Abstract

The Air Force Phillips Laboratory is in the process of demonstrating an advanced space surveillance capability with a heterodyne laser radar (ladar) system. Notable features of this ladar system include its narrow micropulses (<1.5 ns) contained in a pulse-burst wave form that allows high-resolution range data to be obtained and its high power (30 J/pulse burst) that permits reasonable signal returns from satellites. Recently, time-resolved image-domain signal-to-noise ratios have been derived for both the intensity projections calculated from the range-resolved reflective data and image information obtained with linear combinations of the projections. In this paper the signal-to-noise expression for intensity projections is validated by laboratory data.

© 1997 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. K. Parker, E. B. Craig, D. I. Klick, F. K. Knight, S. R. Kulkarni, R. M. Marino, J. R. Senning, and B. K. Tussey, “Reflective tomography: images from range-resolved laser radar measurements,” Appl. Opt. 27, 2642–2643 (1988).
    [CrossRef] [PubMed]
  2. F. K. Knight, D. I. Klick, D. P. Ryan-Howard, J. R. Theriault, Jr., B. K. Tussey, and A. M. Beckman, “Two-dimensional tomographs using range measurements,” in Laser Radar III, R. J. Becherer, ed., Proc. SPIE 999, 269–280 (1988).
  3. R. M. Marino, R. N. Capes, W. E. Keicher, S. R. Kulkarni, J. K. Parker, L. W. Swezey, J. R. Senning, M. F. Reiley, and E. B. Craig, “Tomographic image reconstruction from laser radar reflective projections,” in Laser Radar III, R. J. Becherer, ed., Proc. SPIE 999, 248–268 (1988).
  4. R. M. Gagliardi and S. Karp, Optical Communications, (Wiley, New York, 1976).
  5. A. Yariv, Introduction to Optical Electronics, 2nd ed. (Holt, Rinehart and Winston, New York, 1976).
  6. C. L. Matson, E. P. Magee, and D. E. Holland, “Reflective tomography using a short-pulselength laser: system analysis for artificial satellite imaging,” Opt. Eng. 34, 2811–2820 (1995).
    [CrossRef]
  7. C. L. Matson, “Short pulselength heterodyne laser radar reflective tomography: projection generation and signal-to-noise ratios,” in Radar/Ladar Processing and Applications, W. J. Miceli, ed., Proc. SPIE 2562, 184–194 (1995).
    [CrossRef]
  8. C. L. Matson and J. Boger, “Laboratory validation of heterodyne laser radar signal-to-noise expressions for intensity projection generation and image reconstruction,” in Radar/Ladar Processing and Applications, W. J. Miceli, ed., Proc. SPIE 2562, 195–202 (1995).
    [CrossRef]
  9. C. L. Matson, “Tomographic satellite image reconstruction using ladar E-field or intensity projections: computer simulation results,” in Advanced Imaging Technologies and Commercial Applications, N. Clark and J. D. Gonglewski, eds., Proc. SPIE 2566, 166–176 (1995).
    [CrossRef]
  10. C. L. Matson, “Reconstructed image signal-to-noise issues in range-resolved reflective tomography,” Opt. Commun. 137, 343–358 (1988).
    [CrossRef]
  11. H. Z. Cummins and H. L. Swinney, “Light beating spectroscopy,” Vol. 8 of Progress in Optics Series (North-Holland, Amsterdam, 1967).
  12. M. Elbaum and M. C. Teich, “Heterodyne detection of random Gaussian signals in the optical and infrared: optimization of pulse duration,” Opt. Commun. 27, 257–261 (1978).
    [CrossRef]
  13. J. H. Shapiro, B. A. Capron, and R. C. Harney, “Imaging and target detection with a heterodyne-reception optical radar,” Appl. Opt. 20, 3292–3313 (1981).
    [CrossRef] [PubMed]
  14. A. L. Kachelmyer, “Range-Doppler imaging: waveforms and receiver design,” in Laser Radar III, R. J. Becherer, ed., Proc. SPIE 999, 138–161 (1988).
  15. C. L. Matson, D. Holland, S. Czyzak, D. Pierrottet, and D. Ruffatto, “Heterodyne laser radar for space object imaging: results from recent field experiments,” in Optics in Atmospheric Propagation and Adaptive Systems, A. Kohnle, ed., Proc. SPIE 2580, 288–295 (1995).
    [CrossRef]
  16. M. E. Bair, D. Carmer, D. Zuk, and G. Suits, “Determination of satellite observables: Volume IV, optical properties of satellite materials,” NTIS report AD-782 093 (National Technical Information Service, University of Maryland, College Park, Md., 1974).
  17. D. Letalick and I. Renhorn, “Phase front and signal-to-noise measurements in a coherent CO2 laser radar system,” 5th Conference on Coherent Laser Radar: Technology and Applications, J. W. Bilbro and C. Werner, eds., Proc. SPIE 1181, 190–195 (1989).
    [CrossRef]
  18. W. W. Hines and D. C. Montgomery, Probability and Statistics in Engineering and Management Science (Wiley, New York, 1980).

