Abstract

We measure the rotational and translational velocity components of particles moving in helical motion under a Laguerre-Gaussian mode illumination. The moving particle reflects light that acquires an additional frequency shift proportional to the velocity of rotation in the transverse plane, on top of the usual frequency shift due to the longitudinal motion. We determined both the translational and rotational velocities of the particles by switching between two modes: by illuminating with a Gaussian beam, we can isolate the longitudinal frequency shift; and by using a Laguerre-Gaussian mode, the frequency shift due to the rotation can be determined. Our technique can be used to characterize the motility of microorganisms with a full three-dimensional movement.

© 2014 Optical Society of America

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References

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  1. A. Guerrero, J. Carneiro, A. Pimentel, C. D. Wood, G. Corkidi, and A. Darszon, “Strategies for locating the female gamete: the importance of measuring sperm trajectories in three spatial dimensions,” Mol. Hum. Reprod. 17, 511–523 (2011).
    [Crossref] [PubMed]
  2. R. N. Bearon, “Helical swimming can provide robust upwards transport for gravitactic single-cell algae; a mechanistic model,” J. Math. Biol. 66, 1341–1359 (2013).
    [Crossref]
  3. H. C. Crenshaw, “A new look at locomotion in microorganisms: Rotating and translating,” Am. Zool. 36, 608–618 (1996).
  4. H. C. Crenshaw and L. Edelstein-Keshet, “Orientation by helical motion—II. Changing the direction of the axis of motion,” Bull. Math. Biol. 55, 213–230 (1993).
    [Crossref]
  5. H. C. Crenshaw, “Orientyation by helical motion—III. Microorganisms can orient to stimuly by changing the direction of their rotational velocity,” Bull. Math. Biol. 55, 231–255 (1993).
    [Crossref]
  6. E. Lauga and T. R. Powers, “The hydrodynamics of swimming microorganisms,” Rep. Prog. Phys. 72, 096601 (2009).
    [Crossref]
  7. G. S. Farley, “Helical nature of sperm swimming affects the fit of fertilization-kinetics models to empirical data,” Bio. Bull. 203, 51–57 (2002).
    [Crossref]
  8. T. Su, I. Choi, J. Feng, K. Huang, E. McLeod, and A. Ozcan, “Sperm trajectories form chiral ribbons,” Sci. Rep. 36, 1664 (2013).
  9. V. N. Thinh and S. Tanaka, “Speckle method for the measurement of helical motion of a rigid body,” Opt. Acta 24, 1171–1178 (1977).
    [Crossref]
  10. D. F. Katz and H. M. Dott, “Methods of measuring swimming speed of spermatozoa,” Reprod. Fertil. 45, 263–272 (1975).
    [Crossref]
  11. E. Gurarie, D. Grünbaum, and M. T. Nishizaki, “Estimating 3D movements from 2D observations using a continuous model of helical swimming,” Bull. Math. Biol. 73, 1358–1377 (2011).
    [Crossref]
  12. S. J. Lee, K. W. Seo, Y. S. Choi, and M. H. Sohn, “Three-dimensional motion measurements of free-swimming microorganisms using digital holographic microscopy,” Meas. Sci. Technol. 22, 064004 (2011).
    [Crossref]
  13. F. Durst, B. M. Howe, and G. Richter, “Laser-Doppler measurement of crosswind velocity,” Appl. Opt. 21, 2596–2607 (1982).
    [Crossref] [PubMed]
  14. A. Belmonte and J. P. Torres, “Optical Doppler shift with structured light,” Opt. Lett. 36, 4437–4439 (2011).
    [Crossref] [PubMed]
  15. C. Rosales-Guzmán, N. Hermosa, A. Belmonte, and J. P. Torres, “Experimental detection of transverse particle movement with structured light,” Sci. Rep. 3, 2815 (2013).
    [Crossref] [PubMed]
  16. M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of spinning object using light’s orbital angular momentum,” Science 341, 537–540 (2013).
    [Crossref] [PubMed]
  17. B. A. Garetz and S. Arnold, “Variable frequency shifting of circularly polarized laser radiation via a rotating half-wave retardation plate,” Opt. Commun. 31, 1–3 (1979).
    [Crossref]
  18. J. Courtial, K. Dholakia, D. A. Robertson, L. Allen, and M. J. Padgett, “Measurement of the rotational frequency shift imparted to a rotating light beam possessing orbital angular momentum,” Phys. Rev. Lett. 80, 3217–3219 (1998).
    [Crossref]
  19. T.-W. Su, L. Xue, and A. Ozcan, “High-throughput lensfree 3D tracking of human sperms reveals rare statistics of helical trajectories,” Proc. Natl. Acad. Sc. U. S. A. 109, 1–5 (2012).
    [Crossref]

