Abstract

We present an analysis of the shoulder-shaped power spectrum observed in the modulated laser output due to feedback light scattered from dynamic changes in self-mobile phytoplankton with flagella in seawater performed using a self-mixing laser Doppler vibrometry system. The power spectrum occasionally has shoulder-shaped broad frequency components superimposed on a Lorentz-type spectrum. This reflects the translational motion of phytoplankton moving across the beam-focus area. The velocity of phytoplankton in the focus area can be obtained by applying a curve fitting procedure to the power spectrum. Moreover, the average velocity and the velocity distribution of phytoplankton can be determined from curve fitting of the long-term power spectrum.

© 2009 Optical Society of America

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References

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  1. P. B. Ortner and A. Rosencwaig, “Photoacoustic spectroscopic analysis of marine phytoplankton,” Hydrobiologia 56, 3-6(1977).
    [CrossRef]
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    [CrossRef]
  3. E. Bauerfeind, M. Elbrächter, R. Steiner, and J. Throndsen, “Application of laser Doppler spectroscopy (LDS) in determining swimming velocities of motile phytoplankton,” Marine Biol. 93, 323-327 (1986).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  9. L. Fiorani, V. P. Maltsev, V. M. Nekrasov, A. Palucci, K. A. Semyanov, and V. Spizzichino, “Scanning flow cytometer modified to distinguish phytoplankton cells from their effective size, effective refractive index, depolarization, and fluorescence,” Appl. Opt. 47, 4405-4412 (2008).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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2009 (2)

2008 (3)

2007 (1)

2006 (2)

2005 (1)

2003 (2)

K. Abe, K. Otsuka, and J.-Y. Ko, “Self-mixing laser Doppler vibrometry with high optical sensitivity: application to real-time sound reproduction,” New J. Phys. 5, 8(2003).
[CrossRef]

R. E. Green, H. M. Sosik, R. J. Olson, and M. D. DuRand, “Flow cytometric determination of size and complex refractive index for marine particles: comparison with independent and bulk estimates,” Appl. Opt. 42, 526-541 (2003).
[CrossRef] [PubMed]

2002 (1)

1999 (2)

K. Otsuka, R. Kawai, Y. Asakawa, and T. Fukazawa, “Highly sensitive self-mixing measurement of Brillouin scattering with a laser-diode-pumped LiNdP4O12 laser,” Opt. Lett. 24, 1862-1864 (1999).
[CrossRef]

M. F. Wilkins, L. Boddy, C. W. Morris, and R. R. Jonker, “Identification of phytoplankton from flow cytometry data by using radial basis function neural networks,” Appl. Environ. Microbiol. 65, 4404-4410 (1999).
[PubMed]

1995 (1)

1994 (1)

J. W. Hofstraat, W. J. M. van Zeijl, M. E. J. de Vreeze, J. C. H. Peeters, L. Peperzak, F. Colijn, and T. W. M. Rademaker, “Phytoplankton monitoring by flow cytometry,” J. Plankton Res. 16, 1197-1224 (1994).
[CrossRef]

1992 (1)

1988 (1)

1986 (1)

E. Bauerfeind, M. Elbrächter, R. Steiner, and J. Throndsen, “Application of laser Doppler spectroscopy (LDS) in determining swimming velocities of motile phytoplankton,” Marine Biol. 93, 323-327 (1986).
[CrossRef]

1979 (2)

W. H. Wilson and D. A. Kiefe, “Reflectance spectroscopy of marine phytoplankton. Part 2. A simple model of ocean color,” Limnol. Oceanogr. 24, 673-682 (1979).
[CrossRef]

K. Otsuka, “Effects of external perturbations on LiNdP4O12 lasers,” IEEE J. Quantum Electron. 15, 655-663 (1979).
[CrossRef]

1977 (1)

P. B. Ortner and A. Rosencwaig, “Photoacoustic spectroscopic analysis of marine phytoplankton,” Hydrobiologia 56, 3-6(1977).
[CrossRef]

1971 (1)

Abe, K.

Ackleson, S. G.

Asakawa, Y.

Bauerfeind, E.

