Abstract

A reciprocal fiber-optic reflection interferometer for remote measurement of electrical current through the Faraday effect is described. The effects of polarization cross coupling because of nonideal elements are eliminated with a low-coherence source. Nonreciprocal birefringence phase modulation is employed for detection of the Faraday phase shift. The theoretical predictions are confirmed by measurements with a piece of straight fiber as the sensing element in a 100-turn solenoid. Currents from 0 to 40 A have been measured with a linear response and a noise limit of 0.015A/Hz.

© 1994 Optical Society of America

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References

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  1. V. Annovazzi-Lodi, S. Donati, “Fiber current sensors for HV lines,” in Fiber Optic Sensors II, A. M. Scheggi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.798, 270–274 (1987).
    [CrossRef]
  2. A. M. Smith, “Polarization and magneto-optic properties of single-mode optical fiber,” Appl. Opt. 17, 52–57 (1978).
    [CrossRef] [PubMed]
  3. S. C. Rashleigh, R. Ulrich, “Magneto-optic current sensing with birefringent fibers,” Appl. Phys. Lett. 34, 768–770 (1979).
    [CrossRef]
  4. A. Papp, H. Harms, “Magnetooptical current transformers: principles,” Appl. Opt. 19, 3729–3745 (1980).
    [CrossRef] [PubMed]
  5. S. Donati, V. Annovazzi-Lodi, T. Tambasso, “Magnetooptical fiber sensor for electrical industry: analysis of performance,” Proc. Inst. Electr. Eng. 135, 372–382 (1988).
  6. P. Ferdinand, J.-L. Lesne, “Induced circular birefringence and ellipticity measurement in a Faraday effect fiber ring interferometer,” in Fiber-Optic Rotation Sensors, S. Ezekiel, H. J. Arditty, eds. (Springer-Verlag, Berlin, 1982), pp. 215–221.
  7. P. A. Leilabady, A. P. Wayte, M. Berwick, J. D. C. Jones, D. A. Jackson, “A pseudo-reciprocal fiber-optic Faraday rotation sensor: current measurement and data communication applications,” Opt. Commun. 59, 173–176 (1986).
    [CrossRef]
  8. P.-A. Nicatti, P. Robert, “Stabilized current sensor using a Sagnac interferometer,” J. Phys. E 21, 791–796 (1988).
    [CrossRef]
  9. M. P. Varnham, A. J. Barlow, D. N. Payne, K. Okamoto, “Polarimetric strain gauges using high birefringence fiber,” Electron. Lett. 19, 699–700 (1983).
    [CrossRef]
  10. R. Dändliker, “Rotational effects of polarization in optical fibers,” in Anisotropic and Nonlinear Optical Waveguides, G. Stegeman, C. Someda, eds. (Elsevier, Amsterdam, 1992), pp. 39–76.
  11. R. Ulrich, A. Simon, “Polarization optics of twisted single-mode fibers,” Appl. Opt. 18, 2241–2251 (1979).
    [CrossRef] [PubMed]
  12. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), pp. 491–505.
  13. S. Ezekiel, “Fiber-optic rotation sensors. Tutorial review,” in Fiber-Optic Rotation Sensors, S. Ezekiel, H. J. Arditty, eds. (Springer-Verlag, Berlin, 1982), pp. 2–26.
  14. G. Frosio, K. Hug, R. Dändliker, “All-fiber Sagnac current sensor,” in Opto 92 (ESI Publications, Paris, 1992), pp. 560–564.
  15. R. Ulrich, S. C. Rashleigh, W. Eickhoff, “Bending induced birefringence in single-mode fibers,” Opt. Lett. 5, 273–275 (1980).
    [CrossRef] [PubMed]
  16. G. Frosio, “All-fiber adjustable retardation plate,” in Proceedings of the EFOC (IGI Europe, Boston, Mass., 1989), pp. 350–355.

1988 (2)

S. Donati, V. Annovazzi-Lodi, T. Tambasso, “Magnetooptical fiber sensor for electrical industry: analysis of performance,” Proc. Inst. Electr. Eng. 135, 372–382 (1988).

