Abstract

A laser flow cytometer based on scanning flow cytometry has been assembled. The unpolarized and linearly polarized light-scattering profiles, as well as the side emitted light in different spectral bands, were measured, allowing the simultaneous and real-time determination of the effective size and the effective refractive index of each spherelike particle. Additionally, each particle could be identified from depolarization and fluorescence measured simultaneously. The tests with aqueous samples of polystyrene spheres, fluorescent or nonfluorescent, and phytoplankton cells demonstrate that the system is able to retrieve size and refractive index with an accuracy of 1% and that the depolarization and fluorescence measurements allow the classification of particles otherwise indistinguishable.

© 2008 Optical Society of America

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References

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  1. L. Tsang, J. A. Kong, and K.-H. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley, 2001).
  2. T.Provder and J.Texter, eds., Particle Sizing and Characterization (American Chemical Society, 2004).
    [CrossRef]
  3. H. M. Shapiro, Practical Flow Cytometry (Wiley, 2003).
    [CrossRef]
  4. D. E. Burger, J. H. Jett, and P. F. Mullaney, “Extraction of morphological features from biological models and cells by Fourier analysis of static light scatter measurements,” Cytometry 2, 327-336 (1982).
    [CrossRef] [PubMed]
  5. G. C. Salzman, P. F. Mullaney, and В. J. Price, “Light-scattering approaches to cell characterization,” in Flow Cytometry and Sorting, M.R.Melamed, T.Lindmo, and M.Mendelsohn, eds. (Wiley, 1979).
  6. G. B. J. Dubelaar and R. R. Jonker, “Flow cytometry as a tool for the study of phytoplankton,” Sci. Mar. 64, 135-156(2000).
  7. T. J. O'Leary, “Flow cytometry in diagnostic cytology,” Diagn. Cytopathol. 18, 41-46 (1998).
    [CrossRef] [PubMed]
  8. L. Fiorani and A. Palucci, “Local and remote laser sensing of bio-optical parameters in natural waters,” J. Comput. Technol. 11, 39-45 (2006).
  9. L. Fiorani, Une Première Mesure Lidar Combinée d'Ozone et ee Vent, À Partir d'Une Instrumentation et d'Une Méthodologie Coup par Coup (Swiss Federal Institute of Technology, 1996).
    [PubMed]
  10. A. V. Chernyshev, V. I. Prots, A. A. Doroshkin, and V. P. Maltsev, “Measurement of scattering properties of individual particles with a scanning flow cytometer,” Appl. Opt. 34, 6301-6305 (1995).
    [CrossRef] [PubMed]
  11. V. P. Maltsev, “Scanning flow cytometry for individual particle analysis,” Rev. Sci. Instrum. 71, 243-255 (2000).
    [CrossRef]
  12. V. P. Maltsev and K. A. Semyanov, Characterisation of Bio-Particles from Light Scattering, Inverse and Ill-Posed Problems Series (VSP, 2004).
  13. P. Aristipini, L. Fiorani, I. Menicucci, and A. Palucci, “Spettrofluorimetro laser portatile per l'analisi in situ dei liquidi non opachi,” Italian patent RM2005A000269 (30 May 2005).
  14. V. P. Maltsev and A. V. Chernyshev, “Method and device for determination of parameters of individual microparticles,” U.S. patent 5,650,847 (22 July 1997).
  15. F. Barnaba, L. Fiorani, A. Palucci, and P. Tarasov, “First characterization of marine particles by laser scanning flow cytometry,” J. Quant. Spectrosc. Radiat. Transfer 102, 11-17 (2006).
    [CrossRef]
  16. R. Guenther, Modern Optics (Wiley, 1990).
  17. K. A. Semyanov, P. A. Tarasov, A. E. Zharinov, A. V. Chernyshev, A. G. Hoekstra, and V. P. Maltsev, “Single-particle sizing from light scattering by spectral decomposition,” Appl. Opt. 43, 5110-5115 (2004).
    [CrossRef] [PubMed]
  18. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, 1983).
  19. K. A. Semyanov, A. E. Zharinov, P. A. Tarasov, M. A. Yurkin, I. G. Skribunov, D. R. van Bockstaele, A. G. Hoekstra, and V. P. Maltsev, “Optics of leucocytes,” in Optics of Biological Particles, A. G. Hoekstra, V. P. Maltsev, and G. Videen, eds. (Springer, 2006), pp. 253-264, ISBN 978-1-4020-5501-0.
  20. X. Y. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X. H. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48, 4165-4172 (2003).
    [CrossRef]

