Abstract

An optoelectronic in-line imaging system for particle sizing is described. The images are scanned by two CCD cameras viewing the same object field that is illuminated with two pulses. One of the cameras is double exposed and the other is activated only during the second pulse. Two successive analogical subtractions between the video output signals gives the sign of the transverse velocity vector. Out-of-focus images are deconvolved with the assumption of a Gaussian point-spread function (PSF) whose spatial parameter σ increases with the defocusing distance z. In the case of low particle density, an algorithm based on the exploitation of the power spectral density is used to estimate the particle diameter. This method can be applied to the case of fast-moving particles (e.g., υ < 500 m/s). The accuracy of the size measurement is better than 10% in the diameter range 20–160 μm. The main result is that this accuracy is obtained with an amount of defocusing in the range [−2, 2] mm. Thus, the depth of field is significantly extended in comparison with a conventional microscopic imaging system.

© 1996 Optical Society of America

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References

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  1. A. L. Tassin, D. E. Nikitopoulos, “Nonintrusive measurements of bubble size and velocity,” Exp. Fluids 19, 121–132 (1995).
    [CrossRef]
  2. Y. Hardalupas, K. Hishida, M. Maeda, H. Morikita, A. M. K. P. Taylor, J. H. Whitelaw, “Shadow Doppler technique for sizing particles of arbitrary shape,” Appl. Opt. 33, 8417–8426 (1994).
    [CrossRef] [PubMed]
  3. P. Meyer, N. Chigier, “Drop size measurements using a Malvern 2200 particle sizer,” Atomiz. Spray Technol. 2, 261–268 (1986).
  4. L. G. Dodge, “Calibration of the Malvern particle sizer,” Appl. Opt. 23, 2415–2419 (1994).
    [CrossRef]
  5. J. Cornillault, “Particle size analyzer,” Appl. Opt. 11, 265–268 (1972).
    [CrossRef] [PubMed]
  6. J. Swithenbank, J. M. Beer, D. S. Taylor, D. Abbott, C. G. McCreath, “A laser diagnostic technique for the measurement of droplet and particle size distribution,” special issue on Experimental Diagnostic in Gas Phase Combustion Systems, Prog. Astronaut. Aeronaut. 53, 421–427 (1977).
  7. P. N. Wild, J. Swithenbank, “Beam stop and vignetting effects in particle size measurements by laser diffraction,” Appl. Opt. 25, 3520–35261986).
    [CrossRef] [PubMed]
  8. D. Lebrun, S. Belaïd, C. Özkul, K. F. Ren, G. Gréhan, “Enhancement of wire diameter measurements: comparison between Fraunhofer diffraction and Lorentz–Mie theory,” Opt. Eng. 35, 946–950 (1996).
    [CrossRef]
  9. C. S. Vikram, Particle Field Holography (Cambridge U. Press, Cambridge, 1992).
    [CrossRef]
  10. D. Lebrun, C. Özkul, D. Allano, A. Leduc, “Use of the moiré effect to improve the diameter measurements with charge coupled imagers,” J. Opt. (Paris) 22, 175–184 (1991).
    [CrossRef]
  11. C. Özkul, D. Lebrun, D. Allano, A. Abdelghani-Idrissi, A. Leduc, “Processing of glass cylinder diffraction patterns scanned with a photodiode array: influence of the optical transfer function of diodes on dimensional measurements,” Opt. Eng. 30, 1855–1861 (1991).
    [CrossRef]
  12. M. Raffel, M. Gharib, O. Ronneberger, J. Kompenhans, “Feasibility study of three-dimensional PIV by correlating images of particles within parallel light sheet planes,” Exp. Fluids 19, 69–77 (1995).
  13. C. E. Willert, M. Gharib, “Three-dimensional particle imaging with a single camera,” Exp. Fluids 12, 353–358 (1992).
    [CrossRef]
  14. C. Castellini, F. Francini, G. Longobardi, E. Pampaloni, “On-line characterization of the shape and size of particles,” Part. Part. Syst. Charact. 10, 7–10 (1993).
    [CrossRef]
  15. K. S. Kim, S. S. Kim, “Drop sizing and depth-of-field correction in TV imaging,” Atomiz. Sprays 4, 65–78 (1994).
  16. D. Lebrun, C. Özkul, C. E. Touil, J. B. Blaisot, K. Kleitz, “On-line particle size and velocity measurements by the analysis of defocused images: extended depth of field,” in Laser Dimensional Metrology: Recent Advances for Industrial Application, M. J. Downs, ed., Proc. SPIE2088, 139–148 (1993).
  17. D. Lebrun, C. Özkul, A. Kleitz, C. E. Touil, R. Roth, “Une sonde microvideo appliquée à la granulométrie,” J. Opt. (Paris) 26, 39–48 (1995).
    [CrossRef]
  18. A. P. Pentland, “A new sense for depth of field,” IEEE Trans. Pattern Anal. Machine Intell. 9, 523–531 (1987).
    [CrossRef]
  19. K. F. Ren, D. Lebrun, C. Özkul, A. Kleitz, G. Gouesbet, G. Gréhan, “On the measurements of particles by imaging methods: theoretical and experimental aspects,” Part. Part. Syst. Charact. 13, 156–164 (1996).
    [CrossRef]