P.-A. Nicatti, P. Robert, “Stabilized current sensor using a Sagnac interferometer,” J. Phys. E 21, 791–796 (1988).
[CrossRef]

1986 (1)

P. A. Leilabady, A. P. Wayte, M. Berwick, J. D. C. Jones, D. A. Jackson, “A pseudo-reciprocal fiber-optic Faraday rotation sensor: current measurement and data communication applications,” Opt. Commun. 59, 173–176 (1986).
[CrossRef]

1983 (1)

M. P. Varnham, A. J. Barlow, D. N. Payne, K. Okamoto, “Polarimetric strain gauges using high birefringence fiber,” Electron. Lett. 19, 699–700 (1983).
[CrossRef]

1980 (2)

1979 (2)

R. Ulrich, A. Simon, “Polarization optics of twisted single-mode fibers,” Appl. Opt. 18, 2241–2251 (1979).
[CrossRef] [PubMed]

S. C. Rashleigh, R. Ulrich, “Magneto-optic current sensing with birefringent fibers,” Appl. Phys. Lett. 34, 768–770 (1979).
[CrossRef]

1978 (1)

Annovazzi-Lodi, V.

S. Donati, V. Annovazzi-Lodi, T. Tambasso, “Magnetooptical fiber sensor for electrical industry: analysis of performance,” Proc. Inst. Electr. Eng. 135, 372–382 (1988).

V. Annovazzi-Lodi, S. Donati, “Fiber current sensors for HV lines,” in Fiber Optic Sensors II, A. M. Scheggi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.798, 270–274 (1987).
[CrossRef]

Barlow, A. J.

M. P. Varnham, A. J. Barlow, D. N. Payne, K. Okamoto, “Polarimetric strain gauges using high birefringence fiber,” Electron. Lett. 19, 699–700 (1983).
[CrossRef]

Berwick, M.

P. A. Leilabady, A. P. Wayte, M. Berwick, J. D. C. Jones, D. A. Jackson, “A pseudo-reciprocal fiber-optic Faraday rotation sensor: current measurement and data communication applications,” Opt. Commun. 59, 173–176 (1986).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), pp. 491–505.

Dändliker, R.

G. Frosio, K. Hug, R. Dändliker, “All-fiber Sagnac current sensor,” in Opto 92 (ESI Publications, Paris, 1992), pp. 560–564.

R. Dändliker, “Rotational effects of polarization in optical fibers,” in Anisotropic and Nonlinear Optical Waveguides, G. Stegeman, C. Someda, eds. (Elsevier, Amsterdam, 1992), pp. 39–76.

Donati, S.

S. Donati, V. Annovazzi-Lodi, T. Tambasso, “Magnetooptical fiber sensor for electrical industry: analysis of performance,” Proc. Inst. Electr. Eng. 135, 372–382 (1988).

V. Annovazzi-Lodi, S. Donati, “Fiber current sensors for HV lines,” in Fiber Optic Sensors II, A. M. Scheggi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.798, 270–274 (1987).
[CrossRef]

Eickhoff, W.

Ezekiel, S.

S. Ezekiel, “Fiber-optic rotation sensors. Tutorial review,” in Fiber-Optic Rotation Sensors, S. Ezekiel, H. J. Arditty, eds. (Springer-Verlag, Berlin, 1982), pp. 2–26.

Ferdinand, P.

P. Ferdinand, J.-L. Lesne, “Induced circular birefringence and ellipticity measurement in a Faraday effect fiber ring interferometer,” in Fiber-Optic Rotation Sensors, S. Ezekiel, H. J. Arditty, eds. (Springer-Verlag, Berlin, 1982), pp. 215–221.

Frosio, G.

G. Frosio, K. Hug, R. Dändliker, “All-fiber Sagnac current sensor,” in Opto 92 (ESI Publications, Paris, 1992), pp. 560–564.

G. Frosio, “All-fiber adjustable retardation plate,” in Proceedings of the EFOC (IGI Europe, Boston, Mass., 1989), pp. 350–355.

Harms, H.

Hug, K.

G. Frosio, K. Hug, R. Dändliker, “All-fiber Sagnac current sensor,” in Opto 92 (ESI Publications, Paris, 1992), pp. 560–564.

