Abstract

Noise removal and lesser computational run time of the digital holographic numerical reconstruction procedure are the critical issues for effective and efficient identification of three-dimensional (3D) particle fields. The present study suggests an improved reconstruction procedure based on the superposition principle. The effectiveness of this proposed method is evaluated using both simulated and experimental data of a 3D particle field. Influence of object-particle number density and sample volume depth on the reconstructed particle field is investigated. There is a reduction in computational run time (as high as 50%) and significant increase in reconstruction effectiveness (as high as 7 times increase) due to the proposed method as compared to the literature (Opt. Express 18, 2426, 2010 and Opt. Express 12, 2270, 2004).

© 2012 Optical Society of America

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References

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  1. B. Javidi, F. Okano, and J. Y. Son, Three-Dimensional Imaging, Visualization, and Display (Springer, 2009).
  2. T. Latychevskaia and H. W. Fink, “Solution to the twin image problem in holography,” Phys. Rev. Lett. 98, 233901–233904 (2007).
    [CrossRef]
  3. Y. Zhang, G. Shen, A. Schröder, and J. Kompenhans, “Influence of some recording parameters on digital holographic particle image velocimetry,” Opt. Eng. 45, 075801 (2006).
    [CrossRef]
  4. S. Murata and N. Yasuda, “Potential of digital holography in particle measurement,” Opt. Laser Technol. 32, 567–574 (2000).
    [CrossRef]
  5. G. Pan and H. Meng, “Digital in-line holographic PIV for 3D particulate flow diagnostics,” in Proceedings of 4th International Symposium on Particle Image Velocimetry, Germany, September 17–192001, Paper 1008.
  6. G. Pan and H. Meng, “Digital holographic PIV for 3D flow measurement,” in Proceedings of 2002 ASME International Mechanical Engineering Congress & Exposition, New Orleans, Louisiana, 17–22 November2002, 33173.
  7. G. Pan and H. Meng, “Digital holography of particle fields: reconstruction by use of complex amplitude,” Appl. Opt. 42, 827–833 (2003).
    [CrossRef]
  8. V. R. Singh, G. Hegde, and A. Asundi, “Particle field imaging using digital in-line holography,” Curr. Sci. 96, 391–397 (2009).
  9. 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]
  10. T. Latychevskaia, F. Gehri, and H. W. Fink, “Depth-resolved holographic reconstructions by three-dimensional deconvolution,” Opt. Express 18, 22527–22544 (2010).
    [CrossRef]
  11. D. K. Singh and P. K. Panigrahi, “Improved digital holographic reconstruction algorithm for depth error reduction and elimination of out-of-focus particles,” Opt. Express 18, 2426–2448 (2010).
    [CrossRef]
  12. 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, 2270–2279 (2004).
    [CrossRef]
  13. R. Gonzalez and R. Woods, Digital Image Processing (Pearson Education, 2007).
  14. F. Monroy, O. Rincon, Y. M. Torres, and J. G. Sucerquia, “Quantitative assessment of lateral resolution improvement in digital holography,” Opt. Commun. 281, 3454–3460(2008).
    [CrossRef]

2010 (2)

2009 (1)

V. R. Singh, G. Hegde, and A. Asundi, “Particle field imaging using digital in-line holography,” Curr. Sci. 96, 391–397 (2009).

2008 (1)

F. Monroy, O. Rincon, Y. M. Torres, and J. G. Sucerquia, “Quantitative assessment of lateral resolution improvement in digital holography,” Opt. Commun. 281, 3454–3460(2008).
[CrossRef]

2007 (1)

T. Latychevskaia and H. W. Fink, “Solution to the twin image problem in holography,” Phys. Rev. Lett. 98, 233901–233904 (2007).
[CrossRef]

2006 (1)

Y. Zhang, G. Shen, A. Schröder, and J. Kompenhans, “Influence of some recording parameters on digital holographic particle image velocimetry,” Opt. Eng. 45, 075801 (2006).
[CrossRef]

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]

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, 2270–2279 (2004).
[CrossRef]

2003 (1)

2000 (1)

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

Allano, D.

Asundi, A.

V. R. Singh, G. Hegde, and A. Asundi, “Particle field imaging using digital in-line holography,” Curr. Sci. 96, 391–397 (2009).

Coëtmellec, S.

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]

Fink, H. W.

T. Latychevskaia, F. Gehri, and H. W. Fink, “Depth-resolved holographic reconstructions by three-dimensional deconvolution,” Opt. Express 18, 22527–22544 (2010).
[CrossRef]

T. Latychevskaia and H. W. Fink, “Solution to the twin image problem in holography,” Phys. Rev. Lett. 98, 233901–233904 (2007).
[CrossRef]

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]

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]

Gehri, F.

Gonzalez, R.

R. Gonzalez and R. Woods, Digital Image Processing (Pearson Education, 2007).

Hegde, G.

V. R. Singh, G. Hegde, and A. Asundi, “Particle field imaging using digital in-line holography,” Curr. Sci. 96, 391–397 (2009).

Javidi, B.

