Abstract

A detailed comparison of experimental and theoretical SNR in an IR laser heterodyne system has been made with three different signal analyzers. Good agreement, considerably better than a factor of 1.5, is reported. Accurate allowance was made for transmission in the receiver optics, the effective quantum efficiency of the detector due to shot noise domination by the local oscillator, and for coherent speckle effects across the collection aperture. The evaluation of SNR with a surface acoustic wave spectrum analyzer and digital integrator is described in some detail. As an illustration an absolute measurement of backscattering strength in the atmosphere from an airborne equipment at altitudes up to 13.1 km is provided.

© 1983 Optical Society of America

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References

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  1. B. M. Oliver, Proc. IRE 49, 1960 (1961).
  2. A. E. Siegman, Proc. IEEE 54, 1350 (1966).
    [CrossRef]
  3. K. M. van Vliet, Appl. Opt. 6, 1145 (1967).
    [CrossRef] [PubMed]
  4. R. M. Huffaker, Appl. Opt. 9, 1026 (1970).
    [CrossRef] [PubMed]
  5. R. A. Brandewie, W. C. Davis, Appl. Opt. 11, 1526 (1972).
    [CrossRef] [PubMed]
  6. A. J. Hughes, E. R. Pike, Appl. Opt. 12, 597 (1973).
    [CrossRef] [PubMed]
  7. B. J. Rye, Appl. Opt. 17, 3862 (1978).
    [CrossRef] [PubMed]
  8. Discussion session and papers ThB6-8 in Technical Digest, Topical Meeting on Coherent Laser Radar Systems for Atmospheric Sensing (Optical Society of America, Washington, D.C., 1980).
  9. R. L. Schwiesow, R. E. Cupp, Appl. Opt. 19, 3168 (1980).
    [CrossRef] [PubMed]
  10. M. J. Post, R. A. Richter, R. M. Hardesty, T. R. Lawrence, F. F. Hall, Proc. Soc. Photo-Opt. Instrum. Eng. 300, 60 (1981).
  11. It may be noted that to obtain surfaces of reproducible reflectance, the scatterer should preferably be a Lambertian diffuse reflector. Under this condition, differences in small scale surface detail do not cause a variation in reflectance. In a study at RSRE, measurements have been performed on a wide number of materials, using a 10-μm CO2 laser, direct detection of backscattered radiation with pyroelectric detector, and phase sensitive detection for good SNR. Fresnel reflection from a KBr prism was used to provide an accurate system calibration. Of the many surfaces examined, few were found to be Lambertian; flame sprayed aluminum was to a very good approximation, and hot-wire cut expanded polystyrene to a fair approximation. The measured values of ∊(θ) have strictly been obtained for unpolarized incident and scattered radiation, whereas in this work circularly polarized beams are used. Studies with our equipment have shown <1% depolarization in the scattered beam for circularly polarized incident light. It may, however, be noted that if the quite high values of ∊(θ) that we have adopted were too large by up to 20% the minor residual discrepancy found in this work for the observed and calculated values of SNR would be removed. However, the actual agreement of these values is well within experimental error.
  12. R. L. Schwiesow, R. E. Cupp, V. E. Derr, E. W. Barrett, R. F. Pueschel, J. Appl. Meteorol. 20, 184 (1981).
    [CrossRef]
  13. M. J. Post, F. F. Hall, R. A. Richter, T. R. Lawrence, Appl. Opt. 21, 2442 (1982).
    [CrossRef] [PubMed]
  14. R. M. Hardesty, R. J. Keeler, M. J. Post, R. A. Richter, Appl. Opt. 20, 3763 (1981).
    [CrossRef] [PubMed]
  15. R. Callan, J. Cannell, R. Foord, R. Jones, J. M. Vaughan, D. V. Willetts, A. Woodfield, in Proceedings, Fifth National Quantum Electronics ConferenceHull, 1981 (Wiley, Chicester, England, 1981), p 321.
  16. R. Callan et al., RSRE Research Review No. 6 (1982), paper 39.
  17. For detailed description and application to digital signals see M. Alldritt, R. Jones, C. J. Oliver, J. M. Vaughan, J. Phys. E. 11, 116 (1978).
    [CrossRef]
  18. R. D. Brillinger, M. Rosenblatt, in Spectral Analysis of Time Series, B. Harris, Ed. (Wiley, New York, 1967).
  19. C. J. Oliver, J. Phys A 12, 591 (1979).
    [CrossRef]
  20. J. C. Leader, Appl. Opt. 17, 1194 (1978).
    [CrossRef] [PubMed]
  21. J. H. Shapiro, B. A. Capron, R. C. Harney, Appl. Opt. 20, 3292 (1981).
    [CrossRef] [PubMed]
  22. G. Parry, Royal Signals and Radar Establishment (1980), unpublished work.
  23. I. Goldstein, P. A. Miles, A. Chabot, Proc. IEEE 53, 1172 (1965).
    [CrossRef]
  24. R. F. Lutomirski, Appl. Opt. 17, 3915 (1978).
    [CrossRef] [PubMed]
  25. R. L. Schwiesow, R. L. Calfee, Appl. Opt. 18, 3911 (1979).
    [CrossRef] [PubMed]
  26. B. J. Rye, J. Opt. Soc. Am. 71, 687 (1981).
    [CrossRef]
  27. S. C. Cohen, Appl. Opt. 14, 1953 (1975).
    [CrossRef] [PubMed]
  28. See, e.g., S. L. Buckingham, Royal Aircraft Establishment Technical Report 81014 (Feb.1981).
  29. C. M. Sonnenschein, F. A. Horrigan, Appl. Opt. 10, 1600 (1971).
    [CrossRef] [PubMed]
  30. T. R. Lawrence, D. J. Wilson, C. E. Craven, I. P. Jones, R. M. Huffaker, J. A. L. Thomson, Rev. Sci. Instrum. 43, 512 (1972).
    [CrossRef]
  31. R. M. Huffaker et al., FAA report FAA-RD-74-213, NASA TMX-66868 (1975).