2013 (4)

R. N. Bearon, “Helical swimming can provide robust upwards transport for gravitactic single-cell algae; a mechanistic model,” J. Math. Biol. 66, 1341–1359 (2013).
[Crossref]

T. Su, I. Choi, J. Feng, K. Huang, E. McLeod, and A. Ozcan, “Sperm trajectories form chiral ribbons,” Sci. Rep. 36, 1664 (2013).

C. Rosales-Guzmán, N. Hermosa, A. Belmonte, and J. P. Torres, “Experimental detection of transverse particle movement with structured light,” Sci. Rep. 3, 2815 (2013).
[Crossref] [PubMed]

M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of spinning object using light’s orbital angular momentum,” Science 341, 537–540 (2013).
[Crossref] [PubMed]

2012 (1)

T.-W. Su, L. Xue, and A. Ozcan, “High-throughput lensfree 3D tracking of human sperms reveals rare statistics of helical trajectories,” Proc. Natl. Acad. Sc. U. S. A. 109, 1–5 (2012).
[Crossref]

2011 (4)

E. Gurarie, D. Grünbaum, and M. T. Nishizaki, “Estimating 3D movements from 2D observations using a continuous model of helical swimming,” Bull. Math. Biol. 73, 1358–1377 (2011).
[Crossref]

S. J. Lee, K. W. Seo, Y. S. Choi, and M. H. Sohn, “Three-dimensional motion measurements of free-swimming microorganisms using digital holographic microscopy,” Meas. Sci. Technol. 22, 064004 (2011).
[Crossref]

A. Guerrero, J. Carneiro, A. Pimentel, C. D. Wood, G. Corkidi, and A. Darszon, “Strategies for locating the female gamete: the importance of measuring sperm trajectories in three spatial dimensions,” Mol. Hum. Reprod. 17, 511–523 (2011).
[Crossref] [PubMed]

A. Belmonte and J. P. Torres, “Optical Doppler shift with structured light,” Opt. Lett. 36, 4437–4439 (2011).
[Crossref] [PubMed]

2009 (1)

E. Lauga and T. R. Powers, “The hydrodynamics of swimming microorganisms,” Rep. Prog. Phys. 72, 096601 (2009).
[Crossref]

2002 (1)

G. S. Farley, “Helical nature of sperm swimming affects the fit of fertilization-kinetics models to empirical data,” Bio. Bull. 203, 51–57 (2002).
[Crossref]

1998 (1)

J. Courtial, K. Dholakia, D. A. Robertson, L. Allen, and M. J. Padgett, “Measurement of the rotational frequency shift imparted to a rotating light beam possessing orbital angular momentum,” Phys. Rev. Lett. 80, 3217–3219 (1998).
[Crossref]

1996 (1)

H. C. Crenshaw, “A new look at locomotion in microorganisms: Rotating and translating,” Am. Zool. 36, 608–618 (1996).

1993 (2)

H. C. Crenshaw and L. Edelstein-Keshet, “Orientation by helical motion—II. Changing the direction of the axis of motion,” Bull. Math. Biol. 55, 213–230 (1993).
[Crossref]

H. C. Crenshaw, “Orientyation by helical motion—III. Microorganisms can orient to stimuly by changing the direction of their rotational velocity,” Bull. Math. Biol. 55, 231–255 (1993).
[Crossref]

1982 (1)

1979 (1)

B. A. Garetz and S. Arnold, “Variable frequency shifting of circularly polarized laser radiation via a rotating half-wave retardation plate,” Opt. Commun. 31, 1–3 (1979).
[Crossref]

1977 (1)

V. N. Thinh and S. Tanaka, “Speckle method for the measurement of helical motion of a rigid body,” Opt. Acta 24, 1171–1178 (1977).
[Crossref]

1975 (1)

D. F. Katz and H. M. Dott, “Methods of measuring swimming speed of spermatozoa,” Reprod. Fertil. 45, 263–272 (1975).
[Crossref]

Allen, L.

J. Courtial, K. Dholakia, D. A. Robertson, L. Allen, and M. J. Padgett, “Measurement of the rotational frequency shift imparted to a rotating light beam possessing orbital angular momentum,” Phys. Rev. Lett. 80, 3217–3219 (1998).
[Crossref]

Arnold, S.

