Abstract

The distribution of light scattered by a spheroidal particle is sensitive to the orientation of the particle. Based on interference technology, we present a method for obtaining the orientation of the spheroidal particle from in-focus and out-of-focus images. We simulate the in-focus images using the LightTools. From the optical transfer matrix theory, we obtain both the in-focus and corresponding out-of-focus images using Matlab. We find that the glare-point distribution of the in-focus image exhibits axial symmetry for a spheroidal particle and that it is perpendicular to the speckle orientation of the out-of-focus image. We establish an interferometric particle imaging system to experimentally acquire the out-of-focus and in-focus images of the transparent spheroidal particles. The experimental results agree with the simulations. We are thus able to propose a method for obtaining the orientation of a spheroidal particle using either the in-focus image or out-of-focus image. The method has potential applications in particle measurements.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
  7. Y. Hardalupas, S. Sahu, A. M. K. P. Taylor, and K. Zarogoulidis, “Simultaneous planar measurement of droplet velocity and size with gas phase velocities in a spray by combined ILIDS and PIV techniques,” Exp. Fluids 49(2), 417–434 (2010).
    [Crossref]
  8. H. Zhang, J. Liu, M. Zhai, Y. Zhou, D. Jia, and T. Liu, “Theoretical analysis and experimental validation of sampling volume in tilted imaging system,” IEEE Photonics J. 7(6), 1–12 (2015).
  9. H. Zhang, Y. Zhou, J. Liu, D. Jia, and T. Liu, “A new method for determining the sampling volume and the number of particles within it for particle concentration identification in defocused interferometric particle imaging,” IEEE Photonics J. 9(1), 1–15 (2017).
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    [Crossref] [PubMed]
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    [Crossref]
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2017 (3)

H. Zhang, M. Zhai, J. Sun, Y. Zhou, D. Jia, T. Liu, and Y. Zhang, “Discrimination between spheres and spheroids in a detection system for single particles based on polarization characteristics,” J. Quant. Spectrosc. Ra. 187, 62–75 (2017).
[Crossref]

H. Zhang, Y. Zhou, J. Liu, D. Jia, and T. Liu, “A new method for determining the sampling volume and the number of particles within it for particle concentration identification in defocused interferometric particle imaging,” IEEE Photonics J. 9(1), 1–15 (2017).

J. Sun, H. Zhang, J. Li, Y. Zhou, D. Jia, and T. Liu, “Hybrid spherical particle field measurement based on interference technology,” Meas. Sci. Technol. 28(3), 1–7 (2017).
[Crossref]

2016 (1)

2015 (3)

X. Sun, S. Xiao, L. Ma, and B. Su, “Scattering of polarized Gaussian light by a spheroidal particle,” Opt. Commun. 336, 24–29 (2015).
[Crossref]

M. Brunel, S. G. Ruiz, J. Jacquot, and J. V. Beeck, “On the morphology of irregular rough particles from the analysis of speckle-like interferometric out-of-focus images,” Opt. Commun. 338, 193–198 (2015).
[Crossref]

H. Zhang, J. Liu, M. Zhai, Y. Zhou, D. Jia, and T. Liu, “Theoretical analysis and experimental validation of sampling volume in tilted imaging system,” IEEE Photonics J. 7(6), 1–12 (2015).

2014 (3)

K. W. Seo, H. J. Byeon, and S. J. Lee, “Measuring the light scattering and orientation of a spheroidal particle using in-line holography,” Opt. Lett. 39(13), 3915–3918 (2014).
[Crossref] [PubMed]

M. Brunel, S. Coëtmellec, G. Gréhan, and H. Shen, “Interferometric out-of-focus imaging simulator for irregular rough particles,” J. Eur. Opt. Soc-Rapid 9, 14008 (2014).