1982 (2)

1981 (5)

R. M. Hardesty, R. J. Keeler, M. J. Post, R. A. Richter, Appl. Opt. 20, 3763 (1981).
[CrossRef] [PubMed]

M. J. Post, R. A. Richter, R. M. Hardesty, T. R. Lawrence, F. F. Hall, Proc. Soc. Photo-Opt. Instrum. Eng. 300, 60 (1981).

R. L. Schwiesow, R. E. Cupp, V. E. Derr, E. W. Barrett, R. F. Pueschel, J. Appl. Meteorol. 20, 184 (1981).
[CrossRef]

J. H. Shapiro, B. A. Capron, R. C. Harney, Appl. Opt. 20, 3292 (1981).
[CrossRef] [PubMed]

B. J. Rye, J. Opt. Soc. Am. 71, 687 (1981).
[CrossRef]

1980 (1)

1979 (2)

1978 (4)

R. F. Lutomirski, Appl. Opt. 17, 3915 (1978).
[CrossRef] [PubMed]

J. C. Leader, Appl. Opt. 17, 1194 (1978).
[CrossRef] [PubMed]

For detailed description and application to digital signals see M. Alldritt, R. Jones, C. J. Oliver, J. M. Vaughan, J. Phys. E. 11, 116 (1978).
[CrossRef]

B. J. Rye, Appl. Opt. 17, 3862 (1978).
[CrossRef] [PubMed]

1975 (1)

1973 (1)

1972 (2)

R. A. Brandewie, W. C. Davis, Appl. Opt. 11, 1526 (1972).
[CrossRef] [PubMed]

T. R. Lawrence, D. J. Wilson, C. E. Craven, I. P. Jones, R. M. Huffaker, J. A. L. Thomson, Rev. Sci. Instrum. 43, 512 (1972).
[CrossRef]

1971 (1)

1970 (1)

1967 (1)

1966 (1)

A. E. Siegman, Proc. IEEE 54, 1350 (1966).
[CrossRef]

1965 (1)

I. Goldstein, P. A. Miles, A. Chabot, Proc. IEEE 53, 1172 (1965).
[CrossRef]

1961 (1)

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

Alldritt, M.

