Abstract

In this paper we study the improvement in a laser Doppler velocimetry experiment when the Fourier transform of the time interval probability is measured instead of the intensity correlation function. The errors involved in determination of the velocity are found to be greatly improved for low scattered intensities.

© 1989 Optical Society of America

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References

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  1. F. Moreno, M. A. Rebolledo, R. J. Lopez, “Improvement in Laser Doppler Velocimetry by the Use of Time-Interval Photon Statistics,” Phys. Rev. A 33, 416–420 (1986).
    [CrossRef] [PubMed]
  2. M. A. Rebolledo, J. M. Alvarez, J. C. Amare, “Detailed Study of the Fourier Transform of the Time-Interval Photon Statistics Distribution Applied to Laser Doppler Velocimetry,” Phys. Rev. A 38, 2910–2920 (1988).
    [CrossRef] [PubMed]
  3. M. Quintanilla, A. M. Frutos, “Holographic Filter that Transforms a Gaussian into a Uniform Beam,” Appl. Opt. 20, 879–880 (1981).
    [CrossRef] [PubMed]
  4. B. Saleh, Photoelectron Statistics (Springer-Verlag, Berlin, 1978).

1988

M. A. Rebolledo, J. M. Alvarez, J. C. Amare, “Detailed Study of the Fourier Transform of the Time-Interval Photon Statistics Distribution Applied to Laser Doppler Velocimetry,” Phys. Rev. A 38, 2910–2920 (1988).
[CrossRef] [PubMed]

1986

F. Moreno, M. A. Rebolledo, R. J. Lopez, “Improvement in Laser Doppler Velocimetry by the Use of Time-Interval Photon Statistics,” Phys. Rev. A 33, 416–420 (1986).
[CrossRef] [PubMed]

1981

Alvarez, J. M.

M. A. Rebolledo, J. M. Alvarez, J. C. Amare, “Detailed Study of the Fourier Transform of the Time-Interval Photon Statistics Distribution Applied to Laser Doppler Velocimetry,” Phys. Rev. A 38, 2910–2920 (1988).
[CrossRef] [PubMed]

Amare, J. C.

M. A. Rebolledo, J. M. Alvarez, J. C. Amare, “Detailed Study of the Fourier Transform of the Time-Interval Photon Statistics Distribution Applied to Laser Doppler Velocimetry,” Phys. Rev. A 38, 2910–2920 (1988).
[CrossRef] [PubMed]

Frutos, A. M.

Lopez, R. J.

F. Moreno, M. A. Rebolledo, R. J. Lopez, “Improvement in Laser Doppler Velocimetry by the Use of Time-Interval Photon Statistics,” Phys. Rev. A 33, 416–420 (1986).
[CrossRef] [PubMed]

Moreno, F.

F. Moreno, M. A. Rebolledo, R. J. Lopez, “Improvement in Laser Doppler Velocimetry by the Use of Time-Interval Photon Statistics,” Phys. Rev. A 33, 416–420 (1986).
[CrossRef] [PubMed]

Quintanilla, M.

Rebolledo, M. A.

M. A. Rebolledo, J. M. Alvarez, J. C. Amare, “Detailed Study of the Fourier Transform of the Time-Interval Photon Statistics Distribution Applied to Laser Doppler Velocimetry,” Phys. Rev. A 38, 2910–2920 (1988).
[CrossRef] [PubMed]

F. Moreno, M. A. Rebolledo, R. J. Lopez, “Improvement in Laser Doppler Velocimetry by the Use of Time-Interval Photon Statistics,” Phys. Rev. A 33, 416–420 (1986).
[CrossRef] [PubMed]

Saleh, B.

B. Saleh, Photoelectron Statistics (Springer-Verlag, Berlin, 1978).

Appl. Opt.

Phys. Rev. A

F. Moreno, M. A. Rebolledo, R. J. Lopez, “Improvement in Laser Doppler Velocimetry by the Use of Time-Interval Photon Statistics,” Phys. Rev. A 33, 416–420 (1986).
[CrossRef] [PubMed]

M. A. Rebolledo, J. M. Alvarez, J. C. Amare, “Detailed Study of the Fourier Transform of the Time-Interval Photon Statistics Distribution Applied to Laser Doppler Velocimetry,” Phys. Rev. A 38, 2910–2920 (1988).
[CrossRef] [PubMed]

Other

B. Saleh, Photoelectron Statistics (Springer-Verlag, Berlin, 1978).

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Figures (2)

Fig. 1
Fig. 1

Experimented setup: FG, function generator; L, light emitting diode; F, filter; P1,P2 linear polarizers; PM, photomultiplier; AD, amplifier–discriminator; FM1, FM2, frequency meters; CS, correlation system; COM, computer.

