Abstract

Digital holography, which consists of both acquiring the hologram image in a digital camera and numerically reconstructing the information, offers new and faster ways to make the most of a hologram. We describe a new method to determine the rough size of particles in an in-line hologram. This method relies on a property that is specific to interference patterns in Fresnel holograms: Self-correlation of a hologram provides access to size information. The proposed method is both simple and fast and gives results with acceptable precision. It suppresses all the problems related to the numerical depth of focus when large depth volumes are analyzed.

© 2006 Optical Society of America

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  1. B. J. Thompson, "A new method of measuring particle size by diffraction techniques," Jpn. J. Appl. Phys. 4, 302-307 (1965).
    [CrossRef]
  2. C. S. Vikram, Particle Field Holography (Cambridge U. Press, 1992).
  3. K. D. Hinsch, "Holographic particle image velocimetry," Meas. Sci. Technol. 13, R61-R72 (2002).
    [CrossRef]
  4. See the special feature issue K. D. Hinsch and S. F. Herrmann, eds., "Holographic particle image velocimetry," Meas. Sci. Technol. 15, 601-769 (2004).
  5. J. Müller, V. Kebbel, and W. Jüptner, "Characterization of spatial particle distributions in a spray-forming process using digital holography," Meas. Sci. Technol. 15, 706-710 (2004).
    [CrossRef]
  6. G. Pan and H. Meng, "Digital holography of particle fields: reconstruction by use of complex amplitude," Appl. Opt. 42, 827-833 (2003).
    [CrossRef] [PubMed]
  7. C. Fournier, C. Ducottet, and T. Fournel, "Digital in-line holography: influence of the reconstruction function on the axial profile of a reconstructed particle image," Meas. Sci. Technol. 15, 686-693 (2004).
    [CrossRef]
  8. T. M. Kreis, M. Adams, and W. Juptner, "Methods of digital holography: a comparison," in Optical Inspection and Micromeasurements II, C. Gorecki, ed., Proc. SPIE 3098, 224-233 (1997).
    [CrossRef]
  9. S. Murata and N. Yasuda, "Potential of digital holography in particle measurement," Opt. Laser Technol. 32, 567-574 (2000).
    [CrossRef]
  10. M. Malek, S. Coëtmellec, D. Allano, and D. Lebrun, "Formulation of in-line holography process by a linear shift invariant system: application to the measurement of fiber diameter," Opt. Commun. 223, 263-271 (2003).
    [CrossRef]
  11. H. Royer, "An application of high-speed microholography: the metrology of fogs," Nouv. Rev. Opt. 5, 87-93 (1974).
    [CrossRef]
  12. L. Onural and P. D. Scott, "Digital decoding of in-line holograms," Opt. Eng. 26, 1124-1132 (1987).
  13. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
  14. C. Buraga-Lefebvre, S. Coëtmellec, D. Lebrun, and C. Özkul, "Application of wavelet transform to hologram analysis: three-dimensional location of particles," Opt. Lasers Eng. 33, 409-421 (2000).
    [CrossRef]
  15. J. Serra, Image Analysis and Mathematical Morphology (Academic, 1982).
  16. D. Jeulin, "Random models for the morphological analysis of powders," J. Microsc. 172, 13-21 (1993).
    [CrossRef]
  17. M. Liebling, T. Blu, and M. Unser, "Fresnelets: new multiresolution wavelet bases for digital holography," IEEE Trans. Image Process. 12, 29-43 (2003).
    [CrossRef]
  18. T.-C. Poon and T. Kim, "Optical image recognition of three-dimensional objects," Appl. Opt. 38, 370-381 (1999).
    [CrossRef]
  19. T. Kim and T.-C. Poon, "Three-dimensional matching by use of phase-only holographic information and the Wigner distribution," J. Opt. Soc. Am. A 17, 2520-2528 (2000).
    [CrossRef]
  20. C. Fournier, C. Barat, C. Ducottet, and T. Fournel, "Digital holography applied to PIV: hologram reconstruction and selection of a cloud of particles in the reconstructed volume," presented at the Fourth Pacific Symposium on Flow Visualization and Image Processing, Chamonix, France, 2-5 June 2003, paper F4093.

