Abstract

We report the first experimental validation of the Vectorial Complex Ray Model (VCRM) using the scattering patterns of large oblate droplets trapped in an acoustic field. The two principal radii and refractive index of the droplets are retrieved with a minimization method that involves VCRM predictions and experimental light scattering patterns. The latter are recorded in the droplet equatorial plane between the primary rainbow region and the associated hyperbolic-umbilic diffraction catastrophe. The results demonstrate that the VCRM can predict the fine and coarse stuctures of scattering patterns with good precision, opening up perspectives for the characterization of large non-spherical particles.

© 2015 Optical Society of America

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References

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2014 (1)

G. Derkachov, D. Jakubczyk, M. Woźniak, J. Archer, and M. Kolwas, “High-precision temperature determination of evaporating light-absorbing and non-light-absorbing droplets,” J. Phys. Chem. B 118(43), 12566–12574 (2014).
[Crossref] [PubMed]

2013 (3)

2012 (1)

2011 (2)

2010 (1)

N. Fdida and J.-B. Blaisot, “Drop size distribution measured by imaging: determination of the measurement volume by the calibration of the point spread function,” Meas. Sci. Technol. 21(2), 025501 (2010).
[Crossref]

2005 (1)

1999 (1)

A. L. Yarin, G. Brenn, O. Kastner, D. Rensink, and C. Tropea, “Evaporation of acoustically levitated droplets,” J. Fluid Mech. 399, 151–204 (1999).
[Crossref]

1994 (2)

1992 (1)

1991 (1)

1984 (2)

P. L. Marston and E. H. Trinh, “Hyperbolic umbilic diffraction catastrophe and rainbow scattering from spheroidal drops,” Nature 312(5994), 529–531 (1984).
[Crossref]

J. F. Nye, “Rainbow scattering from spheroidal drops - an explanation of the hyperbolic umbilic foci,” Nature 312(5994), 531–532 (1984).
[Crossref]

1980 (1)

1979 (1)

M. V. Berry, J. F. Nye, and F. J. Wright, “The Elliptic Umbilic Diffraction Catastrophe,” Philos. Trans. R. Soc. Lond. A 291(1382), 453–484 (1979).
[Crossref]

Archer, J.

G. Derkachov, D. Jakubczyk, M. Woźniak, J. Archer, and M. Kolwas, “High-precision temperature determination of evaporating light-absorbing and non-light-absorbing droplets,” J. Phys. Chem. B 118(43), 12566–12574 (2014).
[Crossref] [PubMed]

Barbosa, S.

Berry, M. V.

M. V. Berry, J. F. Nye, and F. J. Wright, “The Elliptic Umbilic Diffraction Catastrophe,” Philos. Trans. R. Soc. Lond. A 291(1382), 453–484 (1979).
[Crossref]

Blaisot, J.-B.

N. Fdida and J.-B. Blaisot, “Drop size distribution measured by imaging: determination of the measurement volume by the calibration of the point spread function,” Meas. Sci. Technol. 21(2), 025501 (2010).
[Crossref]

Brenn, G.

A. L. Yarin, G. Brenn, O. Kastner, D. Rensink, and C. Tropea, “Evaporation of acoustically levitated droplets,” J. Fluid Mech. 399, 151–204 (1999).
[Crossref]

Dean, C. E.

Derkachov, G.

G. Derkachov, D. Jakubczyk, M. Woźniak, J. Archer, and M. Kolwas, “High-precision temperature determination of evaporating light-absorbing and non-light-absorbing droplets,” J. Phys. Chem. B 118(43), 12566–12574 (2014).
[Crossref] [PubMed]

Fdida, N.

N. Fdida and J.-B. Blaisot, “Drop size distribution measured by imaging: determination of the measurement volume by the calibration of the point spread function,” Meas. Sci. Technol. 21(2), 025501 (2010).
[Crossref]

Girasole, T.

Han, X.

Hovenac, E. A.

Jakubczyk, D.

G. Derkachov, D. Jakubczyk, M. Woźniak, J. Archer, and M. Kolwas, “High-precision temperature determination of evaporating light-absorbing and non-light-absorbing droplets,” J. Phys. Chem. B 118(43), 12566–12574 (2014).
[Crossref] [PubMed]

Jiang, K.

Kaduchak, G.

Kastner, O.

A. L. Yarin, G. Brenn, O. Kastner, D. Rensink, and C. Tropea, “Evaporation of acoustically levitated droplets,” J. Fluid Mech. 399, 151–204 (1999).
[Crossref]

Kolwas, M.