B. A. Garetz and S. Arnold, “Variable frequency shifting of circularly polarized laser radiation via a rotating half-wave retardation plate,” Opt. Commun. 31, 1–3 (1979).
[Crossref]

Barnett, S. M.

M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of spinning object using light’s orbital angular momentum,” Science 341, 537–540 (2013).
[Crossref] [PubMed]

Bearon, R. N.

R. N. Bearon, “Helical swimming can provide robust upwards transport for gravitactic single-cell algae; a mechanistic model,” J. Math. Biol. 66, 1341–1359 (2013).
[Crossref]

Belmonte, A.

C. Rosales-Guzmán, N. Hermosa, A. Belmonte, and J. P. Torres, “Experimental detection of transverse particle movement with structured light,” Sci. Rep. 3, 2815 (2013).
[Crossref] [PubMed]

A. Belmonte and J. P. Torres, “Optical Doppler shift with structured light,” Opt. Lett. 36, 4437–4439 (2011).
[Crossref] [PubMed]

Carneiro, J.

A. Guerrero, J. Carneiro, A. Pimentel, C. D. Wood, G. Corkidi, and A. Darszon, “Strategies for locating the female gamete: the importance of measuring sperm trajectories in three spatial dimensions,” Mol. Hum. Reprod. 17, 511–523 (2011).
[Crossref] [PubMed]

Choi, I.

T. Su, I. Choi, J. Feng, K. Huang, E. McLeod, and A. Ozcan, “Sperm trajectories form chiral ribbons,” Sci. Rep. 36, 1664 (2013).

Choi, Y. S.

S. J. Lee, K. W. Seo, Y. S. Choi, and M. H. Sohn, “Three-dimensional motion measurements of free-swimming microorganisms using digital holographic microscopy,” Meas. Sci. Technol. 22, 064004 (2011).
[Crossref]

Corkidi, G.

A. Guerrero, J. Carneiro, A. Pimentel, C. D. Wood, G. Corkidi, and A. Darszon, “Strategies for locating the female gamete: the importance of measuring sperm trajectories in three spatial dimensions,” Mol. Hum. Reprod. 17, 511–523 (2011).
[Crossref] [PubMed]

Courtial, J.

J. Courtial, K. Dholakia, D. A. Robertson, L. Allen, and M. J. Padgett, “Measurement of the rotational frequency shift imparted to a rotating light beam possessing orbital angular momentum,” Phys. Rev. Lett. 80, 3217–3219 (1998).
[Crossref]

Crenshaw, H. C.

H. C. Crenshaw, “A new look at locomotion in microorganisms: Rotating and translating,” Am. Zool. 36, 608–618 (1996).

H. C. Crenshaw and L. Edelstein-Keshet, “Orientation by helical motion—II. Changing the direction of the axis of motion,” Bull. Math. Biol. 55, 213–230 (1993).
[Crossref]

H. C. Crenshaw, “Orientyation by helical motion—III. Microorganisms can orient to stimuly by changing the direction of their rotational velocity,” Bull. Math. Biol. 55, 231–255 (1993).
[Crossref]

Darszon, A.

A. Guerrero, J. Carneiro, A. Pimentel, C. D. Wood, G. Corkidi, and A. Darszon, “Strategies for locating the female gamete: the importance of measuring sperm trajectories in three spatial dimensions,” Mol. Hum. Reprod. 17, 511–523 (2011).
[Crossref] [PubMed]

Dholakia, K.

J. Courtial, K. Dholakia, D. A. Robertson, L. Allen, and M. J. Padgett, “Measurement of the rotational frequency shift imparted to a rotating light beam possessing orbital angular momentum,” Phys. Rev. Lett. 80, 3217–3219 (1998).
[Crossref]

Dott, H. M.

D. F. Katz and H. M. Dott, “Methods of measuring swimming speed of spermatozoa,” Reprod. Fertil. 45, 263–272 (1975).
[Crossref]

Durst, F.

Edelstein-Keshet, L.

H. C. Crenshaw and L. Edelstein-Keshet, “Orientation by helical motion—II. Changing the direction of the axis of motion,” Bull. Math. Biol. 55, 213–230 (1993).
[Crossref]

Farley, G. S.

G. S. Farley, “Helical nature of sperm swimming affects the fit of fertilization-kinetics models to empirical data,” Bio. Bull. 203, 51–57 (2002).
[Crossref]

Feng, J.