E. Bauerfeind, M. Elbrächter, R. Steiner, and J. Throndsen, “Application of laser Doppler spectroscopy (LDS) in determining swimming velocities of motile phytoplankton,” Marine Biol. 93, 323-327 (1986).
[CrossRef]

Boddy, L.

M. F. Wilkins, L. Boddy, C. W. Morris, and R. R. Jonker, “Identification of phytoplankton from flow cytometry data by using radial basis function neural networks,” Appl. Environ. Microbiol. 65, 4404-4410 (1999).
[PubMed]

Colijn, F.

J. W. Hofstraat, W. J. M. van Zeijl, M. E. J. de Vreeze, J. C. H. Peeters, L. Peperzak, F. Colijn, and T. W. M. Rademaker, “Phytoplankton monitoring by flow cytometry,” J. Plankton Res. 16, 1197-1224 (1994).
[CrossRef]

de Vreeze, M. E. J.

J. W. Hofstraat, W. J. M. van Zeijl, M. E. J. de Vreeze, J. C. H. Peeters, L. Peperzak, F. Colijn, and T. W. M. Rademaker, “Phytoplankton monitoring by flow cytometry,” J. Plankton Res. 16, 1197-1224 (1994).
[CrossRef]

DuRand, M. D.

Elbrächter, M.

E. Bauerfeind, M. Elbrächter, R. Steiner, and J. Throndsen, “Application of laser Doppler spectroscopy (LDS) in determining swimming velocities of motile phytoplankton,” Marine Biol. 93, 323-327 (1986).
[CrossRef]

Estes, L. E.

Fiorani, L.

Fukazawa, T.

Garcia-Sucerquia, J.

Green, R. E.

Heidmann, S.

Hofstraat, J. W.

J. W. Hofstraat, W. J. M. van Zeijl, M. E. J. de Vreeze, J. C. H. Peeters, L. Peperzak, F. Colijn, and T. W. M. Rademaker, “Phytoplankton monitoring by flow cytometry,” J. Plankton Res. 16, 1197-1224 (1994).
[CrossRef]

Howard, R. G.

Hugon, O.

Iturriaga, R. H.

Jacquin, O.

Jericho, M. H.

Jonker, R. R.

M. F. Wilkins, L. Boddy, C. W. Morris, and R. R. Jonker, “Identification of phytoplankton from flow cytometry data by using radial basis function neural networks,” Appl. Environ. Microbiol. 65, 4404-4410 (1999).
[PubMed]

Kamikariya, K.

Kawai, R.

Kiefe, D. A.

W. H. Wilson and D. A. Kiefe, “Reflectance spectroscopy of marine phytoplankton. Part 2. A simple model of ocean color,” Limnol. Oceanogr. 24, 673-682 (1979).
[CrossRef]

Klages, P.

Ko, J.-Y.

Kreuzer, H. J.

Lacot, E.

Lim, T.-S.

Liu, Y.

Maltsev, V. P.

Miyasaka, Y.

Morris, C. W.

M. F. Wilkins, L. Boddy, C. W. Morris, and R. R. Jonker, “Identification of phytoplankton from flow cytometry data by using radial basis function neural networks,” Appl. Environ. Microbiol. 65, 4404-4410 (1999).
[PubMed]

Narducci, L. M.

Nekrasov, V. M.

Nemoto, K.

Ohtomo, T.

Oishi, T.

Olson, R. J.

Ortner, P. B.

P. B. Ortner and A. Rosencwaig, “Photoacoustic spectroscopic analysis of marine phytoplankton,” Hydrobiologia 56, 3-6(1977).
[CrossRef]

Otsuka, K.

