Abstract

The 3D distribution of a particle field by digital holography is obtained by 3D numerical reconstruction of a 2D hologram. The proper identification of particles from the background during numerical reconstruction influences the overall effectiveness of the technique. The selection of a suitable threshold value to segment particles from the background of reconstructed images during 3D holographic reconstruction process is a critical issue, which influences the accuracy of particle size and number density of reconstructed particles. The object particle field parameters, such as depth of sample volume and density of object particles, influence the optimal threshold value. The present study proposes a novel technique for the determination of the optimal threshold value of a reconstructed image. The effectiveness of the proposed technique is demonstrated using both simulated and experimental data. The proposed technique is robust to variation in optical properties of particle and background, depth of sample volume, and number density of object particle field. The particle diameter obtained from the proposed threshold technique is within 5% of that obtained from the particle size analyzer. There is a maximum ten times increase in reconstruction effectiveness by using the proposed automatic threshold technique in comparison with the fixed manual threshold technique.

© 2012 Optical Society of America

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References

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  1. S. Murata and N. Yasuda, “Potential of digital holography in particle measurement,” Opt. Laser Technol. 32, 567–574 (2000).
    [CrossRef]
  2. Y. Zhang, G. Shen, and A. Schroder, “Influence of some recording parameters on digital holographic particle image velocimetry,” Opt. Eng. 45, 075801 (2006).
    [CrossRef]
  3. 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]
  4. M. Malek, D. Allano, S. Coetmellec, and D. Lebrun, “Digital in-line holography: influence of the shadow density on particle field extraction,” Opt. Express 12, 2270–2279 (2004).
    [CrossRef]
  5. E. Malkiel, J. N. Abras, and J. Katz, “Automated scanning and measurements of particle distributions within a holographic reconstructed volume,” Meas. Sci. Technol. 15, 601–612 (2004).
    [CrossRef]
  6. G. Pan and H. Meng, “Digital in-line holographic PIV for 3D particulate flow diagnostics,” in Proceedings of the Fourth International Symposium on Particle Image Velocimetry (PIV) (DLR, Institute of Aerodynamics and Flow Technology, 2001), paper 1008.
  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. T. Latychevskaia, F. Gehri, and H. W. Fink, “Depth-resolved holographic reconstructions by three-dimensional deconvolution,” Opt. Express 18, 22527–22544 (2010).
    [CrossRef]
  9. T. Kreis, Handbook of Holographic Interferometry Optical and Digital Methods (Wiley, 2005).
  10. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).
  11. R. Gonzalez and R. Woods, Digital Image Processing (Pearson Education, 2007).

2010

2006

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

2004

M. Malek, D. Allano, S. Coetmellec, and D. Lebrun, “Digital in-line holography: influence of the shadow density on particle field extraction,” Opt. Express 12, 2270–2279 (2004).
[CrossRef]

E. Malkiel, J. N. Abras, and J. Katz, “Automated scanning and measurements of particle distributions within a holographic reconstructed volume,” Meas. Sci. Technol. 15, 601–612 (2004).
[CrossRef]

2003

2000

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

Abras, J. N.

E. Malkiel, J. N. Abras, and J. Katz, “Automated scanning and measurements of particle distributions within a holographic reconstructed volume,” Meas. Sci. Technol. 15, 601–612 (2004).
[CrossRef]

Allano, D.

Coetmellec, S.

Fink, H. W.

Gehri, F.

Gonzalez, R.

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

Goodman, J. W.

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

Katz, J.

E. Malkiel, J. N. Abras, and J. Katz, “Automated scanning and measurements of particle distributions within a holographic reconstructed volume,” Meas. Sci. Technol. 15, 601–612 (2004).
[CrossRef]

Kreis, T.

T. Kreis, Handbook of Holographic Interferometry Optical and Digital Methods (Wiley, 2005).

Latychevskaia, T.

Lebrun, D.

Malek, M.

Malkiel, E.

E. Malkiel, J. N. Abras, and J. Katz, “Automated scanning and measurements of particle distributions within a holographic reconstructed volume,” Meas. Sci. Technol. 15, 601–612 (2004).
[CrossRef]

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 in-line holographic PIV for 3D particulate flow diagnostics,” in Proceedings of the Fourth International Symposium on Particle Image Velocimetry (PIV) (DLR, Institute of Aerodynamics and Flow Technology, 2001), paper 1008.