T. Su, I. Choi, J. Feng, K. Huang, E. McLeod, and A. Ozcan, “Sperm trajectories form chiral ribbons,” Sci. Rep. 36, 1664 (2013).

Garetz, B. A.

B. A. Garetz and S. Arnold, “Variable frequency shifting of circularly polarized laser radiation via a rotating half-wave retardation plate,” Opt. Commun. 31, 1–3 (1979).
[Crossref]

Grünbaum, D.

E. Gurarie, D. Grünbaum, and M. T. Nishizaki, “Estimating 3D movements from 2D observations using a continuous model of helical swimming,” Bull. Math. Biol. 73, 1358–1377 (2011).
[Crossref]

Guerrero, A.

A. Guerrero, J. Carneiro, A. Pimentel, C. D. Wood, G. Corkidi, and A. Darszon, “Strategies for locating the female gamete: the importance of measuring sperm trajectories in three spatial dimensions,” Mol. Hum. Reprod. 17, 511–523 (2011).
[Crossref] [PubMed]

Gurarie, E.

E. Gurarie, D. Grünbaum, and M. T. Nishizaki, “Estimating 3D movements from 2D observations using a continuous model of helical swimming,” Bull. Math. Biol. 73, 1358–1377 (2011).
[Crossref]

Hermosa, N.

C. Rosales-Guzmán, N. Hermosa, A. Belmonte, and J. P. Torres, “Experimental detection of transverse particle movement with structured light,” Sci. Rep. 3, 2815 (2013).
[Crossref] [PubMed]

Howe, B. M.

Huang, K.

T. Su, I. Choi, J. Feng, K. Huang, E. McLeod, and A. Ozcan, “Sperm trajectories form chiral ribbons,” Sci. Rep. 36, 1664 (2013).

Katz, D. F.

D. F. Katz and H. M. Dott, “Methods of measuring swimming speed of spermatozoa,” Reprod. Fertil. 45, 263–272 (1975).
[Crossref]

Lauga, E.

E. Lauga and T. R. Powers, “The hydrodynamics of swimming microorganisms,” Rep. Prog. Phys. 72, 096601 (2009).
[Crossref]

Lavery, M. P. J.

M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of spinning object using light’s orbital angular momentum,” Science 341, 537–540 (2013).
[Crossref] [PubMed]

Lee, S. J.

S. J. Lee, K. W. Seo, Y. S. Choi, and M. H. Sohn, “Three-dimensional motion measurements of free-swimming microorganisms using digital holographic microscopy,” Meas. Sci. Technol. 22, 064004 (2011).
[Crossref]

McLeod, E.

T. Su, I. Choi, J. Feng, K. Huang, E. McLeod, and A. Ozcan, “Sperm trajectories form chiral ribbons,” Sci. Rep. 36, 1664 (2013).

Nishizaki, M. T.

E. Gurarie, D. Grünbaum, and M. T. Nishizaki, “Estimating 3D movements from 2D observations using a continuous model of helical swimming,” Bull. Math. Biol. 73, 1358–1377 (2011).
[Crossref]

Ozcan, A.

T. Su, I. Choi, J. Feng, K. Huang, E. McLeod, and A. Ozcan, “Sperm trajectories form chiral ribbons,” Sci. Rep. 36, 1664 (2013).

T.-W. Su, L. Xue, and A. Ozcan, “High-throughput lensfree 3D tracking of human sperms reveals rare statistics of helical trajectories,” Proc. Natl. Acad. Sc. U. S. A. 109, 1–5 (2012).
[Crossref]

Padgett, M. J.

M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of spinning object using light’s orbital angular momentum,” Science 341, 537–540 (2013).
[Crossref] [PubMed]

J. Courtial, K. Dholakia, D. A. Robertson, L. Allen, and M. J. Padgett, “Measurement of the rotational frequency shift imparted to a rotating light beam possessing orbital angular momentum,” Phys. Rev. Lett. 80, 3217–3219 (1998).
[Crossref]

Pimentel, A.

A. Guerrero, J. Carneiro, A. Pimentel, C. D. Wood, G. Corkidi, and A. Darszon, “Strategies for locating the female gamete: the importance of measuring sperm trajectories in three spatial dimensions,” Mol. Hum. Reprod. 17, 511–523 (2011).
[Crossref] [PubMed]

Powers, T. R.

E. Lauga and T. R. Powers, “The hydrodynamics of swimming microorganisms,” Rep. Prog. Phys. 72, 096601 (2009).
[Crossref]

Richter, G.

Robertson, D. A.