T. Ohtomo, S. Sudo, and K. Otsuka, “Three-channel three-dimensional self-mixing thin-slice solid-state laser-Doppler measurements,” Appl. Opt. 48, 609-616 (2009).
[CrossRef] [PubMed]

S. Sudo, Y. Miyasaka, K. Nemoto, K. Kamikariya, and K. Otsuka, “Detection of small particles in fluid flow using a self-mixing laser,” Opt. Express 15, 8135-8145 (2007).
[CrossRef] [PubMed]

S. Sudo, Y. Miyasaka, K. Otsuka, Y. Takahashi, T. Oishi, and J.-Y. Ko, “Quick and easy measurement of particle size of Brownian particles and plankton in water using a self-mixing laser,” Opt. Express 14, 1044-1054 (2006).
[CrossRef]

K. Otsuka, K. Abe, N. Sano, S. Sudo, and J.-Y. Ko, “Two-channel self-mixing laser Doppler measurement with carrier-frequency-division multiplexing,” Appl. Opt. 44, 1709-1714(2005).
[CrossRef] [PubMed]

K. Abe, K. Otsuka, and J.-Y. Ko, “Self-mixing laser Doppler vibrometry with high optical sensitivity: application to real-time sound reproduction,” New J. Phys. 5, 8(2003).
[CrossRef]

K. Otsuka, K. Abe, J.-Y. Ko, and T.-S. Lim, “Real-time nanometer vibration measurement with a self-mixing microchip solid-state laser,” Opt. Lett. 27, 1339-1341 (2002).
[CrossRef]

K. Otsuka, R. Kawai, Y. Asakawa, and T. Fukazawa, “Highly sensitive self-mixing measurement of Brillouin scattering with a laser-diode-pumped LiNdP4O12 laser,” Opt. Lett. 24, 1862-1864 (1999).
[CrossRef]

K. Otsuka, “Effects of external perturbations on LiNdP4O12 lasers,” IEEE J. Quantum Electron. 15, 655-663 (1979).
[CrossRef]

Palucci, A.

Peeters, J. C. H.

J. W. Hofstraat, W. J. M. van Zeijl, M. E. J. de Vreeze, J. C. H. Peeters, L. Peperzak, F. Colijn, and T. W. M. Rademaker, “Phytoplankton monitoring by flow cytometry,” J. Plankton Res. 16, 1197-1224 (1994).
[CrossRef]

Peperzak, L.

J. W. Hofstraat, W. J. M. van Zeijl, M. E. J. de Vreeze, J. C. H. Peeters, L. Peperzak, F. Colijn, and T. W. M. Rademaker, “Phytoplankton monitoring by flow cytometry,” J. Plankton Res. 16, 1197-1224 (1994).
[CrossRef]

Rademaker, T. W. M.

J. W. Hofstraat, W. J. M. van Zeijl, M. E. J. de Vreeze, J. C. H. Peeters, L. Peperzak, F. Colijn, and T. W. M. Rademaker, “Phytoplankton monitoring by flow cytometry,” J. Plankton Res. 16, 1197-1224 (1994).
[CrossRef]

Rosencwaig, A.

P. B. Ortner and A. Rosencwaig, “Photoacoustic spectroscopic analysis of marine phytoplankton,” Hydrobiologia 56, 3-6(1977).
[CrossRef]

Sano, N.

Semyanov, K. A.

Sonek, G. J.

Sosik, H. M.

Spinrad, R. W.

Spizzichino, V.

Steiner, R.

E. Bauerfeind, M. Elbrächter, R. Steiner, and J. Throndsen, “Application of laser Doppler spectroscopy (LDS) in determining swimming velocities of motile phytoplankton,” Marine Biol. 93, 323-327 (1986).
[CrossRef]

Stephan, K. J.

Sudo, S.

Takahashi, Y.

Throndsen, J.

E. Bauerfeind, M. Elbrächter, R. Steiner, and J. Throndsen, “Application of laser Doppler spectroscopy (LDS) in determining swimming velocities of motile phytoplankton,” Marine Biol. 93, 323-327 (1986).
[CrossRef]

Tuft, R. A.

van Zeijl, W. J. M.

J. W. Hofstraat, W. J. M. van Zeijl, M. E. J. de Vreeze, J. C. H. Peeters, L. Peperzak, F. Colijn, and T. W. M. Rademaker, “Phytoplankton monitoring by flow cytometry,” J. Plankton Res. 16, 1197-1224 (1994).
[CrossRef]

Wilkins, M. F.

