Abstract

A symmetrical method of optical heterodyning of the doppler shifted signal has been developed possessing minimal instrumental spectral broadening and high SNR. These advantages can be gainfully employed in measuring turbulence structure using a cw laser. The method employs two beams incident on the moving scatterer. The doppler signal frequency is independent of the scattering angle and the signal possesses no receiving aperture broadening. Typical values of signal-to-noise ratio are around 30 dB for a signal strength of 3 × 10−9 W. Optical alignment is simple. Relative merits of this technique compared to the local oscillator heterodyning method are briefly described.

© 1970 Optical Society of America

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References

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  1. Y. Yeh, H. Z. Cummins, Appl. Phys. Lett. 4, 176 (1964).
    [CrossRef]
  2. J. W. Foreman, W. W. George, R. R. Lewis, Appl. Phys. Lett. 7, 77 (1965).
    [CrossRef]
  3. R. J. Goldstein, W. F. Hagen, Phys. Fluids 10, 1349 (1967).
    [CrossRef]
  4. J. D. Fridman, R. M. Huffaker, R. F. Kinnard, Laser Focus 4, 36 (1968).
  5. D. T. Davis, ISA Trans. 7, 43 (1968).
  6. E. X. Raymond, “Study of Techniques for Detection and Measurements of Clear Air Turbulence,” DDC Rept. No. AD 63625, January1966.
  7. R. T. H. Collis, Science J. 4, 72 (1968).
  8. R. L. Bond, Ph.D. dissertation, University of Arkansas, 1968, NASA Acc. No. N68-27651.
  9. M. K. Mazumder, University of Arkansas Progress Rept. for NASA Grant NGR-04-001-015, 30June1968, NASA Acc. No. X69-10039.
  10. E. R. Pike et al.J. Sci. Instrum. 1 (2) (1968).
  11. M. E. Monroe, DDC Rept. No. AD 474465, October1965.
  12. B. M. Oliver, Proc. IRE 49, 1960 (1961).
  13. H. A. Hans, C. H. Townes, Proc. IRE 50, 1544 (1962).
  14. M. Ross, Laser Receivers (John Wiley & Sons, Inc., New York, 1966).
  15. H. L. Dryden, Ind. Eng. Chem. 31, 416 (1939).
    [CrossRef]

1968 (4)

J. D. Fridman, R. M. Huffaker, R. F. Kinnard, Laser Focus 4, 36 (1968).

D. T. Davis, ISA Trans. 7, 43 (1968).

R. T. H. Collis, Science J. 4, 72 (1968).

E. R. Pike et al.J. Sci. Instrum. 1 (2) (1968).

1967 (1)

R. J. Goldstein, W. F. Hagen, Phys. Fluids 10, 1349 (1967).
[CrossRef]

1965 (1)

J. W. Foreman, W. W. George, R. R. Lewis, Appl. Phys. Lett. 7, 77 (1965).
[CrossRef]

1964 (1)

Y. Yeh, H. Z. Cummins, Appl. Phys. Lett. 4, 176 (1964).
[CrossRef]

1962 (1)

H. A. Hans, C. H. Townes, Proc. IRE 50, 1544 (1962).

1961 (1)

B. M. Oliver, Proc. IRE 49, 1960 (1961).

1939 (1)

H. L. Dryden, Ind. Eng. Chem. 31, 416 (1939).
[CrossRef]

Bond, R. L.

R. L. Bond, Ph.D. dissertation, University of Arkansas, 1968, NASA Acc. No. N68-27651.

Collis, R. T. H.

R. T. H. Collis, Science J. 4, 72 (1968).

Cummins, H. Z.

Y. Yeh, H. Z. Cummins, Appl. Phys. Lett. 4, 176 (1964).
[CrossRef]

Davis, D. T.

D. T. Davis, ISA Trans. 7, 43 (1968).

Dryden, H. L.

H. L. Dryden, Ind. Eng. Chem. 31, 416 (1939).
[CrossRef]

Foreman, J. W.

J. W. Foreman, W. W. George, R. R. Lewis, Appl. Phys. Lett. 7, 77 (1965).
[CrossRef]

Fridman, J. D.

J. D. Fridman, R. M. Huffaker, R. F. Kinnard, Laser Focus 4, 36 (1968).

George, W. W.

J. W. Foreman, W. W. George, R. R. Lewis, Appl. Phys. Lett. 7, 77 (1965).
[CrossRef]

Goldstein, R. J.

R. J. Goldstein, W. F. Hagen, Phys. Fluids 10, 1349 (1967).
[CrossRef]

Hagen, W. F.

R. J. Goldstein, W. F. Hagen, Phys. Fluids 10, 1349 (1967).
[CrossRef]

Hans, H. A.

H. A. Hans, C. H. Townes, Proc. IRE 50, 1544 (1962).

Huffaker, R. M.

J. D. Fridman, R. M. Huffaker, R. F. Kinnard, Laser Focus 4, 36 (1968).

Kinnard, R. F.

J. D. Fridman, R. M. Huffaker, R. F. Kinnard, Laser Focus 4, 36 (1968).

Lewis, R. R.

J. W. Foreman, W. W. George, R. R. Lewis, Appl. Phys. Lett. 7, 77 (1965).
[CrossRef]

Mazumder, M. K.

