Abstract

A method based on unidirectional gradient-matched algorithm and Fourier transform technique is proposed to simultaneously extract the location and the number of fringes/fringe spacing of a particle interferogram. The position coordinate (x,y) of a particle can be determined with high accuracy because of the elimination of the fringe within the particle fringe pattern. Furthermore, the method can be employed to achieve sub-pixel frequency extraction when combined with an improved Rife algorithm. The performance of the method has been verified by numerical simulations and experimental measurements. The results suggest that the method presented here is highly beneficial to applications such as spray, in accurately measuring both the particle size and its location.

© 2016 Optical Society of America

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References

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  1. G. Konig, K. Anders, and A. Frohn, “A new light-scattering technique to measurement the diameter of periodically generated moving droplets,” J. Aerosol Sci. 17(2), 157–167 (1986).
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    [Crossref]
  3. 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]
  4. A. V. Bilsky, Yu. A. Lozhkin, and D. M. Markovich, “Interferometric technique for measurement of droplet diameter,” Thermophys. Aeromech. 18(1), 1–12 (2011).
    [Crossref]
  5. A. R. Glover, S. M. Skippon, and R. D. Boyle, “Interferometric laser imaging for droplet sizing: a method for droplet-size measurement in sparse spray systems,” Appl. Opt. 34(36), 8409–8421 (1995).
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  8. S. Dehaeck and J. P. A. J. van Beeck, “Multifrequency interferometric particle imaging for gas bubble sizing,” Exp. Fluids 45(5), 823–831 (2008).
    [Crossref]
  9. 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]
  10. R. E. H. Miles, A. E. Carrithers, and J. P. Reid, “Novel optical techniques for measurements of light extinction, scattering and absorption by single aerosol particles,” Laser Photonics Rev. 5(4), 534–552 (2011).
    [Crossref]
  11. G. Lacagnina, S. Grizzi, M. Falchi, F. Di Felice, and G. P. Romano, “Simultaneous size and velocity measurements of cavitating microbubbles using interferometric laser imaging,” Exp. Fluids 50(4), 1153–1167 (2011).
    [Crossref]
  12. A. Quérel, P. Lemaitre, M. Brunel, E. Porcheron, and G. Gréhan, “Real-time global interferometric laser imaging for the droplet sizing(ILIDS) algorithm for airborne research,” Meas. Sci. Technol. 21(1), 015306 (2010).
    [Crossref]
  13. H. Bocanegra Evans, N. Dam, D. van der Voort, G. Bertens, and W. van de Water, “Measuring droplet size distributions from overlapping interferometric particle images,” Rev. Sci. Instrum. 86(2), 023709 (2015).
    [Crossref] [PubMed]
  14. Q. Lu, X. Wang, T. Lu, Z. Li, and Y. Zhang, “Linear interferometric image processing for analysis of a particle in a volume,” J. Opt. 16(4), 045703 (2014).
    [Crossref]
  15. Q. Lu, B. Ge, Y. Chen, and Y. Zhang, “A algorithm for interferometric image processing of interferometric particle imaging,” Acta Opt. Sin. 31(4), 0412009 (2011).
    [Crossref]
  16. Q. Lu, W. Jing, T. Lu, X. Wang, and Y. Zhang, “High-accuracy particle sizing by interferometric particle imaging,” Opt. Commun. 312(2), 312–318 (2014).
  17. N. Damaschke, H. Nobach, T. I. Nonn, N. Semidetnov, and C. Tropea, “Multi-dimensional particle sizing technique,” Exp. Fluids 39(2), 336–350 (2005).
    [Crossref]
  18. K. H. Hesselbacher, K. Anders, and A. Frohn, “Experimental investigation of Gaussian beam effects on the accuracy of a droplet sizing method,” Appl. Opt. 30(33), 4930–4935 (1991).
    [Crossref] [PubMed]
  19. N. Semidetnov and C. Tropea, “Conversion relationships for multidimensional particle sizing techniques,” Meas. Sci. Technol. 15(1), 112–118 (2004).
    [Crossref]
  20. Z. Deng, Y. Liu, and Z. Wang, “Modified Rife algorithm for frequency estimation of sinusoid wave,” J. Data Acquis. Process. 21(4), 473–477 (2006, in Chinese).
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  22. H. Wang and G. Zhao, “Improved Rife algorithm for frequency estimation of sinusoid wave,” Signal Process. 26(10), 1573–1576 (2010).
  23. D. C. Rife and G. A. Vincent, “Use of the discrete Fourier transform in the measurement of frequencies and levels of tones,” Bell Syst. Tech. J. 49(2), 197–228 (1970).
    [Crossref]
  24. S. Dehaeck and J. P. A. J. van Beeck, “Designing a maximum precision interferometric particle imaging set-up,” Exp. Fluids 42(5), 767–781 (2007).
    [Crossref]

