Abstract

A transverse scanning laser Doppler velocimeter (LDV) that does not require any moving mechanism in its sensor probe is proposed, and the scanning function is demonstrated theoretically and experimentally. In the proposed scanning LDV, the measurement position is transversely scanned on the basis of a wavelength change induced by a tunable laser and a combination of a grating and a Dove prism. To demonstrate the scanning function in the transverse direction, an experiment was carried out using a setup of the sensor probe consisting of bulk optical components. The experimental results indicate that a transverse scanning function was successfully obtained. The scanning range in the vertical direction is estimated to be 11.3mm over wavelengths of 1520 to 1570nm.

© 2011 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
  3. M. Uchiyama and K. Hakomori, “A beam scanning LDV to measure velocity profile of unsteady flow,” Precis. Eng. 48, 939–944 (1982).
    [CrossRef]
  4. P. Sriram, S. Hanagud, J. Craig, and N. M. Komerath, “Scanning laser Doppler technique for velocity profile sensing on a moving surface,” Appl. Opt. 29, 2409–2417 (1990).
    [CrossRef] [PubMed]
  5. N. Nakatani, T. Nishikawa, Y. Yoneda, Y. Nakano, and T. Yamada, “Space-correlation measurement of attaching jets by the new scanning laser Doppler velocimeter using a diffraction grating,” in Proceedings of 7th Symposium on Turbulence (1981), pp. 380–389.
  6. E. B. Li, A. K. Tieu, and W. Y. D. Yuen, “Measurements of velocity distributions in the deformation zone in cold rolling by a scanning LDV,” Opt. Lasers Eng. 35, 41–49 (2001).
    [CrossRef]
  7. M. Tirabassi and S. J. Rothberg, “Scanning LDV using wedge prisms,” Opt. Lasers Eng. 47, 454–460 (2009).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  14. E. Gutierrez-Herrera and M. Strojnik, “Interferometric tolerance determination for a Dove prism using exact ray trace,” Opt. Commun. 281, 897–905 (2008).
    [CrossRef]
  15. E. Hecht, Optics, 4th ed. (Addison-Wesley, 2002), Section 10.2.8.
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    [CrossRef] [PubMed]
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2011

2009

M. Tirabassi and S. J. Rothberg, “Scanning LDV using wedge prisms,” Opt. Lasers Eng. 47, 454–460 (2009).
[CrossRef]

2008

E. Gutierrez-Herrera and M. Strojnik, “Interferometric tolerance determination for a Dove prism using exact ray trace,” Opt. Commun. 281, 897–905 (2008).
[CrossRef]

2006

2003

I. Moreno, G. Paez, and M. Strojnik, “Polarization transforming properties of Dove prisms,” Opt. Commun. 220, 257–268(2003).
[CrossRef]

2001

E. B. Li, A. K. Tieu, and W. Y. D. Yuen, “Measurements of velocity distributions in the deformation zone in cold rolling by a scanning LDV,” Opt. Lasers Eng. 35, 41–49 (2001).
[CrossRef]

1994

1992

1990

1982

1981

F. Durst, B. Lehmann, and C. Tropea, “Laser-Doppler system for rapid scanning of flow fields,” Rev. Sci. Instrum. 52, 1676–1681 (1981).
[CrossRef]

1973

Aarnoudse, J. G.

Albrecht, H.-E.

H.-E. Albrecht, M. Borys, N. Damaschke, and C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques(Springer, 2003), Section 7.3.

H.-E. Albrecht, M. Borys, N. Damaschke, and C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques (Springer, 2003), Section 2.1.

Borys, M.

H.-E. Albrecht, M. Borys, N. Damaschke, and C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques (Springer, 2003), Section 2.1.

H.-E. Albrecht, M. Borys, N. Damaschke, and C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques(Springer, 2003), Section 7.3.

Craig, J.

Damaschke, N.

H.-E. Albrecht, M. Borys, N. Damaschke, and C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques(Springer, 2003), Section 7.3.

H.-E. Albrecht, M. Borys, N. Damaschke, and C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques (Springer, 2003), Section 2.1.