G. Derkachov, D. Jakubczyk, M. Woźniak, J. Archer, and M. Kolwas, “High-precision temperature determination of evaporating light-absorbing and non-light-absorbing droplets,” J. Phys. Chem. B 118(43), 12566–12574 (2014).
[Crossref] [PubMed]

Krzysiek, M. A.

Lock, J. A.

Marston, P. L.

Messager, V.

Mroczka, J.

Nye, J. F.

J. F. Nye, “Rainbow scattering from spheroidal drops - an explanation of the hyperbolic umbilic foci,” Nature 312(5994), 531–532 (1984).
[Crossref]

M. V. Berry, J. F. Nye, and F. J. Wright, “The Elliptic Umbilic Diffraction Catastrophe,” Philos. Trans. R. Soc. Lond. A 291(1382), 453–484 (1979).
[Crossref]

Onofri, F.

Onofri, F. R. A.

Radev, S.

Ren, K. F.

Rensink, D.

A. L. Yarin, G. Brenn, O. Kastner, D. Rensink, and C. Tropea, “Evaporation of acoustically levitated droplets,” J. Fluid Mech. 399, 151–204 (1999).
[Crossref]

Riethmuller, M. L.

Rozé, C.

K. F. Ren, F. Onofri, C. Rozé, and T. Girasole, “Vectorial complex ray model and application to two-dimensional scattering of plane wave by a spheroidal particle,” Opt. Lett. 36(3), 370–372 (2011).
[Crossref] [PubMed]

Y. Yuan, K. F. Ren, and C. Rozé, “Fraunhofer diffraction of irregular apertures by Heisenberg uncertainty Monte Carlo model” (in press) (2015).

Sentis, M.

Sheng, X.

M. Yang, Y. Wu, X. Sheng, and K. F. Ren, “Comparison of scattering diagrams of large non-spherical particles calculated by VCRM and MLFMA,” J. Quant. Spectrosc. Radiat. Transf.in press.

Simpson, H. J.

Trinh, E. H.

P. L. Marston and E. H. Trinh, “Hyperbolic umbilic diffraction catastrophe and rainbow scattering from spheroidal drops,” Nature 312(5994), 529–531 (1984).
[Crossref]

Tropea, C.

H. Yu, F. Xu, and C. Tropea, “Spheroidal droplet measurements based on generalized rainbow patterns,” J. Quant. Spectrosc. Radiat. Transf. 126, 105–112 (2013).
[Crossref]

H. Yu, F. Xu, and C. Tropea, “Optical caustics associated with the primary rainbow of oblate droplets: simulation and application in non-sphericity measurement,” Opt. Express 21(22), 25761–25771 (2013).
[Crossref] [PubMed]

A. L. Yarin, G. Brenn, O. Kastner, D. Rensink, and C. Tropea, “Evaporation of acoustically levitated droplets,” J. Fluid Mech. 399, 151–204 (1999).
[Crossref]

van Beeck, J. P.

Vetrano, M. R.

Wozniak, M.

G. Derkachov, D. Jakubczyk, M. Woźniak, J. Archer, and M. Kolwas, “High-precision temperature determination of evaporating light-absorbing and non-light-absorbing droplets,” J. Phys. Chem. B 118(43), 12566–12574 (2014).
[Crossref] [PubMed]

Wright, F. J.

M. V. Berry, J. F. Nye, and F. J. Wright, “The Elliptic Umbilic Diffraction Catastrophe,” Philos. Trans. R. Soc. Lond. A 291(1382), 453–484 (1979).
[Crossref]

Wu, Y.

M. Yang, Y. Wu, X. Sheng, and K. F. Ren, “Comparison of scattering diagrams of large non-spherical particles calculated by VCRM and MLFMA,” J. Quant. Spectrosc. Radiat. Transf.in press.

Xu, F.

H. Yu, F. Xu, and C. Tropea, “Spheroidal droplet measurements based on generalized rainbow patterns,” J. Quant. Spectrosc. Radiat. Transf. 126, 105–112 (2013).
[Crossref]

H. Yu, F. Xu, and C. Tropea, “Optical caustics associated with the primary rainbow of oblate droplets: simulation and application in non-sphericity measurement,” Opt. Express 21(22), 25761–25771 (2013).
[Crossref] [PubMed]

Yang, M.