2015 (1)

H. Bocanegra Evans, N. Dam, D. van der Voort, G. Bertens, and W. van de Water, “Measuring droplet size distributions from overlapping interferometric particle images,” Rev. Sci. Instrum. 86(2), 023709 (2015).
[Crossref] [PubMed]

2014 (2)

Q. Lu, X. Wang, T. Lu, Z. Li, and Y. Zhang, “Linear interferometric image processing for analysis of a particle in a volume,” J. Opt. 16(4), 045703 (2014).
[Crossref]

Q. Lu, W. Jing, T. Lu, X. Wang, and Y. Zhang, “High-accuracy particle sizing by interferometric particle imaging,” Opt. Commun. 312(2), 312–318 (2014).

2012 (1)

2011 (5)

C. Lacour, D. Durox, S. Ducruix, and M. Massot, “Interaction of a polydisperse spray with vortices,” Exp. Fluids 51(2), 295–311 (2011).
[Crossref]

Q. Lu, B. Ge, Y. Chen, and Y. Zhang, “A algorithm for interferometric image processing of interferometric particle imaging,” Acta Opt. Sin. 31(4), 0412009 (2011).
[Crossref]

R. E. H. Miles, A. E. Carrithers, and J. P. Reid, “Novel optical techniques for measurements of light extinction, scattering and absorption by single aerosol particles,” Laser Photonics Rev. 5(4), 534–552 (2011).
[Crossref]

G. Lacagnina, S. Grizzi, M. Falchi, F. Di Felice, and G. P. Romano, “Simultaneous size and velocity measurements of cavitating microbubbles using interferometric laser imaging,” Exp. Fluids 50(4), 1153–1167 (2011).
[Crossref]

A. V. Bilsky, Yu. A. Lozhkin, and D. M. Markovich, “Interferometric technique for measurement of droplet diameter,” Thermophys. Aeromech. 18(1), 1–12 (2011).
[Crossref]

2010 (3)

H. Wang and G. Zhao, “Improved Rife algorithm for frequency estimation of sinusoid wave,” Signal Process. 26(10), 1573–1576 (2010).

A. Quérel, P. Lemaitre, M. Brunel, E. Porcheron, and G. Gréhan, “Real-time global interferometric laser imaging for the droplet sizing(ILIDS) algorithm for airborne research,” Meas. Sci. Technol. 21(1), 015306 (2010).
[Crossref]

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]

2008 (1)

S. Dehaeck and J. P. A. J. van Beeck, “Multifrequency interferometric particle imaging for gas bubble sizing,” Exp. Fluids 45(5), 823–831 (2008).
[Crossref]

2007 (1)

S. Dehaeck and J. P. A. J. van Beeck, “Designing a maximum precision interferometric particle imaging set-up,” Exp. Fluids 42(5), 767–781 (2007).
[Crossref]

2006 (1)

Z. Deng, Y. Liu, and Z. Wang, “Modified Rife algorithm for frequency estimation of sinusoid wave,” J. Data Acquis. Process. 21(4), 473–477 (2006, in Chinese).

