Abstract

A theoretical and experimental study is presented of a Doppler velocimeter that uses a single-mode optical fiber to transmit the probe beam and collect the signal light. The performance is discussed in two cases: (i) for negligible and (ii) for strong probe beam distortion caused by surface scattering. The results suggest that in medical use the assessment of blood velocity is possible for thin superficial vessels.

© 1988 Optical Society of America

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References

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  1. F. Durst, A. Melling, J. H. Whitelaw, Principles of Laser-Doppler Anemometry (Academic, London, 1981).
  2. C. Riva, B. Ross, G. B. Benedek, “Laser Doppler Measurements of Blood Flow in Capillary Tubes and Retinal Arteries,” J. Invest. Ophthalmol 11, 936 (1971).
  3. T. Koyama, H. Mishina, T. Asakura, “A Study of Micro-Circulation in Web of Frog (Xenopus laevis Daudin) by Using Laser Doppler Microscopy,” Experientia 31, 1420 (1975).
    [CrossRef] [PubMed]
  4. M. D. Stern, “In Vivo Evaluation of Microcirculations by Coherent Light Scattering,” Nature London 254, 56 (1975).
    [CrossRef] [PubMed]
  5. G. E. Nilsson, T. Tenland, P. A. Oberg, “Evaluation of a Laser Doppler Flowmeter for Measurement of Tissue Blood Flow,” IEEE Trans. Biomed. Eng. BE-27, 12 (1980).
    [CrossRef]
  6. M. V. Evdokimov, V. G. Kolinko, M. Yu. Poroshina, A. V. Priezzhev, “Energy Characteristics of a Signal from a Laser Doppler Anemometer for the Case of Partial Spatial Coherence of the Probe Radiation,” Sov. J. Quantum Electron. 15, 1352 (1985).
    [CrossRef]
  7. J. H. Shapiro, B. A. Capron, R. C. Harney, “Imaging and Target Detection with a Heterodyne-Reception Optical Radar,” Appl. Opt. 20, 3292 (1981).
    [CrossRef] [PubMed]
  8. R. Bättig, R. Stierlin, P.-D. Henchoz, H. P. Weber, “New Monostatic Balanced Doppler Velocimeter Using a High Birefringence Fiber,” IEEE OSA J. Lightwave Technol. LT-6, 8 (1988).
    [CrossRef]
  9. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968).
  10. R. F. Lutomirski, H. T. Yura, “Propagation of a Finite Optical Beam in an Inhomogeneous Medium,” Appl. Opt. 10, 1652 (1971).
    [CrossRef] [PubMed]
  11. H. T. Yura, “Optical Heterodyne Signal Power Obtained from Finite Sized Sources of Radiation,” Appl. Opt. 13, 150 (1974).
    [CrossRef] [PubMed]
  12. A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).
  13. A. Yariv, Introduction to Optical Electronics (Holt, Rinehart, & Winston, New York1971).
  14. P. O. Rice, “Mathematical Theory of Random Noise,” Bell Syst. Tech. J. 23, 282 (1945).
  15. J. W. Goodman, “Statistical Properties of Easy Speckle Patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer-Verlag, Berlin, 1984).
  16. N. B. Baranova, B. Ya. Zeldovich, V. V. Shkunov, “Phase Conjugation by Stimulated Light Scattering in a Focused Spatially Inhomogeneous Pump Beam,” Sov. J. Quantum Electron. 8, 559 (1978).
    [CrossRef]
  17. B. Ya. Zeldovich, N. F. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, Berlin, 1985).
  18. M. Abramowitz, I. A. Stegun, Eds., Handbook of Mathematical Functions (Dover, New York, 1972).

