Abstract

We propose a microparticle localization scheme in digital holography. Most conventional digital holography methods are based on Fresnel transform and present several problems such as twin-image noise, border effects, and other effects. To avoid these difficulties, we propose an inverse-problem approach, which yields the optimal particle set that best models the observed hologram image. We resolve this global optimization problem by conventional particle detection followed by a local refinement for each particle. Results for both simulated and real digital holograms show strong improvement in the localization of the particles, particularly along the depth dimension. In our simulations, the position precision is 1μm rms. Our results also show that the localization precision does not deteriorate for particles near the edge of the field of view.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. B. J. Thompson, "A new method of measuring particle size by diffraction techniques," Jpn. J. Appl. Phys. 4, 302-307 (1965).
  2. C. S. Vikram, ed., Selected Papers on Holographic Particle Diagnostics, SPIE Milestone Series, Vol. MS21 (1990).
  3. K. D. Hinsch, "Holographic particle image velocimetry," Meas. Sci. Technol. 13, R61-R72 (2002).
    [CrossRef]
  4. T. M. Kreis, M. Adams, and W. Jüptner, Methods of Digital Holography: A Comparison, SPIE (Munich, Germany, 1997).
  5. M. Liebling, T. Blu, and M. Unser, "Fresnelets: new multiresolution wavelet bases for digital holography," IEEE Trans. Image Process. 12, 29-43 (2003).
    [CrossRef]
  6. 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]
  7. W. Yang, A. B. Kostinski, and R. A. Shaw, "Depth-of-focus reduction for digital in-line holography of particle fields," Opt. Lett. 30, 1303-1305 (2005).
    [CrossRef] [PubMed]
  8. L. Denis, C. Fournier, T. Fournel, and C. Ducottet, "Twin-image noise reduction by phase retrieval in in-line digital holography," Proc. SPIE 5914, 148-161 (2005).
  9. S. Murata and N. Yasuda, "Development of full-volume digital holography for particle measurement," in Optical Methods and Data Processing in Heat and Fluid Flow, C.Greated, J.Buick, and J.Cosgrove, eds., (Professional Engineering Publishing, 2002), pp. 69-77.
  10. M. Malek, D. Allano, S. Coëtmellec, and D. Lebrun, "Digital in-line holography: influence of the shadow density on particle field extraction," Opt. Express 12, 2270-2280 (2004).
    [CrossRef] [PubMed]
  11. G. Pan and H. Meng, "Digital holography of particle fields: reconstruction by use of complex amplitude," Appl. Opt. 42, 827-833 (2003).
    [CrossRef] [PubMed]
  12. S. Murata and N. Takeuchi, "A neural network approach to the detection of the depth of tracer particles from in-line hologram patterns," IMechE Conf. Trans. 53, 377-382 (1996).
  13. L. Denis, C. Fournier, T. Fournel, C. Ducottet, and D. Jeulin, "Direct extraction of mean particle size from a digital hologram," Appl. Opt. 45, 944-952 (2006).
    [CrossRef] [PubMed]
  14. C. S. Vikram, Particle Field Holography (Cambridge U. Press, 1992).
    [CrossRef]
  15. S. Sotthivirat and J. A. Fessler, "Penalized-likelihood image reconstruction for digital holography," J. Opt. Soc. Am. A 21, 737-750 (2004).
    [CrossRef]
  16. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
  17. G. A. Tayler and B. J. Thompson, "Fraunhofer holography applied to particle size analysis: a reassessment," Opt. Acta 23, 261-304 (1976).
  18. J. J. Moré and D. C. Sorensen, "Computing a trust region step," SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. 4, 553-572 (1983).
    [CrossRef]

2006 (1)

2005 (2)

W. Yang, A. B. Kostinski, and R. A. Shaw, "Depth-of-focus reduction for digital in-line holography of particle fields," Opt. Lett. 30, 1303-1305 (2005).
[CrossRef] [PubMed]

L. Denis, C. Fournier, T. Fournel, and C. Ducottet, "Twin-image noise reduction by phase retrieval in in-line digital holography," Proc. SPIE 5914, 148-161 (2005).