2005 (1)

N. Damaschke, H. Nobach, T. I. Nonn, N. Semidetnov, and C. Tropea, “Multi-dimensional particle sizing technique,” Exp. Fluids 39(2), 336–350 (2005).
[Crossref]

2004 (1)

N. Semidetnov and C. Tropea, “Conversion relationships for multidimensional particle sizing techniques,” Meas. Sci. Technol. 15(1), 112–118 (2004).
[Crossref]

2002 (1)

N. Damaschke, H. Nobach, and C. Tropea, “Optical limits of particle concentration for multi-dimensional particle sizing techniques in fluid mechanics,” Exp. Fluids 32(2), 143–152 (2002).
[Crossref]

1995 (1)

1991 (1)

1986 (1)

G. Konig, K. Anders, and A. Frohn, “A new light-scattering technique to measurement the diameter of periodically generated moving droplets,” J. Aerosol Sci. 17(2), 157–167 (1986).
[Crossref]

1970 (1)

D. C. Rife and G. A. Vincent, “Use of the discrete Fourier transform in the measurement of frequencies and levels of tones,” Bell Syst. Tech. J. 49(2), 197–228 (1970).
[Crossref]

Anders, K.

K. H. Hesselbacher, K. Anders, and A. Frohn, “Experimental investigation of Gaussian beam effects on the accuracy of a droplet sizing method,” Appl. Opt. 30(33), 4930–4935 (1991).
[Crossref] [PubMed]

G. Konig, K. Anders, and A. Frohn, “A new light-scattering technique to measurement the diameter of periodically generated moving droplets,” J. Aerosol Sci. 17(2), 157–167 (1986).
[Crossref]

Bertens, G.

H. Bocanegra Evans, N. Dam, D. van der Voort, G. Bertens, and W. van de Water, “Measuring droplet size distributions from overlapping interferometric particle images,” Rev. Sci. Instrum. 86(2), 023709 (2015).
[Crossref] [PubMed]

Bilsky, A. V.

A. V. Bilsky, Yu. A. Lozhkin, and D. M. Markovich, “Interferometric technique for measurement of droplet diameter,” Thermophys. Aeromech. 18(1), 1–12 (2011).
[Crossref]

Bocanegra Evans, H.

H. Bocanegra Evans, N. Dam, D. van der Voort, G. Bertens, and W. van de Water, “Measuring droplet size distributions from overlapping interferometric particle images,” Rev. Sci. Instrum. 86(2), 023709 (2015).
[Crossref] [PubMed]

Boyle, R. D.

Brunel, M.

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]

A. Quérel, P. Lemaitre, M. Brunel, E. Porcheron, and G. Gréhan, “Real-time global interferometric laser imaging for the droplet sizing(ILIDS) algorithm for airborne research,” Meas. Sci. Technol. 21(1), 015306 (2010).
[Crossref]

Carrithers, A. E.

R. E. H. Miles, A. E. Carrithers, and J. P. Reid, “Novel optical techniques for measurements of light extinction, scattering and absorption by single aerosol particles,” Laser Photonics Rev. 5(4), 534–552 (2011).
[Crossref]

Chen, Y.

Q. Lu, B. Ge, Y. Chen, and Y. Zhang, “A algorithm for interferometric image processing of interferometric particle imaging,” Acta Opt. Sin. 31(4), 0412009 (2011).
[Crossref]

Coëtmellec, S.

Dam, N.

H. Bocanegra Evans, N. Dam, D. van der Voort, G. Bertens, and W. van de Water, “Measuring droplet size distributions from overlapping interferometric particle images,” Rev. Sci. Instrum. 86(2), 023709 (2015).
[Crossref] [PubMed]

Damaschke, N.