For detailed description and application to digital signals see M. Alldritt, R. Jones, C. J. Oliver, J. M. Vaughan, J. Phys. E. 11, 116 (1978).
[CrossRef]

Barrett, E. W.

R. L. Schwiesow, R. E. Cupp, V. E. Derr, E. W. Barrett, R. F. Pueschel, J. Appl. Meteorol. 20, 184 (1981).
[CrossRef]

Brandewie, R. A.

Brillinger, R. D.

R. D. Brillinger, M. Rosenblatt, in Spectral Analysis of Time Series, B. Harris, Ed. (Wiley, New York, 1967).

Buckingham, S. L.

See, e.g., S. L. Buckingham, Royal Aircraft Establishment Technical Report 81014 (Feb.1981).

Calfee, R. L.

Callan, R.

R. Callan et al., RSRE Research Review No. 6 (1982), paper 39.

R. Callan, J. Cannell, R. Foord, R. Jones, J. M. Vaughan, D. V. Willetts, A. Woodfield, in Proceedings, Fifth National Quantum Electronics ConferenceHull, 1981 (Wiley, Chicester, England, 1981), p 321.

Cannell, J.

R. Callan, J. Cannell, R. Foord, R. Jones, J. M. Vaughan, D. V. Willetts, A. Woodfield, in Proceedings, Fifth National Quantum Electronics ConferenceHull, 1981 (Wiley, Chicester, England, 1981), p 321.

Capron, B. A.

Chabot, A.

I. Goldstein, P. A. Miles, A. Chabot, Proc. IEEE 53, 1172 (1965).
[CrossRef]

Cohen, S. C.

Craven, C. E.

T. R. Lawrence, D. J. Wilson, C. E. Craven, I. P. Jones, R. M. Huffaker, J. A. L. Thomson, Rev. Sci. Instrum. 43, 512 (1972).
[CrossRef]

Cupp, R. E.

R. L. Schwiesow, R. E. Cupp, V. E. Derr, E. W. Barrett, R. F. Pueschel, J. Appl. Meteorol. 20, 184 (1981).
[CrossRef]

R. L. Schwiesow, R. E. Cupp, Appl. Opt. 19, 3168 (1980).
[CrossRef] [PubMed]

Davis, W. C.

Derr, V. E.

R. L. Schwiesow, R. E. Cupp, V. E. Derr, E. W. Barrett, R. F. Pueschel, J. Appl. Meteorol. 20, 184 (1981).
[CrossRef]

Foord, R.

R. Callan, J. Cannell, R. Foord, R. Jones, J. M. Vaughan, D. V. Willetts, A. Woodfield, in Proceedings, Fifth National Quantum Electronics ConferenceHull, 1981 (Wiley, Chicester, England, 1981), p 321.

Goldstein, I.

I. Goldstein, P. A. Miles, A. Chabot, Proc. IEEE 53, 1172 (1965).
[CrossRef]

Hall, F. F.

M. J. Post, F. F. Hall, R. A. Richter, T. R. Lawrence, Appl. Opt. 21, 2442 (1982).
[CrossRef] [PubMed]

M. J. Post, R. A. Richter, R. M. Hardesty, T. R. Lawrence, F. F. Hall, Proc. Soc. Photo-Opt. Instrum. Eng. 300, 60 (1981).

Hardesty, R. M.

M. J. Post, R. A. Richter, R. M. Hardesty, T. R. Lawrence, F. F. Hall, Proc. Soc. Photo-Opt. Instrum. Eng. 300, 60 (1981).

R. M. Hardesty, R. J. Keeler, M. J. Post, R. A. Richter, Appl. Opt. 20, 3763 (1981).
[CrossRef] [PubMed]

Harney, R. C.

Horrigan, F. A.

Huffaker, R. M.

T. R. Lawrence, D. J. Wilson, C. E. Craven, I. P. Jones, R. M. Huffaker, J. A. L. Thomson, Rev. Sci. Instrum. 43, 512 (1972).
[CrossRef]

R. M. Huffaker, Appl. Opt. 9, 1026 (1970).
[CrossRef] [PubMed]

R. M. Huffaker et al., FAA report FAA-RD-74-213, NASA TMX-66868 (1975).

Hughes, A. J.

