Abstract

Fundamental relationships between backscattered power, range, wavelength, and number of scatter centers in the probe volume for the self-aligning, dual-scatter, laser doppler velocimeter are developed. It is shown that not all power scattered from the velocimeter probe volume contributes to a doppler signal. This fact leads to significant deviations in calculations involving signal-to-noise power ratios as compared to the case when only gross backscattered power is considered.

© 1971 Optical Society of America

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Errata

W. M. Farmer, "Errata to: Analysis of Atmospheric Laser Doppler Velocimeters," Appl. Opt. 11, 1872-1872 (1972)
https://www.osapublishing.org/ao/abstract.cfm?uri=ao-11-8-1872

References

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  1. D. B. Brayton, W. H. Goethert, Trans. Inst. Soc. Am. (in press).
  2. A. E. Lennert, D. B. Brayton, W. H. Goethert, F. H. Smith, Laser J. 2, 19 (1970).
  3. F. H. Smith, J. A. Parsons, AEDC-TR-70-119 (1970).
  4. W. H. GoethertAEDC-TR-71- (to be published).
  5. A. S. Hugh, C. S. Oliver, E. R. Pike, J. J. B. O’Shaughnessy, RRE Newsletter and Res. Rev. No. 9, 7/i (1970).
  6. J. F. Meyers, “Investigation of Basic Parameters for the Application of a Laser Doppler Velocimeter,” AIAA 6th Aerodynamic Testing Conference (Albuquerque, N. Mex.10–12 March 1971).
  7. J. C. Owens, Proc. IEEE 57, 530 (1969).
    [CrossRef]
  8. J. D. Fridman, K. F. Kinnard, K. Meister, in Proc. Electro-Optical Systems Design Conference, 128 (1969).
  9. R. M. Huffaker, A. V. Jelalion, J. A. L. Thomson, Proc. IEEE 58, 322 (1970).
    [CrossRef]
  10. M. J. Rudd, J. Phys. E 2, 55 (1969).
    [CrossRef]
  11. R. D. Present, Kinetic Theory of Gases (McGraw-Hill, New York, 1958), p. 67.
  12. G. A. Massey, Appl. Opt. 4, 781 (1965).
    [CrossRef]
  13. D. T. Davis, Trans. Inst. Soc. Am. 7, 43 (1968).
  14. M. P. McCormick, “Laser Backscatter Measurements of the Lower Atmosphere,” Ph.D. Thesis (Dept. of Physics, College of William & Mary in Virginia, 1967), p. 9.
  15. Ref. 14, pp. 11 and 13.
  16. The last two terms in Eq. (23) serve only to define the doppler frequency and width of the probe volume.

1970 (3)

A. E. Lennert, D. B. Brayton, W. H. Goethert, F. H. Smith, Laser J. 2, 19 (1970).

A. S. Hugh, C. S. Oliver, E. R. Pike, J. J. B. O’Shaughnessy, RRE Newsletter and Res. Rev. No. 9, 7/i (1970).

R. M. Huffaker, A. V. Jelalion, J. A. L. Thomson, Proc. IEEE 58, 322 (1970).
[CrossRef]

1969 (2)

M. J. Rudd, J. Phys. E 2, 55 (1969).
[CrossRef]

J. C. Owens, Proc. IEEE 57, 530 (1969).
[CrossRef]

1968 (1)

D. T. Davis, Trans. Inst. Soc. Am. 7, 43 (1968).

1965 (1)

Brayton, D. B.

A. E. Lennert, D. B. Brayton, W. H. Goethert, F. H. Smith, Laser J. 2, 19 (1970).

D. B. Brayton, W. H. Goethert, Trans. Inst. Soc. Am. (in press).

Davis, D. T.

D. T. Davis, Trans. Inst. Soc. Am. 7, 43 (1968).

Fridman, J. D.

J. D. Fridman, K. F. Kinnard, K. Meister, in Proc. Electro-Optical Systems Design Conference, 128 (1969).

Goethert, W. H.

A. E. Lennert, D. B. Brayton, W. H. Goethert, F. H. Smith, Laser J. 2, 19 (1970).

W. H. GoethertAEDC-TR-71- (to be published).

D. B. Brayton, W. H. Goethert, Trans. Inst. Soc. Am. (in press).

Huffaker, R. M.

R. M. Huffaker, A. V. Jelalion, J. A. L. Thomson, Proc. IEEE 58, 322 (1970).
[CrossRef]

Hugh, A. S.