M. Brunel, H. Shen, S. Coëtmellec, G. Gréhan, and T. Delobel, “Determination of the size of irregular particles using interferometric out-of-focus imaging,” Int. J. Opt. 2014, 1–8 (2014).
[Crossref]

2012 (1)

2010 (1)

Y. Hardalupas, S. Sahu, A. M. K. P. Taylor, and K. Zarogoulidis, “Simultaneous planar measurement of droplet velocity and size with gas phase velocities in a spray by combined ILIDS and PIV techniques,” Exp. Fluids 49(2), 417–434 (2010).
[Crossref]

2004 (1)

Y. Zama, M. Kawahashi, and H. Hirahara, “Simultaneous measurement of droplet size and three-components of velocity in spray,” Opt. Rev. 11(6), 358–364 (2004).
[Crossref]

2000 (1)

S. Borrmann, B. Luo, and M. Mishchenko, “Application of the T-matrix method to the measurement of aspherical (ellipsoidal) particles with forward scattering optical particle counters,” J. Aerosol Sci. 31(7), 789–799 (2000).
[Crossref]

1998 (1)

1997 (1)

1988 (1)

J. J. Wen and M. A. Breazeale, “A diffraction beam field expressed as the superposition of Gaussian beams,” J. Acoust. Soc. Am. 83(5), 1752–1756 (1988).
[Crossref]

1987 (1)

Bagini, V.

Beeck, J. V.

M. Brunel, S. G. Ruiz, J. Jacquot, and J. V. Beeck, “On the morphology of irregular rough particles from the analysis of speckle-like interferometric out-of-focus images,” Opt. Commun. 338, 193–198 (2015).
[Crossref]

Borrmann, S.

S. Borrmann, B. Luo, and M. Mishchenko, “Application of the T-matrix method to the measurement of aspherical (ellipsoidal) particles with forward scattering optical particle counters,” J. Aerosol Sci. 31(7), 789–799 (2000).
[Crossref]

Breazeale, M. A.

J. J. Wen and M. A. Breazeale, “A diffraction beam field expressed as the superposition of Gaussian beams,” J. Acoust. Soc. Am. 83(5), 1752–1756 (1988).
[Crossref]

J. J. Wen and M. A. Breazeale, “Gaussian beam functions as a base function set for acoustical field calculations,” in Proceedings of IEEE Conference on Ultrasonics Symposium (IEEE, 1987), pp. 1137–1140.
[Crossref]

Brunel, M.

M. Brunel, S. G. Ruiz, J. Jacquot, and J. V. Beeck, “On the morphology of irregular rough particles from the analysis of speckle-like interferometric out-of-focus images,” Opt. Commun. 338, 193–198 (2015).
[Crossref]

M. Brunel, S. Coëtmellec, G. Gréhan, and H. Shen, “Interferometric out-of-focus imaging simulator for irregular rough particles,” J. Eur. Opt. Soc-Rapid 9, 14008 (2014).

M. Brunel, H. Shen, S. Coëtmellec, G. Gréhan, and T. Delobel, “Determination of the size of irregular particles using interferometric out-of-focus imaging,” Int. J. Opt. 2014, 1–8 (2014).
[Crossref]

H. Shen, S. Coëtmellec, G. Gréhan, and M. Brunel, “Interferometric laser imaging for droplet sizing revisited: elaboration of transfer matrix models for the description of complete systems,” Appl. Opt. 51(22), 5357–5368 (2012).
[Crossref] [PubMed]

Byeon, H.

Byeon, H. J.

Coëtmellec, S.

M. Brunel, S. Coëtmellec, G. Gréhan, and H. Shen, “Interferometric out-of-focus imaging simulator for irregular rough particles,” J. Eur. Opt. Soc-Rapid 9, 14008 (2014).

M. Brunel, H. Shen, S. Coëtmellec, G. Gréhan, and T. Delobel, “Determination of the size of irregular particles using interferometric out-of-focus imaging,” Int. J. Opt. 2014, 1–8 (2014).
[Crossref]

H. Shen, S. Coëtmellec, G. Gréhan, and M. Brunel, “Interferometric laser imaging for droplet sizing revisited: elaboration of transfer matrix models for the description of complete systems,” Appl. Opt. 51(22), 5357–5368 (2012).
[Crossref] [PubMed]

Delobel, T.