1988 (1)

R. Bättig, R. Stierlin, P.-D. Henchoz, H. P. Weber, “New Monostatic Balanced Doppler Velocimeter Using a High Birefringence Fiber,” IEEE OSA J. Lightwave Technol. LT-6, 8 (1988).
[CrossRef]

1985 (1)

M. V. Evdokimov, V. G. Kolinko, M. Yu. Poroshina, A. V. Priezzhev, “Energy Characteristics of a Signal from a Laser Doppler Anemometer for the Case of Partial Spatial Coherence of the Probe Radiation,” Sov. J. Quantum Electron. 15, 1352 (1985).
[CrossRef]

1981 (1)

1980 (1)

G. E. Nilsson, T. Tenland, P. A. Oberg, “Evaluation of a Laser Doppler Flowmeter for Measurement of Tissue Blood Flow,” IEEE Trans. Biomed. Eng. BE-27, 12 (1980).
[CrossRef]

1978 (1)

N. B. Baranova, B. Ya. Zeldovich, V. V. Shkunov, “Phase Conjugation by Stimulated Light Scattering in a Focused Spatially Inhomogeneous Pump Beam,” Sov. J. Quantum Electron. 8, 559 (1978).
[CrossRef]

1975 (2)

T. Koyama, H. Mishina, T. Asakura, “A Study of Micro-Circulation in Web of Frog (Xenopus laevis Daudin) by Using Laser Doppler Microscopy,” Experientia 31, 1420 (1975).
[CrossRef] [PubMed]

M. D. Stern, “In Vivo Evaluation of Microcirculations by Coherent Light Scattering,” Nature London 254, 56 (1975).
[CrossRef] [PubMed]

1974 (1)

1971 (2)

C. Riva, B. Ross, G. B. Benedek, “Laser Doppler Measurements of Blood Flow in Capillary Tubes and Retinal Arteries,” J. Invest. Ophthalmol 11, 936 (1971).

R. F. Lutomirski, H. T. Yura, “Propagation of a Finite Optical Beam in an Inhomogeneous Medium,” Appl. Opt. 10, 1652 (1971).
[CrossRef] [PubMed]

1945 (1)

P. O. Rice, “Mathematical Theory of Random Noise,” Bell Syst. Tech. J. 23, 282 (1945).

Asakura, T.

T. Koyama, H. Mishina, T. Asakura, “A Study of Micro-Circulation in Web of Frog (Xenopus laevis Daudin) by Using Laser Doppler Microscopy,” Experientia 31, 1420 (1975).
[CrossRef] [PubMed]

Baranova, N. B.

N. B. Baranova, B. Ya. Zeldovich, V. V. Shkunov, “Phase Conjugation by Stimulated Light Scattering in a Focused Spatially Inhomogeneous Pump Beam,” Sov. J. Quantum Electron. 8, 559 (1978).
[CrossRef]

Bättig, R.

R. Bättig, R. Stierlin, P.-D. Henchoz, H. P. Weber, “New Monostatic Balanced Doppler Velocimeter Using a High Birefringence Fiber,” IEEE OSA J. Lightwave Technol. LT-6, 8 (1988).
[CrossRef]

Benedek, G. B.

C. Riva, B. Ross, G. B. Benedek, “Laser Doppler Measurements of Blood Flow in Capillary Tubes and Retinal Arteries,” J. Invest. Ophthalmol 11, 936 (1971).

Capron, B. A.

Durst, F.

F. Durst, A. Melling, J. H. Whitelaw, Principles of Laser-Doppler Anemometry (Academic, London, 1981).

Evdokimov, M. V.

M. V. Evdokimov, V. G. Kolinko, M. Yu. Poroshina, A. V. Priezzhev, “Energy Characteristics of a Signal from a Laser Doppler Anemometer for the Case of Partial Spatial Coherence of the Probe Radiation,” Sov. J. Quantum Electron. 15, 1352 (1985).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968).

J. W. Goodman, “Statistical Properties of Easy Speckle Patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer-Verlag, Berlin, 1984).

Harney, R. C.

Henchoz, P.-D.

R. Bättig, R. Stierlin, P.-D. Henchoz, H. P. Weber, “New Monostatic Balanced Doppler Velocimeter Using a High Birefringence Fiber,” IEEE OSA J. Lightwave Technol. LT-6, 8 (1988).
[CrossRef]

Kolinko, V. G.