M. F. Wilkins, L. Boddy, C. W. Morris, and R. R. Jonker, “Identification of phytoplankton from flow cytometry data by using radial basis function neural networks,” Appl. Environ. Microbiol. 65, 4404-4410 (1999).
[PubMed]

Wilson, W. H.

W. H. Wilson and D. A. Kiefe, “Reflectance spectroscopy of marine phytoplankton. Part 2. A simple model of ocean color,” Limnol. Oceanogr. 24, 673-682 (1979).
[CrossRef]

Witomski, A.

Xu, W.

Appl. Environ. Microbiol. (1)

M. F. Wilkins, L. Boddy, C. W. Morris, and R. R. Jonker, “Identification of phytoplankton from flow cytometry data by using radial basis function neural networks,” Appl. Environ. Microbiol. 65, 4404-4410 (1999).
[PubMed]

Appl. Opt. (11)

R. G. Howard, “Diffuse reflectance of the ocean: influence of nonuniform phytoplankton pigment profile,” Appl. Opt. 31, 1419 (1992).
[CrossRef] [PubMed]

G. J. Sonek, Y. Liu, and R. H. Iturriaga, “In situ microparticle analysis of marine phytoplankton cells with infrared laser-based optical tweezers,” Appl. Opt. 34, 7731-7741 (1995).
[CrossRef] [PubMed]

J. Garcia-Sucerquia, W. Xu, K. J. Stephan, P. Klages, M. H. Jericho, and H. J. Kreuzer, “Digital in-line holographic microscopy,” Appl. Opt. 45, 836-850 (2006).
[CrossRef] [PubMed]

S. G. Ackleson and R. W. Spinrad, “Size and refractive index of individual marine participates: a flow cytometric approach,” Appl. Opt. 27, 1270-1277 (1988).
[CrossRef] [PubMed]

R. E. Green, H. M. Sosik, R. J. Olson, and M. D. DuRand, “Flow cytometric determination of size and complex refractive index for marine particles: comparison with independent and bulk estimates,” Appl. Opt. 42, 526-541 (2003).
[CrossRef] [PubMed]

L. Fiorani, V. P. Maltsev, V. M. Nekrasov, A. Palucci, K. A. Semyanov, and V. Spizzichino, “Scanning flow cytometer modified to distinguish phytoplankton cells from their effective size, effective refractive index, depolarization, and fluorescence,” Appl. Opt. 47, 4405-4412 (2008).
[CrossRef] [PubMed]

K. Otsuka, K. Abe, N. Sano, S. Sudo, and J.-Y. Ko, “Two-channel self-mixing laser Doppler measurement with carrier-frequency-division multiplexing,” Appl. Opt. 44, 1709-1714(2005).
[CrossRef] [PubMed]

T. Ohtomo, S. Sudo, and K. Otsuka, “Three-channel three-dimensional self-mixing thin-slice solid-state laser-Doppler measurements,” Appl. Opt. 48, 609-616 (2009).
[CrossRef] [PubMed]

O. Jacquin, S. Heidmann, E. Lacot, and O. Hugon, “Self-aligned setup for laser optical feedback imaging insensitive to parasitic optical feedback,” Appl. Opt. 48, 64-68(2009).
[CrossRef]

E. Lacot, O. Hugon, and O. Jacquin, “Resolution of a synthetic aperture laser optical feedback imaging using a galvanometric scanning,” Appl. Opt. 47, 4025-4030 (2008).
[CrossRef] [PubMed]

A. Witomski, E. Lacot, O. Hugon, and O. Jacquin, “Two-dimensional synthetic aperture laser optical feedback imaging using galvanometric scanning,” Appl. Opt. 47, 860-869(2008).
[CrossRef] [PubMed]

Hydrobiologia (1)

P. B. Ortner and A. Rosencwaig, “Photoacoustic spectroscopic analysis of marine phytoplankton,” Hydrobiologia 56, 3-6(1977).
[CrossRef]

IEEE J. Quantum Electron. (1)

K. Otsuka, “Effects of external perturbations on LiNdP4O12 lasers,” IEEE J. Quantum Electron. 15, 655-663 (1979).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Plankton Res. (1)

