbet, J. A. Lock, G. Gréhan, “Partial wave representation of laser beams for use in light scattering calculation,” Appl. Opt. 34, 2113–2143 (1995).
[CrossRef]

K. F. Ren, G. Gréhan, G. Gouesbet, “Electromagnetic field expression of a laser sheet and the order of approximation,” J. Opt. (Paris) 25, 165–176 (1994).
[CrossRef]

K. F. Ren, G. Gréhan, G. Gouesbet, “Evaluation of laser laser-sheet beam shape coefficients in generalized Lorenz–Mie theory by use of a localized approximation,” J. Opt. Soc. Am. A 11, 2072–2079 (1994).
[CrossRef]

G. Gouesbet, G. Gréhan, B. Maheu, “Localized interpretation to compute all the coefficients gnm in the generalized Lorenz–Mie theory,” J. Opt. Soc. Am. A 7, 998–1007 (1990).
[CrossRef]

G. Gouesbet, B. Maheu, G. Gréhan, “Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation,” J. Opt. Soc. Am. A 5, 1427–1443 (1988).
[CrossRef]

G. Gréhan, B. Maheu, G. Gouesbet, “Scattering of laser beams by Mie scatters centers: numerical results using a localized approximation,” Appl. Opt. 25, 3539–3548 (1986).
[CrossRef]

G. Gouesbet, G. Gréhan, “Sur la généralisation de la théorie de Lorentz–Mie,” J. Opt. (Paris) 13, 97–103 (1982).
[CrossRef]

Guerrero, J. A.

J. A. Guerrero, F. Mendoza Santoyo, D. Moreno, M. Funes-Gallanzi, “Particle positioning from CCD images: experiments and comparison to the generalized Lorenz–Mie theory,” Meas. Sci. Technol. 11, 568–575 (2000).
[CrossRef]

Guezennec, Y. G.

Y. G. Guezennec, Y. Zhao, T. J. Gieseke, “High-speed 3D scanning particle image velocimetry (3-D PIV) technique,” presented at the Seventh International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 11–14 July 1994.

Hinsch, K. D.

K. D. Hinsch, “Three-dimensional particle velocimetry,” Meas. Sci. Technol. 6, 742–753 (1995).
[CrossRef]

Hovenac, E. A.

B. Ovryn, E. A. Hovenac, “Coherent forward scattering particle image velocimetry: application of Poisson’s spot for velocity measurements in fluids,” in Optical Diagnostics in Fluid and Thermal Flow, S. S. Cha, J. D. Trolinger, eds., Proc. SPIE2005, 338–348 (1993).
[CrossRef]

Hussain, F.

H. Meng, F. Hussain, “Holographic particle velocimetry: a 3D measurement technique for vortex interactions, coherent structures and turbulence,” Fluid Dynam. Res. 8, 33–52 (1991).
[CrossRef]

Jensen, K.

Judge, T. R.

P. J. Bryanston-Cross, M. Funes-Gallanzi, T. R. Quan, T. R. Judge, “Holographic particle image velocimetry (HPIV),” Opt. Laser Technol. 24, 251–256 (1992).
[CrossRef]

Ketterle, W.

F. Dinkelaker, M. Schaffer, W. Ketterle, J. Wolfrum, “Determination of the third velocity component with PTA using an intensity graded light sheet,” Exp. Fluids 13, 357–359 (1992).

Lecerf, A.

A. Lecerf, B. Renou, D. Allano, A. Boukhalfa, M. Trinité, “Stereoscopic PIV: validation and application to an isotropic turbulent flow,” Exp. Fluids 26, 107–115 (1999).
[CrossRef]

Letellier, C.

Lock, J. A.

Maheu, B.

McCluskey, D. R.

C. Gray, C. A. Greated, D. R. McCluskey, W. J. Easson, “An analysis of the scanning beam PIV illumination system,” Meas. Sci. Technol. 2, 717–724 (1991).
[CrossRef]

Meinhart, C. D.

R. J. Adrian, C. D. Meinhart, D. H. Barnhart, G. C. Papen, “An HPIV system for turbulence research,” in Proceedings of Conference on Holographic Particle Velicometry (American Socieyt of Mechanical Engineers, New York, 1993), pp. 17–22.

Mendoza Santoyo, F.

J. A. Guerrero, F. Mendoza Santoyo, D. Moreno, M. Funes-Gallanzi, “Particle positioning from CCD images: experiments and comparison to the generalized Lorenz–Mie theory,” Meas. Sci. Technol. 11, 568–575 (2000).
[CrossRef]

Meng, H.

H. Meng, F. Hussain, “Holographic particle velocimetry: a 3D measurement technique for vortex interactions, coherent structures and turbulence,” Fluid Dynam. Res. 8, 33–52 (1991).
[CrossRef]

Mie, G.

G. Mie, “Bietrage zur Optik trüber Medien, speziell kolloidaler Metallosungen,” Ann. Phys. (Leipzig) 25, 377–445 (1908).
[CrossRef]

Moreno, D.