M. V. Evdokimov, V. G. Kolinko, M. Yu. Poroshina, A. V. Priezzhev, “Energy Characteristics of a Signal from a Laser Doppler Anemometer for the Case of Partial Spatial Coherence of the Probe Radiation,” Sov. J. Quantum Electron. 15, 1352 (1985).
[CrossRef]

Koyama, T.

T. Koyama, H. Mishina, T. Asakura, “A Study of Micro-Circulation in Web of Frog (Xenopus laevis Daudin) by Using Laser Doppler Microscopy,” Experientia 31, 1420 (1975).
[CrossRef] [PubMed]

Love, J. D.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

Lutomirski, R. F.

Melling, A.

F. Durst, A. Melling, J. H. Whitelaw, Principles of Laser-Doppler Anemometry (Academic, London, 1981).

Mishina, H.

T. Koyama, H. Mishina, T. Asakura, “A Study of Micro-Circulation in Web of Frog (Xenopus laevis Daudin) by Using Laser Doppler Microscopy,” Experientia 31, 1420 (1975).
[CrossRef] [PubMed]

Nilsson, G. E.

G. E. Nilsson, T. Tenland, P. A. Oberg, “Evaluation of a Laser Doppler Flowmeter for Measurement of Tissue Blood Flow,” IEEE Trans. Biomed. Eng. BE-27, 12 (1980).
[CrossRef]

Oberg, P. A.

G. E. Nilsson, T. Tenland, P. A. Oberg, “Evaluation of a Laser Doppler Flowmeter for Measurement of Tissue Blood Flow,” IEEE Trans. Biomed. Eng. BE-27, 12 (1980).
[CrossRef]

Pilipetsky, N. F.

B. Ya. Zeldovich, N. F. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, Berlin, 1985).

Poroshina, M. Yu.

M. V. Evdokimov, V. G. Kolinko, M. Yu. Poroshina, A. V. Priezzhev, “Energy Characteristics of a Signal from a Laser Doppler Anemometer for the Case of Partial Spatial Coherence of the Probe Radiation,” Sov. J. Quantum Electron. 15, 1352 (1985).
[CrossRef]

Priezzhev, A. V.

M. V. Evdokimov, V. G. Kolinko, M. Yu. Poroshina, A. V. Priezzhev, “Energy Characteristics of a Signal from a Laser Doppler Anemometer for the Case of Partial Spatial Coherence of the Probe Radiation,” Sov. J. Quantum Electron. 15, 1352 (1985).
[CrossRef]

Rice, P. O.

P. O. Rice, “Mathematical Theory of Random Noise,” Bell Syst. Tech. J. 23, 282 (1945).

Riva, C.

C. Riva, B. Ross, G. B. Benedek, “Laser Doppler Measurements of Blood Flow in Capillary Tubes and Retinal Arteries,” J. Invest. Ophthalmol 11, 936 (1971).

Ross, B.

C. Riva, B. Ross, G. B. Benedek, “Laser Doppler Measurements of Blood Flow in Capillary Tubes and Retinal Arteries,” J. Invest. Ophthalmol 11, 936 (1971).

Shapiro, J. H.

Shkunov, V. V.

N. B. Baranova, B. Ya. Zeldovich, V. V. Shkunov, “Phase Conjugation by Stimulated Light Scattering in a Focused Spatially Inhomogeneous Pump Beam,” Sov. J. Quantum Electron. 8, 559 (1978).
[CrossRef]

B. Ya. Zeldovich, N. F. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, Berlin, 1985).

Snyder, A. W.

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

Stern, M. D.

M. D. Stern, “In Vivo Evaluation of Microcirculations by Coherent Light Scattering,” Nature London 254, 56 (1975).
[CrossRef] [PubMed]

Stierlin, R.

R. Bättig, R. Stierlin, P.-D. Henchoz, H. P. Weber, “New Monostatic Balanced Doppler Velocimeter Using a High Birefringence Fiber,” IEEE OSA J. Lightwave Technol. LT-6, 8 (1988).
[CrossRef]

Tenland, T.