1996 (2)

D. Lebrun, S. Belaïd, C. Özkul, K. F. Ren, G. Gréhan, “Enhancement of wire diameter measurements: comparison between Fraunhofer diffraction and Lorentz–Mie theory,” Opt. Eng. 35, 946–950 (1996).
[CrossRef]

K. F. Ren, D. Lebrun, C. Özkul, A. Kleitz, G. Gouesbet, G. Gréhan, “On the measurements of particles by imaging methods: theoretical and experimental aspects,” Part. Part. Syst. Charact. 13, 156–164 (1996).
[CrossRef]

1995 (3)

A. L. Tassin, D. E. Nikitopoulos, “Nonintrusive measurements of bubble size and velocity,” Exp. Fluids 19, 121–132 (1995).
[CrossRef]

M. Raffel, M. Gharib, O. Ronneberger, J. Kompenhans, “Feasibility study of three-dimensional PIV by correlating images of particles within parallel light sheet planes,” Exp. Fluids 19, 69–77 (1995).

D. Lebrun, C. Özkul, A. Kleitz, C. E. Touil, R. Roth, “Une sonde microvideo appliquée à la granulométrie,” J. Opt. (Paris) 26, 39–48 (1995).
[CrossRef]

1994 (3)

1993 (1)

C. Castellini, F. Francini, G. Longobardi, E. Pampaloni, “On-line characterization of the shape and size of particles,” Part. Part. Syst. Charact. 10, 7–10 (1993).
[CrossRef]

1992 (1)

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

1991 (2)

D. Lebrun, C. Özkul, D. Allano, A. Leduc, “Use of the moiré effect to improve the diameter measurements with charge coupled imagers,” J. Opt. (Paris) 22, 175–184 (1991).
[CrossRef]

C. Özkul, D. Lebrun, D. Allano, A. Abdelghani-Idrissi, A. Leduc, “Processing of glass cylinder diffraction patterns scanned with a photodiode array: influence of the optical transfer function of diodes on dimensional measurements,” Opt. Eng. 30, 1855–1861 (1991).
[CrossRef]

1987 (1)

A. P. Pentland, “A new sense for depth of field,” IEEE Trans. Pattern Anal. Machine Intell. 9, 523–531 (1987).
[CrossRef]

1986 (2)

P. N. Wild, J. Swithenbank, “Beam stop and vignetting effects in particle size measurements by laser diffraction,” Appl. Opt. 25, 3520–35261986).
[CrossRef] [PubMed]

P. Meyer, N. Chigier, “Drop size measurements using a Malvern 2200 particle sizer,” Atomiz. Spray Technol. 2, 261–268 (1986).

1977 (1)

J. Swithenbank, J. M. Beer, D. S. Taylor, D. Abbott, C. G. McCreath, “A laser diagnostic technique for the measurement of droplet and particle size distribution,” special issue on Experimental Diagnostic in Gas Phase Combustion Systems, Prog. Astronaut. Aeronaut. 53, 421–427 (1977).

1972 (1)

Abbott, D.