Jones, I. P.

T. R. Lawrence, D. J. Wilson, C. E. Craven, I. P. Jones, R. M. Huffaker, J. A. L. Thomson, Rev. Sci. Instrum. 43, 512 (1972).
[CrossRef]

Jones, R.

For detailed description and application to digital signals see M. Alldritt, R. Jones, C. J. Oliver, J. M. Vaughan, J. Phys. E. 11, 116 (1978).
[CrossRef]

R. Callan, J. Cannell, R. Foord, R. Jones, J. M. Vaughan, D. V. Willetts, A. Woodfield, in Proceedings, Fifth National Quantum Electronics ConferenceHull, 1981 (Wiley, Chicester, England, 1981), p 321.

Keeler, R. J.

Lawrence, T. R.

M. J. Post, F. F. Hall, R. A. Richter, T. R. Lawrence, Appl. Opt. 21, 2442 (1982).
[CrossRef] [PubMed]

M. J. Post, R. A. Richter, R. M. Hardesty, T. R. Lawrence, F. F. Hall, Proc. Soc. Photo-Opt. Instrum. Eng. 300, 60 (1981).

T. R. Lawrence, D. J. Wilson, C. E. Craven, I. P. Jones, R. M. Huffaker, J. A. L. Thomson, Rev. Sci. Instrum. 43, 512 (1972).
[CrossRef]

Leader, J. C.

Lutomirski, R. F.

Miles, P. A.

I. Goldstein, P. A. Miles, A. Chabot, Proc. IEEE 53, 1172 (1965).
[CrossRef]

Oliver, B. M.

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

Oliver, C. J.

C. J. Oliver, J. Phys A 12, 591 (1979).
[CrossRef]

For detailed description and application to digital signals see M. Alldritt, R. Jones, C. J. Oliver, J. M. Vaughan, J. Phys. E. 11, 116 (1978).
[CrossRef]

Parry, G.

G. Parry, Royal Signals and Radar Establishment (1980), unpublished work.

Pike, E. R.

Post, M. J.

Pueschel, R. F.

R. L. Schwiesow, R. E. Cupp, V. E. Derr, E. W. Barrett, R. F. Pueschel, J. Appl. Meteorol. 20, 184 (1981).
[CrossRef]

Richter, R. A.

Rosenblatt, M.

R. D. Brillinger, M. Rosenblatt, in Spectral Analysis of Time Series, B. Harris, Ed. (Wiley, New York, 1967).

Rye, B. J.

Schwiesow, R. L.

R. L. Schwiesow, R. E. Cupp, V. E. Derr, E. W. Barrett, R. F. Pueschel, J. Appl. Meteorol. 20, 184 (1981).
[CrossRef]

R. L. Schwiesow, R. E. Cupp, Appl. Opt. 19, 3168 (1980).
[CrossRef] [PubMed]

R. L. Schwiesow, R. L. Calfee, Appl. Opt. 18, 3911 (1979).
[CrossRef] [PubMed]

Shapiro, J. H.

Siegman, A. E.

A. E. Siegman, Proc. IEEE 54, 1350 (1966).
[CrossRef]

Sonnenschein, C. M.

Thomson, J. A. L.

T. R. Lawrence, D. J. Wilson, C. E. Craven, I. P. Jones, R. M. Huffaker, J. A. L. Thomson, Rev. Sci. Instrum. 43, 512 (1972).
[CrossRef]

van Vliet, K. M.

Vaughan, J. M.

For detailed description and application to digital signals see M. Alldritt, R. Jones, C. J. Oliver, J. M. Vaughan, J. Phys. E. 11, 116 (1978).
[CrossRef]

R. Callan, J. Cannell, R. Foord, R. Jones, J. M. Vaughan, D. V. Willetts, A. Woodfield, in Proceedings, Fifth National Quantum Electronics ConferenceHull, 1981 (Wiley, Chicester, England, 1981), p 321.