Murata, S.

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

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 in-line holographic PIV for 3D particulate flow diagnostics,” in Proceedings of the Fourth International Symposium on Particle Image Velocimetry (PIV) (DLR, Institute of Aerodynamics and Flow Technology, 2001), paper 1008.

Panigrahi, P. K.

Schroder, A.

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

Shen, G.

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

Singh, D. K.

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, and A. Schroder, “Influence of some recording parameters on digital holographic particle image velocimetry,” Opt. Eng. 45, 075801 (2006).
[CrossRef]

Appl. Opt.

Meas. Sci. Technol.

E. Malkiel, J. N. Abras, and J. Katz, “Automated scanning and measurements of particle distributions within a holographic reconstructed volume,” Meas. Sci. Technol. 15, 601–612 (2004).
[CrossRef]

Opt. Eng.

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

Opt. Express

Opt. Laser Technol.

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

Other

T. Kreis, Handbook of Holographic Interferometry Optical and Digital Methods (Wiley, 2005).

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

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

G. Pan and H. Meng, “Digital in-line holographic PIV for 3D particulate flow diagnostics,” in Proceedings of the Fourth International Symposium on Particle Image Velocimetry (PIV) (DLR, Institute of Aerodynamics and Flow Technology, 2001), paper 1008.

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Figures (13)

Fig. 1.
Fig. 1.

Schematic of recording and reconstruction of particle field [10]: (a) hologram generation of 3D particle field using plane wave illumination, (b) plane-wise 3D numerical reconstruction of particle field from digital hologram of (a).

Fig. 2.
Fig. 2.

Average intensity of particles (Iavg,p) and background (Iavg,b) at different reconstruction planes (plane number) and the corresponding threshold value (Th) obtained using the proposed algorithm. The error bars show the standard deviation in intensity distribution of extracted particles (σp) and background noise (σb). The 3D reconstruction has been carried out at a depth interval of 15 μm using simulated hologram of object sample having sample volume size L×W×H=10mm×9.2mm×9.2mm, object particle diameter Dp=18μm, number density of particles no=0.1particles/mm3, and recording distance d=102mm.

Fig. 3.
Fig. 3.

Average intensity of particles (Iavg,p) and background (Iavg,b) at different reconstruction planes (plane number) and corresponding automatic threshold value (Th) using the experimental hologram of object sample having sample volume size L×W×H=3mm×9.6mm×9.6mm, object particle diameter Dp=15μm, number density of particles no=10particles/mm3, and recording distance d=90mm. The 3D reconstruction has been carried out at a depth interval of 15 μm. The error bars show the standard deviation in intensity distribution of extracted particles (σp) and background noise (σb).

Fig. 4.
Fig. 4.

Average intensity level of reconstructed particles (Iavg,p), background (Iavg,b), and the corresponding average threshold value (T¯h) using the proposed algorithm for experimental holograms having different shadow density (sd). The error bars show the standard deviation in intensity distribution of extracted particles (σp) and background noise (σb).

Fig. 5.
Fig. 5.

Percentage reconstruction effectiveness (Nr) as a function of number density of particles (no) at different tolerance level () using the proposed automatic threshold technique and manual threshold technique with fixed threshold value Th. The object sample volume size (L×W×H) and object particle size (Dp) are set equal to 10  mm×9.2mm×9.2mm and 18 μm respectively. The recording distance d=102mm.

Fig. 6.
Fig. 6.

Effect of globally set tolerance value () on number of iterations and percent reconstruction effectiveness (Nr) for the object sample with volume L×W×H=3mm×9.2mm×9.2mm, number density of particles no=5particles/mm3, and particle diameter Dp=18μm. The numerical reconstruction has been carried out for 200 transverse planes at an interval of 15 μm.

Fig. 7.
Fig. 7.

Histogram of reconstructed particles (Nr) using simulated particle field (Dp=18μm) at different sample volume depth (L) and object particle density (ns): (a) L=1mm, no=10particles/mm3, (b) L=3mm, no=10particles/mm3, and (c) L=3mm, no=30particles/mm3. The lateral size of object volume is W×H=9.2mm×9.2mm, and the recording distance d=102mm.

Fig. 8.
Fig. 8.