2004 (2)

C. Fournier, C. Ducottet, and T. Fournel, "Digital in-line holography: influence of the reconstruction function on the axial profile of a reconstructed particle image," Meas. Sci. Technol. 15, 686-693 (2004).
[CrossRef]

J. Müller, V. Kebbel, and W. Jüptner, "Characterization of spatial particle distributions in a spray-forming process using digital holography," Meas. Sci. Technol. 15, 706-710 (2004).
[CrossRef]

2003 (3)

G. Pan and H. Meng, "Digital holography of particle fields: reconstruction by use of complex amplitude," Appl. Opt. 42, 827-833 (2003).
[CrossRef] [PubMed]

M. Liebling, T. Blu, and M. Unser, "Fresnelets: new multiresolution wavelet bases for digital holography," IEEE Trans. Image Process. 12, 29-43 (2003).
[CrossRef]

M. Malek, S. Coëtmellec, D. Allano, and D. Lebrun, "Formulation of in-line holography process by a linear shift invariant system: application to the measurement of fiber diameter," Opt. Commun. 223, 263-271 (2003).
[CrossRef]

2002 (1)

K. D. Hinsch, "Holographic particle image velocimetry," Meas. Sci. Technol. 13, R61-R72 (2002).
[CrossRef]

2000 (3)

T. Kim and T.-C. Poon, "Three-dimensional matching by use of phase-only holographic information and the Wigner distribution," J. Opt. Soc. Am. A 17, 2520-2528 (2000).
[CrossRef]

S. Murata and N. Yasuda, "Potential of digital holography in particle measurement," Opt. Laser Technol. 32, 567-574 (2000).
[CrossRef]

C. Buraga-Lefebvre, S. Coëtmellec, D. Lebrun, and C. Özkul, "Application of wavelet transform to hologram analysis: three-dimensional location of particles," Opt. Lasers Eng. 33, 409-421 (2000).
[CrossRef]

1999 (1)

1997 (1)

T. M. Kreis, M. Adams, and W. Juptner, "Methods of digital holography: a comparison," in Optical Inspection and Micromeasurements II, C. Gorecki, ed., Proc. SPIE 3098, 224-233 (1997).
[CrossRef]

1993 (1)

D. Jeulin, "Random models for the morphological analysis of powders," J. Microsc. 172, 13-21 (1993).
[CrossRef]

1992 (1)

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

1987 (1)

L. Onural and P. D. Scott, "Digital decoding of in-line holograms," Opt. Eng. 26, 1124-1132 (1987).

1974 (1)

H. Royer, "An application of high-speed microholography: the metrology of fogs," Nouv. Rev. Opt. 5, 87-93 (1974).
[CrossRef]

1965 (1)

B. J. Thompson, "A new method of measuring particle size by diffraction techniques," Jpn. J. Appl. Phys. 4, 302-307 (1965).
[CrossRef]

Adams, M.

T. M. Kreis, M. Adams, and W. Juptner, "Methods of digital holography: a comparison," in Optical Inspection and Micromeasurements II, C. Gorecki, ed., Proc. SPIE 3098, 224-233 (1997).
[CrossRef]

Allano, D.

M. Malek, S. Coëtmellec, D. Allano, and D. Lebrun, "Formulation of in-line holography process by a linear shift invariant system: application to the measurement of fiber diameter," Opt. Commun. 223, 263-271 (2003).
[CrossRef]

Barat, C.

C. Fournier, C. Barat, C. Ducottet, and T. Fournel, "Digital holography applied to PIV: hologram reconstruction and selection of a cloud of particles in the reconstructed volume," presented at the Fourth Pacific Symposium on Flow Visualization and Image Processing, Chamonix, France, 2-5 June 2003, paper F4093.

Blu, T.

M. Liebling, T. Blu, and M. Unser, "Fresnelets: new multiresolution wavelet bases for digital holography," IEEE Trans. Image Process. 12, 29-43 (2003).
[CrossRef]

Buraga-Lefebvre, C.

C. Buraga-Lefebvre, S. Coëtmellec, D. Lebrun, and C. Özkul, "Application of wavelet transform to hologram analysis: three-dimensional location of particles," Opt. Lasers Eng. 33, 409-421 (2000).
[CrossRef]

Coëtmellec, S.