A. S. Hugh, C. S. Oliver, E. R. Pike, J. J. B. O’Shaughnessy, RRE Newsletter and Res. Rev. No. 9, 7/i (1970).

Jelalion, A. V.

R. M. Huffaker, A. V. Jelalion, J. A. L. Thomson, Proc. IEEE 58, 322 (1970).
[CrossRef]

Kinnard, K. F.

J. D. Fridman, K. F. Kinnard, K. Meister, in Proc. Electro-Optical Systems Design Conference, 128 (1969).

Lennert, A. E.

A. E. Lennert, D. B. Brayton, W. H. Goethert, F. H. Smith, Laser J. 2, 19 (1970).

Massey, G. A.

McCormick, M. P.

M. P. McCormick, “Laser Backscatter Measurements of the Lower Atmosphere,” Ph.D. Thesis (Dept. of Physics, College of William & Mary in Virginia, 1967), p. 9.

Meister, K.

J. D. Fridman, K. F. Kinnard, K. Meister, in Proc. Electro-Optical Systems Design Conference, 128 (1969).

Meyers, J. F.

J. F. Meyers, “Investigation of Basic Parameters for the Application of a Laser Doppler Velocimeter,” AIAA 6th Aerodynamic Testing Conference (Albuquerque, N. Mex.10–12 March 1971).

O’Shaughnessy, J. J. B.

A. S. Hugh, C. S. Oliver, E. R. Pike, J. J. B. O’Shaughnessy, RRE Newsletter and Res. Rev. No. 9, 7/i (1970).

Oliver, C. S.

A. S. Hugh, C. S. Oliver, E. R. Pike, J. J. B. O’Shaughnessy, RRE Newsletter and Res. Rev. No. 9, 7/i (1970).

Owens, J. C.

J. C. Owens, Proc. IEEE 57, 530 (1969).
[CrossRef]

Parsons, J. A.

F. H. Smith, J. A. Parsons, AEDC-TR-70-119 (1970).

Pike, E. R.

A. S. Hugh, C. S. Oliver, E. R. Pike, J. J. B. O’Shaughnessy, RRE Newsletter and Res. Rev. No. 9, 7/i (1970).

Present, R. D.

R. D. Present, Kinetic Theory of Gases (McGraw-Hill, New York, 1958), p. 67.

Rudd, M. J.

M. J. Rudd, J. Phys. E 2, 55 (1969).
[CrossRef]

Smith, F. H.

A. E. Lennert, D. B. Brayton, W. H. Goethert, F. H. Smith, Laser J. 2, 19 (1970).

F. H. Smith, J. A. Parsons, AEDC-TR-70-119 (1970).

Thomson, J. A. L.

R. M. Huffaker, A. V. Jelalion, J. A. L. Thomson, Proc. IEEE 58, 322 (1970).
[CrossRef]

Appl. Opt. (1)

J. Phys. E (1)

M. J. Rudd, J. Phys. E 2, 55 (1969).
[CrossRef]

Laser J. (1)

A. E. Lennert, D. B. Brayton, W. H. Goethert, F. H. Smith, Laser J. 2, 19 (1970).

Proc. IEEE (2)

J. C. Owens, Proc. IEEE 57, 530 (1969).
[CrossRef]

R. M. Huffaker, A. V. Jelalion, J. A. L. Thomson, Proc. IEEE 58, 322 (1970).
[CrossRef]

RRE Newsletter and Res. Rev. No. 9, 7/i (1)

A. S. Hugh, C. S. Oliver, E. R. Pike, J. J. B. O’Shaughnessy, RRE Newsletter and Res. Rev. No. 9, 7/i (1970).

Trans. Inst. Soc. Am. (1)

D. T. Davis, Trans. Inst. Soc. Am. 7, 43 (1968).

Other (9)

M. P. McCormick, “Laser Backscatter Measurements of the Lower Atmosphere,” Ph.D. Thesis (Dept. of Physics, College of William & Mary in Virginia, 1967), p. 9.

Ref. 14, pp. 11 and 13.

The last two terms in Eq. (23) serve only to define the doppler frequency and width of the probe volume.

R. D. Present, Kinetic Theory of Gases (McGraw-Hill, New York, 1958), p. 67.

J. F. Meyers, “Investigation of Basic Parameters for the Application of a Laser Doppler Velocimeter,” AIAA 6th Aerodynamic Testing Conference (Albuquerque, N. Mex.10–12 March 1971).