2004 (3)

2003 (2)

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]

2002 (2)

S. Murata and N. Yasuda, "Development of full-volume digital holography for particle measurement," in Optical Methods and Data Processing in Heat and Fluid Flow, C.Greated, J.Buick, and J.Cosgrove, eds., (Professional Engineering Publishing, 2002), pp. 69-77.

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

1997 (1)

T. M. Kreis, M. Adams, and W. Jüptner, Methods of Digital Holography: A Comparison, SPIE (Munich, Germany, 1997).

1996 (2)

S. Murata and N. Takeuchi, "A neural network approach to the detection of the depth of tracer particles from in-line hologram patterns," IMechE Conf. Trans. 53, 377-382 (1996).

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

1992 (1)

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

1990 (1)

C. S. Vikram, ed., Selected Papers on Holographic Particle Diagnostics, SPIE Milestone Series, Vol. MS21 (1990).

1983 (1)

J. J. Moré and D. C. Sorensen, "Computing a trust region step," SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. 4, 553-572 (1983).
[CrossRef]

1976 (1)

G. A. Tayler and B. J. Thompson, "Fraunhofer holography applied to particle size analysis: a reassessment," Opt. Acta 23, 261-304 (1976).

1965 (1)

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

Adams, M.

T. M. Kreis, M. Adams, and W. Jüptner, Methods of Digital Holography: A Comparison, SPIE (Munich, Germany, 1997).

Allano, D.

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]

Coëtmellec, S.

Denis, L.

L. Denis, C. Fournier, T. Fournel, C. Ducottet, and D. Jeulin, "Direct extraction of mean particle size from a digital hologram," Appl. Opt. 45, 944-952 (2006).
[CrossRef] [PubMed]

L. Denis, C. Fournier, T. Fournel, and C. Ducottet, "Twin-image noise reduction by phase retrieval in in-line digital holography," Proc. SPIE 5914, 148-161 (2005).

Ducottet, C.

L. Denis, C. Fournier, T. Fournel, C. Ducottet, and D. Jeulin, "Direct extraction of mean particle size from a digital hologram," Appl. Opt. 45, 944-952 (2006).
[CrossRef] [PubMed]

L. Denis, C. Fournier, T. Fournel, and C. Ducottet, "Twin-image noise reduction by phase retrieval in in-line digital holography," Proc. SPIE 5914, 148-161 (2005).

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]

Fessler, J. A.

Fournel, T.

L. Denis, C. Fournier, T. Fournel, C. Ducottet, and D. Jeulin, "Direct extraction of mean particle size from a digital hologram," Appl. Opt. 45, 944-952 (2006).
[CrossRef] [PubMed]

L. Denis, C. Fournier, T. Fournel, and C. Ducottet, "Twin-image noise reduction by phase retrieval in in-line digital holography," Proc. SPIE 5914, 148-161 (2005).

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]

Fournier, C.

L. Denis, C. Fournier, T. Fournel, C. Ducottet, and D. Jeulin, "Direct extraction of mean particle size from a digital hologram," Appl. Opt. 45, 944-952 (2006).
[CrossRef] [PubMed]

L. Denis, C. Fournier, T. Fournel, and C. Ducottet, "Twin-image noise reduction by phase retrieval in in-line digital holography," Proc. SPIE 5914, 148-161 (2005).

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]

Goodman, J. W.

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

Hinsch, K. D.

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

Jeulin, D.

Jüptner, W.

T. M. Kreis, M. Adams, and W. Jüptner, Methods of Digital Holography: A Comparison, SPIE (Munich, Germany, 1997).

Kostinski, A. B.

Kreis, T. M.

T. M. Kreis, M. Adams, and W. Jüptner, Methods of Digital Holography: A Comparison, SPIE (Munich, Germany, 1997).

Lebrun, D.

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.

Meng, H.

Moré, J. J.

J. J. Moré and D. C. Sorensen, "Computing a trust region step," SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. 4, 553-572 (1983).
[CrossRef]

Murata, S.

S. Murata and N. Yasuda, "Development of full-volume digital holography for particle measurement," in Optical Methods and Data Processing in Heat and Fluid Flow, C.Greated, J.Buick, and J.Cosgrove, eds., (Professional Engineering Publishing, 2002), pp. 69-77.

S. Murata and N. Takeuchi, "A neural network approach to the detection of the depth of tracer particles from in-line hologram patterns," IMechE Conf. Trans. 53, 377-382 (1996).

