Abstract

Based on the rotational Doppler effect, an orbital angular momentum beam can measure the lateral rotation velocity of an object, which has broad application prospects. However, all existing research focus on the light spot center coinciding with the rotation center, or only with small center offset. This is difficult to ensure in remote detection applications. In this paper, the rotational Doppler frequency shifts under three cases, including no center offset, small center offset and large center offset, are analyzed theoretically. Through theoretical research results, a novel method of measuring rotation velocity is proposed, with the light spot completely deviated out of the rotation center. A laboratory verification experiment shows that this proposed method breaks the limit of center offset of lateral rotation velocity measurement and is of great significance to the remote detection of non-cooperative rotation object.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Influence of lateral misalignment on the optical rotational Doppler effect

Song Qiu, Tong Liu, Zhimeng Li, Chen Wang, Yuan Ren, Qiongling Shao, and Chaoyang Xing
Appl. Opt. 58(10) 2650-2655 (2019)

Detection of spinning objects at oblique light incidence using the optical rotational Doppler effect

Song Qiu, Tong Liu, Yuan Ren, Zhimeng Li, Chen Wang, and Qiongling Shao
Opt. Express 27(17) 24781-24792 (2019)

Design and experimental demonstration of Doppler cloak from spatiotemporally modulated metamaterials based on rotational Doppler effect

Baiyang Liu, Henry Giddens, Yin Li, Yejun He, Sai-Wai Wong, and Yang Hao
Opt. Express 28(3) 3745-3755 (2020)

References

  • View by:
  • |
  • |
  • |

  1. T. Asakura and N. Takai, “Dynamic laser speckles and their application to velocity measurements of the diffuse object,” Appl. Phys. 25(3), 179–194 (1981).
    [Crossref]
  2. R. Meynart, “Instantaneous velocity field measurements in unsteady gas flow by speckle velocimetry,” Appl. Opt. 22(4), 535–540 (1983).
    [Crossref]
  3. G. Nienhuis, “Doppler effect induced by rotating lenses,” Opt. Commun. 132(1-2), 8–14 (1996).
    [Crossref]
  4. I. Bialynicki-Birula and Z. Bialynicka-Birula, “Rotational frequency shift,” Phys. Rev. Lett. 78(13), 2539–2542 (1997).
    [Crossref]
  5. J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Rotational frequency shift of a light beam,” Phys. Rev. Lett. 81(22), 4828–4830 (1998).
    [Crossref]
  6. L. Marrucci, “Spinning the Doppler Effect,” Science 341(6145), 464–465 (2013).
    [Crossref]
  7. S. Barreiro, J. W. R. Tabosa, H. Failache, and A. Lezama, “Spectroscopic observation of the rotational Doppler effect,” Phys. Rev. Lett. 97(11), 113601 (2006).
    [Crossref]
  8. A. Y. Okulov, “Rotational Doppler shift of a phase-conjugated photon,” J. Opt. Soc. Am. B 29(4), 714–718 (2012).
    [Crossref]
  9. F. C. Speirits, M. P. Lavery, M. J. Padgett, and S. M. Barnett, “Optical angular momentum in a rotating frame,” Opt. Lett. 39(10), 2944–2946 (2014).
    [Crossref]
  10. M. P. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341(6145), 537–540 (2013).
    [Crossref]
  11. M. P. Lavery, S. M. Barnett, F. C. Speirits, and M. J. Padgett, “Observation of the rotational Doppler shift of a white-light, orbital-angular-momentum-carrying beam backscattered from a rotating body,” Optica 1(1), 1–4 (2014).
    [Crossref]
  12. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
    [Crossref]
  13. M. J. Padgett, “Orbital angular momentum 25 years on,” Opt. Express 25(10), 11265–11274 (2017).
    [Crossref]
  14. H. Zhou, D. Fu, J. Dong, P. Zhang, and X. Zhang, “Theoretical analysis and experimental verification on optical rotational Doppler effect,” Opt. Express 24(9), 10050–10056 (2016).
    [Crossref]
  15. L. Fang, M. J. Padgett, and J. Wang, “Sharing a common origin between the rotational and linear Doppler effects,” Laser Photonics Rev. 11(6), 1700183 (2017).
    [Crossref]
  16. R. Neo, S. Leon-Saval, J. Bland-Hawthorn, and G. Molina-Terriza, “OAM interferometry: the detection of the rotational Doppler shift,” Opt. Express 25(18), 21159–21170 (2017).
    [Crossref]
  17. M. Seghilani, M. Myara, I. Sagnes, B. Chomet, R. Bendoula, and A. Garnache, “Self-mixing in low-noise semiconductor vortex laser: detection of a rotational Doppler shift in backscattered light,” Opt. Lett. 40(24), 5778–5781 (2015).
    [Crossref]
  18. S. Qiu, T. Liu, Z. Li, C. Wang, Y. Ren, Q. Shao, and C. Xing, “Influence of lateral misalignment on the optical rotational Doppler effect,” Appl. Opt. 58(10), 2650–2655 (2019).
    [Crossref]
  19. M. V. Vasnetsov, V. A. Pas’Ko, and M. S. Soskin, “Analysis of orbital angular momentum of a misaligned optical beam,” New J. Phys. 7(1), 46 (2005).
    [Crossref]
  20. M. P. Lavery, G. C. Berkhout, J. Courtial, and M. J. Padgett, “Measurement of the light orbital angular momentum spectrum using an optical geometric transformation,” J. Opt. 13(6), 064006 (2011).
    [Crossref]
  21. M. Padgett, “A new twist on the Doppler shift,” Phys. Today 67(2), 58–59 (2014).
    [Crossref]

