Abstract

Poor axial resolution in holographic particle imaging applications makes particle positioning in 3D space more complex since the positions are not directly obtained. In this paper we estimate the axial position of micrometer particles by finding the location where the wavefront curvature from the scattered light becomes zero. By recording scattered light at 90° using off-axis holography, the complex amplitude of the light is obtained. By reconstruction of the imaged scene, a complex valued volume is produced. From this volume, phase gradients are calculated for each particle and used to estimate the wavefront curvature. From simulations it is found that the wavefront curvature became zero at the true axial position of the particle. We applied this metric to track an axial translation experimentally using a telecentric off-axis holographic imaging system with a lateral magnification of M=1.33. A silicon cube with molded particles inside was used as sample. Holographic recordings are performed both before and after a 100 μm axial translation. From the estimated positions, it was found that the mean displacement of particles between recordings was 105.0 μm with a standard deviation of 25.3 μm.

© 2016 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  15. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).
  16. L. Cao, G. Pan, J. de Jong, S. Woodward, and H. Meng, “Hybrid digital holographic imaging system for three-dimensional dense particle field measurement,” Appl. Opt. 47, 4501–4508 (2008).
    [Crossref]

2013 (2)

Y. S. Bae, J. I. Song, and D. Y. Kim, “Volumetric reconstruction of Brownian motion of a micrometer-size bead in water,” Opt. Commun. 309, 291–297 (2013).
[Crossref]

J. K. Abrantes, M. Stanislas, S. Coudert, and L. F. A. Azevedo, “Digital microscopic holography for micrometer particles in air,” Appl. Opt. 52, A397–A409 (2013).
[Crossref]

2012 (2)

L. Wilson and R. Zhang, “3D Localization of weak scatterers in digital holographic microscopy using Rayleigh-Sommerfield back-propagation,” Opt. Express 20, 16735–16744 (2012).
[Crossref]

N. Buchmann, C. Atkinson, and J. Soria, “Ultra-high-speed tomographic digital holographic velocimetry in supersonic particle-laden jet flows,” Meas. Sci. Technol. 24, 024005 (2012).
[Crossref]

2010 (1)

2008 (1)

2007 (2)

2006 (1)

2004 (1)

H. Meng, G. Pan, Y. Pu, and S. H. Woodward, “Holographic particle image velocimetry: from film to digital recording,” Meas. Sci. Technol. 15, 673–685 (2004).
[Crossref]

2003 (1)

1991 (1)

C. E. Willert and M. Gharib, “Digital particle image velocimetry,” Exp. Fluids 10, 181–193 (1991).

1948 (1)

D. Gabor, “A new microscopic principle,” Nature 161, 777–778 (1948).
[Crossref]

Abrantes, J. K.

Atkinson, C.

N. Buchmann, C. Atkinson, and J. Soria, “Ultra-high-speed tomographic digital holographic velocimetry in supersonic particle-laden jet flows,” Meas. Sci. Technol. 24, 024005 (2012).
[Crossref]

Azevedo, L. F. A.

Bae, Y. S.

Y. S. Bae, J. I. Song, and D. Y. Kim, “Volumetric reconstruction of Brownian motion of a micrometer-size bead in water,” Opt. Commun. 309, 291–297 (2013).
[Crossref]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University, 1999).

Buchmann, N.

N. Buchmann, C. Atkinson, and J. Soria, “Ultra-high-speed tomographic digital holographic velocimetry in supersonic particle-laden jet flows,” Meas. Sci. Technol. 24, 024005 (2012).
[Crossref]

Cao, L.

Cheong, F. C.

Coudert, S.

de Jong, J.

Gabor, D.

D. Gabor, “A new microscopic principle,” Nature 161, 777–778 (1948).
[Crossref]

Gharib, M.

C. E. Willert and M. Gharib, “Digital particle image velocimetry,” Exp. Fluids 10, 181–193 (1991).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

Grier, D. G.

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).

Kim, D. Y.

Y. S. Bae, J. I. Song, and D. Y. Kim, “Volumetric reconstruction of Brownian motion of a micrometer-size bead in water,” Opt. Commun. 309, 291–297 (2013).
[Crossref]

Kim, S.-H.

Kostinski, A. B.

Krishnatreya, B. J.

Lee, S.-H.

Meng, H.

Pan, G.

Pu, Y.

H. Meng, G. Pan, Y. Pu, and S. H. Woodward, “Holographic particle image velocimetry: from film to digital recording,” Meas. Sci. Technol. 15, 673–685 (2004).
[Crossref]

Roichman, Y.

Shaw, R. A.

Song, J. I.

Y. S. Bae, J. I. Song, and D. Y. Kim, “Volumetric reconstruction of Brownian motion of a micrometer-size bead in water,” Opt. Commun. 309, 291–297 (2013).
[Crossref]

Soria, J.

N. Buchmann, C. Atkinson, and J. Soria, “Ultra-high-speed tomographic digital holographic velocimetry in supersonic particle-laden jet flows,” Meas. Sci. Technol. 24, 024005 (2012).
[Crossref]

Stanislas, M.

van Blaaderen, A.

van Oostrum, P.

