Abstract

Side scattered light from micrometer-sized particles is recorded using an off-axis digital holographic setup. From holograms, a volume is reconstructed with information about both intensity and phase. Finding particle positions is non-trivial, since poor axial resolution elongates particles in the reconstruction. To overcome this problem, the reconstructed wavefront around a particle is used to find the axial position. The method is based on the change in the sign of the curvature around the true particle position plane. The wavefront curvature is directly linked to the phase response in the reconstruction. In this paper we propose a new method of estimating the curvature based on a parametric model. The model is based on Chebyshev polynomials and is fit to the phase anomaly and compared to a plane wave in the reconstructed volume. From the model coefficients, it is possible to find particle locations. Simulated results show increased performance in the presence of noise, compared to the use of finite difference methods. The standard deviation is decreased from 3–39 μm to 6–10 μm for varying noise levels. Experimental results show a corresponding improvement where the standard deviation is decreased from 18 μm to 13 μm.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2017 (4)

Y. Wu, M. Brunel, R. Li, L. Lan, W. Ao, J. Chen, X. Wu, and G. Gréhan, “Simultaneous amplitude and phase contrast imaging of burning fuel particle and flame with digital inline holography: model and verification,” J. Quant. Spectrosc. Radiat. Transfer 199, 26–35 (2017).
[Crossref]

Y. Wu, L. Yao, X. Wu, J. Chen, G. Gréhan, and K. Cen, “3D imaging of individual burning char and volatile plume in a pulverized coal flame with digital inline holography,” Fuel 206, 429–436 (2017).
[Crossref]

O. Kemppinen, Y. Heinson, and M. Berg, “Quasi-three-dimensional particle imaging with digital holography,” Appl. Opt. 56, F53–F60 (2017).
[Crossref]

M. J. Berg, N. R. Subedi, and P. A. Anderson, “Measuring extinction with digital holography: nonspherical particles and experimental validation,” Opt. Lett. 42, 1011–1014 (2017).
[Crossref]

2016 (2)

2015 (1)

2013 (2)

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]

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]

2012 (2)

Y.-S. Choi, K.-W. Seo, M.-H. Sohn, and S.-J. Lee, “Advances in digital holographic micro-PTV for analyzing microscale flows,” Opt. Lasers Eng. 50, 39–45 (2012).
[Crossref]

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

2011 (3)

2010 (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 (2)

1967 (1)

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[Crossref]

1948 (1)

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

Abramowitz, M.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, 1972), Vol. 9.

Abrantes, J. K.

Anderson, P. A.

Ao, W.

Y. Wu, M. Brunel, R. Li, L. Lan, W. Ao, J. Chen, X. Wu, and G. Gréhan, “Simultaneous amplitude and phase contrast imaging of burning fuel particle and flame with digital inline holography: model and verification,” J. Quant. Spectrosc. Radiat. Transfer 199, 26–35 (2017).
[Crossref]

Atlan, M.

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]

Berg, M.

Berg, M. J.

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).

Brunel, M.

Y. Wu, M. Brunel, R. Li, L. Lan, W. Ao, J. Chen, X. Wu, and G. Gréhan, “Simultaneous amplitude and phase contrast imaging of burning fuel particle and flame with digital inline holography: model and verification,” J. Quant. Spectrosc. Radiat. Transfer 199, 26–35 (2017).
[Crossref]

Caprio, G. D.

Cen, K.

Y. Wu, L. Yao, X. Wu, J. Chen, G. Gréhan, and K. Cen, “3D imaging of individual burning char and volatile plume in a pulverized coal flame with digital inline holography,” Fuel 206, 429–436 (2017).
[Crossref]

Chen, J.

Y. Wu, L. Yao, X. Wu, J. Chen, G. Gréhan, and K. Cen, “3D imaging of individual burning char and volatile plume in a pulverized coal flame with digital inline holography,” Fuel 206, 429–436 (2017).
[Crossref]

Y. Wu, M. Brunel, R. Li, L. Lan, W. Ao, J. Chen, X. Wu, and G. Gréhan, “Simultaneous amplitude and phase contrast imaging of burning fuel particle and flame with digital inline holography: model and verification,” J. Quant. Spectrosc. Radiat. Transfer 199, 26–35 (2017).
[Crossref]

Cheong, F. C.

Choi, Y.-S.

Y.-S. Choi, K.-W. Seo, M.-H. Sohn, and S.-J. Lee, “Advances in digital holographic micro-PTV for analyzing microscale flows,” Opt. Lasers Eng. 50, 39–45 (2012).
[Crossref]

Coppola, G.