Pan, G.

Shaw, R. A.

Sorensen, D. C.

J. J. Moré and D. C. Sorensen, "Computing a trust region step," SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. 4, 553-572 (1983).
[CrossRef]

Sotthivirat, S.

Takeuchi, N.

S. Murata and N. Takeuchi, "A neural network approach to the detection of the depth of tracer particles from in-line hologram patterns," IMechE Conf. Trans. 53, 377-382 (1996).

Tayler, G. A.

G. A. Tayler and B. J. Thompson, "Fraunhofer holography applied to particle size analysis: a reassessment," Opt. Acta 23, 261-304 (1976).

Thompson, B. J.

G. A. Tayler and B. J. Thompson, "Fraunhofer holography applied to particle size analysis: a reassessment," Opt. Acta 23, 261-304 (1976).

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

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).
[CrossRef]

C. S. Vikram, ed., Selected Papers on Holographic Particle Diagnostics, SPIE Milestone Series, Vol. MS21 (1990).

Yang, W.

Yasuda, N.

S. Murata and N. Yasuda, "Development of full-volume digital holography for particle measurement," in Optical Methods and Data Processing in Heat and Fluid Flow, C.Greated, J.Buick, and J.Cosgrove, eds., (Professional Engineering Publishing, 2002), pp. 69-77.

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]

IMechE Conf. Trans. (1)

S. Murata and N. Takeuchi, "A neural network approach to the detection of the depth of tracer particles from in-line hologram patterns," IMechE Conf. Trans. 53, 377-382 (1996).

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).

Meas. Sci. Technol. (2)

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]

Opt. Acta (1)

G. A. Tayler and B. J. Thompson, "Fraunhofer holography applied to particle size analysis: a reassessment," Opt. Acta 23, 261-304 (1976).

Opt. Express (1)

Opt. Lett. (1)

SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. (1)

J. J. Moré and D. C. Sorensen, "Computing a trust region step," SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. 4, 553-572 (1983).
[CrossRef]

Other (6)

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

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

L. Denis, C. Fournier, T. Fournel, and C. Ducottet, "Twin-image noise reduction by phase retrieval in in-line digital holography," Proc. SPIE 5914, 148-161 (2005).

S. Murata and N. Yasuda, "Development of full-volume digital holography for particle measurement," in Optical Methods and Data Processing in Heat and Fluid Flow, C.Greated, J.Buick, and J.Cosgrove, eds., (Professional Engineering Publishing, 2002), pp. 69-77.

T. M. Kreis, M. Adams, and W. Jüptner, Methods of Digital Holography: A Comparison, SPIE (Munich, Germany, 1997).

C. S. Vikram, ed., Selected Papers on Holographic Particle Diagnostics, SPIE Milestone Series, Vol. MS21 (1990).

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 (8)

Fig. 1
Fig. 1

In-line holography setup.

Fig. 2
Fig. 2

Notations used in the hologram model.

Fig. 3
Fig. 3

Synopsis of the method.

Fig. 4
Fig. 4

Small particle simulations. Left, 10 particles; right, 100 particles.

Fig. 5
Fig. 5

Pair of experimental holograms separated by a delay of 100 μ s .

Fig. 6
Fig. 6

Iterative particle removal in real hologram image.

Fig. 7
Fig. 7

Droplet jet reconstruction.

Fig. 8
Fig. 8

Measured diameter histogram.

Tables (1)

Tables Icon

Table 1 Rms Errors for the Estimated Particle Parameters in Several Simulation Configurations

Equations (32)