M. Brunel, H. Shen, S. Coëtmellec, G. Gréhan, and T. Delobel, “Determination of the size of irregular particles using interferometric out-of-focus imaging,” Int. J. Opt. 2014, 1–8 (2014).
[Crossref]

Fraser, D.

Go, T.

Gong, Y.

Y. Gong and Z. Wu, “Optical properties of ellipsoidal particles in the geometrical optics approximation,” in Proceedings of IEEE Conference on Microwave and Millimeter Wave Technology (IEEE, 2007), pp. 1–3.
[Crossref]

Gréhan, G.

M. Brunel, H. Shen, S. Coëtmellec, G. Gréhan, and T. Delobel, “Determination of the size of irregular particles using interferometric out-of-focus imaging,” Int. J. Opt. 2014, 1–8 (2014).
[Crossref]

M. Brunel, S. Coëtmellec, G. Gréhan, and H. Shen, “Interferometric out-of-focus imaging simulator for irregular rough particles,” J. Eur. Opt. Soc-Rapid 9, 14008 (2014).

H. Shen, S. Coëtmellec, G. Gréhan, and M. Brunel, “Interferometric laser imaging for droplet sizing revisited: elaboration of transfer matrix models for the description of complete systems,” Appl. Opt. 51(22), 5357–5368 (2012).
[Crossref] [PubMed]

Hanson, S. G.

Hardalupas, Y.

Y. Hardalupas, S. Sahu, A. M. K. P. Taylor, and K. Zarogoulidis, “Simultaneous planar measurement of droplet velocity and size with gas phase velocities in a spray by combined ILIDS and PIV techniques,” Exp. Fluids 49(2), 417–434 (2010).
[Crossref]

Hirahara, H.

Y. Zama, M. Kawahashi, and H. Hirahara, “Simultaneous measurement of droplet size and three-components of velocity in spray,” Opt. Rev. 11(6), 358–364 (2004).
[Crossref]

Jacquot, J.

M. Brunel, S. G. Ruiz, J. Jacquot, and J. V. Beeck, “On the morphology of irregular rough particles from the analysis of speckle-like interferometric out-of-focus images,” Opt. Commun. 338, 193–198 (2015).
[Crossref]

Jia, D.

H. Zhang, M. Zhai, J. Sun, Y. Zhou, D. Jia, T. Liu, and Y. Zhang, “Discrimination between spheres and spheroids in a detection system for single particles based on polarization characteristics,” J. Quant. Spectrosc. Ra. 187, 62–75 (2017).
[Crossref]

H. Zhang, Y. Zhou, J. Liu, D. Jia, and T. Liu, “A new method for determining the sampling volume and the number of particles within it for particle concentration identification in defocused interferometric particle imaging,” IEEE Photonics J. 9(1), 1–15 (2017).

J. Sun, H. Zhang, J. Li, Y. Zhou, D. Jia, and T. Liu, “Hybrid spherical particle field measurement based on interference technology,” Meas. Sci. Technol. 28(3), 1–7 (2017).
[Crossref]

H. Zhang, J. Liu, M. Zhai, Y. Zhou, D. Jia, and T. Liu, “Theoretical analysis and experimental validation of sampling volume in tilted imaging system,” IEEE Photonics J. 7(6), 1–12 (2015).

Kawahashi, M.

Y. Zama, M. Kawahashi, and H. Hirahara, “Simultaneous measurement of droplet size and three-components of velocity in spray,” Opt. Rev. 11(6), 358–364 (2004).
[Crossref]

Lambert, A. J.

Lee, S. J.

Li, J.