J. Swithenbank, J. M. Beer, D. S. Taylor, D. Abbott, C. G. McCreath, “A laser diagnostic technique for the measurement of droplet and particle size distribution,” special issue on Experimental Diagnostic in Gas Phase Combustion Systems, Prog. Astronaut. Aeronaut. 53, 421–427 (1977).

Abdelghani-Idrissi, A.

C. Özkul, D. Lebrun, D. Allano, A. Abdelghani-Idrissi, A. Leduc, “Processing of glass cylinder diffraction patterns scanned with a photodiode array: influence of the optical transfer function of diodes on dimensional measurements,” Opt. Eng. 30, 1855–1861 (1991).
[CrossRef]

Allano, D.

D. Lebrun, C. Özkul, D. Allano, A. Leduc, “Use of the moiré effect to improve the diameter measurements with charge coupled imagers,” J. Opt. (Paris) 22, 175–184 (1991).
[CrossRef]

C. Özkul, D. Lebrun, D. Allano, A. Abdelghani-Idrissi, A. Leduc, “Processing of glass cylinder diffraction patterns scanned with a photodiode array: influence of the optical transfer function of diodes on dimensional measurements,” Opt. Eng. 30, 1855–1861 (1991).
[CrossRef]

Beer, J. M.

J. Swithenbank, J. M. Beer, D. S. Taylor, D. Abbott, C. G. McCreath, “A laser diagnostic technique for the measurement of droplet and particle size distribution,” special issue on Experimental Diagnostic in Gas Phase Combustion Systems, Prog. Astronaut. Aeronaut. 53, 421–427 (1977).

Belaïd, S.

D. Lebrun, S. Belaïd, C. Özkul, K. F. Ren, G. Gréhan, “Enhancement of wire diameter measurements: comparison between Fraunhofer diffraction and Lorentz–Mie theory,” Opt. Eng. 35, 946–950 (1996).
[CrossRef]

Blaisot, J. B.

D. Lebrun, C. Özkul, C. E. Touil, J. B. Blaisot, K. Kleitz, “On-line particle size and velocity measurements by the analysis of defocused images: extended depth of field,” in Laser Dimensional Metrology: Recent Advances for Industrial Application, M. J. Downs, ed., Proc. SPIE2088, 139–148 (1993).

Castellini, C.

C. Castellini, F. Francini, G. Longobardi, E. Pampaloni, “On-line characterization of the shape and size of particles,” Part. Part. Syst. Charact. 10, 7–10 (1993).
[CrossRef]

Chigier, N.

P. Meyer, N. Chigier, “Drop size measurements using a Malvern 2200 particle sizer,” Atomiz. Spray Technol. 2, 261–268 (1986).

Cornillault, J.

Dodge, L. G.

Francini, F.

C. Castellini, F. Francini, G. Longobardi, E. Pampaloni, “On-line characterization of the shape and size of particles,” Part. Part. Syst. Charact. 10, 7–10 (1993).
[CrossRef]

Gharib, M.

M. Raffel, M. Gharib, O. Ronneberger, J. Kompenhans, “Feasibility study of three-dimensional PIV by correlating images of particles within parallel light sheet planes,” Exp. Fluids 19, 69–77 (1995).

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

Gouesbet, G.

K. F. Ren, D. Lebrun, C. Özkul, A. Kleitz, G. Gouesbet, G. Gréhan, “On the measurements of particles by imaging methods: theoretical and experimental aspects,” Part. Part. Syst. Charact. 13, 156–164 (1996).
[CrossRef]

Gréhan, G.

K. F. Ren, D. Lebrun, C. Özkul, A. Kleitz, G. Gouesbet, G. Gréhan, “On the measurements of particles by imaging methods: theoretical and experimental aspects,” Part. Part. Syst. Charact. 13, 156–164 (1996).
[CrossRef]

D. Lebrun, S. Belaïd, C. Özkul, K. F. Ren, G. Gréhan, “Enhancement of wire diameter measurements: comparison between Fraunhofer diffraction and Lorentz–Mie theory,” Opt. Eng. 35, 946–950 (1996).
[CrossRef]

Hardalupas, Y.