2006 (2)

L. Fiorani and A. Palucci, “Local and remote laser sensing of bio-optical parameters in natural waters,” J. Comput. Technol. 11, 39-45 (2006).

F. Barnaba, L. Fiorani, A. Palucci, and P. Tarasov, “First characterization of marine particles by laser scanning flow cytometry,” J. Quant. Spectrosc. Radiat. Transfer 102, 11-17 (2006).
[CrossRef]

2004 (1)

2003 (1)

X. Y. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X. H. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

2000 (2)

V. P. Maltsev, “Scanning flow cytometry for individual particle analysis,” Rev. Sci. Instrum. 71, 243-255 (2000).
[CrossRef]

G. B. J. Dubelaar and R. R. Jonker, “Flow cytometry as a tool for the study of phytoplankton,” Sci. Mar. 64, 135-156(2000).

1998 (1)

T. J. O'Leary, “Flow cytometry in diagnostic cytology,” Diagn. Cytopathol. 18, 41-46 (1998).
[CrossRef] [PubMed]

1995 (1)

1982 (1)

D. E. Burger, J. H. Jett, and P. F. Mullaney, “Extraction of morphological features from biological models and cells by Fourier analysis of static light scatter measurements,” Cytometry 2, 327-336 (1982).
[CrossRef] [PubMed]

Aristipini, P.

P. Aristipini, L. Fiorani, I. Menicucci, and A. Palucci, “Spettrofluorimetro laser portatile per l'analisi in situ dei liquidi non opachi,” Italian patent RM2005A000269 (30 May 2005).

Barnaba, F.

F. Barnaba, L. Fiorani, A. Palucci, and P. Tarasov, “First characterization of marine particles by laser scanning flow cytometry,” J. Quant. Spectrosc. Radiat. Transfer 102, 11-17 (2006).
[CrossRef]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, 1983).

Brock, R. S.

X. Y. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X. H. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

Burger, D. E.

D. E. Burger, J. H. Jett, and P. F. Mullaney, “Extraction of morphological features from biological models and cells by Fourier analysis of static light scatter measurements,” Cytometry 2, 327-336 (1982).
[CrossRef] [PubMed]

Chernyshev, A. V.

Ding, K.-H.

L. Tsang, J. A. Kong, and K.-H. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley, 2001).

Doroshkin, A. A.

Dubelaar, G. B. J.

G. B. J. Dubelaar and R. R. Jonker, “Flow cytometry as a tool for the study of phytoplankton,” Sci. Mar. 64, 135-156(2000).

Fiorani, L.

L. Fiorani and A. Palucci, “Local and remote laser sensing of bio-optical parameters in natural waters,” J. Comput. Technol. 11, 39-45 (2006).

F. Barnaba, L. Fiorani, A. Palucci, and P. Tarasov, “First characterization of marine particles by laser scanning flow cytometry,” J. Quant. Spectrosc. Radiat. Transfer 102, 11-17 (2006).
[CrossRef]

P. Aristipini, L. Fiorani, I. Menicucci, and A. Palucci, “Spettrofluorimetro laser portatile per l'analisi in situ dei liquidi non opachi,” Italian patent RM2005A000269 (30 May 2005).

L. Fiorani, Une Première Mesure Lidar Combinée d'Ozone et ee Vent, À Partir d'Une Instrumentation et d'Une Méthodologie Coup par Coup (Swiss Federal Institute of Technology, 1996).
[PubMed]

Guenther, R.

R. Guenther, Modern Optics (Wiley, 1990).

Hoekstra, A. G.

