Abstract

A new and computationally efficient approach is proposed for determining the refractive index of spherical and transparent particles, in addition to their size and 3D position, using digital in-line holography. The method is based on the localization of the maximum intensity position of the photonic jet with respect to the particle center retrieved from the back propagation of recorded holograms. Rigorous electromagnetic calculations and experimental results demonstrate that for liquid-liquid systems and droplets with a radius > 30µm, a refractive index measurement with a resolution inferior to 4 × 10−3 is achievable, revealing a significant potential for the use of this method to investigate multiphase flows. The resolution for solid or liquid particles in gas is expected to be lower but sufficient for the recognition of particle material.

© 2017 Optical Society of America

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References

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2017 (1)

M. P. Sentis, L. Bruel, S. Charton, F. R. Onofri, and F. Lamadie, “Digital in-line holography for the characterization of flowing particles in astigmatic optical systems,” Opt. Lasers Eng. 88, 184–196 (2017).
[Crossref]

2015 (2)

C.-Y. Tan and Y.-X. Huang, “Dependence of refractive index on concentration and temperature in electrolyte solution, polar solution, nonpolar solution, and protein solution,” J. Chem. Eng. Data 60(10), 2827–2833 (2015).
[Crossref]

M. P. Sentis, F. R. Onofri, L. Méès, and S. Radev, “Scattering of light by large bubbles: Coupling of geometrical and physical optics approximations,” J. Quant. Spectrosc. Radiat. Transf. 170, 8–18 (2015).
[Crossref]

2014 (3)

A. Yevick, M. Hannel, and D. G. Grier, “Machine-learning approach to holographic particle characterization,” Opt. Express 22(22), 26884–26890 (2014).
[Crossref] [PubMed]

F. Lamadie and L. Bruel, “Processing method for near-field in-line holograms (Fresnel number≥ 1),” Opt. Lasers Eng. 57, 130–137 (2014).
[Crossref]

Y. Sung, N. Lue, B. Hamza, J. Martel, D. Irimia, R. R. Dasari, W. Choi, Z. Yaqoob, and P. So, “Three-dimensional holographic refractive-index measurement of continuously flowing cells in a microfluidic channel,” Phys. Rev. Appl. 1(1), 014002 (2014).
[Crossref] [PubMed]

2013 (1)

F. Koohyar, “Refractive Index and Its Applications,” J. Thermodyn Catal. 4(02), 117 (2013).
[Crossref]

2012 (2)

H. Shpaisman, B. J. Krishnatreya, and D. G. Grier, “Holographic microrefractometer,” Appl. Phys. Lett. 101(9), 091102 (2012).
[Crossref]

F. Lamadie, L. Bruel, and M. Himbert, “Digital holographic measurement of liquid–liquid two-phase flows,” Opt. Lasers Eng. 50(12), 1716–1725 (2012).
[Crossref]

2010 (2)

Y. E. Geints, E. Panina, and A. Zemlyanov, “Control over parameters of photonic nanojets of dielectric microspheres,” Opt. Commun. 283(23), 4775–4781 (2010).
[Crossref]

H. Ding, L. Dai, and C. Yan, “Properties of the 3D photonic nanojet based on the refractive index of surroundings,” Chin. Opt. Lett. 8(7), 706–708 (2010).
[Crossref]

2009 (1)

A. Heifetz, S.-C. Kong, A. V. Sahakian, A. Taflove, and V. Backman, “Photonic nanojets,” J. Comput. Theor. Nanosci. 6(9), 1979–1992 (2009).
[Crossref] [PubMed]

2008 (2)

2007 (2)

S.-H. Lee, Y. Roichman, G.-R. Yi, S.-H. Kim, S.-M. Yang, A. van Blaaderen, P. van Oostrum, and D. G. Grier, “Characterizing and tracking single colloidal particles with video holographic microscopy,” Opt. Express 15(26), 18275–18282 (2007).
[Crossref] [PubMed]

X. Liang, A. Liu, C. Lim, T. Ayi, and P. Yap, “Determining refractive index of single living cell using an integrated microchip,” Sens. Actuators A Phys. 133(2), 349–354 (2007).
[Crossref]

2006 (2)

D. Subedi, D. Adhikari, U. Joshi, H. Poudel, and B. Niraula, “Study of temperature and concentration dependence of refractive index of liquids using a novel technique,” Kathmandu University Journal of Science, Engineering and Technology 2, 1–7 (2006).