J. Sun, H. Zhang, J. Li, Y. Zhou, D. Jia, and T. Liu, “Hybrid spherical particle field measurement based on interference technology,” Meas. Sci. Technol. 28(3), 1–7 (2017).
[Crossref]

Liu, J.

H. Zhang, Y. Zhou, J. Liu, D. Jia, and T. Liu, “A new method for determining the sampling volume and the number of particles within it for particle concentration identification in defocused interferometric particle imaging,” IEEE Photonics J. 9(1), 1–15 (2017).

H. Zhang, J. Liu, M. Zhai, Y. Zhou, D. Jia, and T. Liu, “Theoretical analysis and experimental validation of sampling volume in tilted imaging system,” IEEE Photonics J. 7(6), 1–12 (2015).

Liu, T.

H. Zhang, M. Zhai, J. Sun, Y. Zhou, D. Jia, T. Liu, and Y. Zhang, “Discrimination between spheres and spheroids in a detection system for single particles based on polarization characteristics,” J. Quant. Spectrosc. Ra. 187, 62–75 (2017).
[Crossref]

J. Sun, H. Zhang, J. Li, Y. Zhou, D. Jia, and T. Liu, “Hybrid spherical particle field measurement based on interference technology,” Meas. Sci. Technol. 28(3), 1–7 (2017).
[Crossref]

H. Zhang, Y. Zhou, J. Liu, D. Jia, and T. Liu, “A new method for determining the sampling volume and the number of particles within it for particle concentration identification in defocused interferometric particle imaging,” IEEE Photonics J. 9(1), 1–15 (2017).

H. Zhang, J. Liu, M. Zhai, Y. Zhou, D. Jia, and T. Liu, “Theoretical analysis and experimental validation of sampling volume in tilted imaging system,” IEEE Photonics J. 7(6), 1–12 (2015).

Luo, B.

S. Borrmann, B. Luo, and M. Mishchenko, “Application of the T-matrix method to the measurement of aspherical (ellipsoidal) particles with forward scattering optical particle counters,” J. Aerosol Sci. 31(7), 789–799 (2000).
[Crossref]

Ma, L.

X. Sun, S. Xiao, L. Ma, and B. Su, “Scattering of polarized Gaussian light by a spheroidal particle,” Opt. Commun. 336, 24–29 (2015).
[Crossref]

Mishchenko, M.

S. Borrmann, B. Luo, and M. Mishchenko, “Application of the T-matrix method to the measurement of aspherical (ellipsoidal) particles with forward scattering optical particle counters,” J. Aerosol Sci. 31(7), 789–799 (2000).
[Crossref]

Palma, C.

Ruiz, S. G.

M. Brunel, S. G. Ruiz, J. Jacquot, and J. V. Beeck, “On the morphology of irregular rough particles from the analysis of speckle-like interferometric out-of-focus images,” Opt. Commun. 338, 193–198 (2015).
[Crossref]

Sahu, S.

Y. Hardalupas, S. Sahu, A. M. K. P. Taylor, and K. Zarogoulidis, “Simultaneous planar measurement of droplet velocity and size with gas phase velocities in a spray by combined ILIDS and PIV techniques,” Exp. Fluids 49(2), 417–434 (2010).
[Crossref]

Seo, K. W.

Shen, H.

M. Brunel, H. Shen, S. Coëtmellec, G. Gréhan, and T. Delobel, “Determination of the size of irregular particles using interferometric out-of-focus imaging,” Int. J. Opt. 2014, 1–8 (2014).
[Crossref]

M. Brunel, S. Coëtmellec, G. Gréhan, and H. Shen, “Interferometric out-of-focus imaging simulator for irregular rough particles,” J. Eur. Opt. Soc-Rapid 9, 14008 (2014).

H. Shen, S. Coëtmellec, G. Gréhan, and M. Brunel, “Interferometric laser imaging for droplet sizing revisited: elaboration of transfer matrix models for the description of complete systems,” Appl. Opt. 51(22), 5357–5368 (2012).
[Crossref] [PubMed]

Su, B.