K. A. Semyanov, P. A. Tarasov, A. E. Zharinov, A. V. Chernyshev, A. G. Hoekstra, and V. P. Maltsev, “Single-particle sizing from light scattering by spectral decomposition,” Appl. Opt. 43, 5110-5115 (2004).
[CrossRef] [PubMed]

K. A. Semyanov, A. E. Zharinov, P. A. Tarasov, M. A. Yurkin, I. G. Skribunov, D. R. van Bockstaele, A. G. Hoekstra, and V. P. Maltsev, “Optics of leucocytes,” in Optics of Biological Particles, A. G. Hoekstra, V. P. Maltsev, and G. Videen, eds. (Springer, 2006), pp. 253-264, ISBN 978-1-4020-5501-0.

Hu, X. H.

X. Y. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X. H. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, 1983).

Jacobs, K. M.

X. Y. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X. H. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

Jett, J. H.

D. E. Burger, J. H. Jett, and P. F. Mullaney, “Extraction of morphological features from biological models and cells by Fourier analysis of static light scatter measurements,” Cytometry 2, 327-336 (1982).
[CrossRef] [PubMed]

Jonker, R. R.

G. B. J. Dubelaar and R. R. Jonker, “Flow cytometry as a tool for the study of phytoplankton,” Sci. Mar. 64, 135-156(2000).

Kong, J. A.

L. Tsang, J. A. Kong, and K.-H. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley, 2001).

Lu, J. Q.

X. Y. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X. H. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

Ma, X. Y.

X. Y. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X. H. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

Maltsev, V. P.

K. A. Semyanov, P. A. Tarasov, A. E. Zharinov, A. V. Chernyshev, A. G. Hoekstra, and V. P. Maltsev, “Single-particle sizing from light scattering by spectral decomposition,” Appl. Opt. 43, 5110-5115 (2004).
[CrossRef] [PubMed]

V. P. Maltsev, “Scanning flow cytometry for individual particle analysis,” Rev. Sci. Instrum. 71, 243-255 (2000).
[CrossRef]

A. V. Chernyshev, V. I. Prots, A. A. Doroshkin, and V. P. Maltsev, “Measurement of scattering properties of individual particles with a scanning flow cytometer,” Appl. Opt. 34, 6301-6305 (1995).
[CrossRef] [PubMed]

V. P. Maltsev and A. V. Chernyshev, “Method and device for determination of parameters of individual microparticles,” U.S. patent 5,650,847 (22 July 1997).

V. P. Maltsev and K. A. Semyanov, Characterisation of Bio-Particles from Light Scattering, Inverse and Ill-Posed Problems Series (VSP, 2004).

K. A. Semyanov, A. E. Zharinov, P. A. Tarasov, M. A. Yurkin, I. G. Skribunov, D. R. van Bockstaele, A. G. Hoekstra, and V. P. Maltsev, “Optics of leucocytes,” in Optics of Biological Particles, A. G. Hoekstra, V. P. Maltsev, and G. Videen, eds. (Springer, 2006), pp. 253-264, ISBN 978-1-4020-5501-0.

Menicucci, I.

P. Aristipini, L. Fiorani, I. Menicucci, and A. Palucci, “Spettrofluorimetro laser portatile per l'analisi in situ dei liquidi non opachi,” Italian patent RM2005A000269 (30 May 2005).

Mullaney, P. F.

D. E. Burger, J. H. Jett, and P. F. Mullaney, “Extraction of morphological features from biological models and cells by Fourier analysis of static light scatter measurements,” Cytometry 2, 327-336 (1982).
[CrossRef] [PubMed]

G. C. Salzman, P. F. Mullaney, and В. J. Price, “Light-scattering approaches to cell characterization,” in Flow Cytometry and Sorting, M.R.Melamed, T.Lindmo, and M.Mendelsohn, eds. (Wiley, 1979).

O'Leary, T. J.

T. J. O'Leary, “Flow cytometry in diagnostic cytology,” Diagn. Cytopathol. 18, 41-46 (1998).
[CrossRef] [PubMed]

Palucci, A.

L. Fiorani and A. Palucci, “Local and remote laser sensing of bio-optical parameters in natural waters,” J. Comput. Technol. 11, 39-45 (2006).