Coudert, S.

de Jong, J.

Denis, L.

Ferraro, P.

Fournier, C.

Fung, J.

Gabor, D.

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

Goepfert, C.

Goodman, J. W.

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[Crossref]

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

Gréhan, G.

Y. Wu, L. Yao, X. Wu, J. Chen, G. Gréhan, and K. Cen, “3D imaging of individual burning char and volatile plume in a pulverized coal flame with digital inline holography,” Fuel 206, 429–436 (2017).
[Crossref]

Y. Wu, M. Brunel, R. Li, L. Lan, W. Ao, J. Chen, X. Wu, and G. Gréhan, “Simultaneous amplitude and phase contrast imaging of burning fuel particle and flame with digital inline holography: model and verification,” J. Quant. Spectrosc. Radiat. Transfer 199, 26–35 (2017).
[Crossref]

Grier, D. G.

Heinson, Y.

Holler, S.

Huffman, D. R.

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

Katz, J.

Kaz, D. M.

Kemppinen, O.

Kikuchi, T.

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]

Krishnatreya, B. J.

Kunugi, T.

Lan, L.

Y. Wu, M. Brunel, R. Li, L. Lan, W. Ao, J. Chen, X. Wu, and G. Gréhan, “Simultaneous amplitude and phase contrast imaging of burning fuel particle and flame with digital inline holography: model and verification,” J. Quant. Spectrosc. Radiat. Transfer 199, 26–35 (2017).
[Crossref]

Lawrence, R. W.

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[Crossref]

Lee, S.-J.

Y.-S. Choi, K.-W. Seo, M.-H. Sohn, and S.-J. Lee, “Advances in digital holographic micro-PTV for analyzing microscale flows,” Opt. Lasers Eng. 50, 39–45 (2012).
[Crossref]

Li, R.

Y. Wu, M. Brunel, R. Li, L. Lan, W. Ao, J. Chen, X. Wu, and G. Gréhan, “Simultaneous amplitude and phase contrast imaging of burning fuel particle and flame with digital inline holography: model and verification,” J. Quant. Spectrosc. Radiat. Transfer 199, 26–35 (2017).
[Crossref]

Malkiel, E.

Manoharan, V. N.

Martin, K. E.

McGorty, R.

Memmolo, P.

Meng, H.

Miccio, L.

Netti, P. A.

Öhman, J.

Pan, G.

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]

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

Paturzo, M.

Perry, R. W.

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]

Y. Pu and H. Meng, “Intrinsic aberrations due to Mie scattering in particle holography,” J. Opt. Soc. Am. A 20, 1920–1932 (2003).
[Crossref]

Satake, S. I.

Seo, K.-W.

Y.-S. Choi, K.-W. Seo, M.-H. Sohn, and S.-J. Lee, “Advances in digital holographic micro-PTV for analyzing microscale flows,” Opt. Lasers Eng. 50, 39–45 (2012).
[Crossref]

Sheng, J.

Sjödahl, M.

Sohn, M.-H.

Y.-S. Choi, K.-W. Seo, M.-H. Sohn, and S.-J. Lee, “Advances in digital holographic micro-PTV for analyzing microscale flows,” Opt. Lasers Eng. 50, 39–45 (2012).
[Crossref]

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]

Soulez, F.

Stanislas, M.

Stegun, I. A.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, 1972), Vol. 9.

Subedi, N. R.

Thiébaut, É.

Verrier, N.

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. 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]

Wu, X.

Y. Wu, L. Yao, X. Wu, J. Chen, G. Gréhan, and K. Cen, “3D imaging of individual burning char and volatile plume in a pulverized coal flame with digital inline holography,” Fuel 206, 429–436 (2017).
[Crossref]

Y. Wu, M. Brunel, R. Li, L. Lan, W. Ao, J. Chen, X. Wu, and G. Gréhan, “Simultaneous amplitude and phase contrast imaging of burning fuel particle and flame with digital inline holography: model and verification,” J. Quant. Spectrosc. Radiat. Transfer 199, 26–35 (2017).
[Crossref]

Wu, Y.

Y. Wu, M. Brunel, R. Li, L. Lan, W. Ao, J. Chen, X. Wu, and G. Gréhan, “Simultaneous amplitude and phase contrast imaging of burning fuel particle and flame with digital inline holography: model and verification,” J. Quant. Spectrosc. Radiat. Transfer 199, 26–35 (2017).
[Crossref]

Y. Wu, L. Yao, X. Wu, J. Chen, G. Gréhan, and K. Cen, “3D imaging of individual burning char and volatile plume in a pulverized coal flame with digital inline holography,” Fuel 206, 429–436 (2017).
[Crossref]

Yao, L.