B. Javidi, F. Okano, and J. Y. Son, Three-Dimensional Imaging, Visualization, and Display (Springer, 2009).

Kompenhans, J.

Y. Zhang, G. Shen, A. Schröder, and J. Kompenhans, “Influence of some recording parameters on digital holographic particle image velocimetry,” Opt. Eng. 45, 075801 (2006).
[CrossRef]

Latychevskaia, T.

T. Latychevskaia, F. Gehri, and H. W. Fink, “Depth-resolved holographic reconstructions by three-dimensional deconvolution,” Opt. Express 18, 22527–22544 (2010).
[CrossRef]

T. Latychevskaia and H. W. Fink, “Solution to the twin image problem in holography,” Phys. Rev. Lett. 98, 233901–233904 (2007).
[CrossRef]

Lebrun, D.

Malek, M.

Meng, H.

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

G. Pan and H. Meng, “Digital holographic PIV for 3D flow measurement,” in Proceedings of 2002 ASME International Mechanical Engineering Congress & Exposition, New Orleans, Louisiana, 17–22 November2002, 33173.

G. Pan and H. Meng, “Digital in-line holographic PIV for 3D particulate flow diagnostics,” in Proceedings of 4th International Symposium on Particle Image Velocimetry, Germany, September 17–192001, Paper 1008.

Monroy, F.

F. Monroy, O. Rincon, Y. M. Torres, and J. G. Sucerquia, “Quantitative assessment of lateral resolution improvement in digital holography,” Opt. Commun. 281, 3454–3460(2008).
[CrossRef]

Murata, S.

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

Okano, F.

B. Javidi, F. Okano, and J. Y. Son, Three-Dimensional Imaging, Visualization, and Display (Springer, 2009).

Pan, G.

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

G. Pan and H. Meng, “Digital holographic PIV for 3D flow measurement,” in Proceedings of 2002 ASME International Mechanical Engineering Congress & Exposition, New Orleans, Louisiana, 17–22 November2002, 33173.

G. Pan and H. Meng, “Digital in-line holographic PIV for 3D particulate flow diagnostics,” in Proceedings of 4th International Symposium on Particle Image Velocimetry, Germany, September 17–192001, Paper 1008.

Panigrahi, P. K.

Rincon, O.

F. Monroy, O. Rincon, Y. M. Torres, and J. G. Sucerquia, “Quantitative assessment of lateral resolution improvement in digital holography,” Opt. Commun. 281, 3454–3460(2008).
[CrossRef]

Schröder, A.

Y. Zhang, G. Shen, A. Schröder, and J. Kompenhans, “Influence of some recording parameters on digital holographic particle image velocimetry,” Opt. Eng. 45, 075801 (2006).
[CrossRef]

Shen, G.

Y. Zhang, G. Shen, A. Schröder, and J. Kompenhans, “Influence of some recording parameters on digital holographic particle image velocimetry,” Opt. Eng. 45, 075801 (2006).
[CrossRef]

Singh, D. K.

Singh, V. R.

V. R. Singh, G. Hegde, and A. Asundi, “Particle field imaging using digital in-line holography,” Curr. Sci. 96, 391–397 (2009).

Son, J. Y.

B. Javidi, F. Okano, and J. Y. Son, Three-Dimensional Imaging, Visualization, and Display (Springer, 2009).

Sucerquia, J. G.

F. Monroy, O. Rincon, Y. M. Torres, and J. G. Sucerquia, “Quantitative assessment of lateral resolution improvement in digital holography,” Opt. Commun. 281, 3454–3460(2008).
[CrossRef]

Torres, Y. M.

F. Monroy, O. Rincon, Y. M. Torres, and J. G. Sucerquia, “Quantitative assessment of lateral resolution improvement in digital holography,” Opt. Commun. 281, 3454–3460(2008).
[CrossRef]

Woods, R.

R. Gonzalez and R. Woods, Digital Image Processing (Pearson Education, 2007).

Yasuda, N.

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

Zhang, Y.

Y. Zhang, G. Shen, A. Schröder, and J. Kompenhans, “Influence of some recording parameters on digital holographic particle image velocimetry,” Opt. Eng. 45, 075801 (2006).
[CrossRef]

Appl. Opt. (1)

Curr. Sci. (1)

V. R. Singh, G. Hegde, and A. Asundi, “Particle field imaging using digital in-line holography,” Curr. Sci. 96, 391–397 (2009).

Meas. Sci. Technol. (1)

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. Commun. (1)

F. Monroy, O. Rincon, Y. M. Torres, and J. G. Sucerquia, “Quantitative assessment of lateral resolution improvement in digital holography,” Opt. Commun. 281, 3454–3460(2008).
[CrossRef]

Opt. Eng. (1)

Y. Zhang, G. Shen, A. Schröder, and J. Kompenhans, “Influence of some recording parameters on digital holographic particle image velocimetry,” Opt. Eng. 45, 075801 (2006).
[CrossRef]

Opt. Express (3)

Opt. Laser Technol. (1)

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

Phys. Rev. Lett. (1)

T. Latychevskaia and H. W. Fink, “Solution to the twin image problem in holography,” Phys. Rev. Lett. 98, 233901–233904 (2007).
[CrossRef]

Other (4)

B. Javidi, F. Okano, and J. Y. Son, Three-Dimensional Imaging, Visualization, and Display (Springer, 2009).

G. Pan and H. Meng, “Digital in-line holographic PIV for 3D particulate flow diagnostics,” in Proceedings of 4th International Symposium on Particle Image Velocimetry, Germany, September 17–192001, Paper 1008.