X. Sun, S. Xiao, L. Ma, and B. Su, “Scattering of polarized Gaussian light by a spheroidal particle,” Opt. Commun. 336, 24–29 (2015).
[Crossref]

Sun, J.

H. Zhang, M. Zhai, J. Sun, Y. Zhou, D. Jia, T. Liu, and Y. Zhang, “Discrimination between spheres and spheroids in a detection system for single particles based on polarization characteristics,” J. Quant. Spectrosc. Ra. 187, 62–75 (2017).
[Crossref]

J. Sun, H. Zhang, J. Li, Y. Zhou, D. Jia, and T. Liu, “Hybrid spherical particle field measurement based on interference technology,” Meas. Sci. Technol. 28(3), 1–7 (2017).
[Crossref]

Sun, X.

X. Sun, S. Xiao, L. Ma, and B. Su, “Scattering of polarized Gaussian light by a spheroidal particle,” Opt. Commun. 336, 24–29 (2015).
[Crossref]

Taylor, A. M. K. P.

Y. Hardalupas, S. Sahu, A. M. K. P. Taylor, and K. Zarogoulidis, “Simultaneous planar measurement of droplet velocity and size with gas phase velocities in a spray by combined ILIDS and PIV techniques,” Exp. Fluids 49(2), 417–434 (2010).
[Crossref]

Wen, J. J.

J. J. Wen and M. A. Breazeale, “A diffraction beam field expressed as the superposition of Gaussian beams,” J. Acoust. Soc. Am. 83(5), 1752–1756 (1988).
[Crossref]

J. J. Wen and M. A. Breazeale, “Gaussian beam functions as a base function set for acoustical field calculations,” in Proceedings of IEEE Conference on Ultrasonics Symposium (IEEE, 1987), pp. 1137–1140.
[Crossref]

Wu, Z.

Y. Gong and Z. Wu, “Optical properties of ellipsoidal particles in the geometrical optics approximation,” in Proceedings of IEEE Conference on Microwave and Millimeter Wave Technology (IEEE, 2007), pp. 1–3.
[Crossref]

Xiao, S.

X. Sun, S. Xiao, L. Ma, and B. Su, “Scattering of polarized Gaussian light by a spheroidal particle,” Opt. Commun. 336, 24–29 (2015).
[Crossref]

Yura, H. T.

Zama, Y.

Y. Zama, M. Kawahashi, and H. Hirahara, “Simultaneous measurement of droplet size and three-components of velocity in spray,” Opt. Rev. 11(6), 358–364 (2004).
[Crossref]

Zarogoulidis, K.

Y. Hardalupas, S. Sahu, A. M. K. P. Taylor, and K. Zarogoulidis, “Simultaneous planar measurement of droplet velocity and size with gas phase velocities in a spray by combined ILIDS and PIV techniques,” Exp. Fluids 49(2), 417–434 (2010).
[Crossref]

Zhai, M.

H. Zhang, M. Zhai, J. Sun, Y. Zhou, D. Jia, T. Liu, and Y. Zhang, “Discrimination between spheres and spheroids in a detection system for single particles based on polarization characteristics,” J. Quant. Spectrosc. Ra. 187, 62–75 (2017).
[Crossref]

H. Zhang, J. Liu, M. Zhai, Y. Zhou, D. Jia, and T. Liu, “Theoretical analysis and experimental validation of sampling volume in tilted imaging system,” IEEE Photonics J. 7(6), 1–12 (2015).

Zhang, H.

H. Zhang, Y. Zhou, J. Liu, D. Jia, and T. Liu, “A new method for determining the sampling volume and the number of particles within it for particle concentration identification in defocused interferometric particle imaging,” IEEE Photonics J. 9(1), 1–15 (2017).