Willetts, D. V.

R. Callan, J. Cannell, R. Foord, R. Jones, J. M. Vaughan, D. V. Willetts, A. Woodfield, in Proceedings, Fifth National Quantum Electronics ConferenceHull, 1981 (Wiley, Chicester, England, 1981), p 321.

Wilson, D. J.

T. R. Lawrence, D. J. Wilson, C. E. Craven, I. P. Jones, R. M. Huffaker, J. A. L. Thomson, Rev. Sci. Instrum. 43, 512 (1972).
[CrossRef]

Woodfield, A.

R. Callan, J. Cannell, R. Foord, R. Jones, J. M. Vaughan, D. V. Willetts, A. Woodfield, in Proceedings, Fifth National Quantum Electronics ConferenceHull, 1981 (Wiley, Chicester, England, 1981), p 321.

Appl. Opt. (14)

J. Appl. Meteorol. (1)

R. L. Schwiesow, R. E. Cupp, V. E. Derr, E. W. Barrett, R. F. Pueschel, J. Appl. Meteorol. 20, 184 (1981).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Phys A (1)

C. J. Oliver, J. Phys A 12, 591 (1979).
[CrossRef]

J. Phys. E. (1)

For detailed description and application to digital signals see M. Alldritt, R. Jones, C. J. Oliver, J. M. Vaughan, J. Phys. E. 11, 116 (1978).
[CrossRef]

Proc. IEEE (2)

A. E. Siegman, Proc. IEEE 54, 1350 (1966).
[CrossRef]

I. Goldstein, P. A. Miles, A. Chabot, Proc. IEEE 53, 1172 (1965).
[CrossRef]

Proc. IRE (1)

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

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

M. J. Post, R. A. Richter, R. M. Hardesty, T. R. Lawrence, F. F. Hall, Proc. Soc. Photo-Opt. Instrum. Eng. 300, 60 (1981).

Rev. Sci. Instrum. (1)

T. R. Lawrence, D. J. Wilson, C. E. Craven, I. P. Jones, R. M. Huffaker, J. A. L. Thomson, Rev. Sci. Instrum. 43, 512 (1972).
[CrossRef]

RSRE Research Review No. 6 (1)

R. Callan et al., RSRE Research Review No. 6 (1982), paper 39.

Other (7)

R. Callan, J. Cannell, R. Foord, R. Jones, J. M. Vaughan, D. V. Willetts, A. Woodfield, in Proceedings, Fifth National Quantum Electronics ConferenceHull, 1981 (Wiley, Chicester, England, 1981), p 321.

R. D. Brillinger, M. Rosenblatt, in Spectral Analysis of Time Series, B. Harris, Ed. (Wiley, New York, 1967).

G. Parry, Royal Signals and Radar Establishment (1980), unpublished work.

It may be noted that to obtain surfaces of reproducible reflectance, the scatterer should preferably be a Lambertian diffuse reflector. Under this condition, differences in small scale surface detail do not cause a variation in reflectance. In a study at RSRE, measurements have been performed on a wide number of materials, using a 10-μm CO2 laser, direct detection of backscattered radiation with pyroelectric detector, and phase sensitive detection for good SNR. Fresnel reflection from a KBr prism was used to provide an accurate system calibration. Of the many surfaces examined, few were found to be Lambertian; flame sprayed aluminum was to a very good approximation, and hot-wire cut expanded polystyrene to a fair approximation. The measured values of ∊(θ) have strictly been obtained for unpolarized incident and scattered radiation, whereas in this work circularly polarized beams are used. Studies with our equipment have shown <1% depolarization in the scattered beam for circularly polarized incident light. It may, however, be noted that if the quite high values of ∊(θ) that we have adopted were too large by up to 20% the minor residual discrepancy found in this work for the observed and calculated values of SNR would be removed. However, the actual agreement of these values is well within experimental error.

Discussion session and papers ThB6-8 in Technical Digest, Topical Meeting on Coherent Laser Radar Systems for Atmospheric Sensing (Optical Society of America, Washington, D.C., 1980).