M. Malek, S. Coëtmellec, D. Allano, and D. Lebrun, "Formulation of in-line holography process by a linear shift invariant system: application to the measurement of fiber diameter," Opt. Commun. 223, 263-271 (2003).
[CrossRef]

C. Buraga-Lefebvre, S. Coëtmellec, D. Lebrun, and C. Özkul, "Application of wavelet transform to hologram analysis: three-dimensional location of particles," Opt. Lasers Eng. 33, 409-421 (2000).
[CrossRef]

Ducottet, C.

C. Fournier, C. Ducottet, and T. Fournel, "Digital in-line holography: influence of the reconstruction function on the axial profile of a reconstructed particle image," Meas. Sci. Technol. 15, 686-693 (2004).
[CrossRef]

C. Fournier, C. Barat, C. Ducottet, and T. Fournel, "Digital holography applied to PIV: hologram reconstruction and selection of a cloud of particles in the reconstructed volume," presented at the Fourth Pacific Symposium on Flow Visualization and Image Processing, Chamonix, France, 2-5 June 2003, paper F4093.

Fournel, T.

C. Fournier, C. Ducottet, and T. Fournel, "Digital in-line holography: influence of the reconstruction function on the axial profile of a reconstructed particle image," Meas. Sci. Technol. 15, 686-693 (2004).
[CrossRef]

C. Fournier, C. Barat, C. Ducottet, and T. Fournel, "Digital holography applied to PIV: hologram reconstruction and selection of a cloud of particles in the reconstructed volume," presented at the Fourth Pacific Symposium on Flow Visualization and Image Processing, Chamonix, France, 2-5 June 2003, paper F4093.

Fournier, C.

C. Fournier, C. Ducottet, and T. Fournel, "Digital in-line holography: influence of the reconstruction function on the axial profile of a reconstructed particle image," Meas. Sci. Technol. 15, 686-693 (2004).
[CrossRef]

C. Fournier, C. Barat, C. Ducottet, and T. Fournel, "Digital holography applied to PIV: hologram reconstruction and selection of a cloud of particles in the reconstructed volume," presented at the Fourth Pacific Symposium on Flow Visualization and Image Processing, Chamonix, France, 2-5 June 2003, paper F4093.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Herrmann, S. F.

See the special feature issue K. D. Hinsch and S. F. Herrmann, eds., "Holographic particle image velocimetry," Meas. Sci. Technol. 15, 601-769 (2004).

Hinsch, K. D.

K. D. Hinsch, "Holographic particle image velocimetry," Meas. Sci. Technol. 13, R61-R72 (2002).
[CrossRef]

See the special feature issue K. D. Hinsch and S. F. Herrmann, eds., "Holographic particle image velocimetry," Meas. Sci. Technol. 15, 601-769 (2004).

Jeulin, D.

D. Jeulin, "Random models for the morphological analysis of powders," J. Microsc. 172, 13-21 (1993).
[CrossRef]

Juptner, W.

T. M. Kreis, M. Adams, and W. Juptner, "Methods of digital holography: a comparison," in Optical Inspection and Micromeasurements II, C. Gorecki, ed., Proc. SPIE 3098, 224-233 (1997).
[CrossRef]

Jüptner, W.

J. Müller, V. Kebbel, and W. Jüptner, "Characterization of spatial particle distributions in a spray-forming process using digital holography," Meas. Sci. Technol. 15, 706-710 (2004).
[CrossRef]

Kebbel, V.

J. Müller, V. Kebbel, and W. Jüptner, "Characterization of spatial particle distributions in a spray-forming process using digital holography," Meas. Sci. Technol. 15, 706-710 (2004).
[CrossRef]

Kim, T.

Kreis, T. M.

T. M. Kreis, M. Adams, and W. Juptner, "Methods of digital holography: a comparison," in Optical Inspection and Micromeasurements II, C. Gorecki, ed., Proc. SPIE 3098, 224-233 (1997).
[CrossRef]

Lebrun, D.

M. Malek, S. Coëtmellec, D. Allano, and D. Lebrun, "Formulation of in-line holography process by a linear shift invariant system: application to the measurement of fiber diameter," Opt. Commun. 223, 263-271 (2003).
[CrossRef]

C. Buraga-Lefebvre, S. Coëtmellec, D. Lebrun, and C. Özkul, "Application of wavelet transform to hologram analysis: three-dimensional location of particles," Opt. Lasers Eng. 33, 409-421 (2000).
[CrossRef]

Liebling, M.