J. Sheng, E. Malkiel, and J. Katz, “Digital holographic microscope for measuring three-dimensional particle distributions and motions,” Appl. Opt. 45(16), 3893–3901 (2006).
[Crossref] [PubMed]

2005 (2)

2000 (1)

1997 (1)

1996 (1)

F. Onofri, T. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, T. H. Xu, and C. Tropea, “Phase‐Doppler Anemometry with the Dual Burst Technique for measurement of refractive index and absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Char. 13(2), 112–124 (1996).
[Crossref]

1974 (1)

B. J. Thompson, “Holographic particle sizing techniques,” J. Phys. E Sci. Instrum. 7(10), 781–788 (1974).
[Crossref]

Adhikari, D.

D. Subedi, D. Adhikari, U. Joshi, H. Poudel, and B. Niraula, “Study of temperature and concentration dependence of refractive index of liquids using a novel technique,” Kathmandu University Journal of Science, Engineering and Technology 2, 1–7 (2006).

Adler, C. L.

Ayi, T.

X. Liang, A. Liu, C. Lim, T. Ayi, and P. Yap, “Determining refractive index of single living cell using an integrated microchip,” Sens. Actuators A Phys. 133(2), 349–354 (2007).
[Crossref]

Backman, V.

A. Heifetz, S.-C. Kong, A. V. Sahakian, A. Taflove, and V. Backman, “Photonic nanojets,” J. Comput. Theor. Nanosci. 6(9), 1979–1992 (2009).
[Crossref] [PubMed]

Bonod, N.

Brenn, G.

F. Onofri, T. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, T. H. Xu, and C. Tropea, “Phase‐Doppler Anemometry with the Dual Burst Technique for measurement of refractive index and absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Char. 13(2), 112–124 (1996).
[Crossref]

Bruel, L.

M. P. Sentis, L. Bruel, S. Charton, F. R. Onofri, and F. Lamadie, “Digital in-line holography for the characterization of flowing particles in astigmatic optical systems,” Opt. Lasers Eng. 88, 184–196 (2017).
[Crossref]

F. Lamadie and L. Bruel, “Processing method for near-field in-line holograms (Fresnel number≥ 1),” Opt. Lasers Eng. 57, 130–137 (2014).
[Crossref]

F. Lamadie, L. Bruel, and M. Himbert, “Digital holographic measurement of liquid–liquid two-phase flows,” Opt. Lasers Eng. 50(12), 1716–1725 (2012).
[Crossref]

Challener, W. A.

Charton, S.

M. P. Sentis, L. Bruel, S. Charton, F. R. Onofri, and F. Lamadie, “Digital in-line holography for the characterization of flowing particles in astigmatic optical systems,” Opt. Lasers Eng. 88, 184–196 (2017).
[Crossref]

Choi, W.

Y. Sung, N. Lue, B. Hamza, J. Martel, D. Irimia, R. R. Dasari, W. Choi, Z. Yaqoob, and P. So, “Three-dimensional holographic refractive-index measurement of continuously flowing cells in a microfluidic channel,” Phys. Rev. Appl. 1(1), 014002 (2014).
[Crossref] [PubMed]

Dai, L.

Dasari, R. R.

Y. Sung, N. Lue, B. Hamza, J. Martel, D. Irimia, R. R. Dasari, W. Choi, Z. Yaqoob, and P. So, “Three-dimensional holographic refractive-index measurement of continuously flowing cells in a microfluidic channel,” Phys. Rev. Appl. 1(1), 014002 (2014).
[Crossref] [PubMed]

Devilez, A.

Ding, H.

Domnick, J.

F. Onofri, T. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, T. H. Xu, and C. Tropea, “Phase‐Doppler Anemometry with the Dual Burst Technique for measurement of refractive index and absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Char. 13(2), 112–124 (1996).
[Crossref]

Ferrand, P.

Garcia, C. J.

Geints, Y. E.

Y. E. Geints, E. Panina, and A. Zemlyanov, “Control over parameters of photonic nanojets of dielectric microspheres,” Opt. Commun. 283(23), 4775–4781 (2010).
[Crossref]

Girasole, T.

F. Onofri, T. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, T. H. Xu, and C. Tropea, “Phase‐Doppler Anemometry with the Dual Burst Technique for measurement of refractive index and absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Char. 13(2), 112–124 (1996).
[Crossref]

Gouesbet, G.