N. Damaschke, H. Nobach, T. I. Nonn, N. Semidetnov, and C. Tropea, “Multi-dimensional particle sizing technique,” Exp. Fluids 39(2), 336–350 (2005).
[Crossref]

N. Damaschke, H. Nobach, and C. Tropea, “Optical limits of particle concentration for multi-dimensional particle sizing techniques in fluid mechanics,” Exp. Fluids 32(2), 143–152 (2002).
[Crossref]

Dehaeck, S.

S. Dehaeck and J. P. A. J. van Beeck, “Multifrequency interferometric particle imaging for gas bubble sizing,” Exp. Fluids 45(5), 823–831 (2008).
[Crossref]

S. Dehaeck and J. P. A. J. van Beeck, “Designing a maximum precision interferometric particle imaging set-up,” Exp. Fluids 42(5), 767–781 (2007).
[Crossref]

Deng, Z.

Z. Deng, Y. Liu, and Z. Wang, “Modified Rife algorithm for frequency estimation of sinusoid wave,” J. Data Acquis. Process. 21(4), 473–477 (2006, in Chinese).

Di Felice, F.

G. Lacagnina, S. Grizzi, M. Falchi, F. Di Felice, and G. P. Romano, “Simultaneous size and velocity measurements of cavitating microbubbles using interferometric laser imaging,” Exp. Fluids 50(4), 1153–1167 (2011).
[Crossref]

Ducruix, S.

C. Lacour, D. Durox, S. Ducruix, and M. Massot, “Interaction of a polydisperse spray with vortices,” Exp. Fluids 51(2), 295–311 (2011).
[Crossref]

Durox, D.

C. Lacour, D. Durox, S. Ducruix, and M. Massot, “Interaction of a polydisperse spray with vortices,” Exp. Fluids 51(2), 295–311 (2011).
[Crossref]

Falchi, M.

G. Lacagnina, S. Grizzi, M. Falchi, F. Di Felice, and G. P. Romano, “Simultaneous size and velocity measurements of cavitating microbubbles using interferometric laser imaging,” Exp. Fluids 50(4), 1153–1167 (2011).
[Crossref]

Frohn, A.

K. H. Hesselbacher, K. Anders, and A. Frohn, “Experimental investigation of Gaussian beam effects on the accuracy of a droplet sizing method,” Appl. Opt. 30(33), 4930–4935 (1991).
[Crossref] [PubMed]

G. Konig, K. Anders, and A. Frohn, “A new light-scattering technique to measurement the diameter of periodically generated moving droplets,” J. Aerosol Sci. 17(2), 157–167 (1986).
[Crossref]

Ge, B.

Q. Lu, B. Ge, Y. Chen, and Y. Zhang, “A algorithm for interferometric image processing of interferometric particle imaging,” Acta Opt. Sin. 31(4), 0412009 (2011).
[Crossref]

Glover, A. R.

Gréhan, G.

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]

A. Quérel, P. Lemaitre, M. Brunel, E. Porcheron, and G. Gréhan, “Real-time global interferometric laser imaging for the droplet sizing(ILIDS) algorithm for airborne research,” Meas. Sci. Technol. 21(1), 015306 (2010).
[Crossref]

Grizzi, S.

G. Lacagnina, S. Grizzi, M. Falchi, F. Di Felice, and G. P. Romano, “Simultaneous size and velocity measurements of cavitating microbubbles using interferometric laser imaging,” Exp. Fluids 50(4), 1153–1167 (2011).
[Crossref]

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]

Hesselbacher, K. H.

Jing, W.

Q. Lu, W. Jing, T. Lu, X. Wang, and Y. Zhang, “High-accuracy particle sizing by interferometric particle imaging,” Opt. Commun. 312(2), 312–318 (2014).

Konig, G.

G. Konig, K. Anders, and A. Frohn, “A new light-scattering technique to measurement the diameter of periodically generated moving droplets,” J. Aerosol Sci. 17(2), 157–167 (1986).
[Crossref]

Lacagnina, G.

G. Lacagnina, S. Grizzi, M. Falchi, F. Di Felice, and G. P. Romano, “Simultaneous size and velocity measurements of cavitating microbubbles using interferometric laser imaging,” Exp. Fluids 50(4), 1153–1167 (2011).
[Crossref]

Lacour, C.