Jackson, D. A.

P. A. Leilabady, A. P. Wayte, M. Berwick, J. D. C. Jones, D. A. Jackson, “A pseudo-reciprocal fiber-optic Faraday rotation sensor: current measurement and data communication applications,” Opt. Commun. 59, 173–176 (1986).
[CrossRef]

Jones, J. D. C.

P. A. Leilabady, A. P. Wayte, M. Berwick, J. D. C. Jones, D. A. Jackson, “A pseudo-reciprocal fiber-optic Faraday rotation sensor: current measurement and data communication applications,” Opt. Commun. 59, 173–176 (1986).
[CrossRef]

Leilabady, P. A.

P. A. Leilabady, A. P. Wayte, M. Berwick, J. D. C. Jones, D. A. Jackson, “A pseudo-reciprocal fiber-optic Faraday rotation sensor: current measurement and data communication applications,” Opt. Commun. 59, 173–176 (1986).
[CrossRef]

Lesne, J.-L.

P. Ferdinand, J.-L. Lesne, “Induced circular birefringence and ellipticity measurement in a Faraday effect fiber ring interferometer,” in Fiber-Optic Rotation Sensors, S. Ezekiel, H. J. Arditty, eds. (Springer-Verlag, Berlin, 1982), pp. 215–221.

Nicatti, P.-A.

P.-A. Nicatti, P. Robert, “Stabilized current sensor using a Sagnac interferometer,” J. Phys. E 21, 791–796 (1988).
[CrossRef]

Okamoto, K.

M. P. Varnham, A. J. Barlow, D. N. Payne, K. Okamoto, “Polarimetric strain gauges using high birefringence fiber,” Electron. Lett. 19, 699–700 (1983).
[CrossRef]

Papp, A.

Payne, D. N.

M. P. Varnham, A. J. Barlow, D. N. Payne, K. Okamoto, “Polarimetric strain gauges using high birefringence fiber,” Electron. Lett. 19, 699–700 (1983).
[CrossRef]

Rashleigh, S. C.

R. Ulrich, S. C. Rashleigh, W. Eickhoff, “Bending induced birefringence in single-mode fibers,” Opt. Lett. 5, 273–275 (1980).
[CrossRef] [PubMed]

S. C. Rashleigh, R. Ulrich, “Magneto-optic current sensing with birefringent fibers,” Appl. Phys. Lett. 34, 768–770 (1979).
[CrossRef]

Robert, P.

P.-A. Nicatti, P. Robert, “Stabilized current sensor using a Sagnac interferometer,” J. Phys. E 21, 791–796 (1988).
[CrossRef]

Simon, A.

Smith, A. M.

Tambasso, T.

S. Donati, V. Annovazzi-Lodi, T. Tambasso, “Magnetooptical fiber sensor for electrical industry: analysis of performance,” Proc. Inst. Electr. Eng. 135, 372–382 (1988).

Ulrich, R.

Varnham, M. P.

M. P. Varnham, A. J. Barlow, D. N. Payne, K. Okamoto, “Polarimetric strain gauges using high birefringence fiber,” Electron. Lett. 19, 699–700 (1983).
[CrossRef]

Wayte, A. P.

P. A. Leilabady, A. P. Wayte, M. Berwick, J. D. C. Jones, D. A. Jackson, “A pseudo-reciprocal fiber-optic Faraday rotation sensor: current measurement and data communication applications,” Opt. Commun. 59, 173–176 (1986).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), pp. 491–505.

