Abstract

When a light beam with a transverse spatially varying phase is considered for optical remote sensing, in addition to the usual longitudinal Doppler frequency shift of the returned signal induced by the motion of the scatter along the beam axis, a new transversal Doppler shift appears associated to the motion of the scatterer in the plane perpendicular to the beam axis. We discuss here how this new effect can be used to enhance the current capabilities of optical measurement systems, adding the capacity to detect more complex movements of scatters.

© 2011 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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  10. J. W. Goodman, Statistical Optics (Wiley-Interscience, 2000).
  11. R. Loudon, Phys. Rev. A 68, 013806 (2003).
    [CrossRef]

2007 (1)

Y. Wang, B. Bower, J. Izatt, O. Tan, and D. Huang, J. Biomed. Opt. 12, 041215 (2007).
[CrossRef] [PubMed]

2003 (2)

2002 (1)

M. Harris, R. Young, F. Köpp, A. Dolfi, and J. Cariou, Aerospace Sci. Technol. 6, 325 (2002).
[CrossRef]

1999 (1)

Y. R. Chemla, H. L. Grossman, T. S. Lee, J. Clarke, M. Adamkiewicz, and B. B. Buchanan, Biophys. J. 76, 3323(1999).
[CrossRef] [PubMed]

1998 (1)

J. Courtial, K. Dholakia, D. A. Robertson, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 80, 3217 (1998).
[CrossRef]

1992 (1)

1982 (1)

Adamkiewicz, M.

Y. R. Chemla, H. L. Grossman, T. S. Lee, J. Clarke, M. Adamkiewicz, and B. B. Buchanan, Biophys. J. 76, 3323(1999).
[CrossRef] [PubMed]

Allen, L.

J. Courtial, K. Dholakia, D. A. Robertson, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 80, 3217 (1998).
[CrossRef]

Bower, B.

Y. Wang, B. Bower, J. Izatt, O. Tan, and D. Huang, J. Biomed. Opt. 12, 041215 (2007).
[CrossRef] [PubMed]

Buchanan, B. B.

Y. R. Chemla, H. L. Grossman, T. S. Lee, J. Clarke, M. Adamkiewicz, and B. B. Buchanan, Biophys. J. 76, 3323(1999).
[CrossRef] [PubMed]

Cariou, J.

M. Harris, R. Young, F. Köpp, A. Dolfi, and J. Cariou, Aerospace Sci. Technol. 6, 325 (2002).
[CrossRef]

Chemla, Y. R.

Y. R. Chemla, H. L. Grossman, T. S. Lee, J. Clarke, M. Adamkiewicz, and B. B. Buchanan, Biophys. J. 76, 3323(1999).
[CrossRef] [PubMed]

Clarke, J.

Y. R. Chemla, H. L. Grossman, T. S. Lee, J. Clarke, M. Adamkiewicz, and B. B. Buchanan, Biophys. J. 76, 3323(1999).
[CrossRef] [PubMed]

Courtial, J.

J. Courtial, K. Dholakia, D. A. Robertson, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 80, 3217 (1998).
[CrossRef]

Dholakia, K.

J. Courtial, K. Dholakia, D. A. Robertson, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 80, 3217 (1998).
[CrossRef]

Dolfi, A.

M. Harris, R. Young, F. Köpp, A. Dolfi, and J. Cariou, Aerospace Sci. Technol. 6, 325 (2002).
[CrossRef]

Durst, F.

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley-Interscience, 2000).

Grant, W. B.

W. B. Grant, in Tunable Laser Applications, F.J.Duarte, ed. (CRC, 2009).

Grossman, H. L.

Y. R. Chemla, H. L. Grossman, T. S. Lee, J. Clarke, M. Adamkiewicz, and B. B. Buchanan, Biophys. J. 76, 3323(1999).
[CrossRef] [PubMed]

Harris, M.

M. Harris, R. Young, F. Köpp, A. Dolfi, and J. Cariou, Aerospace Sci. Technol. 6, 325 (2002).
[CrossRef]

Heckenberg, N. R.

Howe, B. M.

Huang, D.

Y. Wang, B. Bower, J. Izatt, O. Tan, and D. Huang, J. Biomed. Opt. 12, 041215 (2007).
[CrossRef] [PubMed]

Izatt, J.