G. Pan and H. Meng, “Digital holographic PIV for 3D flow measurement,” in Proceedings of 2002 ASME International Mechanical Engineering Congress & Exposition, New Orleans, Louisiana, 17–22 November2002, 33173.

R. Gonzalez and R. Woods, Digital Image Processing (Pearson Education, 2007).

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Figures (8)

Fig. 1.
Fig. 1.

(a) Schematic of the in-line holographic setup and (b) schematic with photographic image of the sample explaining the sample preparation process for evaluating the holographic reconstruction procedure.

Fig. 2.
Fig. 2.

Schematic explaining the overall implementation of holographic reconstruction of a 3D particle field.

Fig. 3.
Fig. 3.

Intensity profiles for explaining the benefits of the proposed superposition algorithm: (a) 3D nonuniform object particle field with five particles (two particles, P1 and P2, with diameter dp=3pixels; two particles, P3 and P4, with diameter dp=5pixels; one particle, P5, with diameter dp=7pixels), (b) hologram image of object particle field in (a), (c) intensity image at the reference plane after numerical reconstruction, (d) normalized average intensity distribution of particles along the depth of sample volume, and (e)–(i) show the axial intensity distribution in the reference plane and focal plane for particles P1, P2, P3, P4, and P5, respectively.

Fig. 4.
Fig. 4.

Example illustrating the intensity profile of a missing particle (x/Δξ=21, y/Δξ=125, z/Δξ=21) and an extracted particle (x/Δξ=10, y/Δξ=195, z/Δξ=7) from the simulated hologram of an object volume with random 3D particle distribution (particle density n0=30mm3 and sample volume depth L=3mm) for illustrating the benefits achieved by the proposed algorithm: (a) object particle field, (b) reconstructed particle field, and (c) intensity profile of an extracted particle and a missing particle in the reference plane and focal plane. (d) The normalized average intensity distribution of an extracted particle against a missing particle along the depth of the sample volume. The hologram is reconstructed for 171 reconstruction planes, and the distance between two successive reconstruction planes δz=3pixels.

Fig. 5.
Fig. 5.

Experimentally generated hologram image of silver-coated particles (diameter 14 μm) inside gelatin solution [concentration 5% w(gm)/v(ml)] between two cover slips with their corresponding reconstructed particle field for different object particle density (n0) and sample volume depth (L): (a) L=1.2mm and n0=11particles/mm3, (b) L=1.2mm and n0=27particles/mm3, (c) L=2.8mm and n0=8particles/mm3, and (d) L=2.8mm and n0=10particles/mm3.

Fig. 6.
Fig. 6.

SNR values and percentage increase in SNR values between reference plane and focal plane as a function of object particle number density (n0) inside the sample volume of depth L=1mm.

Fig. 7.
Fig. 7.

Comparison of reconstructed particle bar charts from the present study with that of Singh and Panigrahi [11] for different recording distances: (a) z0/zc=0.65, (b) z0/zc=0.75, and (c) z0/zc=1.35. The object volume consists of 310 particles (100 particles of 1 pixel size, 100 particles of 2 pixel size, and 110 particles of 3 pixel size).

Fig. 8.
Fig. 8.

Comparison of reconstruction effectiveness (Nr) between the present study and those of Singh and Panigrahi [11] and Malik [12] as a function of object particle number density (n0) and sample volume depth (L).

Tables (2)

Tables Icon

Table 1. Comparison of Percentage Increase in SNR Values, Percentage Reconstruction Effectiveness (Nr), and Average Particle Diameter (dp) as a Function of Object Particle Density (n0) for Two Different Sample Volume Depths (L) of Both Numerically and Experimentally Generated Holograms

Tables Icon

Table 2. Comparison of Computational Time for Holographic Reconstruction Between the Proposed Algorithm and the Literature [11] as a Function of Object Particle Density (n0) and Sample Volume Depth (L)

Equations (6)

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E0(ξ,η)=exp(ikz0)iλz0++Er(x0,y0)t(x0,y0)exp{ik2z0((ξx0)2+(ηy0)2)}dx0dy0,
IH(ξ,η)=|Er+E0(ξ,η)|2=Ar2+|E0(ξ,η)|2+ArE0*(ξ,η)+ArE0(ξ,η).
Ei(xi,yi)=exp(ikzr)iλzr++Er*(ξ,η)IH(ξ,η)exp{ik2zr((xiξ)2+(yiη)2)}dξdη.
In,x,y,i=Ix,y,iImin,iImax,iImin,i,
IR=I1+I2+I3+I4+I5++IP,
SNR=x¯1Ni=1N(xix¯)2,

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