M. K. Mazumder, University of Arkansas Progress Rept. for NASA Grant NGR-04-001-015, 30June1968, NASA Acc. No. X69-10039.

Monroe, M. E.

M. E. Monroe, DDC Rept. No. AD 474465, October1965.

Oliver, B. M.

B. M. Oliver, Proc. IRE 49, 1960 (1961).

Pike, E. R.

E. R. Pike et al.J. Sci. Instrum. 1 (2) (1968).

Raymond, E. X.

E. X. Raymond, “Study of Techniques for Detection and Measurements of Clear Air Turbulence,” DDC Rept. No. AD 63625, January1966.

Ross, M.

M. Ross, Laser Receivers (John Wiley & Sons, Inc., New York, 1966).

Townes, C. H.

H. A. Hans, C. H. Townes, Proc. IRE 50, 1544 (1962).

Yeh, Y.

Y. Yeh, H. Z. Cummins, Appl. Phys. Lett. 4, 176 (1964).
[CrossRef]

Appl. Phys. Lett. (2)

Y. Yeh, H. Z. Cummins, Appl. Phys. Lett. 4, 176 (1964).
[CrossRef]

J. W. Foreman, W. W. George, R. R. Lewis, Appl. Phys. Lett. 7, 77 (1965).
[CrossRef]

Ind. Eng. Chem. (1)

H. L. Dryden, Ind. Eng. Chem. 31, 416 (1939).
[CrossRef]

ISA Trans. (1)

D. T. Davis, ISA Trans. 7, 43 (1968).

J. Sci. Instrum. (1)

E. R. Pike et al.J. Sci. Instrum. 1 (2) (1968).

Laser Focus (1)

J. D. Fridman, R. M. Huffaker, R. F. Kinnard, Laser Focus 4, 36 (1968).

Phys. Fluids (1)

R. J. Goldstein, W. F. Hagen, Phys. Fluids 10, 1349 (1967).
[CrossRef]

Proc. IRE (2)

B. M. Oliver, Proc. IRE 49, 1960 (1961).

H. A. Hans, C. H. Townes, Proc. IRE 50, 1544 (1962).

Science J. (1)

R. T. H. Collis, Science J. 4, 72 (1968).

Other (5)

R. L. Bond, Ph.D. dissertation, University of Arkansas, 1968, NASA Acc. No. N68-27651.

M. K. Mazumder, University of Arkansas Progress Rept. for NASA Grant NGR-04-001-015, 30June1968, NASA Acc. No. X69-10039.

M. E. Monroe, DDC Rept. No. AD 474465, October1965.

E. X. Raymond, “Study of Techniques for Detection and Measurements of Clear Air Turbulence,” DDC Rept. No. AD 63625, January1966.

M. Ross, Laser Receivers (John Wiley & Sons, Inc., New York, 1966).

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Figures (7)

Fig. 1
Fig. 1

Local oscillator heterodyning.

Fig. 2
Fig. 2

Symmetrical heterodyning system type I.

Fig. 3
Fig. 3

Symmetrical heterodyning system type II.

Fig. 4
Fig. 4

The expected nature of the variation of frequency spread (δf) with convergence angle (α).

Fig. 5
Fig. 5

Instrumental broadening (δf) vs transmission aperture diameter.

Fig. 6
Fig. 6

Instrumental broadening (δfa) vs receiving aperture diameter.

Fig. 7
Fig. 7

Signal-to-noise ratio vs signal power for the two different heterodyning methods.

Tables (1)

Tables Icon

Table I Typical Values of SNR and δf for the Three Different Systems of Heterodyning a

Equations (17)

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f D = ( 1 / 2 π ) ( K s K o ) · V ,
λ o λ s , | K s | = | K o | = K o = 2 π n / λ o f D = ( 1 / λ o ) ( i s i o ) · V ,
f c = U / λ o sin ψ + V / λ o cos ψ + W / λ o
δ f a = δ f Δ ϕ + δ f Δ Ω ,
δ f Δ ϕ = 2 V λ o sin ψ sin α 2 + 2 [ ( V sin ψ U cos ψ ) 2 + W 2 ] 1 2 λ o × sin α 2 ,
δ f Δ Ω = 2 [ U 2 + V 2 ] 1 2 λ o sin Δ θ 2 .
f c = ( 2 U / λ o ) sin ( θ / 2 )
δ f Δ Ω = 0.
δ f a = δ f Δ ϕ = 4 ( U 2 + V 2 ) 1 2 λ o sin α 2 cos θ 2 .
( δ f τ / f c ) K τ sin ( α / 2 ) cot ( θ / 2 )
( δ f Δ ϕ / f c ) = 2 sin ( α / 2 ) cot ( θ / 2 ) .
SNR i s 2 R 4 K T δ f + 2 q i d δ f R + 2 q i b δ f R + 2 q i d c δ f R + a ( e n 2 / R ) ,
SNR C ( ν o , , η ) ( P s / δ f L ) ,
SNR C ( ν o , , η ) ( P s / 2 δ f s ) ,
V = V ¯ + V o sin p t .
f V = 2 V ¯ λ o sin α 2 + 2 V o sin p t λ o sin α 2
e υ = e υ ¯ + A n = 2,4,6 J n ( M ) cos n p t ,

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