Dassel, A. C. M.

de Mul, F. F. M.

Durst, F.

F. Durst, B. Lehmann, and C. Tropea, “Laser-Doppler system for rapid scanning of flow fields,” Rev. Sci. Instrum. 52, 1676–1681 (1981).
[CrossRef]

González, N.

Graaff, R.

Grant, G. R.

Greve, J.

Gutierrez-Herrera, E.

E. Gutierrez-Herrera and M. Strojnik, “Interferometric tolerance determination for a Dove prism using exact ray trace,” Opt. Commun. 281, 897–905 (2008).
[CrossRef]

Hakomori, K.

M. Uchiyama and K. Hakomori, “A beam scanning LDV to measure velocity profile of unsteady flow,” Precis. Eng. 48, 939–944 (1982).
[CrossRef]

Hanagud, S.

Hecht, E.

E. Hecht, Optics, 4th ed. (Addison-Wesley, 2002), Section 10.2.8.

Hironaga, M.

Hoki, N.

Kajiya, F.

Kano, M.

Koelink, M. H.

Komerath, N. M.

Koyama, J.

Lehmann, B.

F. Durst, B. Lehmann, and C. Tropea, “Laser-Doppler system for rapid scanning of flow fields,” Rev. Sci. Instrum. 52, 1676–1681 (1981).
[CrossRef]

Li, E. B.

E. B. Li, A. K. Tieu, and W. Y. D. Yuen, “Measurements of velocity distributions in the deformation zone in cold rolling by a scanning LDV,” Opt. Lasers Eng. 35, 41–49 (2001).
[CrossRef]

Maru, K.

Molina-Terriza, G.

Moreno, I.

I. Moreno, G. Paez, and M. Strojnik, “Polarization transforming properties of Dove prisms,” Opt. Commun. 220, 257–268(2003).
[CrossRef]

Nakano, Y.

N. Nakatani, T. Nishikawa, Y. Yoneda, Y. Nakano, and T. Yamada, “Space-correlation measurement of attaching jets by the new scanning laser Doppler velocimeter using a diffraction grating,” in Proceedings of 7th Symposium on Turbulence (1981), pp. 380–389.

Nakatani, N.

N. Nakatani, T. Nishikawa, Y. Yoneda, Y. Nakano, and T. Yamada, “Space-correlation measurement of attaching jets by the new scanning laser Doppler velocimeter using a diffraction grating,” in Proceedings of 7th Symposium on Turbulence (1981), pp. 380–389.

Nishihara, H.

Nishikawa, T.

N. Nakatani, T. Nishikawa, Y. Yoneda, Y. Nakano, and T. Yamada, “Space-correlation measurement of attaching jets by the new scanning laser Doppler velocimeter using a diffraction grating,” in Proceedings of 7th Symposium on Turbulence (1981), pp. 380–389.

Orloff, K. L.

Paez, G.

I. Moreno, G. Paez, and M. Strojnik, “Polarization transforming properties of Dove prisms,” Opt. Commun. 220, 257–268(2003).
[CrossRef]

Rothberg, S. J.

M. Tirabassi and S. J. Rothberg, “Scanning LDV using wedge prisms,” Opt. Lasers Eng. 47, 454–460 (2009).
[CrossRef]

Sriram, P.

Stiegimeier, M.

Strojnik, M.

E. Gutierrez-Herrera and M. Strojnik, “Interferometric tolerance determination for a Dove prism using exact ray trace,” Opt. Commun. 281, 897–905 (2008).
[CrossRef]

I. Moreno, G. Paez, and M. Strojnik, “Polarization transforming properties of Dove prisms,” Opt. Commun. 220, 257–268(2003).
[CrossRef]

Tieu, A. K.

E. B. Li, A. K. Tieu, and W. Y. D. Yuen, “Measurements of velocity distributions in the deformation zone in cold rolling by a scanning LDV,” Opt. Lasers Eng. 35, 41–49 (2001).
[CrossRef]

Tirabassi, M.