Fig. 2
Fig. 2

Graphs of GF(ν) corresponding to the A1 case in Table I.

Tables (4)

Tables Icon

Table I Cases for Which the Comparison Between Experimental, Simulated and Theoretical Values of GF(ν) was Made

Tables Icon

Table II Cases for Which the Errors Involved in the Determination of ν0 from QF(ν) or G(2)(τ) were Obtained, I0 Being the Mean Intensity in a Period P

Tables Icon

Table III Values of the Systematic es and Statistics σ Errors in ν0 when Obtained from G(2)(τ) or QF(ν)

Tables Icon

Table IV Improvement Factors for the Errors in ν0 When QF(ν) is Measured Instead of G(2)(τ)

Equations (16)

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I ( t ) = I 0 { 1 + V cos [ 2 π ν 0 ( t t j ) + δ ] } ( t j t t j + Δ ) , I ( t ) = 0 otherwise ,
Q F ( ν ) = 0 W ( θ ) cos ( 2 π ν θ ) d θ ,
G ( 2 ) ( τ ) = I ( t ) I ( t + τ )
G ( 2 ) ( τ ) = C 1 0 Δ τ I ( t ) I ( t + τ ) d τ ( τ < Δ ) , G ( 2 ) ( τ ) = 0 ( τ Δ ) ,
G ( 2 ) ( τ ) = C 2 { V [ sin ( 2 π ν 0 Δ + δ ) sin δ ] + 2 π ν 0 ( Δ τ ) [ 1 + ( V 2 / 2 ) cos ( 2 π ν 0 τ ) ] 2 V cos ( π ν 0 Δ + δ ) sin [ 2 π ν 0 ( τ Δ / 2 ) ] ( V 2 / 2 ) cos ( 2 π ν 0 Δ + 2 δ ) sin [ 2 π ν 0 ( τ Δ ) ] } .
G F ( ν ) = 0 G ( 2 ) ( τ ) cos ( 2 π ν τ ) d τ .
G F ( ν ) = C 3 i = 1 6 I i ( ν ) ,
I 1 ( ν ) = { 2 π ν 0 Δ + V [ sin ( 2 π ν 0 Δ + δ ) sin δ ] } F 1 ( ν ) ,
I 2 ( ν ) = 2 π ν 0 [ Δ F 1 ( ν ) + F 2 ( ν ) ] ,
I 3 ( ν ) = ( π ν 0 Δ V 2 / 2 ) [ F 1 ( ν 0 ν ) + F 1 ( ν 0 + ν ) ] ,
I 4 ( ν ) = ( π ν 0 V 2 / 2 ) { Δ [ F 1 ( ν 0 ν ) + F 1 ( ν 0 + ν ) ] + F 2 ( ν 0 ν ) + F 2 ( ν 0 + ν ) } ,
I 5 ( ν ) = V cos ( π ν 0 Δ δ ) × { cos ( π ν 0 Δ ) [ F 2 ( ν 0 ν ) + F 2 ( ν 0 + ν ) ] + sin ( π ν 0 Δ ) [ F 1 ( ν 0 ν ) + F 1 ( ν 0 + ν ) ] } ,
I 6 ( ν ) = ( V 2 / 4 ) cos ( 2 π ν 0 Δ + 2 δ ) × { cos ( 2 π ν 0 Δ ) [ F 2 ( ν 0 ν ) + F 2 ( ν 0 + ν ) ] + sin ( 2 π ν 0 Δ ) [ F 1 ( ν 0 ν ) + F 1 ( ν 0 + ν ) ] } ,
F 1 ( x ) = sin ( 2 π x Δ ) / 2 π x ,
F 2 ( x ) = [ cos ( 2 π x Δ ) 1 ] / ( 2 π x ) 2 .
e s = | 10 4 ν 0 10 4 |

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