F. Barnaba, L. Fiorani, A. Palucci, and P. Tarasov, “First characterization of marine particles by laser scanning flow cytometry,” J. Quant. Spectrosc. Radiat. Transfer 102, 11-17 (2006).
[CrossRef]

P. Aristipini, L. Fiorani, I. Menicucci, and A. Palucci, “Spettrofluorimetro laser portatile per l'analisi in situ dei liquidi non opachi,” Italian patent RM2005A000269 (30 May 2005).

Price, ?. J.

G. C. Salzman, P. F. Mullaney, and В. J. Price, “Light-scattering approaches to cell characterization,” in Flow Cytometry and Sorting, M.R.Melamed, T.Lindmo, and M.Mendelsohn, eds. (Wiley, 1979).

Prots, V. I.

Salzman, G. C.

G. C. Salzman, P. F. Mullaney, and В. J. Price, “Light-scattering approaches to cell characterization,” in Flow Cytometry and Sorting, M.R.Melamed, T.Lindmo, and M.Mendelsohn, eds. (Wiley, 1979).

Semyanov, K. A.

K. A. Semyanov, P. A. Tarasov, A. E. Zharinov, A. V. Chernyshev, A. G. Hoekstra, and V. P. Maltsev, “Single-particle sizing from light scattering by spectral decomposition,” Appl. Opt. 43, 5110-5115 (2004).
[CrossRef] [PubMed]

V. P. Maltsev and K. A. Semyanov, Characterisation of Bio-Particles from Light Scattering, Inverse and Ill-Posed Problems Series (VSP, 2004).

K. A. Semyanov, A. E. Zharinov, P. A. Tarasov, M. A. Yurkin, I. G. Skribunov, D. R. van Bockstaele, A. G. Hoekstra, and V. P. Maltsev, “Optics of leucocytes,” in Optics of Biological Particles, A. G. Hoekstra, V. P. Maltsev, and G. Videen, eds. (Springer, 2006), pp. 253-264, ISBN 978-1-4020-5501-0.

Shapiro, H. M.

H. M. Shapiro, Practical Flow Cytometry (Wiley, 2003).
[CrossRef]

Skribunov, I. G.

K. A. Semyanov, A. E. Zharinov, P. A. Tarasov, M. A. Yurkin, I. G. Skribunov, D. R. van Bockstaele, A. G. Hoekstra, and V. P. Maltsev, “Optics of leucocytes,” in Optics of Biological Particles, A. G. Hoekstra, V. P. Maltsev, and G. Videen, eds. (Springer, 2006), pp. 253-264, ISBN 978-1-4020-5501-0.

Tarasov, P.

F. Barnaba, L. Fiorani, A. Palucci, and P. Tarasov, “First characterization of marine particles by laser scanning flow cytometry,” J. Quant. Spectrosc. Radiat. Transfer 102, 11-17 (2006).
[CrossRef]

Tarasov, P. A.

K. A. Semyanov, P. A. Tarasov, A. E. Zharinov, A. V. Chernyshev, A. G. Hoekstra, and V. P. Maltsev, “Single-particle sizing from light scattering by spectral decomposition,” Appl. Opt. 43, 5110-5115 (2004).
[CrossRef] [PubMed]

K. A. Semyanov, A. E. Zharinov, P. A. Tarasov, M. A. Yurkin, I. G. Skribunov, D. R. van Bockstaele, A. G. Hoekstra, and V. P. Maltsev, “Optics of leucocytes,” in Optics of Biological Particles, A. G. Hoekstra, V. P. Maltsev, and G. Videen, eds. (Springer, 2006), pp. 253-264, ISBN 978-1-4020-5501-0.

Tsang, L.

L. Tsang, J. A. Kong, and K.-H. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley, 2001).

van Bockstaele, D. R.

K. A. Semyanov, A. E. Zharinov, P. A. Tarasov, M. A. Yurkin, I. G. Skribunov, D. R. van Bockstaele, A. G. Hoekstra, and V. P. Maltsev, “Optics of leucocytes,” in Optics of Biological Particles, A. G. Hoekstra, V. P. Maltsev, and G. Videen, eds. (Springer, 2006), pp. 253-264, ISBN 978-1-4020-5501-0.