Comparison of reconstruction effectiveness Nr (%) as a function of shadow density, Sd from the present study with that of Malek et al. [4] and Malkiel et al. [5] for sample volume size L×W×H=3mm×9.2mm×9.2mm and particle diameter Dp=30μm. The number density of particles corresponding to the shadow density is no=(5,10,20,25,30)mm3, and the recording distance d=102mm. The reconstruction has been carried out using the proposed automatic threshold technique at tolerance level =0.05.

Fig. 9.
Fig. 9.

(a) Schematic of inline digital holography setup and (b) the sample image of 3D object particles (silver coated particles, diameter Dp=14μm) embedded in gelatin for sample volume size L×W×H=1mm×6.96mm×6.96mm.

Fig. 10.
Fig. 10.

Hologram generated from using silver particles suspended in (a) gelatin and (b) water. The variation of iteration number and reconstruction effectiveness with respect to the tolerance value are shown in (c) and (d), respectively. The sample volume size and particle density for both the samples are L×W×H=1mm×6.96mm×6.96mm and no=4.75particle/mm3, respectively.

Fig. 11.
Fig. 11.

Histogram of reconstructed particles as a function of particle diameter at different sample volume depth (L) and object particle number density (no): (a) L=0.5mm and no=9particles/mm3, b) L=1mm and no=2.25particles/mm3. The lateral size W×H=6.96mm×6.96mm, and the recording distance d=80mm.

Fig. 12.
Fig. 12.

Experimentally generated hologram and corresponding reconstructed particle field for different sample volume depth (L) and object particle number density (no): (a) L=0.5mm, no=2.12particles/mm3, (b) L=0.5mm, no=9.0particles/mm3, (c) L=1mm, no=1.0particles/mm3, d) L=1mm, no=2.25particles/mm3. The lateral size of object sample W×H=6.96mm×6.96mm.

Fig. 13.
Fig. 13.

Comparison of reconstruction effectiveness (Nr) between proposed automatic threshold technique and manual threshold technique at fixed threshold value Th as a function of object particle number density (no) using experimental holograms of object volume size L×W×H=1mm×6.96mm×6.96mm. The recording distance d=80mm.

Tables (4)

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Table 1. The Automatic Threshold Value (T¯h) Averaged over All Planes in the Reconstruction Volume, Reconstructed Particle Diameter (Dp), Its Standard Deviation (σ), and Percentage Reconstruction Effectiveness (Nr) as a Function of Sample Volume Depth (L), Object Particle Number Density (no), and Tolerance Level ()a

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Table 2. Average Depth Error (δr) of Reconstructed Particles for Different Sample Volume Depth (L) and Object Particle Number Density (no) for Tolerance Level =0.01 and 0.1a

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Table 3. Comparison of Size Distribution of Silver-Coated Particles Obtained from Digital Holography (DH) with That from Particle Size Analyzer (PSA) and Manufacturer Specifications

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Table 4. The Reconstruction Effectiveness (Nr) and Average Threshold Value (T¯h) Obtained from the Iterative Algorithm for Tolerance, =0.01, as a Function of Sample Volume Depth (L) and Object Particle Number Density (no) from the Experimental Hologram of Silver Coated Particles Embedded in Gelatin 10% (w/v)a

Equations (14)

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E(ξ,η)=exp(ikd)iλd++t(x,y)exp{ik2d[(ξx)2+(ηy)2]}dxdy,
h(ξ,η)=|r+E(ξ,η)|2=Ar2+|E(ξ,η)|2+ArE*(ξ,η)+ArE(ξ,η),
E(x,y)=exp(ikd)iλd++h(ξ,η)exp{ik2d[(xξ)2+(yη)2)]}dξdη.
I(x,y)=|E(x,y)|2.
In,p(z)=Iavg,p(z)Imin,pImax,pImin,p,
I(x,y)=Ip(x,y)+Ib(x,y),
I(k)=Ip(k)+Ib(k);where,k=1,2,,(M×N),
Iavg,p=1Npk=1NpIp(k)andIavg,b=1Nbk=1NbIb(k),
Th=12(Iavg,p+Iavg,b).
Th=12(Imax+Imin).
A1=1NG1k=1NG1I(k)andA2=1NG2k=1NG2I(k).
Th=12(A1+A2).
sd=L*no*Dp2.
ThI¯o=4.2(I¯imageI¯o),

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