C. Lacour, D. Durox, S. Ducruix, and M. Massot, “Interaction of a polydisperse spray with vortices,” Exp. Fluids 51(2), 295–311 (2011).
[Crossref]

Lemaitre, P.

A. Quérel, P. Lemaitre, M. Brunel, E. Porcheron, and G. Gréhan, “Real-time global interferometric laser imaging for the droplet sizing(ILIDS) algorithm for airborne research,” Meas. Sci. Technol. 21(1), 015306 (2010).
[Crossref]

Li, Z.

Q. Lu, X. Wang, T. Lu, Z. Li, and Y. Zhang, “Linear interferometric image processing for analysis of a particle in a volume,” J. Opt. 16(4), 045703 (2014).
[Crossref]

Liu, Y.

Z. Deng, Y. Liu, and Z. Wang, “Modified Rife algorithm for frequency estimation of sinusoid wave,” J. Data Acquis. Process. 21(4), 473–477 (2006, in Chinese).

Lozhkin, Yu. A.

A. V. Bilsky, Yu. A. Lozhkin, and D. M. Markovich, “Interferometric technique for measurement of droplet diameter,” Thermophys. Aeromech. 18(1), 1–12 (2011).
[Crossref]

Lu, Q.

Q. Lu, W. Jing, T. Lu, X. Wang, and Y. Zhang, “High-accuracy particle sizing by interferometric particle imaging,” Opt. Commun. 312(2), 312–318 (2014).

Q. Lu, X. Wang, T. Lu, Z. Li, and Y. Zhang, “Linear interferometric image processing for analysis of a particle in a volume,” J. Opt. 16(4), 045703 (2014).
[Crossref]

Q. Lu, B. Ge, Y. Chen, and Y. Zhang, “A algorithm for interferometric image processing of interferometric particle imaging,” Acta Opt. Sin. 31(4), 0412009 (2011).
[Crossref]

Lu, T.

Q. Lu, X. Wang, T. Lu, Z. Li, and Y. Zhang, “Linear interferometric image processing for analysis of a particle in a volume,” J. Opt. 16(4), 045703 (2014).
[Crossref]

Q. Lu, W. Jing, T. Lu, X. Wang, and Y. Zhang, “High-accuracy particle sizing by interferometric particle imaging,” Opt. Commun. 312(2), 312–318 (2014).

Markovich, D. M.

A. V. Bilsky, Yu. A. Lozhkin, and D. M. Markovich, “Interferometric technique for measurement of droplet diameter,” Thermophys. Aeromech. 18(1), 1–12 (2011).
[Crossref]

Massot, M.

C. Lacour, D. Durox, S. Ducruix, and M. Massot, “Interaction of a polydisperse spray with vortices,” Exp. Fluids 51(2), 295–311 (2011).
[Crossref]

Miles, R. E. H.

R. E. H. Miles, A. E. Carrithers, and J. P. Reid, “Novel optical techniques for measurements of light extinction, scattering and absorption by single aerosol particles,” Laser Photonics Rev. 5(4), 534–552 (2011).
[Crossref]

Nobach, H.

N. Damaschke, H. Nobach, T. I. Nonn, N. Semidetnov, and C. Tropea, “Multi-dimensional particle sizing technique,” Exp. Fluids 39(2), 336–350 (2005).
[Crossref]

N. Damaschke, H. Nobach, and C. Tropea, “Optical limits of particle concentration for multi-dimensional particle sizing techniques in fluid mechanics,” Exp. Fluids 32(2), 143–152 (2002).
[Crossref]

Nonn, T. I.

N. Damaschke, H. Nobach, T. I. Nonn, N. Semidetnov, and C. Tropea, “Multi-dimensional particle sizing technique,” Exp. Fluids 39(2), 336–350 (2005).
[Crossref]

Porcheron, E.