2019 (1)

2017 (3)

2016 (1)

2015 (1)

2014 (3)

2013 (2)

M. P. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341(6145), 537–540 (2013).
[Crossref]

L. Marrucci, “Spinning the Doppler Effect,” Science 341(6145), 464–465 (2013).
[Crossref]

2012 (1)

2011 (1)

M. P. Lavery, G. C. Berkhout, J. Courtial, and M. J. Padgett, “Measurement of the light orbital angular momentum spectrum using an optical geometric transformation,” J. Opt. 13(6), 064006 (2011).
[Crossref]

2006 (1)

S. Barreiro, J. W. R. Tabosa, H. Failache, and A. Lezama, “Spectroscopic observation of the rotational Doppler effect,” Phys. Rev. Lett. 97(11), 113601 (2006).
[Crossref]

2005 (1)

M. V. Vasnetsov, V. A. Pas’Ko, and M. S. Soskin, “Analysis of orbital angular momentum of a misaligned optical beam,” New J. Phys. 7(1), 46 (2005).
[Crossref]

1998 (1)

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Rotational frequency shift of a light beam,” Phys. Rev. Lett. 81(22), 4828–4830 (1998).
[Crossref]

1997 (1)

I. Bialynicki-Birula and Z. Bialynicka-Birula, “Rotational frequency shift,” Phys. Rev. Lett. 78(13), 2539–2542 (1997).
[Crossref]

1996 (1)

G. Nienhuis, “Doppler effect induced by rotating lenses,” Opt. Commun. 132(1-2), 8–14 (1996).
[Crossref]

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref]

1983 (1)

1981 (1)

T. Asakura and N. Takai, “Dynamic laser speckles and their application to velocity measurements of the diffuse object,” Appl. Phys. 25(3), 179–194 (1981).
[Crossref]

Allen, L.

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Rotational frequency shift of a light beam,” Phys. Rev. Lett. 81(22), 4828–4830 (1998).
[Crossref]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref]

Asakura, T.

T. Asakura and N. Takai, “Dynamic laser speckles and their application to velocity measurements of the diffuse object,” Appl. Phys. 25(3), 179–194 (1981).
[Crossref]

Barnett, S. M.

Barreiro, S.

S. Barreiro, J. W. R. Tabosa, H. Failache, and A. Lezama, “Spectroscopic observation of the rotational Doppler effect,” Phys. Rev. Lett. 97(11), 113601 (2006).
[Crossref]

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref]

Bendoula, R.