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

A j ̱ ( x , y ) = A 0 ̱ [ 1 η j ( ϑ j * h z j ̱ ) ( x x j , y y j ) ] ,
ϑ j ( x , y ) = { 1 , x 2 + y 2 r j 0 , x 2 + y 2 > r j ,
h z j ̱ ( x , y ) = 1 i λ z j exp ( i π λ z j ( x 2 + y 2 ) ) ,
A ̱ ( x , y ) = A 0 ̱ [ 1 j = 1 n η j ( ϑ j * h z j ̱ ) ( x x j , y y j ) ] .
( ϑ j * h z j ̱ ) ( x , y ) r j λ z j 2 x 2 + y 2 J 1 ( 2 π r j x 2 + y 2 λ z j ) h z j ̱ ( x , y ) ,
f j ̱ ( x , y ) = r j 2 i ρ j ( x , y ) J 1 ( 2 π r j ρ j ( x , y ) λ z j ) exp ( i π ρ j 2 ( x , y ) λ z j ) ,
A ̱ ( x , y ) = A 0 ̱ [ 1 j = 1 n η j f j ̱ ( x , y ) ] .
I ( x , y ) = γ A ̱ ( x , y ) 2 + I bg = γ A 0 ̱ 2 + I bg 2 γ A 0 ̱ 2 j = 1 n η j Re [ f j ̱ ( x , y ) ] + γ A 0 ̱ 2 i = 1 n j = 1 n η i f i ̱ ( x , y ) η j f j * ̱ ( x , y ) ,
2 j = 1 n η j Re [ f j ̱ ( x , y ) ] i = 1 n j = 1 n η i f i ̱ ( x , y ) η j f j * ̱ ( x , y )
I ( x , y ) = I 0 j = 1 n α j Re [ f j ̱ ( x , y ) ] ,
P n = k = 1 N pixel W k [ M n , k D k ] 2 ,
M n , k = I 0 j = 1 n α j Re [ f j ̱ ( X k , Y k ) ] ,
x = x ω , y = y ω , z = λ z ω 2 , r = r ω ,
g j ( x , y ) = Re [ f j ̱ ( ω x , ω y ) ] = r j 2 ρ j J 1 ( 2 π r j ρ j z j ) sin ( π ρ j 2 z j ) ,
M n , k = I 0 j = 1 n α j g j ( X k , Y k ) ,
R n 1 , k = D k + j = 1 n 1 α j g j ( X k , Y k ) ,
P n = k = 1 N pixel W k [ R n 1 , k I 0 + α n g n ( X k , Y k ) ] 2 .
P n + = P n I 0 = I 0 + , α n = α n + = k = 1 N pixel W k [ R n 1 , k I 0 + + α n + g n ( X k , Y k ) ] 2 ,
I 0 + = 1 Q n ( k W k G n , k 2 ) ( k W k R n 1 , k ) 1 Q n ( k W k G n , k ) ( k W k R n 1 , k G n , k ) ,
α n + = 1 Q n ( k W k G n , k ) ( k W k R n 1 , k ) 1 Q n ( k W k ) ( k W k R n 1 , k G n , k ) ,
Q n = ( k W k ) ( k W k G n , k 2 ) ( k W k G n , k ) 2 .
P n + θ = P n θ I 0 = I 0 + α n = α n + + α n + θ P n α n I 0 = I 0 + α n = α n + + I 0 + θ P n I 0 I 0 = I 0 + α n = α n + .
{ α n + , I 0 + } = arg min α n , I 0 P n ,
P n + θ = P n θ I 0 = I 0 + α n = α n + = 2 α n + k = 1 N pixel W k [ R n 1 , k I 0 + + α n + g n , k ] g n , k θ ,
g n , k x n = ( x n X k ) r n 2 ρ n , k 3 [ ϕ n , k J 0 ( ϕ n , k ) sin θ n , k 2 J 1 ( ϕ n , k ) ( sin θ n , k θ n , k cos θ n , k ) ] ,
g n , k y n = ( y n Y k ) r n 2 ρ n , k 3 [ ϕ n , k J 0 ( ϕ n , k ) sin θ n , k 2 J 1 ( ϕ n , k ) ( sin θ n , k θ n , k cos θ n , k ) ] ,
g n , k z n = r n 2 ρ n , k z n [ J 1 ( ϕ n , k ) ( sin θ n , k θ n , k cos θ n , k ) ϕ n , k J 0 ( ϕ n , k ) sin θ n , k ] ,
g n , k r n = π r n z n J 0 ( ϕ n , k ) sin θ n , k ,
θ n , k = π ρ n , k 2 z n ,
ϕ n , k = 2 π r n ρ n , k z n ,
ρ n , k = ( x n X k ) 2 + ( y n Y k ) 2 .
2 P n + θ 1 θ 2 2 α n + 2 k = 1 N pixel W k g n , k θ 1 g n , k θ 2 ,

Metrics