G. E. Nilsson, T. Tenland, P. A. Oberg, “Evaluation of a Laser Doppler Flowmeter for Measurement of Tissue Blood Flow,” IEEE Trans. Biomed. Eng. BE-27, 12 (1980).
[CrossRef]

Weber, H. P.

R. Bättig, R. Stierlin, P.-D. Henchoz, H. P. Weber, “New Monostatic Balanced Doppler Velocimeter Using a High Birefringence Fiber,” IEEE OSA J. Lightwave Technol. LT-6, 8 (1988).
[CrossRef]

Whitelaw, J. H.

F. Durst, A. Melling, J. H. Whitelaw, Principles of Laser-Doppler Anemometry (Academic, London, 1981).

Yariv, A.

A. Yariv, Introduction to Optical Electronics (Holt, Rinehart, & Winston, New York1971).

Yura, H. T.

Zeldovich, B. Ya.

N. B. Baranova, B. Ya. Zeldovich, V. V. Shkunov, “Phase Conjugation by Stimulated Light Scattering in a Focused Spatially Inhomogeneous Pump Beam,” Sov. J. Quantum Electron. 8, 559 (1978).
[CrossRef]

B. Ya. Zeldovich, N. F. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, Berlin, 1985).

Appl. Opt. (3)

Bell Syst. Tech. J. (1)

P. O. Rice, “Mathematical Theory of Random Noise,” Bell Syst. Tech. J. 23, 282 (1945).

Experientia (1)

T. Koyama, H. Mishina, T. Asakura, “A Study of Micro-Circulation in Web of Frog (Xenopus laevis Daudin) by Using Laser Doppler Microscopy,” Experientia 31, 1420 (1975).
[CrossRef] [PubMed]

IEEE OSA J. Lightwave Technol. (1)

R. Bättig, R. Stierlin, P.-D. Henchoz, H. P. Weber, “New Monostatic Balanced Doppler Velocimeter Using a High Birefringence Fiber,” IEEE OSA J. Lightwave Technol. LT-6, 8 (1988).
[CrossRef]

IEEE Trans. Biomed. Eng. (1)

G. E. Nilsson, T. Tenland, P. A. Oberg, “Evaluation of a Laser Doppler Flowmeter for Measurement of Tissue Blood Flow,” IEEE Trans. Biomed. Eng. BE-27, 12 (1980).
[CrossRef]

J. Invest. Ophthalmol (1)

C. Riva, B. Ross, G. B. Benedek, “Laser Doppler Measurements of Blood Flow in Capillary Tubes and Retinal Arteries,” J. Invest. Ophthalmol 11, 936 (1971).

Nature London (1)

M. D. Stern, “In Vivo Evaluation of Microcirculations by Coherent Light Scattering,” Nature London 254, 56 (1975).
[CrossRef] [PubMed]

Sov. J. Quantum Electron. (2)

M. V. Evdokimov, V. G. Kolinko, M. Yu. Poroshina, A. V. Priezzhev, “Energy Characteristics of a Signal from a Laser Doppler Anemometer for the Case of Partial Spatial Coherence of the Probe Radiation,” Sov. J. Quantum Electron. 15, 1352 (1985).
[CrossRef]

N. B. Baranova, B. Ya. Zeldovich, V. V. Shkunov, “Phase Conjugation by Stimulated Light Scattering in a Focused Spatially Inhomogeneous Pump Beam,” Sov. J. Quantum Electron. 8, 559 (1978).
[CrossRef]

Other (7)

B. Ya. Zeldovich, N. F. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, Berlin, 1985).

M. Abramowitz, I. A. Stegun, Eds., Handbook of Mathematical Functions (Dover, New York, 1972).

J. W. Goodman, “Statistical Properties of Easy Speckle Patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, Ed. (Springer-Verlag, Berlin, 1984).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968).