Berkhout, G. C.

M. P. Lavery, G. C. Berkhout, J. Courtial, and M. J. Padgett, “Measurement of the light orbital angular momentum spectrum using an optical geometric transformation,” J. Opt. 13(6), 064006 (2011).
[Crossref]

Bialynicka-Birula, Z.

I. Bialynicki-Birula and Z. Bialynicka-Birula, “Rotational frequency shift,” Phys. Rev. Lett. 78(13), 2539–2542 (1997).
[Crossref]

Bialynicki-Birula, I.

I. Bialynicki-Birula and Z. Bialynicka-Birula, “Rotational frequency shift,” Phys. Rev. Lett. 78(13), 2539–2542 (1997).
[Crossref]

Bland-Hawthorn, J.

Chomet, B.

Courtial, J.

M. P. Lavery, G. C. Berkhout, J. Courtial, and M. J. Padgett, “Measurement of the light orbital angular momentum spectrum using an optical geometric transformation,” J. Opt. 13(6), 064006 (2011).
[Crossref]

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Rotational frequency shift of a light beam,” Phys. Rev. Lett. 81(22), 4828–4830 (1998).
[Crossref]

Dholakia, K.

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Rotational frequency shift of a light beam,” Phys. Rev. Lett. 81(22), 4828–4830 (1998).
[Crossref]

Dong, J.

Failache, H.

S. Barreiro, J. W. R. Tabosa, H. Failache, and A. Lezama, “Spectroscopic observation of the rotational Doppler effect,” Phys. Rev. Lett. 97(11), 113601 (2006).
[Crossref]

Fang, L.

L. Fang, M. J. Padgett, and J. Wang, “Sharing a common origin between the rotational and linear Doppler effects,” Laser Photonics Rev. 11(6), 1700183 (2017).
[Crossref]

Fu, D.

Garnache, A.

Lavery, M. P.

F. C. Speirits, M. P. Lavery, M. J. Padgett, and S. M. Barnett, “Optical angular momentum in a rotating frame,” Opt. Lett. 39(10), 2944–2946 (2014).
[Crossref]

M. P. Lavery, S. M. Barnett, F. C. Speirits, and M. J. Padgett, “Observation of the rotational Doppler shift of a white-light, orbital-angular-momentum-carrying beam backscattered from a rotating body,” Optica 1(1), 1–4 (2014).
[Crossref]

M. P. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341(6145), 537–540 (2013).
[Crossref]

M. P. Lavery, G. C. Berkhout, J. Courtial, and M. J. Padgett, “Measurement of the light orbital angular momentum spectrum using an optical geometric transformation,” J. Opt. 13(6), 064006 (2011).
[Crossref]

Leon-Saval, S.

Lezama, A.

S. Barreiro, J. W. R. Tabosa, H. Failache, and A. Lezama, “Spectroscopic observation of the rotational Doppler effect,” Phys. Rev. Lett. 97(11), 113601 (2006).
[Crossref]

Li, Z.

Liu, T.

Marrucci, L.

L. Marrucci, “Spinning the Doppler Effect,” Science 341(6145), 464–465 (2013).
[Crossref]

Meynart, R.

Molina-Terriza, G.

Myara, M.

Neo, R.

Nienhuis, G.

G. Nienhuis, “Doppler effect induced by rotating lenses,” Opt. Commun. 132(1-2), 8–14 (1996).
[Crossref]

Okulov, A. Y.

Padgett, M.

M. Padgett, “A new twist on the Doppler shift,” Phys. Today 67(2), 58–59 (2014).
[Crossref]

Padgett, M. J.