F. Onofri, T. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, T. H. Xu, and C. Tropea, “Phase‐Doppler Anemometry with the Dual Burst Technique for measurement of refractive index and absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Char. 13(2), 112–124 (1996).
[Crossref]

Gréhan, G.

F. Onofri, T. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, T. H. Xu, and C. Tropea, “Phase‐Doppler Anemometry with the Dual Burst Technique for measurement of refractive index and absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Char. 13(2), 112–124 (1996).
[Crossref]

Grier, D. G.

Hamza, B.

Y. Sung, N. Lue, B. Hamza, J. Martel, D. Irimia, R. R. Dasari, W. Choi, Z. Yaqoob, and P. So, “Three-dimensional holographic refractive-index measurement of continuously flowing cells in a microfluidic channel,” Phys. Rev. Appl. 1(1), 014002 (2014).
[Crossref] [PubMed]

Hannel, M.

Heifetz, A.

A. Heifetz, S.-C. Kong, A. V. Sahakian, A. Taflove, and V. Backman, “Photonic nanojets,” J. Comput. Theor. Nanosci. 6(9), 1979–1992 (2009).
[Crossref] [PubMed]

Himbert, M.

F. Lamadie, L. Bruel, and M. Himbert, “Digital holographic measurement of liquid–liquid two-phase flows,” Opt. Lasers Eng. 50(12), 1716–1725 (2012).
[Crossref]

Hovenac, E. A.

Huang, Y.-X.

C.-Y. Tan and Y.-X. Huang, “Dependence of refractive index on concentration and temperature in electrolyte solution, polar solution, nonpolar solution, and protein solution,” J. Chem. Eng. Data 60(10), 2827–2833 (2015).
[Crossref]

Irimia, D.

Y. Sung, N. Lue, B. Hamza, J. Martel, D. Irimia, R. R. Dasari, W. Choi, Z. Yaqoob, and P. So, “Three-dimensional holographic refractive-index measurement of continuously flowing cells in a microfluidic channel,” Phys. Rev. Appl. 1(1), 014002 (2014).
[Crossref] [PubMed]

Itagi, A. V.

Joshi, U.

D. Subedi, D. Adhikari, U. Joshi, H. Poudel, and B. Niraula, “Study of temperature and concentration dependence of refractive index of liquids using a novel technique,” Kathmandu University Journal of Science, Engineering and Technology 2, 1–7 (2006).

Katz, J.

Kim, S.-H.

Kong, S.-C.

A. Heifetz, S.-C. Kong, A. V. Sahakian, A. Taflove, and V. Backman, “Photonic nanojets,” J. Comput. Theor. Nanosci. 6(9), 1979–1992 (2009).
[Crossref] [PubMed]

Koohyar, F.

F. Koohyar, “Refractive Index and Its Applications,” J. Thermodyn Catal. 4(02), 117 (2013).
[Crossref]

Krishnatreya, B. J.

H. Shpaisman, B. J. Krishnatreya, and D. G. Grier, “Holographic microrefractometer,” Appl. Phys. Lett. 101(9), 091102 (2012).
[Crossref]

Lamadie, F.

M. P. Sentis, L. Bruel, S. Charton, F. R. Onofri, and F. Lamadie, “Digital in-line holography for the characterization of flowing particles in astigmatic optical systems,” Opt. Lasers Eng. 88, 184–196 (2017).
[Crossref]

F. Lamadie and L. Bruel, “Processing method for near-field in-line holograms (Fresnel number≥ 1),” Opt. Lasers Eng. 57, 130–137 (2014).
[Crossref]

F. Lamadie, L. Bruel, and M. Himbert, “Digital holographic measurement of liquid–liquid two-phase flows,” Opt. Lasers Eng. 50(12), 1716–1725 (2012).
[Crossref]

Lecler, S.

Lee, S.-H.

Liang, X.

X. Liang, A. Liu, C. Lim, T. Ayi, and P. Yap, “Determining refractive index of single living cell using an integrated microchip,” Sens. Actuators A Phys. 133(2), 349–354 (2007).
[Crossref]

Lim, C.

X. Liang, A. Liu, C. Lim, T. Ayi, and P. Yap, “Determining refractive index of single living cell using an integrated microchip,” Sens. Actuators A Phys. 133(2), 349–354 (2007).
[Crossref]

Liu, A.

X. Liang, A. Liu, C. Lim, T. Ayi, and P. Yap, “Determining refractive index of single living cell using an integrated microchip,” Sens. Actuators A Phys. 133(2), 349–354 (2007).
[Crossref]

Lock, J. A.