Hishida, K.

Kim, K. S.

K. S. Kim, S. S. Kim, “Drop sizing and depth-of-field correction in TV imaging,” Atomiz. Sprays 4, 65–78 (1994).

Kim, S. S.

K. S. Kim, S. S. Kim, “Drop sizing and depth-of-field correction in TV imaging,” Atomiz. Sprays 4, 65–78 (1994).

Kleitz, A.

K. F. Ren, D. Lebrun, C. Özkul, A. Kleitz, G. Gouesbet, G. Gréhan, “On the measurements of particles by imaging methods: theoretical and experimental aspects,” Part. Part. Syst. Charact. 13, 156–164 (1996).
[CrossRef]

D. Lebrun, C. Özkul, A. Kleitz, C. E. Touil, R. Roth, “Une sonde microvideo appliquée à la granulométrie,” J. Opt. (Paris) 26, 39–48 (1995).
[CrossRef]

Kleitz, K.

D. Lebrun, C. Özkul, C. E. Touil, J. B. Blaisot, K. Kleitz, “On-line particle size and velocity measurements by the analysis of defocused images: extended depth of field,” in Laser Dimensional Metrology: Recent Advances for Industrial Application, M. J. Downs, ed., Proc. SPIE2088, 139–148 (1993).

Kompenhans, J.

M. Raffel, M. Gharib, O. Ronneberger, J. Kompenhans, “Feasibility study of three-dimensional PIV by correlating images of particles within parallel light sheet planes,” Exp. Fluids 19, 69–77 (1995).

Lebrun, D.

D. Lebrun, S. Belaïd, C. Özkul, K. F. Ren, G. Gréhan, “Enhancement of wire diameter measurements: comparison between Fraunhofer diffraction and Lorentz–Mie theory,” Opt. Eng. 35, 946–950 (1996).
[CrossRef]

K. F. Ren, D. Lebrun, C. Özkul, A. Kleitz, G. Gouesbet, G. Gréhan, “On the measurements of particles by imaging methods: theoretical and experimental aspects,” Part. Part. Syst. Charact. 13, 156–164 (1996).
[CrossRef]

D. Lebrun, C. Özkul, A. Kleitz, C. E. Touil, R. Roth, “Une sonde microvideo appliquée à la granulométrie,” J. Opt. (Paris) 26, 39–48 (1995).
[CrossRef]

C. Özkul, D. Lebrun, D. Allano, A. Abdelghani-Idrissi, A. Leduc, “Processing of glass cylinder diffraction patterns scanned with a photodiode array: influence of the optical transfer function of diodes on dimensional measurements,” Opt. Eng. 30, 1855–1861 (1991).
[CrossRef]

D. Lebrun, C. Özkul, D. Allano, A. Leduc, “Use of the moiré effect to improve the diameter measurements with charge coupled imagers,” J. Opt. (Paris) 22, 175–184 (1991).
[CrossRef]

D. Lebrun, C. Özkul, C. E. Touil, J. B. Blaisot, K. Kleitz, “On-line particle size and velocity measurements by the analysis of defocused images: extended depth of field,” in Laser Dimensional Metrology: Recent Advances for Industrial Application, M. J. Downs, ed., Proc. SPIE2088, 139–148 (1993).

Leduc, A.

D. Lebrun, C. Özkul, D. Allano, A. Leduc, “Use of the moiré effect to improve the diameter measurements with charge coupled imagers,” J. Opt. (Paris) 22, 175–184 (1991).
[CrossRef]

C. Özkul, D. Lebrun, D. Allano, A. Abdelghani-Idrissi, A. Leduc, “Processing of glass cylinder diffraction patterns scanned with a photodiode array: influence of the optical transfer function of diodes on dimensional measurements,” Opt. Eng. 30, 1855–1861 (1991).
[CrossRef]

Longobardi, G.

C. Castellini, F. Francini, G. Longobardi, E. Pampaloni, “On-line characterization of the shape and size of particles,” Part. Part. Syst. Charact. 10, 7–10 (1993).
[CrossRef]

Maeda, M.

McCreath, C. G.