M. J. Padgett, “Orbital angular momentum 25 years on,” Opt. Express 25(10), 11265–11274 (2017).
[Crossref]

L. Fang, M. J. Padgett, and J. Wang, “Sharing a common origin between the rotational and linear Doppler effects,” Laser Photonics Rev. 11(6), 1700183 (2017).
[Crossref]

M. P. Lavery, S. M. Barnett, F. C. Speirits, and M. J. Padgett, “Observation of the rotational Doppler shift of a white-light, orbital-angular-momentum-carrying beam backscattered from a rotating body,” Optica 1(1), 1–4 (2014).
[Crossref]

F. C. Speirits, M. P. Lavery, M. J. Padgett, and S. M. Barnett, “Optical angular momentum in a rotating frame,” Opt. Lett. 39(10), 2944–2946 (2014).
[Crossref]

M. P. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341(6145), 537–540 (2013).
[Crossref]

M. P. Lavery, G. C. Berkhout, J. Courtial, and M. J. Padgett, “Measurement of the light orbital angular momentum spectrum using an optical geometric transformation,” J. Opt. 13(6), 064006 (2011).
[Crossref]

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Rotational frequency shift of a light beam,” Phys. Rev. Lett. 81(22), 4828–4830 (1998).
[Crossref]

Pas’Ko, V. A.

M. V. Vasnetsov, V. A. Pas’Ko, and M. S. Soskin, “Analysis of orbital angular momentum of a misaligned optical beam,” New J. Phys. 7(1), 46 (2005).
[Crossref]

Qiu, S.

Ren, Y.

Robertson, D. A.

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Rotational frequency shift of a light beam,” Phys. Rev. Lett. 81(22), 4828–4830 (1998).
[Crossref]

Sagnes, I.

Seghilani, M.

Shao, Q.

Soskin, M. S.

M. V. Vasnetsov, V. A. Pas’Ko, and M. S. Soskin, “Analysis of orbital angular momentum of a misaligned optical beam,” New J. Phys. 7(1), 46 (2005).
[Crossref]

Speirits, F. C.

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref]

Tabosa, J. W. R.

S. Barreiro, J. W. R. Tabosa, H. Failache, and A. Lezama, “Spectroscopic observation of the rotational Doppler effect,” Phys. Rev. Lett. 97(11), 113601 (2006).
[Crossref]

Takai, N.

T. Asakura and N. Takai, “Dynamic laser speckles and their application to velocity measurements of the diffuse object,” Appl. Phys. 25(3), 179–194 (1981).
[Crossref]

Vasnetsov, M. V.

M. V. Vasnetsov, V. A. Pas’Ko, and M. S. Soskin, “Analysis of orbital angular momentum of a misaligned optical beam,” New J. Phys. 7(1), 46 (2005).
[Crossref]

Wang, C.

Wang, J.

L. Fang, M. J. Padgett, and J. Wang, “Sharing a common origin between the rotational and linear Doppler effects,” Laser Photonics Rev. 11(6), 1700183 (2017).
[Crossref]

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref]

Xing, C.

Zhang, P.

Zhang, X.

Zhou, H.

Appl. Opt. (2)

Appl. Phys. (1)

T. Asakura and N. Takai, “Dynamic laser speckles and their application to velocity measurements of the diffuse object,” Appl. Phys. 25(3), 179–194 (1981).
[Crossref]

J. Opt. (1)

M. P. Lavery, G. C. Berkhout, J. Courtial, and M. J. Padgett, “Measurement of the light orbital angular momentum spectrum using an optical geometric transformation,” J. Opt. 13(6), 064006 (2011).
[Crossref]

J. Opt. Soc. Am. B (1)

Laser Photonics Rev. (1)

L. Fang, M. J. Padgett, and J. Wang, “Sharing a common origin between the rotational and linear Doppler effects,” Laser Photonics Rev. 11(6), 1700183 (2017).
[Crossref]

New J. Phys. (1)

M. V. Vasnetsov, V. A. Pas’Ko, and M. S. Soskin, “Analysis of orbital angular momentum of a misaligned optical beam,” New J. Phys. 7(1), 46 (2005).
[Crossref]

Opt. Commun. (1)

G. Nienhuis, “Doppler effect induced by rotating lenses,” Opt. Commun. 132(1-2), 8–14 (1996).
[Crossref]

Opt. Express (3)