Willert, C. E.

C. E. Willert and M. Gharib, “Digital particle image velocimetry,” Exp. Fluids 10, 181–193 (1991).

Wilson, L.

Wolf, E.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University, 1999).

Woodward, S.

Woodward, S. H.

H. Meng, G. Pan, Y. Pu, and S. H. Woodward, “Holographic particle image velocimetry: from film to digital recording,” Meas. Sci. Technol. 15, 673–685 (2004).
[Crossref]

Yang, S.-M.

Yang, W.

Yi, G.-R.

Zhang, R.

Appl. Opt. (4)

Exp. Fluids (1)

C. E. Willert and M. Gharib, “Digital particle image velocimetry,” Exp. Fluids 10, 181–193 (1991).

Meas. Sci. Technol. (2)

H. Meng, G. Pan, Y. Pu, and S. H. Woodward, “Holographic particle image velocimetry: from film to digital recording,” Meas. Sci. Technol. 15, 673–685 (2004).
[Crossref]

N. Buchmann, C. Atkinson, and J. Soria, “Ultra-high-speed tomographic digital holographic velocimetry in supersonic particle-laden jet flows,” Meas. Sci. Technol. 24, 024005 (2012).
[Crossref]

Nature (1)

D. Gabor, “A new microscopic principle,” Nature 161, 777–778 (1948).
[Crossref]

Opt. Commun. (1)

Y. S. Bae, J. I. Song, and D. Y. Kim, “Volumetric reconstruction of Brownian motion of a micrometer-size bead in water,” Opt. Commun. 309, 291–297 (2013).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Other (3)

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1998).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University, 1999).

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Figures (7)

Fig. 1.
Fig. 1. Definition of scattering plane with the illumination direction s i and scattering direction s s .
Fig. 2.
Fig. 2. Coordinate systems, where U i is the field at the focus plane, U a is the field in the joint focal plane, and U o is the field at the detector. L 1 and L 2 are imaging lenses with focal lengths f 1 and f 2 , respectively. Δ z is the defocus distance of the particle. (a) Shows the coordinates in the object- and image-domains and (b) shows the propagation of a image plane by a distance Δ z .
Fig. 3.
Fig. 3. Evaluation from simulated data; (a) shows the phase-gradient tilt for parallel direction (dashed) and orthogonal direction (solid), (b) shows a zoomed-in version of (a), and (c) shows the centroid intensity.
Fig. 4.
Fig. 4. Histograms of simulated data with Gaussian distribution fits for both phase-gradient method (a) and centroid intensity method (b). The solid lines are the fitted Gaussian distributions.
Fig. 5.
Fig. 5. Experimental setup used in the recordings. BS is a beam splitter, L1 is a f = 150    mm lens, L2 is a f = 20    mm lens, L3 is a f = 60    mm lens, L4 is a f = 80    mm lens, A is the aperture, M is a mirror, and FC is a fiber collimator.
Fig. 6.
Fig. 6. Evaluation of parameter B 2 for 17 particles from an experimental recording. The z axis is shifted so that all particles have their zero-crossing at z * = 0 .
Fig. 7.
Fig. 7. 3D scatter plot of particle positions before and after the axial translation. Links between paired particles are also indicated.

Tables (1)

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Table 1. Simulated Standard Deviation for Different Peak-to-Peak Noise Ratios

Equations (16)

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( E s ( θ ) E s ( θ ) ) = ( S 1 ( θ ) 0 0 S 2 ( θ ) ) ( E i E i ) ,
E s ( θ ) = S 2 ( θ ) · E i .
U a ( η , ξ ) = E i · S 2 ( f x , f y ) · exp ( i k s z Δ z ) ,
U i ( x , y ) = F 1 { U a ( η , ξ ) } .
U o ( x , y ) = f 1 f 2 U i ( f 1 f 2 x , f 1 f 2 y ) ,
U o ( x , y ) = 1 M U i ( x M , y M ) .
I ( x , y ) = | U ( x , y ) R ( x , y ) | 2 = | U ( x , y ) | 2 + | R ( x , y ) | 2 + U ( x , y ) * R ( x , y ) + U ( x , y ) R * ( x , y ) .
U ( x , y ) R * ( x , y ) U ( x , y ) .
U ( x , y , Δ z ) = F 1 [ F ( U ( x , y , 0 ) ) exp ( j k s z Δ z ) ] ,
δ φ i , j δ x = ( E i 1 , j E i + 1 , j * ) 2 d ,
δ φ i , j δ y = ( E i , j 1 E i , j + 1 * ) 2 d ,
δ φ i , j δ x = A 1 ( i 1 ) d + B 1 ( j 1 ) d + C 1 ,
δ φ i , j δ y = A 2 ( i 1 ) d + B 2 ( j 1 ) d + C 2 ,
NA 0 = NA 0 n silicon = 0.025 1.4 0.0179 .
z * = z z 0 ,
σ scaled = σ NA 0 2 λ ,

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