Appl. Opt. (3)

Appl. Phys. Lett. (1)

S. C. Rashleigh, R. Ulrich, “Magneto-optic current sensing with birefringent fibers,” Appl. Phys. Lett. 34, 768–770 (1979).
[CrossRef]

Electron. Lett. (1)

M. P. Varnham, A. J. Barlow, D. N. Payne, K. Okamoto, “Polarimetric strain gauges using high birefringence fiber,” Electron. Lett. 19, 699–700 (1983).
[CrossRef]

J. Phys. E (1)

P.-A. Nicatti, P. Robert, “Stabilized current sensor using a Sagnac interferometer,” J. Phys. E 21, 791–796 (1988).
[CrossRef]

Opt. Commun. (1)

P. A. Leilabady, A. P. Wayte, M. Berwick, J. D. C. Jones, D. A. Jackson, “A pseudo-reciprocal fiber-optic Faraday rotation sensor: current measurement and data communication applications,” Opt. Commun. 59, 173–176 (1986).
[CrossRef]

Opt. Lett. (1)

Proc. Inst. Electr. Eng. (1)

S. Donati, V. Annovazzi-Lodi, T. Tambasso, “Magnetooptical fiber sensor for electrical industry: analysis of performance,” Proc. Inst. Electr. Eng. 135, 372–382 (1988).

Other (7)

P. Ferdinand, J.-L. Lesne, “Induced circular birefringence and ellipticity measurement in a Faraday effect fiber ring interferometer,” in Fiber-Optic Rotation Sensors, S. Ezekiel, H. J. Arditty, eds. (Springer-Verlag, Berlin, 1982), pp. 215–221.

V. Annovazzi-Lodi, S. Donati, “Fiber current sensors for HV lines,” in Fiber Optic Sensors II, A. M. Scheggi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.798, 270–274 (1987).
[CrossRef]

R. Dändliker, “Rotational effects of polarization in optical fibers,” in Anisotropic and Nonlinear Optical Waveguides, G. Stegeman, C. Someda, eds. (Elsevier, Amsterdam, 1992), pp. 39–76.

G. Frosio, “All-fiber adjustable retardation plate,” in Proceedings of the EFOC (IGI Europe, Boston, Mass., 1989), pp. 350–355.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), pp. 491–505.

S. Ezekiel, “Fiber-optic rotation sensors. Tutorial review,” in Fiber-Optic Rotation Sensors, S. Ezekiel, H. J. Arditty, eds. (Springer-Verlag, Berlin, 1982), pp. 2–26.

G. Frosio, K. Hug, R. Dändliker, “All-fiber Sagnac current sensor,” in Opto 92 (ESI Publications, Paris, 1992), pp. 560–564.

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Figures (8)

Fig. 1
Fig. 1

Principle of the reciprocal reflection interferometer for Faraday effect detection. (a) Initial version: C, coupler; M, mirror. (b) Improved version: PMC, polarization-maintaining coupler; P, all-fiber polarizer; B-PhM, birefringent phase modulator; M, mirror.

Fig. 2
Fig. 2

Block diagram representation of the reflection interferometer: (a) corresponding to Fig. 1(a), (b) corresponding to Fig. 1(b). A–D, ports of the fiber-optic coupler; I, output intensity; r , input linear retarder; f , high-birefringent fiber; q , quarter-wave retarder; c , Faraday sensing coil; p , linear polarizer; r ( + ) , modulated linear retarder.

Fig. 3
Fig. 3

Calculated relative phase error versus the Faraday effect for a twisted fiber coil.

Fig. 4
Fig. 4

Experimental setup with high-coherence source: LD, single-mode laser diode (λ = 780 nm); L1, antireflection-coated lens; OI, optical isolator; P1, P2, Glan–Thompson polarizers; BS, beam-splitter cube; SFP, scanning Fabry–Perot analyzer, D S , D F , photodiodes; L2, low-bi microscope objective; I, electrical current.

Fig. 5
Fig. 5

Measured output voltage versus electrical current.

Fig. 6
Fig. 6

Effects of coherent polarization cross coupling: (a) detected voltage versus time for zero Faraday effect and for different values of the quarter-wave loop retardation error ΔR; (b) relative fluctuation of the detected voltage versus loop retardation error ΔR.

Fig. 7
Fig. 7

Experimental setup with nonreciprocal birefringence modulation: LD, multimode laser diode (λ = 780 nm, Δλ ≈ 3 nm); P, Glan–Thompson polarizers; BS, beam-splitter cube; D F , photodiode; L, low-bi microscope objective; I, electrical current.

Fig. 8
Fig. 8

Experimental results for a low-coherence source and phase modulation: (a) demodulated voltage versus electrical current; (b) relative demodulated voltage U/U0′ versus loop retardation error ΔR.