Lue, N.

Y. Sung, N. Lue, B. Hamza, J. Martel, D. Irimia, R. R. Dasari, W. Choi, Z. Yaqoob, and P. So, “Three-dimensional holographic refractive-index measurement of continuously flowing cells in a microfluidic channel,” Phys. Rev. Appl. 1(1), 014002 (2014).
[Crossref] [PubMed]

Malkiel, E.

Martel, J.

Y. Sung, N. Lue, B. Hamza, J. Martel, D. Irimia, R. R. Dasari, W. Choi, Z. Yaqoob, and P. So, “Three-dimensional holographic refractive-index measurement of continuously flowing cells in a microfluidic channel,” Phys. Rev. Appl. 1(1), 014002 (2014).
[Crossref] [PubMed]

Méès, L.

M. P. Sentis, F. R. Onofri, L. Méès, and S. Radev, “Scattering of light by large bubbles: Coupling of geometrical and physical optics approximations,” J. Quant. Spectrosc. Radiat. Transf. 170, 8–18 (2015).
[Crossref]

Meyrueis, P.

Niraula, B.

D. Subedi, D. Adhikari, U. Joshi, H. Poudel, and B. Niraula, “Study of temperature and concentration dependence of refractive index of liquids using a novel technique,” Kathmandu University Journal of Science, Engineering and Technology 2, 1–7 (2006).

Onofri, F.

F. Onofri, T. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, T. H. Xu, and C. Tropea, “Phase‐Doppler Anemometry with the Dual Burst Technique for measurement of refractive index and absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Char. 13(2), 112–124 (1996).
[Crossref]

Onofri, F. R.

M. P. Sentis, L. Bruel, S. Charton, F. R. Onofri, and F. Lamadie, “Digital in-line holography for the characterization of flowing particles in astigmatic optical systems,” Opt. Lasers Eng. 88, 184–196 (2017).
[Crossref]

M. P. Sentis, F. R. Onofri, L. Méès, and S. Radev, “Scattering of light by large bubbles: Coupling of geometrical and physical optics approximations,” J. Quant. Spectrosc. Radiat. Transf. 170, 8–18 (2015).
[Crossref]

Panina, E.

Y. E. Geints, E. Panina, and A. Zemlyanov, “Control over parameters of photonic nanojets of dielectric microspheres,” Opt. Commun. 283(23), 4775–4781 (2010).
[Crossref]

Pianta, M.

Popov, E.

Poudel, H.

D. Subedi, D. Adhikari, U. Joshi, H. Poudel, and B. Niraula, “Study of temperature and concentration dependence of refractive index of liquids using a novel technique,” Kathmandu University Journal of Science, Engineering and Technology 2, 1–7 (2006).

Radev, S.

M. P. Sentis, F. R. Onofri, L. Méès, and S. Radev, “Scattering of light by large bubbles: Coupling of geometrical and physical optics approximations,” J. Quant. Spectrosc. Radiat. Transf. 170, 8–18 (2015).
[Crossref]

Rigneault, H.

Roichman, Y.

Sahakian, A. V.

A. Heifetz, S.-C. Kong, A. V. Sahakian, A. Taflove, and V. Backman, “Photonic nanojets,” J. Comput. Theor. Nanosci. 6(9), 1979–1992 (2009).
[Crossref] [PubMed]

Sentis, M. P.

M. P. Sentis, L. Bruel, S. Charton, F. R. Onofri, and F. Lamadie, “Digital in-line holography for the characterization of flowing particles in astigmatic optical systems,” Opt. Lasers Eng. 88, 184–196 (2017).
[Crossref]

M. P. Sentis, F. R. Onofri, L. Méès, and S. Radev, “Scattering of light by large bubbles: Coupling of geometrical and physical optics approximations,” J. Quant. Spectrosc. Radiat. Transf. 170, 8–18 (2015).
[Crossref]

Sheng, J.

Shpaisman, H.

H. Shpaisman, B. J. Krishnatreya, and D. G. Grier, “Holographic microrefractometer,” Appl. Phys. Lett. 101(9), 091102 (2012).
[Crossref]

So, P.

Y. Sung, N. Lue, B. Hamza, J. Martel, D. Irimia, R. R. Dasari, W. Choi, Z. Yaqoob, and P. So, “Three-dimensional holographic refractive-index measurement of continuously flowing cells in a microfluidic channel,” Phys. Rev. Appl. 1(1), 014002 (2014).
[Crossref] [PubMed]

Stone, B. R.