Opt. Lett. (2)

Optica (1)

Phys. Rev. A (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref]

Phys. Rev. Lett. (3)

S. Barreiro, J. W. R. Tabosa, H. Failache, and A. Lezama, “Spectroscopic observation of the rotational Doppler effect,” Phys. Rev. Lett. 97(11), 113601 (2006).
[Crossref]

I. Bialynicki-Birula and Z. Bialynicka-Birula, “Rotational frequency shift,” Phys. Rev. Lett. 78(13), 2539–2542 (1997).
[Crossref]

J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, “Rotational frequency shift of a light beam,” Phys. Rev. Lett. 81(22), 4828–4830 (1998).
[Crossref]

Phys. Today (1)

M. Padgett, “A new twist on the Doppler shift,” Phys. Today 67(2), 58–59 (2014).
[Crossref]

Science (2)

L. Marrucci, “Spinning the Doppler Effect,” Science 341(6145), 464–465 (2013).
[Crossref]

M. P. Lavery, F. C. Speirits, S. M. Barnett, and M. J. Padgett, “Detection of a spinning object using light’s orbital angular momentum,” Science 341(6145), 537–540 (2013).
[Crossref]

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1.
Fig. 1. OAM light beam illuminates at different positions of the rotating object. The point O is the rotation center of object, and the point $O^{\prime}$ is the center of OAM light beam, and thus the offset between two centers $d = |{OO^{\prime}} |$ . (a) Without the offset, the center of OAM light beam coincides with the rotation center of object $O({O^{\prime}} )$ , also $d = 0$ . (b) With the small offset, $0\;<\;d\;\le\;r$ . (c) With the large offset, $d\;>\;r$ . (d) The schematic diagram of the angle $\phi$ between the Poynting vector $\vec{S}$ and the velocity vector ${\vec{v}_{o^{\prime}}}$
Fig. 2.
Fig. 2. Experiment system. SMF: single mode fiber, SLM: spatial light modulator
Fig. 3.
Fig. 3. The curve of measurement error and signal-to-clutter ratio (SCR) under different offsets between the light spot center and rotation center.
Fig. 4.
Fig. 4. The rotational Doppler frequency spectrum. (a) the center offset $d\textrm{ = }0.15r$ . (b) the center offset $d\textrm{ = }0.2r$ . (c) the center offset $d\textrm{ = }0.25r$ . (d) the center offset $d\textrm{ = }0.3r$ . Rotation angular velocity and rotational Doppler frequency shift satisfy $\Delta f = {{\Omega |{{l_1} - {l_2}} |} \mathord{\left/ {\vphantom {{\Omega |{{l_1} - {l_2}} |} {({2\pi } )}}} \right.} {({2\pi } )}}$ . The rotational angular velocity to be measured is 300 rad/s.
Fig. 5.
Fig. 5. The rotational Doppler frequency spectrum. (a) the center offset $d\textrm{ = }0.9r$ . (b) the center offset $d\textrm{ = }r$ . The rotational angular velocity to be measured is 300 rad/s.
Fig. 6.
Fig. 6. The curve of measurement error and signal-to-clutter ratio (SCR) with OAM light spot completely deviated out of the rotation center.
Fig. 7.
Fig. 7. The rotational Doppler frequency spectrum. (a) the center offset $d\textrm{ = }5r$ . (b) the center offset $d\textrm{ = }10r$ . (c) the center offset $d\textrm{ = }15r$ . (d) the center offset $d\textrm{ = }20r$ . The rotational angular velocity to be measured is 300 rad/s.

Equations (5)

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

Δ f = cos ϕ f 0 v c
Δ f = cos ϕ f 0 v c = l λ 2 π r f 0 v c = l v 2 π r
Δ f = l v 2 π r = l Ω r 2 π r = l Ω 2 π
Δ f = l v 2 π r = l Ω d 2 + r 2 + 2 d r cos θ 2 π r
Δ f = l v r 2 π r = l Ω r 2 π r = l Ω 2 π

Metrics