Y. Wang, B. Bower, J. Izatt, O. Tan, and D. Huang, J. Biomed. Opt. 12, 041215 (2007).
[CrossRef] [PubMed]

Köpp, F.

M. Harris, R. Young, F. Köpp, A. Dolfi, and J. Cariou, Aerospace Sci. Technol. 6, 325 (2002).
[CrossRef]

Lee, T. S.

Y. R. Chemla, H. L. Grossman, T. S. Lee, J. Clarke, M. Adamkiewicz, and B. B. Buchanan, Biophys. J. 76, 3323(1999).
[CrossRef] [PubMed]

Loudon, R.

R. Loudon, Phys. Rev. A 68, 013806 (2003).
[CrossRef]

McDuff, R.

Padgett, M. J.

J. Courtial, K. Dholakia, D. A. Robertson, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 80, 3217 (1998).
[CrossRef]

Petrov, D.

Richter, G.

Robertson, D. A.

J. Courtial, K. Dholakia, D. A. Robertson, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 80, 3217 (1998).
[CrossRef]

Smith, C. P.

Tan, O.

Y. Wang, B. Bower, J. Izatt, O. Tan, and D. Huang, J. Biomed. Opt. 12, 041215 (2007).
[CrossRef] [PubMed]

Torner, L.

Torres, J. P.

Vasnetsov, M.

Wang, Y.

Y. Wang, B. Bower, J. Izatt, O. Tan, and D. Huang, J. Biomed. Opt. 12, 041215 (2007).
[CrossRef] [PubMed]

White, A. G.

Young, R.

M. Harris, R. Young, F. Köpp, A. Dolfi, and J. Cariou, Aerospace Sci. Technol. 6, 325 (2002).
[CrossRef]

Aerospace Sci. Technol. (1)

M. Harris, R. Young, F. Köpp, A. Dolfi, and J. Cariou, Aerospace Sci. Technol. 6, 325 (2002).
[CrossRef]

Appl. Opt. (1)

Biophys. J. (1)

Y. R. Chemla, H. L. Grossman, T. S. Lee, J. Clarke, M. Adamkiewicz, and B. B. Buchanan, Biophys. J. 76, 3323(1999).
[CrossRef] [PubMed]

J. Biomed. Opt. (1)

Y. Wang, B. Bower, J. Izatt, O. Tan, and D. Huang, J. Biomed. Opt. 12, 041215 (2007).
[CrossRef] [PubMed]

Opt. Lett. (2)

Phys. Rev. A (1)

R. Loudon, Phys. Rev. A 68, 013806 (2003).
[CrossRef]

Phys. Rev. Lett. (1)

J. Courtial, K. Dholakia, D. A. Robertson, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 80, 3217 (1998).
[CrossRef]

Other (3)

J. W. Goodman, Statistical Optics (Wiley-Interscience, 2000).

W. B. Grant, in Tunable Laser Applications, F.J.Duarte, ed. (CRC, 2009).

J.P.Torres and L.Torner, eds., Twisted Light (Wiley, 2010).

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Figures (1)

Fig. 1
Fig. 1

Sketch of the movement of a target (white solid line) in a beam with a spatially varying phase- gradient (as indicated by color scales) and the corresponding Doppler shift of the returned signal for three different times t 1 < t 2 < t 3 . (a) Target with constant velocity moves v in a constant phase gradient γ, induces a time-independent Doppler shift of value v γ / ( 2 π ) . (b) Target rotates with angular velocity ω in an LG beam and induces a time-independent Doppler shift of value m ω / ( 2 π ) . (c) Doppler shift induced by the uniform movement of a scatterer on a twisted LG beam. The frequency shift depends on time ( t 1 , t 2 , t 3 ) as the scatterer moves across the LG beam.

Equations (7)

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E ( r , t ) = E 0 exp { i [ 2 π f t k z Φ ( r ) ] } ,
i ( t ) = i 0 exp ( i { 2 k z ( t ) + Φ [ r ( t ) ] } ) ,
Ψ t = 2 k v z + Φ · v ,
Δ f = 1 2 π Φ · v .
Δ f = γ v 2 π x
Δ f = m ω 2 π ,
Δ f = m d 0 v 2 π ρ 2 .

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