M. Tirabassi and S. J. Rothberg, “Scanning LDV using wedge prisms,” Opt. Lasers Eng. 47, 454–460 (2009).
[CrossRef]

Torres, J. P.

Tropea, C.

M. Stiegimeier and C. Tropea, “Mobile fiber-optic laser Doppler anemometer,” Appl. Opt. 31, 4096–4105 (1992).
[CrossRef]

F. Durst, B. Lehmann, and C. Tropea, “Laser-Doppler system for rapid scanning of flow fields,” Rev. Sci. Instrum. 52, 1676–1681 (1981).
[CrossRef]

H.-E. Albrecht, M. Borys, N. Damaschke, and C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques (Springer, 2003), Section 2.1.

H.-E. Albrecht, M. Borys, N. Damaschke, and C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques(Springer, 2003), Section 7.3.

Uchiyama, M.

M. Uchiyama and K. Hakomori, “A beam scanning LDV to measure velocity profile of unsteady flow,” Precis. Eng. 48, 939–944 (1982).
[CrossRef]

Yamada, T.

N. Nakatani, T. Nishikawa, Y. Yoneda, Y. Nakano, and T. Yamada, “Space-correlation measurement of attaching jets by the new scanning laser Doppler velocimeter using a diffraction grating,” in Proceedings of 7th Symposium on Turbulence (1981), pp. 380–389.

Yoneda, Y.

N. Nakatani, T. Nishikawa, Y. Yoneda, Y. Nakano, and T. Yamada, “Space-correlation measurement of attaching jets by the new scanning laser Doppler velocimeter using a diffraction grating,” in Proceedings of 7th Symposium on Turbulence (1981), pp. 380–389.

Yuen, W. Y. D.

E. B. Li, A. K. Tieu, and W. Y. D. Yuen, “Measurements of velocity distributions in the deformation zone in cold rolling by a scanning LDV,” Opt. Lasers Eng. 35, 41–49 (2001).
[CrossRef]

Appl. Opt.

Opt. Commun.

I. Moreno, G. Paez, and M. Strojnik, “Polarization transforming properties of Dove prisms,” Opt. Commun. 220, 257–268(2003).
[CrossRef]

E. Gutierrez-Herrera and M. Strojnik, “Interferometric tolerance determination for a Dove prism using exact ray trace,” Opt. Commun. 281, 897–905 (2008).
[CrossRef]

Opt. Express

Opt. Lasers Eng.

E. B. Li, A. K. Tieu, and W. Y. D. Yuen, “Measurements of velocity distributions in the deformation zone in cold rolling by a scanning LDV,” Opt. Lasers Eng. 35, 41–49 (2001).
[CrossRef]

M. Tirabassi and S. J. Rothberg, “Scanning LDV using wedge prisms,” Opt. Lasers Eng. 47, 454–460 (2009).
[CrossRef]

Precis. Eng.

M. Uchiyama and K. Hakomori, “A beam scanning LDV to measure velocity profile of unsteady flow,” Precis. Eng. 48, 939–944 (1982).
[CrossRef]

Rev. Sci. Instrum.

F. Durst, B. Lehmann, and C. Tropea, “Laser-Doppler system for rapid scanning of flow fields,” Rev. Sci. Instrum. 52, 1676–1681 (1981).
[CrossRef]

Other

H.-E. Albrecht, M. Borys, N. Damaschke, and C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques(Springer, 2003), Section 7.3.

E. Hecht, Optics, 4th ed. (Addison-Wesley, 2002), Section 10.2.8.

H.-E. Albrecht, M. Borys, N. Damaschke, and C. Tropea, Laser Doppler and Phase Doppler Measurement Techniques (Springer, 2003), Section 2.1.

Schott Optical Glass Catalogue, http://www.us.schott.com/advanced_optics/english/our_products/materials/data_tools/.

N. Nakatani, T. Nishikawa, Y. Yoneda, Y. Nakano, and T. Yamada, “Space-correlation measurement of attaching jets by the new scanning laser Doppler velocimeter using a diffraction grating,” in Proceedings of 7th Symposium on Turbulence (1981), pp. 380–389.