J. Swithenbank, J. M. Beer, D. S. Taylor, D. Abbott, C. G. McCreath, “A laser diagnostic technique for the measurement of droplet and particle size distribution,” special issue on Experimental Diagnostic in Gas Phase Combustion Systems, Prog. Astronaut. Aeronaut. 53, 421–427 (1977).

Meyer, P.

P. Meyer, N. Chigier, “Drop size measurements using a Malvern 2200 particle sizer,” Atomiz. Spray Technol. 2, 261–268 (1986).

Morikita, H.

Nikitopoulos, D. E.

A. L. Tassin, D. E. Nikitopoulos, “Nonintrusive measurements of bubble size and velocity,” Exp. Fluids 19, 121–132 (1995).
[CrossRef]

Özkul, C.

D. Lebrun, S. Belaïd, C. Özkul, K. F. Ren, G. Gréhan, “Enhancement of wire diameter measurements: comparison between Fraunhofer diffraction and Lorentz–Mie theory,” Opt. Eng. 35, 946–950 (1996).
[CrossRef]

K. F. Ren, D. Lebrun, C. Özkul, A. Kleitz, G. Gouesbet, G. Gréhan, “On the measurements of particles by imaging methods: theoretical and experimental aspects,” Part. Part. Syst. Charact. 13, 156–164 (1996).
[CrossRef]

D. Lebrun, C. Özkul, A. Kleitz, C. E. Touil, R. Roth, “Une sonde microvideo appliquée à la granulométrie,” J. Opt. (Paris) 26, 39–48 (1995).
[CrossRef]

C. Özkul, D. Lebrun, D. Allano, A. Abdelghani-Idrissi, A. Leduc, “Processing of glass cylinder diffraction patterns scanned with a photodiode array: influence of the optical transfer function of diodes on dimensional measurements,” Opt. Eng. 30, 1855–1861 (1991).
[CrossRef]

D. Lebrun, C. Özkul, D. Allano, A. Leduc, “Use of the moiré effect to improve the diameter measurements with charge coupled imagers,” J. Opt. (Paris) 22, 175–184 (1991).
[CrossRef]

D. Lebrun, C. Özkul, C. E. Touil, J. B. Blaisot, K. Kleitz, “On-line particle size and velocity measurements by the analysis of defocused images: extended depth of field,” in Laser Dimensional Metrology: Recent Advances for Industrial Application, M. J. Downs, ed., Proc. SPIE2088, 139–148 (1993).

Pampaloni, E.

C. Castellini, F. Francini, G. Longobardi, E. Pampaloni, “On-line characterization of the shape and size of particles,” Part. Part. Syst. Charact. 10, 7–10 (1993).
[CrossRef]

Pentland, A. P.

A. P. Pentland, “A new sense for depth of field,” IEEE Trans. Pattern Anal. Machine Intell. 9, 523–531 (1987).
[CrossRef]

Raffel, M.

M. Raffel, M. Gharib, O. Ronneberger, J. Kompenhans, “Feasibility study of three-dimensional PIV by correlating images of particles within parallel light sheet planes,” Exp. Fluids 19, 69–77 (1995).

Ren, K. F.

D. Lebrun, S. Belaïd, C. Özkul, K. F. Ren, G. Gréhan, “Enhancement of wire diameter measurements: comparison between Fraunhofer diffraction and Lorentz–Mie theory,” Opt. Eng. 35, 946–950 (1996).
[CrossRef]

K. F. Ren, D. Lebrun, C. Özkul, A. Kleitz, G. Gouesbet, G. Gréhan, “On the measurements of particles by imaging methods: theoretical and experimental aspects,” Part. Part. Syst. Charact. 13, 156–164 (1996).
[CrossRef]

Ronneberger, O.

M. Raffel, M. Gharib, O. Ronneberger, J. Kompenhans, “Feasibility study of three-dimensional PIV by correlating images of particles within parallel light sheet planes,” Exp. Fluids 19, 69–77 (1995).

Roth, R.

D. Lebrun, C. Özkul, A. Kleitz, C. E. Touil, R. Roth, “Une sonde microvideo appliquée à la granulométrie,” J. Opt. (Paris) 26, 39–48 (1995).
[CrossRef]

Swithenbank, J.