Stout, B.

Subedi, D.

D. Subedi, D. Adhikari, U. Joshi, H. Poudel, and B. Niraula, “Study of temperature and concentration dependence of refractive index of liquids using a novel technique,” Kathmandu University Journal of Science, Engineering and Technology 2, 1–7 (2006).

Sung, Y.

Y. Sung, N. Lue, B. Hamza, J. Martel, D. Irimia, R. R. Dasari, W. Choi, Z. Yaqoob, and P. So, “Three-dimensional holographic refractive-index measurement of continuously flowing cells in a microfluidic channel,” Phys. Rev. Appl. 1(1), 014002 (2014).
[Crossref] [PubMed]

Taflove, A.

A. Heifetz, S.-C. Kong, A. V. Sahakian, A. Taflove, and V. Backman, “Photonic nanojets,” J. Comput. Theor. Nanosci. 6(9), 1979–1992 (2009).
[Crossref] [PubMed]

Takakura, Y.

Tan, C.-Y.

C.-Y. Tan and Y.-X. Huang, “Dependence of refractive index on concentration and temperature in electrolyte solution, polar solution, nonpolar solution, and protein solution,” J. Chem. Eng. Data 60(10), 2827–2833 (2015).
[Crossref]

Thompson, B. J.

B. J. Thompson, “Holographic particle sizing techniques,” J. Phys. E Sci. Instrum. 7(10), 781–788 (1974).
[Crossref]

Tropea, C.

F. Onofri, T. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, T. H. Xu, and C. Tropea, “Phase‐Doppler Anemometry with the Dual Burst Technique for measurement of refractive index and absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Char. 13(2), 112–124 (1996).
[Crossref]

van Blaaderen, A.

van Oostrum, P.

Wenger, J.

Xu, T. H.

F. Onofri, T. Girasole, G. Gréhan, G. Gouesbet, G. Brenn, J. Domnick, T. H. Xu, and C. Tropea, “Phase‐Doppler Anemometry with the Dual Burst Technique for measurement of refractive index and absorption coefficient simultaneously with size and velocity,” Part. Part. Syst. Char. 13(2), 112–124 (1996).
[Crossref]

Yan, C.

Yang, S.-M.

Yap, P.

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Supplementary Material (1)

NameDescription
» Visualization 1: AVI (28456 KB)      Illustration of the proposed method to determine particle size, position, and refractive index using DH

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Figures (4)

Fig. 1
Fig. 1 Illustration of the proposed method to determine particle size, position, and refractive index using DH. (a) Direct LMT calculations of the near-field intensity distribution of a droplet with R = 550 µm, m1 = 1.4425, and m2 = 1.3325, (b) corresponding hologram in the sensor plane, and back-propagated holograms in the axial plane of (c) the photonic jet intensity maxima and (d) the particle center. (e)-(h) Similar to (a)-(d) but the hologram in (f) was produced by a real droplet with parameters similar to the droplet in (a). (i) Evolution of the indicators to determine the optimal reconstruction planes (see Visualization 1).
Fig. 2
Fig. 2 Direct calculation and reconstruction of (a) axial and (b) transverse intensity profiles of the near-field region [droplets and other optical parameters the same as in Fig. 1(a) except for R = 250 µm].
Fig. 3
Fig. 3 Numerical evaluation of the resolution of the method with respect to the relative refractive index. (a) Holograms were simulated and processed for 1000 droplets with randomly distributed sizes, relative refractive indices, and 3D positions. (b) Evolution of the dispersion of the retrieved refractive index [data’s were analyzed statistically over refractive index bandwidths of 0.02].
Fig. 4
Fig. 4 Estimation of (a) the refractive index m and (b) the radii R for three series of 500 quasi-monodisperse droplets of different liquids (two pure liquids and a non homogeneous mixture).

Equations (4)

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U z ( x,y )=[ I h ( x,y ) ][ 1 iλz exp( 2iπz λ )exp( iπ( x 2 + y 2 ) λz ) ],
Teng( z )= ( x,y ) ( Sob[ | U z ( x,y ) | ]E{ Sob[ | U z ( x,y ) | ] } ) 2 ,
Var( z )=E ( Im[ U z ( x,y ) ]E{ Im[ U z ( x,y ) ] } ) 2 .
m 2| z max z p | 2| z max z p |R

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