R. M. Huffaker et al., FAA report FAA-RD-74-213, NASA TMX-66868 (1975).

See, e.g., S. L. Buckingham, Royal Aircraft Establishment Technical Report 81014 (Feb.1981).

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Figures (8)

Fig. 1
Fig. 1

Schematic optical arrangement of the airborne monostatic CO2 laser velocimeter. Polarization techniques promote good efficiency. The laser is locked to the P20 transition with the narrowband filter in the local oscillator beam.

Fig. 2
Fig. 2

Typical effective detector quantum efficiency ηeff plotted against detector current at different frequencies. Detector current provides a convenient reproducible measure of the applied local oscillator.

Fig. 3
Fig. 3

Speckle factor Kspec (see text) plotted against the aperture parameter R 2 / 2 ω 0 2 to provide a quantitative measure of the effect of laser speckle on the scattered signal [from G. Parry, Royal Signals and Radar Establishment (1980), unpublished work].

Fig. 4
Fig. 4

Comparison of observed and calculated SNR with different SAW spectrum analyzers and a scanning analyzer. Good agreement with the points close to the 45° line is apparent. The error bars are estimated limit errors.

Fig. 5
Fig. 5

Signal analysis system with the SAW spectrum analyzer and digital integrator. The amplifiers and attenuators are required to keep the signal within the dynamic range of the components.

Fig. 6
Fig. 6

Typical spectra recorded on the oscilloscope with the 6.3-MHz bandwidth SAW spectrum analyzer: (A) noise and (B) signal with additional 50 dB of attenuation. The noise amplitude and variance are readily estimated by expanding the scale of (A).

Fig. 7
Fig. 7

Recordings with the scanning spectrum analyzer: (A) attenuated signal from the rotating expanded polystyrene wheel; (B) noise background with (upper) and without (lower) local oscillator.

Fig. 8
Fig. 8

Atmospheric backscattering coefficient β (π) sr−1 m−1 and static air temperature SAT vs indicated height in feet and kilometers (ASL). These recordings were made during flight 772 from Jefferson County Airport, Colo. on the morning of 2 July 1982 in clear summer conditions with visibility at the surface >130 km (80 miles). The strong return c at 10.4 km (34,000 ft) later in the day became a visible layer of cirrus cloud. It is very noticeable that the signal increases toward the top of many small temperature inversion layers and decreases suddenly as the aircraft passes through the top of the layer.

Tables (1)

Tables Icon

Table I Comparison of Observed and Calculated SNRs Obtained with a Scanned IF Spectrum Analyzer

Equations (18)

Equations on this page are rendered with MathJax. Learn more.

SNR power = η eff P s / ω B ,
i s E LO × E s .
P ( ω ) = lim J 1 J | J / 2 + J / 2 i s ( t ) exp ( i ω t ) d t | 2 ,
SNR power = mean signal mean background standard deviation of background ,
var P ̂ ( ω ) = P ̂ ( ω ) 2 .
SNR power = mean signal mean background [ var P ̂ ( ω ) background ] 1 / 2 = mean signal mean background P ̂ ( ω ) background
= mean signal power mean noise power ,
η eff = ( M 1 M ) η ,
P s = P 0 T atm β ( θ , π ) Ω K opt K spec K het .
K spec = ( heterodyne detection output power ) ensemble averaged with speckle ( heterodyne detection output power ) same mean intensity but constant amplitude and phase
s m = m n ¯ s ,
S volt , 1 = ( 10 A / 10 ) 1 / 2 s m ,
| σ measured 2 | N = σ synch 2 + 1 N [ | σ det 2 | 1 + | σ dig 2 | 1 ] ,
N volt , 1 = m 1 / 2 σ det .
SNR power ( ω ) = η eff [ P ( ω ) s B noise ] ω B noise ,
SNR power max = η eff P s / ω B s ,
P s = P 0 T atm β ( π ) λ [ π / 2 + tan 1 ( π D 2 / 4 λ F ) ] K opt K het .
β ( π ) = [ 44.6 × 10 8 ] 1 × ( SNR ) power , 1 ,

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