Y. Wu, L. Yao, X. Wu, J. Chen, G. Gréhan, and K. Cen, “3D imaging of individual burning char and volatile plume in a pulverized coal flame with digital inline holography,” Fuel 206, 429–436 (2017).
[Crossref]

Yonemoto, Y.

Zhang, R.

Adv. Opt. Photon. (1)

Appl. Opt. (8)

Appl. Phys. Lett. (1)

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77–79 (1967).
[Crossref]

Fuel (1)

Y. Wu, L. Yao, X. Wu, J. Chen, G. Gréhan, and K. Cen, “3D imaging of individual burning char and volatile plume in a pulverized coal flame with digital inline holography,” Fuel 206, 429–436 (2017).
[Crossref]

J. Opt. Soc. Am. A (2)

J. Quant. Spectrosc. Radiat. Transfer (1)

Y. Wu, M. Brunel, R. Li, L. Lan, W. Ao, J. Chen, X. Wu, and G. Gréhan, “Simultaneous amplitude and phase contrast imaging of burning fuel particle and flame with digital inline holography: model and verification,” J. Quant. Spectrosc. Radiat. Transfer 199, 26–35 (2017).
[Crossref]

Meas. Sci. Technol. (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]

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. Lasers Eng. (1)

Y.-S. Choi, K.-W. Seo, M.-H. Sohn, and S.-J. Lee, “Advances in digital holographic micro-PTV for analyzing microscale flows,” Opt. Lasers Eng. 50, 39–45 (2012).
[Crossref]

Opt. Lett. (2)

Other (4)

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

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, 1972), Vol. 9.

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 (8)

Fig. 1.
Fig. 1. Scattering geometry with the defined scattering plane, spanned by vectors s i and s s . Polarization is expressed on component form, parallel, and orthogonal to this plane.
Fig. 2.
Fig. 2. Telecentric imaging system consisting of lenses L 1 and L 2 and aperture A . Solid rays are the object light, and dashed rays are the reference light. Dashed black lines indicate the detector in image space and corresponding conjugate plane in object space.
Fig. 3.
Fig. 3. Different properties in the reconstruction. (a) Intensity on the detector for a simulated hologram, (b) reconstructed phase along the center of the particle, (c) corresponding phase anomaly to (b). (d) Wavefront curvature at Δ z = 100    μm (black), 50    μm (blue), 0 μm (red), 50 μm (green), and 100 μm (magenta). In both (c) and (d), solid lines are polynomial fit, and markers the simulated data.
Fig. 4.
Fig. 4. MSE per voxel for different orders of n .
Fig. 5.
Fig. 5. Evaluation of square terms a 200 and a 020 around particle location.
Fig. 6.
Fig. 6. 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 FP is a fiber port.
Fig. 7.
Fig. 7. Simulated standard deviations of axial position error using both Chebyshev model (blue) and finite difference method (red).
Fig. 8.
Fig. 8. Histogram of experimental error. Error is approximately zero mean with a standard deviation of 12.8 μm.

Equations (10)

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

E ¯ s = ( E s ( θ ) E s ( θ ) ) = e i k ( r z ) i k r ( S 1 ( θ ) 0 0 S 2 ( θ ) ) ( E i E i ) ,
R ¯ = ( R R ) ,
I ( x , y ) = | E ¯ ( x , y ) R ¯ ( x , y ) | 2 = | E ( x , y ) | 2 + | E ( x , y ) | 2 + | R ( x , y ) | 2 + | R ( x , y ) | 2 + E ( x , y ) * R ( x , y ) + E ( x , y ) * R ( x , y ) + E ( x , y ) R * ( x , y ) + E ( x , y ) R * ( x , y ) ,
E ( x , y , z ) = F 1 [ E ˜ ( f x , f y ; z D ) exp ( j k s z Δ z ) ] ,
ϕ a ( x , y , z ) = [ E ( x , y , z ) ] k z ,
ϕ ^ a ( ε , η , ζ ) = i = 0 n j = 0 n k = 0 n a i j k T i ( ε ) T j ( η ) T k ( ζ ) ,
ϕ ^ a ( ε , η , ζ ) = T a .
a ^ i j k = argmin a W ( ϕ a ϕ ^ a ) 2 ,
a ^ = ( T T W T ) 1 T T W ϕ a ,
NA 0 = NA 0 n silicon 0.0179 .

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