M. Liebling, T. Blu, and M. Unser, "Fresnelets: new multiresolution wavelet bases for digital holography," IEEE Trans. Image Process. 12, 29-43 (2003).
[CrossRef]

Malek, M.

M. Malek, S. Coëtmellec, D. Allano, and D. Lebrun, "Formulation of in-line holography process by a linear shift invariant system: application to the measurement of fiber diameter," Opt. Commun. 223, 263-271 (2003).
[CrossRef]

Meng, H.

Müller, J.

J. Müller, V. Kebbel, and W. Jüptner, "Characterization of spatial particle distributions in a spray-forming process using digital holography," Meas. Sci. Technol. 15, 706-710 (2004).
[CrossRef]

Murata, S.

S. Murata and N. Yasuda, "Potential of digital holography in particle measurement," Opt. Laser Technol. 32, 567-574 (2000).
[CrossRef]

Onural, L.

L. Onural and P. D. Scott, "Digital decoding of in-line holograms," Opt. Eng. 26, 1124-1132 (1987).

Özkul, C.

C. Buraga-Lefebvre, S. Coëtmellec, D. Lebrun, and C. Özkul, "Application of wavelet transform to hologram analysis: three-dimensional location of particles," Opt. Lasers Eng. 33, 409-421 (2000).
[CrossRef]

Pan, G.

Poon, T.-C.

Royer, H.

H. Royer, "An application of high-speed microholography: the metrology of fogs," Nouv. Rev. Opt. 5, 87-93 (1974).
[CrossRef]

Scott, P. D.

L. Onural and P. D. Scott, "Digital decoding of in-line holograms," Opt. Eng. 26, 1124-1132 (1987).

Serra, J.

J. Serra, Image Analysis and Mathematical Morphology (Academic, 1982).

Thompson, B. J.

B. J. Thompson, "A new method of measuring particle size by diffraction techniques," Jpn. J. Appl. Phys. 4, 302-307 (1965).
[CrossRef]

Unser, M.

M. Liebling, T. Blu, and M. Unser, "Fresnelets: new multiresolution wavelet bases for digital holography," IEEE Trans. Image Process. 12, 29-43 (2003).
[CrossRef]

Vikram, C. S.

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

Yasuda, N.

S. Murata and N. Yasuda, "Potential of digital holography in particle measurement," Opt. Laser Technol. 32, 567-574 (2000).
[CrossRef]

Appl. Opt. (2)

IEEE Trans. Image Process. (1)

M. Liebling, T. Blu, and M. Unser, "Fresnelets: new multiresolution wavelet bases for digital holography," IEEE Trans. Image Process. 12, 29-43 (2003).
[CrossRef]

J. Microsc. (1)

D. Jeulin, "Random models for the morphological analysis of powders," J. Microsc. 172, 13-21 (1993).
[CrossRef]

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

Jpn. J. Appl. Phys. (1)

B. J. Thompson, "A new method of measuring particle size by diffraction techniques," Jpn. J. Appl. Phys. 4, 302-307 (1965).
[CrossRef]

Meas. Sci. Technol. (3)

K. D. Hinsch, "Holographic particle image velocimetry," Meas. Sci. Technol. 13, R61-R72 (2002).
[CrossRef]

C. Fournier, C. Ducottet, and T. Fournel, "Digital in-line holography: influence of the reconstruction function on the axial profile of a reconstructed particle image," Meas. Sci. Technol. 15, 686-693 (2004).
[CrossRef]

J. Müller, V. Kebbel, and W. Jüptner, "Characterization of spatial particle distributions in a spray-forming process using digital holography," Meas. Sci. Technol. 15, 706-710 (2004).
[CrossRef]

Nouv. Rev. Opt. (1)

H. Royer, "An application of high-speed microholography: the metrology of fogs," Nouv. Rev. Opt. 5, 87-93 (1974).
[CrossRef]

Opt. Commun. (1)

M. Malek, S. Coëtmellec, D. Allano, and D. Lebrun, "Formulation of in-line holography process by a linear shift invariant system: application to the measurement of fiber diameter," Opt. Commun. 223, 263-271 (2003).
[CrossRef]

Opt. Eng. (1)

L. Onural and P. D. Scott, "Digital decoding of in-line holograms," Opt. Eng. 26, 1124-1132 (1987).

Opt. Laser Technol. (1)