F. H. Smith, J. A. Parsons, AEDC-TR-70-119 (1970).

W. H. GoethertAEDC-TR-71- (to be published).

D. B. Brayton, W. H. Goethert, Trans. Inst. Soc. Am. (in press).

J. D. Fridman, K. F. Kinnard, K. Meister, in Proc. Electro-Optical Systems Design Conference, 128 (1969).

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Figures (2)

Fig. 1
Fig. 1

A one-velocity component long range, dual-scatter backscatter LDV system.

Fig. 2
Fig. 2

Comparison of (a) actual and (b) model fringe intensity at the geometric center of a dual scatter LDV.

Equations (35)

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P + g = n ,
P - g = m ,             m > 0.
P n , m = n ! / ( P ! g ! ) ( 1 2 ) P ( 1 2 ) g ,
P n , m = n ! / ( P ! g ! ) ( 1 2 ) n .
n ! ( 2 π n ) 1 2 ( n e ) n .
P n , m 1 ( 1 + m n ) P + 1 2 ( 1 - m n ) g + 1 2 ( 2 π n ) 1 2 .
ln [ ( n π 2 ) 1 2 P n , m ] - m 2 2 n
P n , m ( 2 n π ) 1 2 exp ( - m 2 / 2 n ) ,             m n .
( m ¯ ) 2 = 0 m 2 P n , m d m .
( m ¯ 2 ) 1 2 = ( n ) 1 2 ,
P s = I 0 σ V P T Ω ,
I 0 = 8 P 0 T π D 2 cos 2 [ k sin ( θ 2 ) cos ( ψ ) r p ] exp ( - a r p 2 ) ,
D = ( 4 λ R ) / ( π d ) .
σ = σ R + σ m ,
σ Mie = λ 2 4 π 2 r i ( 2 π r λ , n ¯ , π ) N Mie ( r , z ) ,
z = R sin φ ,
σ Mie = N Mie ( 0 ) exp ( - β R sin φ ) 3 π r 1 3 λ ϕ [ i ( 2 π r λ , n ¯ , π ) ] ,
V P = ( π / 6 ) ( D 3 / sin θ ) ,
sin θ θ = b / R ,
Ω = A R / R 2 ,
T = exp ( - β R ) ,
P s = 8 d b P 0 N Mie ( 0 ) A R r 1 3 ϕ [ i ( 2 π r λ , n ¯ , π ) ] × exp [ - ( β sin φ + 2 β ) R ] .
P s 1 = I 0 σ 1 T Ω ,
σ 1 = 3 π r 1 3 λ ϕ [ i ( 2 π r λ , n ¯ , π ) ] .
P s 1 = 3 π 2 d 2 A R r 1 3 P 0 2 ϕ [ i ( 2 π r λ , n ¯ , π ) ] exp - ( 2 β R ) λ 3 R 4 × cos 2 [ k sin ( θ 2 ) cos ( ψ ) r p ] exp ( - a r p 2 ) .
P s s = n P s 1 ,
n = N ( z ) V P .
N ( z ) = N Mie ( 0 ) exp ( - β R sin φ ) .
n = 32 N Mie ( 0 ) 3 π 2 d 3 b λ 3 R 4 exp ( - β R sin ρ ) .
P s s = 6 π P 0 A r r 1 3 [ N Mie ( 0 ) d 3 b ] 1 2 ϕ ( i ) λ / 2 3 R 2 exp [ - R ( 2 β + β sin φ 2 ) ] × cos 2 [ k sin ( θ 2 ) cos ( ψ ) r p ] exp ( - a r p 2 ) .
S / N q h f 1 Δ f [ ( P s s ) 2 P s + P B G ] ,
S / N q h f 1 Δ f ( 1 1 + P B G P s ) ( P s s ) 2 P s .
S / N q h f 1 Δ f ( 1 1 + P B G P s ) × ( 3 π 2 d 2 A R P 0 r 1 3 2 ) ϕ [ i ( 2 π r λ , n ¯ , π ) ] exp ( - 2 β R ) λ 3 R 4 .
S / N q h f 1 Δ f ( 1 1 + P B G P s ) × ( 3 π 2 d 2 P 0 A R r 1 3 2 ) ϕ [ i ( 2 π r λ , n ¯ , π ) ] exp ( - 2 β R ) λ 3 R 4 .
S / N = q h f 1 Δ f ( 1 1 + P B G P s ) ( 8 r 1 3 d b A R N Mie ( 0 ) P 0 ) × ϕ [ i ( 2 π r λ , n ¯ , π ) ] exp [ - R ( 2 β + β sin φ ) .

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