J. A. Guerrero, F. Mendoza Santoyo, D. Moreno, M. Funes-Gallanzi, “Particle positioning from CCD images: experiments and comparison to the generalized Lorenz–Mie theory,” Meas. Sci. Technol. 11, 568–575 (2000).
[CrossRef]

Nieuwstadt, F. T. M.

J. Westerweel, F. T. M. Nieuwstadt, “Performance tests on 3-dimensional velocity measurements with a two-camera digital particle image velocimeter,” in Laser Anemometry: Advances and Applications, A. Dybbs, B. Ghorashi, eds. (American Society of Mechanical Engineers, New York, 1991), Vol. 1, pp. 349–355.

Ovryn, B.

B. Ovryn, E. A. Hovenac, “Coherent forward scattering particle image velocimetry: application of Poisson’s spot for velocity measurements in fluids,” in Optical Diagnostics in Fluid and Thermal Flow, S. S. Cha, J. D. Trolinger, eds., Proc. SPIE2005, 338–348 (1993).
[CrossRef]

Padilla Sosa, P.

P. Padilla Sosa, M. Funes-Gallanzi are preparing a manuscript to be called “High accuracy at low magnification 3D PIV measurement using the concept of locales.”

Papen, G. C.

R. J. Adrian, C. D. Meinhart, D. H. Barnhart, G. C. Papen, “An HPIV system for turbulence research,” in Proceedings of Conference on Holographic Particle Velicometry (American Socieyt of Mechanical Engineers, New York, 1993), pp. 17–22.

Prasad, A. K.

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[CrossRef]

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J. Westerweel, F. T. M. Nieuwstadt, “Performance tests on 3-dimensional velocity measurements with a two-camera digital particle image velocimeter,” in Laser Anemometry: Advances and Applications, A. Dybbs, B. Ghorashi, eds. (American Society of Mechanical Engineers, New York, 1991), Vol. 1, pp. 349–355.

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[CrossRef]

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Y. G. Guezennec, Y. Zhao, T. J. Gieseke, “High-speed 3D scanning particle image velocimetry (3-D PIV) technique,” presented at the Seventh International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 11–14 July 1994.

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[CrossRef]

Appl. Opt.

Exp. Fluids

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[CrossRef]

A. Lecerf, B. Renou, D. Allano, A. Boukhalfa, M. Trinité, “Stereoscopic PIV: validation and application to an isotropic turbulent flow,” Exp. Fluids 26, 107–115 (1999).
[CrossRef]

C. Brucker, “Study of vortex breakdown by particle tracking velocimetry,” Exp. Fluids 13, 339–349 (1992).
[CrossRef]

F. Dinkelaker, M. Schaffer, W. Ketterle, J. Wolfrum, “Determination of the third velocity component with PTA using an intensity graded light sheet,” Exp. Fluids 13, 357–359 (1992).

C. E. Willert, M. Gharib, “Three-dimensional particle imaging with a single camera,” Exp. Fluids 12, 353–358 (1992).
[CrossRef]

Fluid Dynam. Res.

H. Meng, F. Hussain, “Holographic particle velocimetry: a 3D measurement technique for vortex interactions, coherent structures and turbulence,” Fluid Dynam. Res. 8, 33–52 (1991).
[CrossRef]

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[CrossRef]

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S. A. Schaub, D. R. Alexander, J. P. Barton, “Theoretical model for the image formed by a spherical particle in a coherent imaging system: comparison to experiment,” Opt. Eng. 23, 565–571 (1989).

Opt. Laser Technol.

P. J. Bryanston-Cross, M. Funes-Gallanzi, T. R. Quan, T. R. Judge, “Holographic particle image velocimetry (HPIV),” Opt. Laser Technol. 24, 251–256 (1992).
[CrossRef]

Other

B. Ovryn, E. A. Hovenac, “Coherent forward scattering particle image velocimetry: application of Poisson’s spot for velocity measurements in fluids,” in Optical Diagnostics in Fluid and Thermal Flow, S. S. Cha, J. D. Trolinger, eds., Proc. SPIE2005, 338–348 (1993).
[CrossRef]

V. Gauthier, M. L. Riethmuller, “Application of PIDV to complex flows: measurements of third component,” von Karman Institute for Fluid Dynamics, Vol. 1988-06 of Lecture Series on Particle Image Displacement Velicometry (Rhode Saint Genese, Belgium, 1988).

J. Westerweel, F. T. M. Nieuwstadt, “Performance tests on 3-dimensional velocity measurements with a two-camera digital particle image velocimeter,” in Laser Anemometry: Advances and Applications, A. Dybbs, B. Ghorashi, eds. (American Society of Mechanical Engineers, New York, 1991), Vol. 1, pp. 349–355.

R. J. Adrian, C. D. Meinhart, D. H. Barnhart, G. C. Papen, “An HPIV system for turbulence research,” in Proceedings of Conference on Holographic Particle Velicometry (American Socieyt of Mechanical Engineers, New York, 1993), pp. 17–22.