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Figures (8)

Fig. 1
Fig. 1

Concept of proposed nonmechanical transverse scanning LDV. (a) Whole system and (b) sensor probe.

Fig. 2
Fig. 2

Model of transmitting optics. (a) Geometrical model and (b) definitions of rotation angle of Dove prism θ, base angle α, and angle of ray ( φ x , φ y ) .

Fig. 3
Fig. 3

Calculated locus of measurement position on ζ y plane when wavelength λ is changed from 1520 to 1570 nm . d = 1.67 μm , ϕ i = 50 ° , m = 1 , L 1 = 30 mm , L D = 64 mm , L 2 = 306 mm , γ = 10 ° , α = 45 ° , and θ = 45.48 ° . The result using the paraxial approximation is also plotted.

Fig. 4
Fig. 4

Calculated locus of ray projected on x y plane for various distances from Dove prism when wavelength λ is changed from 1520 to 1570 nm . d = 1.67 μm , ϕ i = 50 ° , m = 1 , L 1 = 30 mm , L D = 64 mm , α = 45 ° , and θ = 45.48 ° .

Fig. 5
Fig. 5

Experimental setup. (a) Whole setup and (b) measurement position on surface of rotating target.

Fig. 6
Fig. 6

Measured spectra of beat signals. The angular velocity is 14 π rad / s and the wavelengths are 1525, 1545, and 1565 nm .

Fig. 7
Fig. 7

Measured values of F / ω as function of wavelength.

Fig. 8
Fig. 8

Measurement positions in vertical direction y d estimated from measured values of F / ω . Theoretical values are also plotted.

Equations (14)

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ϕ m ( λ ) = sin 1 ( m λ d sin ϕ i ) ,
( x 2 tan φ x 2 ) = ( 1 L 1 0 1 ) ( x 1 tan φ x 1 ) , ( y 2 tan φ y 2 ) = ( 1 L 1 0 1 ) ( y 1 tan φ y 1 ) ,
( X 2 Y 2 ) = R ( θ ) ( x 2 y 2 ) , ( tan φ X 2 tan φ Y 2 ) = R ( θ ) ( tan φ x 2 tan φ y 2 ) ,
R ( θ ) = ( cos θ sin θ sin θ cos θ ) .
X 3 = L D tan φ X 2 + tan α tan φ X 2 tan ( α + φ Y 2 ) 1 + tan α tan ( α + φ Y 2 ) + X 2 , Y 3 = L D tan α tan φ Y 2 1 + tan α tan ( α + φ Y 2 ) Y 2 , φ X 3 = φ X 2 , φ Y 3 = φ Y 2 ,
k ^ i × u ^ n = n ( k ^ t × u ^ n ) ,
k ^ i = 1 1 + tan 2 φ X 2 + tan 2 φ Y 2 ( tan φ X 2 tan φ Y 2 1 ) , k ^ t = 1 1 + tan 2 φ X 2 + tan 2 ( α + φ Y 2 π / 2 ) ( tan φ X 2 tan ( α + φ Y 2 π / 2 ) 1 ) , u ^ n = ( 0 cos α sin α ) .
( x 3 y 3 ) = R ( θ ) ( X 3 Y 3 ) , ( tan φ x 3 tan φ y 3 ) = R ( θ ) ( tan φ X 3 tan φ Y 3 ) .
( x y z ) = s ζ + t y + ( 0 0 L 2 ) ,
( x y z ) = u ( tan φ x 3 tan φ y 3 1 ) + ( x 3 y 3 0 ) .
s = L 2 tan φ x 3 + x 3 sin γ + tan φ x 3 cos γ , t = tan φ y 3 L 2 sin γ x 3 cos γ sin γ + tan φ x 3 cos γ + y 3 .
2 γ = cos 1 ( ( 1 tan 2 φ x 3 ) cos 2 γ 2 tan φ x 3 sin 2 γ + tan 2 φ y 3 1 + tan 2 φ x 3 + tan 2 φ y 3 ) .
F = 2 v sin γ λ .
F ω = 2 y d sin γ λ .

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