H. Zhang, M. Zhai, J. Sun, Y. Zhou, D. Jia, T. Liu, and Y. Zhang, “Discrimination between spheres and spheroids in a detection system for single particles based on polarization characteristics,” J. Quant. Spectrosc. Ra. 187, 62–75 (2017).
[Crossref]

J. Sun, H. Zhang, J. Li, Y. Zhou, D. Jia, and T. Liu, “Hybrid spherical particle field measurement based on interference technology,” Meas. Sci. Technol. 28(3), 1–7 (2017).
[Crossref]

H. Zhang, J. Liu, M. Zhai, Y. Zhou, D. Jia, and T. Liu, “Theoretical analysis and experimental validation of sampling volume in tilted imaging system,” IEEE Photonics J. 7(6), 1–12 (2015).

Zhang, Y.

H. Zhang, M. Zhai, J. Sun, Y. Zhou, D. Jia, T. Liu, and Y. Zhang, “Discrimination between spheres and spheroids in a detection system for single particles based on polarization characteristics,” J. Quant. Spectrosc. Ra. 187, 62–75 (2017).
[Crossref]

Zhou, Y.

H. Zhang, Y. Zhou, J. Liu, D. Jia, and T. Liu, “A new method for determining the sampling volume and the number of particles within it for particle concentration identification in defocused interferometric particle imaging,” IEEE Photonics J. 9(1), 1–15 (2017).

H. Zhang, M. Zhai, J. Sun, Y. Zhou, D. Jia, T. Liu, and Y. Zhang, “Discrimination between spheres and spheroids in a detection system for single particles based on polarization characteristics,” J. Quant. Spectrosc. Ra. 187, 62–75 (2017).
[Crossref]

J. Sun, H. Zhang, J. Li, Y. Zhou, D. Jia, and T. Liu, “Hybrid spherical particle field measurement based on interference technology,” Meas. Sci. Technol. 28(3), 1–7 (2017).
[Crossref]

H. Zhang, J. Liu, M. Zhai, Y. Zhou, D. Jia, and T. Liu, “Theoretical analysis and experimental validation of sampling volume in tilted imaging system,” IEEE Photonics J. 7(6), 1–12 (2015).

Appl. Opt. (2)

Exp. Fluids (1)

Y. Hardalupas, S. Sahu, A. M. K. P. Taylor, and K. Zarogoulidis, “Simultaneous planar measurement of droplet velocity and size with gas phase velocities in a spray by combined ILIDS and PIV techniques,” Exp. Fluids 49(2), 417–434 (2010).
[Crossref]

IEEE Photonics J. (2)

H. Zhang, J. Liu, M. Zhai, Y. Zhou, D. Jia, and T. Liu, “Theoretical analysis and experimental validation of sampling volume in tilted imaging system,” IEEE Photonics J. 7(6), 1–12 (2015).

H. Zhang, Y. Zhou, J. Liu, D. Jia, and T. Liu, “A new method for determining the sampling volume and the number of particles within it for particle concentration identification in defocused interferometric particle imaging,” IEEE Photonics J. 9(1), 1–15 (2017).

Int. J. Opt. (1)

M. Brunel, H. Shen, S. Coëtmellec, G. Gréhan, and T. Delobel, “Determination of the size of irregular particles using interferometric out-of-focus imaging,” Int. J. Opt. 2014, 1–8 (2014).
[Crossref]

J. Acoust. Soc. Am. (1)

J. J. Wen and M. A. Breazeale, “A diffraction beam field expressed as the superposition of Gaussian beams,” J. Acoust. Soc. Am. 83(5), 1752–1756 (1988).
[Crossref]

J. Aerosol Sci. (1)

S. Borrmann, B. Luo, and M. Mishchenko, “Application of the T-matrix method to the measurement of aspherical (ellipsoidal) particles with forward scattering optical particle counters,” J. Aerosol Sci. 31(7), 789–799 (2000).
[Crossref]

J. Eur. Opt. Soc-Rapid (1)

M. Brunel, S. Coëtmellec, G. Gréhan, and H. Shen, “Interferometric out-of-focus imaging simulator for irregular rough particles,” J. Eur. Opt. Soc-Rapid 9, 14008 (2014).