S. Murata and N. Yasuda, "Potential of digital holography in particle measurement," Opt. Laser Technol. 32, 567-574 (2000).
[CrossRef]

Opt. Lasers Eng. (1)

C. Buraga-Lefebvre, S. Coëtmellec, D. Lebrun, and C. Özkul, "Application of wavelet transform to hologram analysis: three-dimensional location of particles," Opt. Lasers Eng. 33, 409-421 (2000).
[CrossRef]

Proc. SPIE (1)

T. M. Kreis, M. Adams, and W. Juptner, "Methods of digital holography: a comparison," in Optical Inspection and Micromeasurements II, C. Gorecki, ed., Proc. SPIE 3098, 224-233 (1997).
[CrossRef]

Other (5)

See the special feature issue K. D. Hinsch and S. F. Herrmann, eds., "Holographic particle image velocimetry," Meas. Sci. Technol. 15, 601-769 (2004).

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

J. Serra, Image Analysis and Mathematical Morphology (Academic, 1982).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

C. Fournier, C. Barat, C. Ducottet, and T. Fournel, "Digital holography applied to PIV: hologram reconstruction and selection of a cloud of particles in the reconstructed volume," presented at the Fourth Pacific Symposium on Flow Visualization and Image Processing, Chamonix, France, 2-5 June 2003, paper F4093.

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Figures (11)

Fig. 1
Fig. 1

(Color online) In-line digital holography setup.

Fig. 2
Fig. 2

Hologram information coding: line profile (solid curve), Fresnel radial frequency-modulation function (dotted–dashed curve) and the diffraction envelope (dashed curve).

Fig. 3
Fig. 3

(a) Patterns of a particle with constant radius r for different recording distances z and (b) their associated self-correlation profile.

Fig. 4
Fig. 4

Centered hologram self-correlation (numerical simulation).

Fig. 5
Fig. 5

Hologram processing chain. (a) Classical hologram processing chain for size measurements. (b) Proposed direct particle-size extraction scheme. FFT, fast Fourier transform.

Fig. 6
Fig. 6

(Color online) (a) Numerically generated hologram and (b) its self-correlation profile.

Fig. 7
Fig. 7

(Color online) Breakdown of Fig. 6(b) correlation profile into its four constituent terms: (a) particle-aperture self-correlation term, (b) twin self-correlation term, (c) cross-correlation term, and (d) nonlinear term.

Fig. 8
Fig. 8

Self-correlation of a disk.

Fig. 9
Fig. 9

Application of the size-extraction method on numerically generated holograms. (a) Parameters used in the numerical simulations. (b) One of the numerically generated holograms. (c) Correlation profiles and best-fitting curves for holograms with particles from ϕ = 70 to 130 μm.

Fig. 10
Fig. 10

Experimental result for a hologram of a water spray: (a) Experimental digital hologrom and (b) correlation profile computed on the hologram in (a).

Fig. 11
Fig. 11

Reconstructed volume from the experimental hologram shown in Fig. 10.

Tables (2)

Tables Icon

Table 1 Results of the Correlation Method on Numerically Generated Holograms a

Tables Icon

Table 2 Positions and Sizes of the Particles in the Experimental Hologram Shown in Fig. 10(a) a

Equations (9)

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

A z r ̲ = I H h z r ̲ ,
A z ̲ = t i h z i ̲ = 1 ϑ r i h z i ̲ δ x i , y i ,
A z ̲ 1 i = 1 N ϑ r i h z i ̲ δ x i , y i .
I H = 1 2 i = 1 N ϑ r i ( h z i ̲ ) δ x i , y i + i = 1 N j = 1 N ( ϑ r i h z i ̲ δ x i , y i ) ( ϑ r j h −z j ̲ δ x j , y j ) ,
I H 1 2 i = 1 N ϑ r i ( h z i ̲ ) δ x i , y i .
I ˜ H I ˜ H = 2 i = 1 N ϑ r i ϑ r i
+ 2 i = 1 N ϑ r i ϑ r i ( h 2z i ̲ )
+ 4 i = 1 N j = 1 j i N ϑ r i ϑ r j ( h z i ̲ ) ( h z j ̲ ) δ x i x j , y i y j .
C r ( h ) = 2 r 2 [ arccos ( h 2 r ) h 1 h 2 ( 2 r ) 2 2 r ],

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