Yang, P.

X. Y. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X. H. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

Yurkin, M. A.

K. A. Semyanov, A. E. Zharinov, P. A. Tarasov, M. A. Yurkin, I. G. Skribunov, D. R. van Bockstaele, A. G. Hoekstra, and V. P. Maltsev, “Optics of leucocytes,” in Optics of Biological Particles, A. G. Hoekstra, V. P. Maltsev, and G. Videen, eds. (Springer, 2006), pp. 253-264, ISBN 978-1-4020-5501-0.

Zharinov, A. E.

K. A. Semyanov, P. A. Tarasov, A. E. Zharinov, A. V. Chernyshev, A. G. Hoekstra, and V. P. Maltsev, “Single-particle sizing from light scattering by spectral decomposition,” Appl. Opt. 43, 5110-5115 (2004).
[CrossRef] [PubMed]

K. A. Semyanov, A. E. Zharinov, P. A. Tarasov, M. A. Yurkin, I. G. Skribunov, D. R. van Bockstaele, A. G. Hoekstra, and V. P. Maltsev, “Optics of leucocytes,” in Optics of Biological Particles, A. G. Hoekstra, V. P. Maltsev, and G. Videen, eds. (Springer, 2006), pp. 253-264, ISBN 978-1-4020-5501-0.

Appl. Opt. (2)

Cytometry (1)

D. E. Burger, J. H. Jett, and P. F. Mullaney, “Extraction of morphological features from biological models and cells by Fourier analysis of static light scatter measurements,” Cytometry 2, 327-336 (1982).
[CrossRef] [PubMed]

Diagn. Cytopathol. (1)

T. J. O'Leary, “Flow cytometry in diagnostic cytology,” Diagn. Cytopathol. 18, 41-46 (1998).
[CrossRef] [PubMed]

J. Comput. Technol. (1)

L. Fiorani and A. Palucci, “Local and remote laser sensing of bio-optical parameters in natural waters,” J. Comput. Technol. 11, 39-45 (2006).

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

F. Barnaba, L. Fiorani, A. Palucci, and P. Tarasov, “First characterization of marine particles by laser scanning flow cytometry,” J. Quant. Spectrosc. Radiat. Transfer 102, 11-17 (2006).
[CrossRef]

Phys. Med. Biol. (1)

X. Y. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X. H. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48, 4165-4172 (2003).
[CrossRef]

Rev. Sci. Instrum. (1)

V. P. Maltsev, “Scanning flow cytometry for individual particle analysis,” Rev. Sci. Instrum. 71, 243-255 (2000).
[CrossRef]

Sci. Mar. (1)

G. B. J. Dubelaar and R. R. Jonker, “Flow cytometry as a tool for the study of phytoplankton,” Sci. Mar. 64, 135-156(2000).

Other (11)

L. Fiorani, Une Première Mesure Lidar Combinée d'Ozone et ee Vent, À Partir d'Une Instrumentation et d'Une Méthodologie Coup par Coup (Swiss Federal Institute of Technology, 1996).
[PubMed]

R. Guenther, Modern Optics (Wiley, 1990).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, 1983).

K. A. Semyanov, A. E. Zharinov, P. A. Tarasov, M. A. Yurkin, I. G. Skribunov, D. R. van Bockstaele, A. G. Hoekstra, and V. P. Maltsev, “Optics of leucocytes,” in Optics of Biological Particles, A. G. Hoekstra, V. P. Maltsev, and G. Videen, eds. (Springer, 2006), pp. 253-264, ISBN 978-1-4020-5501-0.

V. P. Maltsev and K. A. Semyanov, Characterisation of Bio-Particles from Light Scattering, Inverse and Ill-Posed Problems Series (VSP, 2004).

P. Aristipini, L. Fiorani, I. Menicucci, and A. Palucci, “Spettrofluorimetro laser portatile per l'analisi in situ dei liquidi non opachi,” Italian patent RM2005A000269 (30 May 2005).