Equations (48)

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E i = 1 2 ( 1 1 ) ,
r = [ exp ( i ϕ r / 2 ) 0 0 exp ( i ϕ r / 2 ) ] ,
f = f = f = [ exp ( i k Δ n L / 2 ) 0 0 exp ( i k Δ n L / 2 ) ] ,
q = [ cos ( R / 2 ) i sin ( R / 2 ) i sin ( R / 2 ) cos ( R / 2 ) ] , q = [ cos ( R / 2 ) i sin ( R / 2 ) i sin ( R / 2 ) cos ( R / 2 ) ] ,
c = ( cos φ F sin φ F sin φ F cos φ F ) , c = ( cos φ F sin φ F sin φ F cos φ F ) ,
s = ( 1 0 0 1 ) .
p = 1 2 ( 1 1 1 1 )
E 0 = i 2 s f m s m f r E 1 ,
E 0 = i 2 f s m s m f r E i = i 2 f m f r E i ,
m = s m s m = s q c s c q = ( m a m b * m b m a * ) .
E 0 = i 2 2 { m a exp [ i ( k Δ n L + ϕ r / 2 ) ] m b * exp ( i ϕ r / 2 ) m a * exp [ i ( k Δ n L + ϕ r / 2 ) ] + m b exp ( i ϕ r / 2 ) } .
E = p E 0 = i 2 ( Re { m a exp [ i ( k Δ n L + ϕ r / 2 ) ] } + i Im [ m b exp ( i ϕ r / 2 ) ] ) E i .
I = EE * = ¼ ( Re 2 { m a exp [ i ( k Δ n L + ϕ r / 2 ) ] } + Im 2 [ m b exp ( i ϕ r / 2 ) ] ) .
E = i 2 [ Re ( m a ( ν ) exp { i [ 2 π ν τ + ϕ r ( ν ) / 2 ] } ) + i Im { m b ( ν ) exp [ i ϕ r ( ν ) / 2 ] } ] E i ,
E i ( t ) = V ( t ) E i = V ̂ ( ν ) exp ( i 2 π ν t ) d ν E i ,
E ( t ) = U ( t ) E i ,
U ( t ) = i 2 ( Re { m a ( ν ) exp { i [ 2 π ν τ + ϕ r ( ν ) / 2 ] } + i Im { m b ( ν ) exp [ i ϕ r ( ν ) / 2 ] } ) V ̂ ( ν ) × exp ( i 2 π ν t ) d ν .
U ( t ) = i 4 m a ( ν 0 ) exp [ i ϕ r ( ν 0 ) / 2 ] V ( t + τ ) + i 4 m a * ( ν 0 ) exp [ i ϕ r ( ν 0 ) / 2 ] V ( t τ ) 1 2 Im { m b ( ν 0 ) exp [ i ϕ r ( ν 0 ) / 2 ] } V ( t ) .
I = I ( t ) = U ( t ) * U ( t ) = | m a ( ν 0 ) | 2 + ¼ Im 2 { m b ( ν 0 ) exp [ i ϕ r ( ν 0 ) / 2 ] } + | γ ( 2 τ ) | Re ( m a 2 ( ν 0 ) exp { i [ ϕ r ( ν 0 ) 4 π ν 0 τ ] } ) ,
γ ( 2 τ ) = V ( t + τ ) V * ( t τ ) V ( t ) V * ( t ) = | γ ( 2 τ ) | exp ( i 4 π ν 0 τ ) .
I incoh = | m a ( ν 0 ) | 2 + ¼ Im 2 { m b ( ν 0 ) exp [ i ϕ r ( ν 0 ) / 2 ] } .
E 0 = s r ( t ) f m s m f r ( t ) E i .
r ( t ) = { exp [ i ϕ r ( t ) / 2 ] 0 0 exp [ i ϕ r ( t ) / 2 ] } , r ( t ) = { exp [ i ϕ r ( t + T ) / 2 ] 0 0 exp [ i ϕ r ( t + T ) / 2 ] } ,