J. Courtial, K. Dholakia, D. A. Robertson, L. Allen, and M. J. Padgett, “Measurement of the rotational frequency shift imparted to a rotating light beam possessing orbital angular momentum,” Phys. Rev. Lett. 80, 3217–3219 (1998).
[Crossref]

Rosales-Guzmán, C.

C. Rosales-Guzmán, N. Hermosa, A. Belmonte, and J. P. Torres, “Experimental detection of transverse particle movement with structured light,” Sci. Rep. 3, 2815 (2013).
[Crossref] [PubMed]

Seo, K. W.

S. J. Lee, K. W. Seo, Y. S. Choi, and M. H. Sohn, “Three-dimensional motion measurements of free-swimming microorganisms using digital holographic microscopy,” Meas. Sci. Technol. 22, 064004 (2011).
[Crossref]

Sohn, M. H.

S. J. Lee, K. W. Seo, Y. S. Choi, and M. H. Sohn, “Three-dimensional motion measurements of free-swimming microorganisms using digital holographic microscopy,” Meas. Sci. Technol. 22, 064004 (2011).
[Crossref]

Speirits, F. C.

M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of spinning object using light’s orbital angular momentum,” Science 341, 537–540 (2013).
[Crossref] [PubMed]

Su, T.

T. Su, I. Choi, J. Feng, K. Huang, E. McLeod, and A. Ozcan, “Sperm trajectories form chiral ribbons,” Sci. Rep. 36, 1664 (2013).

Su, T.-W.

T.-W. Su, L. Xue, and A. Ozcan, “High-throughput lensfree 3D tracking of human sperms reveals rare statistics of helical trajectories,” Proc. Natl. Acad. Sc. U. S. A. 109, 1–5 (2012).
[Crossref]

Tanaka, S.

V. N. Thinh and S. Tanaka, “Speckle method for the measurement of helical motion of a rigid body,” Opt. Acta 24, 1171–1178 (1977).
[Crossref]

Thinh, V. N.

V. N. Thinh and S. Tanaka, “Speckle method for the measurement of helical motion of a rigid body,” Opt. Acta 24, 1171–1178 (1977).
[Crossref]

Torres, J. P.

C. Rosales-Guzmán, N. Hermosa, A. Belmonte, and J. P. Torres, “Experimental detection of transverse particle movement with structured light,” Sci. Rep. 3, 2815 (2013).
[Crossref] [PubMed]

A. Belmonte and J. P. Torres, “Optical Doppler shift with structured light,” Opt. Lett. 36, 4437–4439 (2011).
[Crossref] [PubMed]

Wood, C. D.

A. Guerrero, J. Carneiro, A. Pimentel, C. D. Wood, G. Corkidi, and A. Darszon, “Strategies for locating the female gamete: the importance of measuring sperm trajectories in three spatial dimensions,” Mol. Hum. Reprod. 17, 511–523 (2011).
[Crossref] [PubMed]

Xue, L.

T.-W. Su, L. Xue, and A. Ozcan, “High-throughput lensfree 3D tracking of human sperms reveals rare statistics of helical trajectories,” Proc. Natl. Acad. Sc. U. S. A. 109, 1–5 (2012).
[Crossref]

Am. Zool. (1)

H. C. Crenshaw, “A new look at locomotion in microorganisms: Rotating and translating,” Am. Zool. 36, 608–618 (1996).

Appl. Opt. (1)

Bio. Bull. (1)

G. S. Farley, “Helical nature of sperm swimming affects the fit of fertilization-kinetics models to empirical data,” Bio. Bull. 203, 51–57 (2002).
[Crossref]

Bull. Math. Biol. (3)

H. C. Crenshaw and L. Edelstein-Keshet, “Orientation by helical motion—II. Changing the direction of the axis of motion,” Bull. Math. Biol. 55, 213–230 (1993).
[Crossref]

H. C. Crenshaw, “Orientyation by helical motion—III. Microorganisms can orient to stimuly by changing the direction of their rotational velocity,” Bull. Math. Biol. 55, 231–255 (1993).
[Crossref]

E. Gurarie, D. Grünbaum, and M. T. Nishizaki, “Estimating 3D movements from 2D observations using a continuous model of helical swimming,” Bull. Math. Biol. 73, 1358–1377 (2011).
[Crossref]

J. Math. Biol. (1)

R. N. Bearon, “Helical swimming can provide robust upwards transport for gravitactic single-cell algae; a mechanistic model,” J. Math. Biol. 66, 1341–1359 (2013).
[Crossref]