M. Yang, Y. Wu, X. Sheng, and K. F. Ren, “Comparison of scattering diagrams of large non-spherical particles calculated by VCRM and MLFMA,” J. Quant. Spectrosc. Radiat. Transf.in press.

Yarin, A. L.

A. L. Yarin, G. Brenn, O. Kastner, D. Rensink, and C. Tropea, “Evaporation of acoustically levitated droplets,” J. Fluid Mech. 399, 151–204 (1999).
[Crossref]

Yu, H.

H. Yu, F. Xu, and C. Tropea, “Spheroidal droplet measurements based on generalized rainbow patterns,” J. Quant. Spectrosc. Radiat. Transf. 126, 105–112 (2013).
[Crossref]

H. Yu, F. Xu, and C. Tropea, “Optical caustics associated with the primary rainbow of oblate droplets: simulation and application in non-sphericity measurement,” Opt. Express 21(22), 25761–25771 (2013).
[Crossref] [PubMed]

Yuan, Y.

Y. Yuan, K. F. Ren, and C. Rozé, “Fraunhofer diffraction of irregular apertures by Heisenberg uncertainty Monte Carlo model” (in press) (2015).

Appl. Opt. (5)

J. Fluid Mech. (1)

A. L. Yarin, G. Brenn, O. Kastner, D. Rensink, and C. Tropea, “Evaporation of acoustically levitated droplets,” J. Fluid Mech. 399, 151–204 (1999).
[Crossref]

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

J. Phys. Chem. B (1)

G. Derkachov, D. Jakubczyk, M. Woźniak, J. Archer, and M. Kolwas, “High-precision temperature determination of evaporating light-absorbing and non-light-absorbing droplets,” J. Phys. Chem. B 118(43), 12566–12574 (2014).
[Crossref] [PubMed]

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

H. Yu, F. Xu, and C. Tropea, “Spheroidal droplet measurements based on generalized rainbow patterns,” J. Quant. Spectrosc. Radiat. Transf. 126, 105–112 (2013).
[Crossref]

Meas. Sci. Technol. (1)

N. Fdida and J.-B. Blaisot, “Drop size distribution measured by imaging: determination of the measurement volume by the calibration of the point spread function,” Meas. Sci. Technol. 21(2), 025501 (2010).
[Crossref]

Nature (2)

P. L. Marston and E. H. Trinh, “Hyperbolic umbilic diffraction catastrophe and rainbow scattering from spheroidal drops,” Nature 312(5994), 529–531 (1984).
[Crossref]

J. F. Nye, “Rainbow scattering from spheroidal drops - an explanation of the hyperbolic umbilic foci,” Nature 312(5994), 531–532 (1984).
[Crossref]

Opt. Express (1)

Opt. Lett. (3)

Philos. Trans. R. Soc. Lond. A (1)

M. V. Berry, J. F. Nye, and F. J. Wright, “The Elliptic Umbilic Diffraction Catastrophe,” Philos. Trans. R. Soc. Lond. A 291(1382), 453–484 (1979).
[Crossref]

Other (3)

M. Yang, Y. Wu, X. Sheng, and K. F. Ren, “Comparison of scattering diagrams of large non-spherical particles calculated by VCRM and MLFMA,” J. Quant. Spectrosc. Radiat. Transf.in press.

H. C. van de Hulst, Light Scattering by Small Particles (Dover Publications, 1957).

Y. Yuan, K. F. Ren, and C. Rozé, “Fraunhofer diffraction of irregular apertures by Heisenberg uncertainty Monte Carlo model” (in press) (2015).

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Figures (4)

Fig. 1
Fig. 1

Experimental setup with coordinate system.

Fig. 2
Fig. 2

Experimental far-field scattering patterns (color coding: intensity) and shadowgraph images (top right corners) of a DEHS droplet. From (a) to (c), the droplet's aspect ratio b/a increases and refractive index decreases when the amplitude of the acoustic field is reduced.

Fig. 3
Fig. 3

Comparison of VCRM and experimental normalized equatorial scattering diagrams for the droplets considered in Fig. 2.

Fig. 4
Fig. 4

(a) Principal radii measured with the RD- and SI-System and (b) corresponding evolution of the droplet refractive index during the course of the experiment.

Equations (2)

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( a,b,m ){ ( a α , b β , m μ )/ min a α b β , m μ ( ε ) } with ε( a α , b β , m μ )= i=v i=w ( S i,α,β,μ E i ) 2
S i,α,β,μ = S i,α,β,μ / i=v i=w S i,α,β,μ , E i = E i / i=v i=w E i .

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