A. Quérel, P. Lemaitre, M. Brunel, E. Porcheron, and G. Gréhan, “Real-time global interferometric laser imaging for the droplet sizing(ILIDS) algorithm for airborne research,” Meas. Sci. Technol. 21(1), 015306 (2010).
[Crossref]

Quérel, A.

A. Quérel, P. Lemaitre, M. Brunel, E. Porcheron, and G. Gréhan, “Real-time global interferometric laser imaging for the droplet sizing(ILIDS) algorithm for airborne research,” Meas. Sci. Technol. 21(1), 015306 (2010).
[Crossref]

Reid, J. P.

R. E. H. Miles, A. E. Carrithers, and J. P. Reid, “Novel optical techniques for measurements of light extinction, scattering and absorption by single aerosol particles,” Laser Photonics Rev. 5(4), 534–552 (2011).
[Crossref]

Rife, D. C.

D. C. Rife and G. A. Vincent, “Use of the discrete Fourier transform in the measurement of frequencies and levels of tones,” Bell Syst. Tech. J. 49(2), 197–228 (1970).
[Crossref]

Romano, G. P.

G. Lacagnina, S. Grizzi, M. Falchi, F. Di Felice, and G. P. Romano, “Simultaneous size and velocity measurements of cavitating microbubbles using interferometric laser imaging,” Exp. Fluids 50(4), 1153–1167 (2011).
[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]

Semidetnov, N.

N. Damaschke, H. Nobach, T. I. Nonn, N. Semidetnov, and C. Tropea, “Multi-dimensional particle sizing technique,” Exp. Fluids 39(2), 336–350 (2005).
[Crossref]

N. Semidetnov and C. Tropea, “Conversion relationships for multidimensional particle sizing techniques,” Meas. Sci. Technol. 15(1), 112–118 (2004).
[Crossref]

Shen, H.

Skippon, S. M.

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]

Tropea, C.

N. Damaschke, H. Nobach, T. I. Nonn, N. Semidetnov, and C. Tropea, “Multi-dimensional particle sizing technique,” Exp. Fluids 39(2), 336–350 (2005).
[Crossref]

N. Semidetnov and C. Tropea, “Conversion relationships for multidimensional particle sizing techniques,” Meas. Sci. Technol. 15(1), 112–118 (2004).
[Crossref]

N. Damaschke, H. Nobach, and C. Tropea, “Optical limits of particle concentration for multi-dimensional particle sizing techniques in fluid mechanics,” Exp. Fluids 32(2), 143–152 (2002).
[Crossref]

van Beeck, J. P. A. J.

S. Dehaeck and J. P. A. J. van Beeck, “Multifrequency interferometric particle imaging for gas bubble sizing,” Exp. Fluids 45(5), 823–831 (2008).
[Crossref]

S. Dehaeck and J. P. A. J. van Beeck, “Designing a maximum precision interferometric particle imaging set-up,” Exp. Fluids 42(5), 767–781 (2007).
[Crossref]

van de Water, W.

H. Bocanegra Evans, N. Dam, D. van der Voort, G. Bertens, and W. van de Water, “Measuring droplet size distributions from overlapping interferometric particle images,” Rev. Sci. Instrum. 86(2), 023709 (2015).
[Crossref] [PubMed]

van der Voort, D.

H. Bocanegra Evans, N. Dam, D. van der Voort, G. Bertens, and W. van de Water, “Measuring droplet size distributions from overlapping interferometric particle images,” Rev. Sci. Instrum. 86(2), 023709 (2015).
[Crossref] [PubMed]

Vincent, G. A.

D. C. Rife and G. A. Vincent, “Use of the discrete Fourier transform in the measurement of frequencies and levels of tones,” Bell Syst. Tech. J. 49(2), 197–228 (1970).
[Crossref]

Wang, H.

H. Wang and G. Zhao, “Improved Rife algorithm for frequency estimation of sinusoid wave,” Signal Process. 26(10), 1573–1576 (2010).