V. P. Maltsev and A. V. Chernyshev, “Method and device for determination of parameters of individual microparticles,” U.S. patent 5,650,847 (22 July 1997).

G. C. Salzman, P. F. Mullaney, and В. J. Price, “Light-scattering approaches to cell characterization,” in Flow Cytometry and Sorting, M.R.Melamed, T.Lindmo, and M.Mendelsohn, eds. (Wiley, 1979).

L. Tsang, J. A. Kong, and K.-H. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley, 2001).

T.Provder and J.Texter, eds., Particle Sizing and Characterization (American Chemical Society, 2004).
[CrossRef]

H. M. Shapiro, Practical Flow Cytometry (Wiley, 2003).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Optical scheme of the system. The elements are described in Table 1. The three bending mirrors M 1 (inserted between D and Q) and bending mirror M 3 (inserted between M 2 and I 1 ) are not influential and have not been indicated.

Fig. 2
Fig. 2

Dependency of phase-shift parameter ρ on parameter J for different values of size parameter α.

Fig. 3
Fig. 3

Images of Chlamydomonas at the optical microscope in Fig. 4 LSPs of Chlamydomonas.

Fig. 4
Fig. 4

Images of Chlamydomonas at the optical microscope just before measurement with CLASS.

Fig. 5
Fig. 5

Depolarization δ I for Chlamydomonas and 2 and 6 μm polystyrene microspheres.

Fig. 6
Fig. 6

Two-dimensional scatterplot (LSP integral J in the range of 10 ° 20 ° versus integral of depolarization δ I in the range 10 ° 70 ° ) obtained analyzing a sample of Chlamydomonas mixed with fluorescent polystyrene spheres, having 6 and 2 μm diameters.

Fig. 7
Fig. 7

Histograms of (a) size, (b) refractive index, (c) fluorescence, and (d) depolarization obtained analyzing a sample of Chlamydomonas mixed with fluorescent and nonfluorescent polystyrene spheres, having 6 and 2 μm diameters.

Fig. 8
Fig. 8

Three-dimensional scatterplot (effective size, depolarization, and fluorescence) obtained analyzing a sample of Chlamydomonas mixed with fluorescent and nonfluorescent polystyrene spheres, having 6 and 2 μm diameters.

Fig. 9
Fig. 9

Three-dimensional scatterplot (size, fluorescence at 530 nm , and fluorescence at 680 nm ) obtained analyzing a sample prepared mixing green fluorescent and nonfluorescent polystyrene spheres, having a 2 μm diameter, with red fluorescent and nonfluorescent polystyrene spheres, having a 6 μm diameter.

Tables (3)

Tables Icon

Table 1 Optical Elements of the System a

Tables Icon

Table 2 Fitting Ccoefficients of Eq. (8) that Correspond to the Minimum Value of χ 2

Tables Icon

Table 3 Measurements of the Effective Size, the Effective Refractive Index, the Depolarization, and the Fluorescence Obtained Analyzing a Sample of C. Reinhardtii Mixed with Fluorescent and Nonfluorescent Polystyrene Spheres, Having 6 and 2 μm Diameters a

Equations (8)

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

I 1 ( θ ) = k 0 2 π [ S 11 S 14 + ( S 21 S 24 ) cos ( 2 φ ) ( S 31 S 34 ) sin ( 2 φ ) ] d φ ,
I 2 ( θ ) = k 0 2 π ( S 11 S 14 ) d φ ,
I 1 ( θ ) = k 0 2 π S 11 d φ = 2 π k S 11 ( θ ) ,
I 2 ( θ ) = k 0 2 π S 11 d φ = 2 π k S 11 ( θ ) .
δ I = I 2 I 1 I 2
δ I ( θ ) = 0 2 π [ ( S 21 S 24 ) cos ( 2 φ ) ( S 31 S 34 ) sin ( 2 φ ) ] d φ 0 2 π ( S 11 S 14 ) d φ .
J = 10 ° 70 ° I 2 ( θ ) · sin ( π · θ 10 ° 60 ° ) d θ .
ρ = A J β [ 1 + k 1 ( 1 + k 2 P f ) J 2 / β ] ,

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