A. W. Snyder, J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

A. Yariv, Introduction to Optical Electronics (Holt, Rinehart, & Winston, New York1971).

F. Durst, A. Melling, J. H. Whitelaw, Principles of Laser-Doppler Anemometry (Academic, London, 1981).

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Figures (7)

Fig. 1
Fig. 1

Experimental setup: BS, beam splitter; LO, local oscillator beam; BC, Bragg cells; ν1,ν2, Bragg cell driver frequencies; SMF, optical single-mode fiber; PD, photodiode; α, angle of incidence.

Fig. 2
Fig. 2

Detailed view of receiving/transmitting geometry: θ, diffraction angle of probe beam; α, angle of incidence; z axis transmitting/receiving fiber (ξx,ζ), local coordinate system for the flow cell; P, particle; v(ζ) particle velocity.

Fig. 3
Fig. 3

Theoretical plot of spectral signal power vs frequency in the narrow duct approximation: (a) Q = 40; (b) Q = 10; (c) Q = 0.707; (d) Q = 0.1.

Fig. 4
Fig. 4

Experimental spectra: (a) Q = 12; (b) Q = 43. Identical ordinate scale for both figures. The arrows indicate fitted spectral pedestals.

Fig. 5
Fig. 5

Ratio of spectral peak power to spectral pedestal vs Q1/2: +, experimental; solid line, theory in the narrow duct approximation.

Fig. 6
Fig. 6

Scaled peak width vs Q−1: +, experimental; solid line, theory in the narrow duct approximation.

Fig. 7
Fig. 7

Doppler spectrum vs frequency recorded through a diffuser screen: broken line, theory fitted for absolute magnitude.

Equations (37)