P. N. Wild, J. Swithenbank, “Beam stop and vignetting effects in particle size measurements by laser diffraction,” Appl. Opt. 25, 3520–35261986).
[CrossRef] [PubMed]

J. Swithenbank, J. M. Beer, D. S. Taylor, D. Abbott, C. G. McCreath, “A laser diagnostic technique for the measurement of droplet and particle size distribution,” special issue on Experimental Diagnostic in Gas Phase Combustion Systems, Prog. Astronaut. Aeronaut. 53, 421–427 (1977).

Tassin, A. L.

A. L. Tassin, D. E. Nikitopoulos, “Nonintrusive measurements of bubble size and velocity,” Exp. Fluids 19, 121–132 (1995).
[CrossRef]

Taylor, A. M. K. P.

Taylor, D. S.

J. Swithenbank, J. M. Beer, D. S. Taylor, D. Abbott, C. G. McCreath, “A laser diagnostic technique for the measurement of droplet and particle size distribution,” special issue on Experimental Diagnostic in Gas Phase Combustion Systems, Prog. Astronaut. Aeronaut. 53, 421–427 (1977).

Touil, C. E.

D. Lebrun, C. Özkul, A. Kleitz, C. E. Touil, R. Roth, “Une sonde microvideo appliquée à la granulométrie,” J. Opt. (Paris) 26, 39–48 (1995).
[CrossRef]

D. Lebrun, C. Özkul, C. E. Touil, J. B. Blaisot, K. Kleitz, “On-line particle size and velocity measurements by the analysis of defocused images: extended depth of field,” in Laser Dimensional Metrology: Recent Advances for Industrial Application, M. J. Downs, ed., Proc. SPIE2088, 139–148 (1993).

Vikram, C. S.

C. S. Vikram, Particle Field Holography (Cambridge U. Press, Cambridge, 1992).
[CrossRef]

Whitelaw, J. H.

Wild, P. N.

Willert, C. E.

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

Appl. Opt. (4)

Atomiz. Spray Technol. (1)

P. Meyer, N. Chigier, “Drop size measurements using a Malvern 2200 particle sizer,” Atomiz. Spray Technol. 2, 261–268 (1986).

Atomiz. Sprays (1)

K. S. Kim, S. S. Kim, “Drop sizing and depth-of-field correction in TV imaging,” Atomiz. Sprays 4, 65–78 (1994).

Exp. Fluids (3)

M. Raffel, M. Gharib, O. Ronneberger, J. Kompenhans, “Feasibility study of three-dimensional PIV by correlating images of particles within parallel light sheet planes,” Exp. Fluids 19, 69–77 (1995).

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

A. L. Tassin, D. E. Nikitopoulos, “Nonintrusive measurements of bubble size and velocity,” Exp. Fluids 19, 121–132 (1995).
[CrossRef]

IEEE Trans. Pattern Anal. Machine Intell. (1)

A. P. Pentland, “A new sense for depth of field,” IEEE Trans. Pattern Anal. Machine Intell. 9, 523–531 (1987).
[CrossRef]

J. Opt. (Paris) (2)

D. Lebrun, C. Özkul, A. Kleitz, C. E. Touil, R. Roth, “Une sonde microvideo appliquée à la granulométrie,” J. Opt. (Paris) 26, 39–48 (1995).
[CrossRef]

D. Lebrun, C. Özkul, D. Allano, A. Leduc, “Use of the moiré effect to improve the diameter measurements with charge coupled imagers,” J. Opt. (Paris) 22, 175–184 (1991).
[CrossRef]

Opt. Eng. (2)

C. Özkul, D. Lebrun, D. Allano, A. Abdelghani-Idrissi, A. Leduc, “Processing of glass cylinder diffraction patterns scanned with a photodiode array: influence of the optical transfer function of diodes on dimensional measurements,” Opt. Eng. 30, 1855–1861 (1991).
[CrossRef]

D. Lebrun, S. Belaïd, C. Özkul, K. F. Ren, G. Gréhan, “Enhancement of wire diameter measurements: comparison between Fraunhofer diffraction and Lorentz–Mie theory,” Opt. Eng. 35, 946–950 (1996).
[CrossRef]