J. W. Hofstraat, W. J. M. van Zeijl, M. E. J. de Vreeze, J. C. H. Peeters, L. Peperzak, F. Colijn, and T. W. M. Rademaker, “Phytoplankton monitoring by flow cytometry,” J. Plankton Res. 16, 1197-1224 (1994).
[CrossRef]

Limnol. Oceanogr. (1)

W. H. Wilson and D. A. Kiefe, “Reflectance spectroscopy of marine phytoplankton. Part 2. A simple model of ocean color,” Limnol. Oceanogr. 24, 673-682 (1979).
[CrossRef]

Marine Biol. (1)

E. Bauerfeind, M. Elbrächter, R. Steiner, and J. Throndsen, “Application of laser Doppler spectroscopy (LDS) in determining swimming velocities of motile phytoplankton,” Marine Biol. 93, 323-327 (1986).
[CrossRef]

New J. Phys. (1)

K. Abe, K. Otsuka, and J.-Y. Ko, “Self-mixing laser Doppler vibrometry with high optical sensitivity: application to real-time sound reproduction,” New J. Phys. 5, 8(2003).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

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Figures (8)

Fig. 1
Fig. 1

Experimental setup for self-mixing laser metrology of phytoplankton motion in seawater: LD, laser diode; AP, anamorphic prism pair; OL, objective lens; SL, 0.3 mm thick LiNd P 4 O 12 (LNP); SG, slide glass; AOM, acousto-optic modulators; PD, photodiode receiver, SA, spectrum analyzer.

Fig. 2
Fig. 2

Power spectra for rotating disk with various disk velocities in the focus area.

Fig. 3
Fig. 3

Velocity of rotating disk versus (a) parameter w and (b)  A G .

Fig. 4
Fig. 4

(a) Power spectra and (b) time dependence of power spectra (JTFA) for Tetraselmis tetrathele in seawater at different times.

Fig. 5
Fig. 5

(a) Power spectrum for Tetraselmis tetrathele in seawater. The dotted line indicates the observed power spectrum. Short-dashed and dot-dashed lines indicate the noise level and the Lorentz term, respectively. Dashed lines indicate the Gaussian terms for the velocity elements. Solid line indicates the sum of Lorentz and Gaussian terms and noise level. (b)  f D versus proportionality constant of each velocity element c i .

Fig. 6
Fig. 6

Particle movement in the focal area.

Fig. 7
Fig. 7

Histogram of v z . Here, v avg = 0.50 mm / s and w s = (a)  0.050 mm / s , (b)  0.10 mm / s , and (c)  0.30 mm / s .

Fig. 8
Fig. 8

(a) Power spectra calculated from the sum of the Gaussian spectra for various velocity distributions: dashed line ( v avg = 0.50 mm / s , w s = 0.050 mm / s ), solid line ( 0.50 mm / s , 0.10 mm / s ), dotted line ( 0.50 mm / s , 0.30 mm / s ), dot-dashed line ( 0.10 mm / s , 0.10 mm / s ), and short dashed line ( 1.0 mm / s , 0.10 mm / s ). (b) Average power spectrum for Tetraselmis tetrathele in seawater. The dotted line indicates the observed power spectrum. The short-dashed and dot-dashed lines indicate the noise level and Lorentz term, respectively. The dashed lines indicate the sum of Gaussian spectra ( v avg = 0.40 mm / s , w s = 0.013 mm / s ). The solid line indicates the sum of Lorentz and Gaussian terms and noise level.

Equations (7)

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

I ( ω ) = A G exp { ( ω 2 π f D ) 2 w 2 } .
f D = 2 v z λ = 2 v sin θ λ ,
I ( ω ) = i A G i exp { [ ω 2 π ( 2 f AOM + f D i ) ] 2 w i 2 } ,
A G = 2.55 × 10 9 v z 1 ,
w = 1.46 × 10 6 v z .
I ( ω ) = A L k 2 D [ ω 2 π ( 2 f AOM ) ] 2 + ( k 2 D ) 2 + i c i A G i exp { [ ω 2 π ( 2 f AOM + f D i ) ] 2 w i 2 } .
p ( v ) = exp { ( v avg v ) 2 2 w s 2 } ,

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