r ( t ) = r ( t ) , r ( t ) = r ( t + T ) .
E 0 = r ( t + T ) f m f r ( t ) E i ,
E 0 = 1 2 × ( m a exp { i [ k Δ n L + ϕ ̅ ( t ) ] } m b * exp [ i Δ ϕ ( t ) / 2 ] m a * exp i [ k Δ n L + ϕ ̅ ( t ) ] + m b exp [ i Δ ϕ ( t ) / 2 ] ) ,
ϕ ̅ ( t ) = ϕ r ( t + T ) + ϕ r ( t ) 2 , Δ ϕ ( t ) = ϕ r ( t + T ) ϕ r ( t ) .
I ( t ) = ¼ | m a ( ν 0 ) | 2 + ½ Im 2 { m b ( ν 0 ) exp [ i Δ ϕ ( t ) / 2 ] } + ¼ | γ ( 2 τ ) | Re ( m a 2 ( ν 0 ) exp { i [ 2 ϕ ̅ ( t ) 2 π ν 0 2 τ ] } ) .
I ( t ) = ¼ | m a ( ν 0 ) | 2 + ½ Im 2 { m b ( ν 0 ) exp [ i Δ ϕ ( t ) / 2 ] } .
I ( t ) = ¼ + ¼ cos [ 4 φ F + Δ ϕ ( t ) ] .
m b = i | m b | exp ( i φ b )
I ( t ) = ¼ | m a | 2 + ¼ | m b | 2 [ 1 cos ( 2 φ b ) cos Δ ϕ ( t ) + sin ( 2 φ b ) sin Δ ϕ ( t ) ] .
ϕ r ( t ) = ϕ 0 sin ( ω m t ) .
Δ ϕ ( t ) = 2 ϕ 0 sin ( ω m T / 2 ) cos [ ω m ( t + T / 2 ) ] = Δ ϕ 0 cos [ ω m ( t + T / 2 ) ] .
I ( t ) = ¼ { | m a | 2 + | m b | 2 [ 1 J 0 ( Δ ϕ 0 ) cos ( 2 φ b ) ] } ½ | m b | 2 sin ( 2 φ b ) μ odd ( 1 ) ( μ + 1 ) / 2 J μ ( Δ ϕ 0 ) × cos [ μ ω m ( t + T / 2 ) ] ½ | m b | 2 cos ( 2 φ b ) × μ even ( 1 ) μ / 2 J μ ( Δ ϕ 0 ) cos [ μ ω m ( t + T / 2 ) ] ,
2 φ b = tan 1 [ J 2 ( Δ ϕ 0 ) J 1 ( Δ ϕ 0 ) I ( ω m ) I ( 2 ω m ) ] ,
2 φ b = 4 φ F = 4 VNI ,
m b = V H z + ξ γ sin ( γ d ) cos ( γ d ) V H z ξ γ sin ( γ d ) cos ( γ d ) i ( V H z ) 2 ξ 2 + η 2 γ γ sin ( γ d ) sin ( γ d ) + i cos ( γ d ) cos ( γ d ) ,
φ = φ b 4 φ F 4 φ F
m a = sin ( Δ R ) cos ( 2 φ F ) ,
m b = sin ( 2 φ F ) + i cos ( Δ R ) cos ( 2 φ F ) .
I = [ 1 + sin ( 4 φ F ) ] ¼ sin 2 ( Δ R / 2 ) sin ( 4 φ F ) + | γ ( 2 τ ) | sin 2 ( Δ R ) cos 2 ( 2 φ F ) sin ( 4 π ν 0 τ ) .
I [ 1 + ( 1 Δ R 2 / 2 ) 4 φ F ] + | γ ( 2 τ ) | Δ R 2 sin ( 4 π ν 0 τ ) .
u ( t ) = u 0 [ 1 + 4 φ F ( t ) ] = u 0 [ 1 + 4 VNI ( t ) ] ,
u ( t ) = u 0 J 1 ( Δ ϕ 0 ) sin φ ( t ) ,
φ ( t ) = 4 φ F ( t ) = 4 VNI ( t ) .
L = c / 4 n f m ,
u ( t ) = u 0 4 VNI ( t ) cos Δ R = u 0 ( t ) cos Δ R .

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