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

J. Quant. Spectrosc. Ra. (1)

H. Zhang, M. Zhai, J. Sun, Y. Zhou, D. Jia, T. Liu, and Y. Zhang, “Discrimination between spheres and spheroids in a detection system for single particles based on polarization characteristics,” J. Quant. Spectrosc. Ra. 187, 62–75 (2017).
[Crossref]

Meas. Sci. Technol. (1)

J. Sun, H. Zhang, J. Li, Y. Zhou, D. Jia, and T. Liu, “Hybrid spherical particle field measurement based on interference technology,” Meas. Sci. Technol. 28(3), 1–7 (2017).
[Crossref]

Opt. Commun. (2)

X. Sun, S. Xiao, L. Ma, and B. Su, “Scattering of polarized Gaussian light by a spheroidal particle,” Opt. Commun. 336, 24–29 (2015).
[Crossref]

M. Brunel, S. G. Ruiz, J. Jacquot, and J. V. Beeck, “On the morphology of irregular rough particles from the analysis of speckle-like interferometric out-of-focus images,” Opt. Commun. 338, 193–198 (2015).
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[Crossref]

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Figures (11)

Fig. 1
Fig. 1 Schematic of the IPI system
Fig. 2
Fig. 2 Definition of the orientation of an arbitrarily oriented spheroidal particle
Fig. 3
Fig. 3 Particle imaging model based on LightTools
Fig. 4
Fig. 4 In-focus image of a spherical particle
Fig. 5
Fig. 5 In-focus images of a spheroidal particle with Θ = 90°. Ψ = (a) 0°, (b) 30°, (c) 60°, (d) 90°, (e) 120°, and (f) 150°.
Fig. 6
Fig. 6 Projection of the emitting points. (a) Five emitting points and (b) symmetric distributions of (a)
Fig. 7
Fig. 7 Out-of-focus and in-focus images simulated by Matlab. (a)–(d) Out-of-focus and (e)–(h) in-focus images. (i)–(l) Magnified combination of the out-of-focus and corresponding in-focus images.
Fig. 8
Fig. 8 Experimental setup
Fig. 9
Fig. 9 Interference images of a spherical particle. (a) Out-of-focus and (b) in-focus images
Fig. 10
Fig. 10 Interference images of a specific spheroidal particle. (a)–(d) Out-of-focus images for different angles of rotation, and (e)–(h) corresponding in-focus images collected by the same CCD. (i)–(l) Magnified combination of the out-of-focus and corresponding in-focus images.
Fig. 11
Fig. 11 Interference images for different spheroidal particles. (a)–(d) Out-of-focus images for different spheroidal particles, and (e)–(h) corresponding in-focus images. (i)–(l) Magnified combination of the out-of-focus and corresponding in-focus images.

Equations (7)

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Δl= M d p 2 { cos θ 2 +sin[ tan 1 ( sin θ 2 cos θ 2 1 m ) ] },
G 1 (x,y,z)= j=1 N gp α j δ(x a j ,y b j ,z) e i φ j ,
G 2 (x',y',u+v)= j=1 N gp k=1 N [ e i 2π λ (u+v) e i π D 2 (x ' 2 +y ' 2 ) λ B 2 (iλ) 2 B 1,j B 2 × P k π γ x,j (k) γ y,j (k) α j e β j (k) e i φ j ],
β j (k)=i π A 1,j λ B 1,j ( a j 2 + b j 2 ) φ j,x' 2 + φ j,y' 2 4 γ j (k) ,
γ j (k)= Q k R 0 2 i π λ ( D 1,j B 1,j + A 2 B 2 ),
φ j,x' = 2π λ ( a j B 1,j + x' B 2 ),
φ j,y' = 2π λ ( b j B 1,j + y' B 2 ).

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