Y. G. Guezennec, Y. Zhao, T. J. Gieseke, “High-speed 3D scanning particle image velocimetry (3-D PIV) technique,” presented at the Seventh International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, 11–14 July 1994.

P. Padilla Sosa, M. Funes-Gallanzi are preparing a manuscript to be called “High accuracy at low magnification 3D PIV measurement using the concept of locales.”

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M. Abramowitz, I. A. Stegun, eds., Handbook of Mathematical Functions (Dover, New York, 1972), pp. 332–334.

R. J. Adrian, C. S. Yao, “Development of pulsed laser velocimetry for measurement of fluid flow,” in Proceedings, Eighth biennial Symposium on Turbulence, G. Patterson, J. L. Zakin, eds. (University of Missouri, Rolla, Mo., 1983).

K. J. Wiles, “Development of a system for secondary liquid injection into a Mach 2 supersonic flow to study drop size and distribution by video imaging techniques,” master’s degree thesis (University of Nebraska, Lincoln, Neb., 1985).

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Figures (5)

Fig. 1
Fig. 1

System geometry for GLMT calculations.

Fig. 2
Fig. 2

Initial layout: z0–z3, planes.

Fig. 3
Fig. 3

Mesh plot of particle image versus defocus (experimentally verified Gaussian-beam generalized Lorenz–Mie calculation: 18-µm glass particle).

Fig. 4
Fig. 4

Comparison of radial intensity for experimental (dashed curve) and theoretical (solid curve) particle images.

Fig. 5
Fig. 5

Typical GLMT toolbox front-end display.

Equations (28)

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E˜rs=-n=1m=-n+n angn,TMmξnαr˜+ξnαr˜Pn|m|cos θexpimφ,
E˜θs=-1αr˜n=1m=-n+nangn,TMmξnαr˜τn|m|cos θ+mbngn,TEmξnαr˜n|m|cos θexpimφ,
E˜ϕs=-iαr˜n=1m=-n+nmangn,TMmξnαr˜n|m|cos θ+bngn,TEmξnαr˜τn|m|cos θexpimφ;
α=ka
an=in-11n2n+1nn+1ψnn¯αψnα-n¯ψnn¯αψnαψnn¯αξnα-n¯ψnn¯αξnα,
bn=in-11n2n+1nn+1n¯ψnn¯αψnα-ψnn¯αψnαn¯ψnn¯αξnα-ψnn¯αξnα,
E˜ri=φ0shcos ϕsinθ1-2Qxl˜x r˜ cos θ+2Qxl˜x x˜0 cos θexpK,
E˜θi=φ0shcos ϕcos θ+2Qxl˜x r˜ sin2θ-2Qxl˜x x˜0 sin θexpK,
E˜φi=-φ0sh sin φ expK,
K=-iαr˜ cos θ-z˜0,
φ0sh=-QxQy1/2 exp-iQxω˜0x2r˜ cos ϕ sin θ-x˜02-iQyω˜0y2r˜ sin ϕ sin θ-y˜02,
Qx=1i+2/l˜xr˜ cos θ-z˜0,
Qy=1i+2/l˜yr˜ cos θ-z˜0,
l˜x=αω˜0x2, l˜y=αω˜0y2,
de=M2dp2+ds21/2,
ds=2.44M+1λf/#
E2x2, y2=expiknΔ0exp-ik2fx12+y12E1x1, y1=expiknΔ0exp-ik2fx22+y22E1x2, y2,
E3x3, y3=expikz3-z2iλz3-z2A E2x2, y2×expik2z3-z2x3-x22+y3-y22dx2dy2,
E3x3, y3=expikz3-z2iλz3-z2AexpiknΔ0×exp-ik2fx22+y22E1x2, y2×expik2z3-z2x3-x22+y3-y22dx2dy2.
E3r3, ϕ3=expikz3-z2iλz3-z202π0raexpiknΔ0×exp-ik2fr2 cos ϕ22+r2 sin ϕ22E1r2, ϕ2×expik2z3-z2r3 cos ϕ3-r2 cos ϕ22+r3 sin ϕ3-r2 sin ϕ32r2dr2dϕ2.
E3r3, ϕ3=1iλz3-z20ra E1r2r2 exp-ik2f r2202π×expik2z3-z2r32+r22-2r2×cosϕ2-ϕ3dϕ2dr.
expia sin x=k=- Jkaexpikx,
Er3=2πiλz3-z2expikr322z3-z20ra E1r2J0β×exp-ikr2221f-1z3-z2r2dr2,
β=kr2r3z3-z2.
I3r3=E3r3E3*r3=2πλz3-z220ra E1r2J0β×exp-ikr2221f-1z3-z2r2dr22,
Ĩ3r˜3=αz˜3-z˜220ra E˜1r˜2J0β˜×exp-iαr˜2221f-1z˜3-z˜2r˜2dr˜22,
β˜=r˜2r˜3αz˜3-z˜2, r˜=ra,  z˜=za,  f˜=fa.
WS, θ=F+Er˜2 cos θ+Dr˜22+Cr˜221+cos2 θ+Br˜23cos θ+Ar˜24,

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