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E i l l ( x , z = 0 ) = ( P i l l ) 1 / 2 e + ( x ) ,
d 2 x e + ( x ) 2 = 1 ,
E i l l ( x P , z P ) = exp ( i Φ ) ( P i l l ) 1 / 2 e + ( x P , z P ) ,
e + ( x P , z P ) = ( i λ ) - 1 d 2 x e + ( x ) K ( x , L ; x P , z P ) ,
K ( x , L ; x P , z P ) = K ( x P , z P ; x , L ) .
E sig ( x , L ) = ( σ / 4 π ) 1 / 2 E i l l ( x P , z P ) K ( x P , z P ; x , L ) ,
A ( z = 0 ) = exp ( i Φ ) d 2 x e - * ( x ) E sig ( x , L ) .
A ( z = 0 ) = i λ ( σ P i l l / 4 π ) 1 / 2 exp ( 2 i Φ ) e + 2 ( x P , z P ) .
S ( x P , z P ) = ½ [ i γ λ exp ( 2 i Φ ) ( P i l l P LO σ / 4 π ) 1 / 2 exp ( 2 π i ν LO t ) · e + 2 ( x P , z P ) ] + c . c . ,             γ = r β .
S j ( t ) = S [ ( t - τ j ) v ( ζ j ) , ξ y j , ζ j ] ,
S D ( t ) = j S [ ( t - τ j ) v ( ζ j ) , ξ y j , ζ j ] .
k S [ ( t - τ k ) v ( ζ ) , ξ y , ζ ]
Δ P D ( ν ) = n P Δ ξ y Δ ζ v ( ζ ) F { S [ t v ( ζ ) , ξ y , ζ ] } 2
P D ( ν ) = n P A d ζ d ξ y v ( ζ ) F { S [ t v ( ζ ) , ξ y , ζ ] } 2 .
P D ( ν ) e = n p A d ζ d ξ y v ( ζ ) - + d τ exp ( - 2 π i ν τ ) s ( ξ y , ζ , τ ) e , s ( ξ y , ζ , τ ) e = P 0 exp ( 2 π i ν L O τ ) - + d t e + 2 [ t v ( ζ ) , ξ y , ζ ] e + * 2 [ ( t - τ ) v ( ζ ) , ξ y , ζ ] e + c . c . , P 0 [ V 2 cm 4 ] = λ 2 σ γ 2 P i l l P LO / 16 π ,
G ( 2 ) ( ξ 1 , ξ 2 , ζ ) = e + 2 ( ξ 1 , ζ ) e 2 * 2 ( ξ 2 , ζ ) e ,
G ( 2 ) ( ξ 1 ξ 2 , ζ ) = 2 [ G ( 1 ) ] 2 + e + 2 ( ξ 1 , ζ ) e + 2 ( ξ 2 , ζ ) e ,
G ( 1 ) ( ξ 1 , ξ 2 , ζ ) = e + ( ξ 1 , ζ ) e + * ( ξ 2 , ζ ) e .
G ( 2 ) ( ξ 1 , ξ 2 , ζ ) = 2 [ G ( 1 ) ( ξ 1 , ξ 2 , ζ ) ] 2 .
G ( 1 ) ( r , ρ , 0 - ) = ( π a 0 2 ) - 1 exp [ - ( r 2 + ρ 2 / 4 ) / a 0 2 + i k ρ x sin α ] ,
r = ½ ( ξ 1 + ξ 2 ) ,             ρ = ( ρ x , ρ y ) = ξ 1 - ξ 2 .
G ( 1 ) ( r , ρ , 0 + ) = ( π a 0 2 ) - 1 exp [ - ( r 2 + M ρ 2 / 4 ) / a 0 2 + i k ρ x sin α ] .
G ( 1 ) ( r , ρ , ζ > 0 ) = [ π a 2 ( ζ ) ] - 1 exp ( i k n ρ q ) exp { - [ ( r - ζ q ) 2 + M ρ 2 / 4 - i n - 1 k ζ θ 0 2 ρ ( r - ζ q ) ] / a 2 ( ζ ) } ,
a 2 ( ζ ) = a 0 2 + ( ζ θ 0 / n ) 2 ,             θ 0 = M 1 / 2 ( k a 0 ) - 1 , q = ( sin α , 0 ) / n .
F { S [ t v ( ζ ) , ξ y , ζ ] } ( ν ) 2 e = R ( ζ , ξ y ) D ( ζ , ν ) ,
D ( ζ , ν ) = exp { - [ ν LO + 2 v ( ζ ) × sin α / λ - ν ] 2 / [ Δ ν ( ζ ) ] 2 } ,
Δ ν ( ζ ) = v ( ζ ) / ( 2 1 / 2 π a 0 / M 1 / 2 ) .
Q = 2 - 1 / 2 sin α / θ 0 2 - 1 / 2 α / [ M 1 / 2 ( k a 0 ) - 1 ] .
P D ( ν ) e = { 2 } M - 1 / 2 ( 2 π ) - 1 / 2 a 0 P 0 × ζ 0 - d ζ 0 + d d ζ a - 2 ( ζ ) v - 1 ( ζ ) D ( ζ , ν ) ,
v ( ζ ) = v m [ 1 - ( ζ - ζ 0 ) 2 / d 2 ] .
ν T = v m / D c = π v m θ 0 / λ .
P D ( p ) e = C Q 0 1 d s [ s ( 1 - s ) 1 / 2 ] - 1 exp [ - 4 Q 2 ( 1 - p / s ) 2 ] ,
P D ( ν ) e C π 1 / 2 [ 1 - p ] - 1 / 2 ,             2 Q - 1 < p < 1 - 2 Q - 1 ,             Q 1.
P D ( ν ) e C ( π 1 / 2 Q 1 / 2 / 8 1 / 4 ) exp [ - 2 Q 2 ( p - 1 ) 2 ] D - 1 / 2 [ 8 1 / 2 ( p - 1 ) ] ,
S p C Q 1 / 2 Γ ( ¼ ) / 8 1 / 2 .
S p / S 0 Q 1 / 2 Γ ( ¼ ) / ( 2 π ) 1 / 2 = 1.44 Q 1 / 2 .
Δ p 1 / 2 { 8 π / [ Γ ( ¼ ) ] 2 + 0.855 / 8 1 / 2 } Q - 1 = 2.21 Q - 1 .

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