Part. Part. Syst. Charact. (2)

C. Castellini, F. Francini, G. Longobardi, E. Pampaloni, “On-line characterization of the shape and size of particles,” Part. Part. Syst. Charact. 10, 7–10 (1993).
[CrossRef]

K. F. Ren, D. Lebrun, C. Özkul, A. Kleitz, G. Gouesbet, G. Gréhan, “On the measurements of particles by imaging methods: theoretical and experimental aspects,” Part. Part. Syst. Charact. 13, 156–164 (1996).
[CrossRef]

Prog. Astronaut. Aeronaut. (1)

J. Swithenbank, J. M. Beer, D. S. Taylor, D. Abbott, C. G. McCreath, “A laser diagnostic technique for the measurement of droplet and particle size distribution,” special issue on Experimental Diagnostic in Gas Phase Combustion Systems, Prog. Astronaut. Aeronaut. 53, 421–427 (1977).

Other (2)

D. Lebrun, C. Özkul, C. E. Touil, J. B. Blaisot, K. Kleitz, “On-line particle size and velocity measurements by the analysis of defocused images: extended depth of field,” in Laser Dimensional Metrology: Recent Advances for Industrial Application, M. J. Downs, ed., Proc. SPIE2088, 139–148 (1993).

C. S. Vikram, Particle Field Holography (Cambridge U. Press, Cambridge, 1992).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Schematic diagram of the experimental setup. The flow axis is parallel to the x axis.

Fig. 2
Fig. 2

Theoretical values of S and C plotted as functions of s . The dimensionless cross-section areas S and s are obtained by the normalization of S and s with respect to the PSF spatial parameter σ2.

Fig. 3
Fig. 3

Theoretical (solid curve) and experimental (symbols) variations of s/S plotted versus C for −25 mm ≤ z ≤ 25 mm.

Fig. 4
Fig. 4

Estimated diameters 2â plotted versus the defocusing distance z (a) without correction and (b) with correction.

Fig. 5
Fig. 5

Digitized images of a circular disk with (a) υτ = 0 μm and (b) υτ = 70 μm (2a = 100 μm).

Fig. 6
Fig. 6

Estimated diameters for different object velocities.

Fig. 7
Fig. 7

Typical power spectrum of a circular opaque-disk image.

Fig. 8
Fig. 8

Diameters estimated from the power-spectrum analysis.

Fig. 9
Fig. 9

Diameters estimated with the power-spectrum method for different velocities.

Equations (15)

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

I ( r ) = A ( r ) * h ( r ) ,
I n ( q ) = ( 1 ) n π 0 2 π exp [ q cos ( θ ) ] cos ( n θ ) d θ .
I 0 ( α q ) = α I 1 ( α q ) .
I ( r ) = 1 + exp ( 8 r 2 ) [ exp ( 8 a 2 ) I 0 ( 16 r a ) 1 ] 16 r ( 8 r 2 ) 0 a exp ( 8 ρ 2 ) I 1 ( 16 r ρ ) d ρ ,
r = r / σ , ρ = ρ / σ , a = a / σ .
C = I ( ) I ( 0 ) I ( ) + I ( 0 ) ,
C = 1 exp ( 8 a 2 ) 1 + exp ( 8 a 2 ) = tanh ( 4 a 2 ) .
s = ( s σ 2 ( z ) ) , S = ( S σ 2 ( z ) ) .
E υ ( x , y ) = τ / 2 τ / 2 I ( x υ t , y ) d t .
E υ ( x , y ) = τ I ( x , y ) * V ( x , y ) ,
E υ ( x , y ) = τ a ( x , y ) * h υ ( x , y ) ,
+ + h υ ( x , y ) d x d y = + + h ( x , y ) d x d y = 1 .
P ( ω , z ) = [ 2 π a 2 J 1 ( 2 π ω a ) 2 π ω a δ ( ω ) ] 2 H 2 ( ω , z ) ,
P ( ω , z ) P 0 = π 2 a 4 H 0 2 ,
H 0 = 0 0 2 π h ( r , θ , z ) d r d θ .

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