Wang, X.

Q. Lu, W. Jing, T. Lu, X. Wang, and Y. Zhang, “High-accuracy particle sizing by interferometric particle imaging,” Opt. Commun. 312(2), 312–318 (2014).

Q. Lu, X. Wang, T. Lu, Z. Li, and Y. Zhang, “Linear interferometric image processing for analysis of a particle in a volume,” J. Opt. 16(4), 045703 (2014).
[Crossref]

Wang, Z.

Z. Deng, Y. Liu, and Z. Wang, “Modified Rife algorithm for frequency estimation of sinusoid wave,” J. Data Acquis. Process. 21(4), 473–477 (2006, in Chinese).

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]

Zhang, Y.

Q. Lu, X. Wang, T. Lu, Z. Li, and Y. Zhang, “Linear interferometric image processing for analysis of a particle in a volume,” J. Opt. 16(4), 045703 (2014).
[Crossref]

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Figures (11)

Fig. 1
Fig. 1 Schematic of interferometric imaging of particle scattering light.
Fig. 2
Fig. 2 Flowchart of particle measurement.
Fig. 3
Fig. 3 Simulation results of the interferogram center-detecting using different algorithm: (a) the interferogram image; (b) the mask image; the results of (c) WMF algorithm, (d) erosion match algorithm and (e) unidirectional gradient-matched algorithm. Shown from left to right are the extracted edge image of (a) and (b), 3D and 2D correlation distribution.
Fig. 4
Fig. 4 (a) Simulation interferogram images; (b) the results of the center detecting using different methods; error distribution in (c) x-direction and (d) y-direction, where the pink “” indicates erosion matching algorithm, the light green “ο” is WMF algorithm, and the red dot “•” is gradient-matched algorithm, respectively.
Fig. 5
Fig. 5 Comparison of recognition ratio Rp of three algorithms.
Fig. 6
Fig. 6 Simulation results of the frequency estimation: (a) interferometric image; (b) 2D frequency spectrum of (a); (c) fine peak detection and frequency estimation.
Fig. 7
Fig. 7 Variation of RMSE (a) and MAE (b) with respect to SNR
Fig. 8
Fig. 8 Experimental setup for particle center detection.
Fig. 9
Fig. 9 (a) A simulated interferogram; (b) the image of (a); (c) the result of the center location for different disk counts; (d) comparison of the location center location with the method in this work and the previously proposed algorithms.
Fig. 10
Fig. 10 Measurement results of the standard particles: (a) the interferometric image; (b) result of the center detection; (c) an interferometric image of particle 3 in (a); (d) 2D frequency spectrum of (c); (e) fine peak detection and frequency estimation; and (f) absolute errors of particle diameter measurement for the i-Rife method and the m-Rife method.
Fig. 11
Fig. 11 Measured diameter distribution of monodisperse polystyrene particle of 45μm.

Equations (10)

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d= 2λN α ( cos θ 2 + msin (θ / 2) m 2 2mcos (θ / 2) +1 ) 1 ,
x {I(x,y)} x {P(x,y)}= I ( x , y ) x P( x +x, y +y) x d x d y ,
S(k)= n=0 N1 s(n)exp(i 2πnk N ) ,
Δδ= 1 2 δ,
δ= | S( k 2 ) | | S( k 1 ) |+| S( k 2 ) | ,
s ( n )=s( n )exp( i 2πn N rΔδ ),
S (k)= n=0 N1 s (n)exp(i 2πnk N ) =S(krΔδ).
δ = | S ( k 2 ) | | S ( k 1 ) |+| S ( k 2 ) | = | S( k 1 rΔδ+r) | | S( k 1 rΔδ) |+| S( k 1 rΔδ+r) | .
f= 1 NΔx ( k 1 rΔδ+r δ ),
I(x,y)=[1+cos(2πfx)]circ(2 (x x 0 ) 2 + (y y 0 ) 2 / d i )

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