Meas. Sci. Technol. (1)

S. J. Lee, K. W. Seo, Y. S. Choi, and M. H. Sohn, “Three-dimensional motion measurements of free-swimming microorganisms using digital holographic microscopy,” Meas. Sci. Technol. 22, 064004 (2011).
[Crossref]

Mol. Hum. Reprod. (1)

A. Guerrero, J. Carneiro, A. Pimentel, C. D. Wood, G. Corkidi, and A. Darszon, “Strategies for locating the female gamete: the importance of measuring sperm trajectories in three spatial dimensions,” Mol. Hum. Reprod. 17, 511–523 (2011).
[Crossref] [PubMed]

Opt. Acta (1)

V. N. Thinh and S. Tanaka, “Speckle method for the measurement of helical motion of a rigid body,” Opt. Acta 24, 1171–1178 (1977).
[Crossref]

Opt. Commun. (1)

B. A. Garetz and S. Arnold, “Variable frequency shifting of circularly polarized laser radiation via a rotating half-wave retardation plate,” Opt. Commun. 31, 1–3 (1979).
[Crossref]

Opt. Lett. (1)

Phys. Rev. Lett. (1)

J. Courtial, K. Dholakia, D. A. Robertson, L. Allen, and M. J. Padgett, “Measurement of the rotational frequency shift imparted to a rotating light beam possessing orbital angular momentum,” Phys. Rev. Lett. 80, 3217–3219 (1998).
[Crossref]

Proc. Natl. Acad. Sc. U. S. A. (1)

T.-W. Su, L. Xue, and A. Ozcan, “High-throughput lensfree 3D tracking of human sperms reveals rare statistics of helical trajectories,” Proc. Natl. Acad. Sc. U. S. A. 109, 1–5 (2012).
[Crossref]

Rep. Prog. Phys. (1)

E. Lauga and T. R. Powers, “The hydrodynamics of swimming microorganisms,” Rep. Prog. Phys. 72, 096601 (2009).
[Crossref]

Reprod. Fertil. (1)

D. F. Katz and H. M. Dott, “Methods of measuring swimming speed of spermatozoa,” Reprod. Fertil. 45, 263–272 (1975).
[Crossref]

Sci. Rep. (2)

C. Rosales-Guzmán, N. Hermosa, A. Belmonte, and J. P. Torres, “Experimental detection of transverse particle movement with structured light,” Sci. Rep. 3, 2815 (2013).
[Crossref] [PubMed]

T. Su, I. Choi, J. Feng, K. Huang, E. McLeod, and A. Ozcan, “Sperm trajectories form chiral ribbons,” Sci. Rep. 36, 1664 (2013).

Science (1)

M. P. J. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of spinning object using light’s orbital angular momentum,” Science 341, 537–540 (2013).
[Crossref] [PubMed]

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Figures (5)

Fig. 1
Fig. 1 (a) Intensity profile of the LG 0 10 beam illuminating the Digital Micromirror Device (DMD). (b) Interference of the LG 0 10 beam with the reference beam. The 10 lobes observed are due to the phase profile Φ = 10φ. (c) Schematic representation of the helical trajectory followed by particles. Z is the propagation axis of the beam.
Fig. 2
Fig. 2 (a) Experimental setup. (b) Raw signal after balanced detection. (c) Autocorrelation function of the signal. (d) Power spectral density. We only show the spectrum above the chopping frequency. PBS: polarizing beam splitter; M: mirror; L: lens; PD: photodetector; SLM: Spatial Light Modulator; SF: spatial filter; OC: optical chopper; QWP: Quarter-Wave Plate; DMD: Digital Micromirror Device. See text for details.
Fig. 3
Fig. 3 Frequency shift measured under illumination with a Gaussian mode ( = 0) for any direction of translation (vz > 0 and vz < 0), and any sense of rotation (Ω > 0 and (Ω < 0). For the sake of comparison, the case with Ω = 0 is also shown.
Fig. 4
Fig. 4 Frequency shift measured under illumination with a LG 0 10 mode for vz > 0 and vz < 0, and for Ω > 0 and (Ω < 0.
Fig. 5
Fig. 5 Frequency shift measured under illumination with a LG 0 10 mode for vz > 0 and vz < 0, and for Ω > 0 and (Ω < 0.

Equations (2)

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Δ f = Δ f + Δ f = 1 2 π ( 2 k v z + Φ v ) ,
Δ f = 1 2 π ( 2 k v z + Ω ) .

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