1995 (1)

C. L. Matson, E. P. Magee, and D. E. Holland, “Reflective tomography using a short-pulselength laser: system analysis for artificial satellite imaging,” Opt. Eng. 34, 2811–2820 (1995).
[CrossRef]

1988 (2)

1981 (1)

1978 (1)

M. Elbaum and M. C. Teich, “Heterodyne detection of random Gaussian signals in the optical and infrared: optimization of pulse duration,” Opt. Commun. 27, 257–261 (1978).
[CrossRef]

Capron, B. A.

Craig, E. B.

Elbaum, M.

M. Elbaum and M. C. Teich, “Heterodyne detection of random Gaussian signals in the optical and infrared: optimization of pulse duration,” Opt. Commun. 27, 257–261 (1978).
[CrossRef]

Gagliardi, R. M.

R. M. Gagliardi and S. Karp, Optical Communications, (Wiley, New York, 1976).

Harney, R. C.

Hines, W. W.

W. W. Hines and D. C. Montgomery, Probability and Statistics in Engineering and Management Science (Wiley, New York, 1980).

Holland, D. E.

C. L. Matson, E. P. Magee, and D. E. Holland, “Reflective tomography using a short-pulselength laser: system analysis for artificial satellite imaging,” Opt. Eng. 34, 2811–2820 (1995).
[CrossRef]

Karp, S.

R. M. Gagliardi and S. Karp, Optical Communications, (Wiley, New York, 1976).

Klick, D. I.

Knight, F. K.

Kulkarni, S. R.

Magee, E. P.

C. L. Matson, E. P. Magee, and D. E. Holland, “Reflective tomography using a short-pulselength laser: system analysis for artificial satellite imaging,” Opt. Eng. 34, 2811–2820 (1995).
[CrossRef]

Marino, R. M.

Matson, C. L.

C. L. Matson, E. P. Magee, and D. E. Holland, “Reflective tomography using a short-pulselength laser: system analysis for artificial satellite imaging,” Opt. Eng. 34, 2811–2820 (1995).
[CrossRef]

C. L. Matson, “Reconstructed image signal-to-noise issues in range-resolved reflective tomography,” Opt. Commun. 137, 343–358 (1988).
[CrossRef]

Montgomery, D. C.

W. W. Hines and D. C. Montgomery, Probability and Statistics in Engineering and Management Science (Wiley, New York, 1980).

Parker, J. K.

Senning, J. R.

Shapiro, J. H.

Teich, M. C.

M. Elbaum and M. C. Teich, “Heterodyne detection of random Gaussian signals in the optical and infrared: optimization of pulse duration,” Opt. Commun. 27, 257–261 (1978).
[CrossRef]

Tussey, B. K.

Yariv, A.

A. Yariv, Introduction to Optical Electronics, 2nd ed. (Holt, Rinehart and Winston, New York, 1976).

Appl. Opt. (2)

Opt. Commun. (2)

C. L. Matson, “Reconstructed image signal-to-noise issues in range-resolved reflective tomography,” Opt. Commun. 137, 343–358 (1988).
[CrossRef]

M. Elbaum and M. C. Teich, “Heterodyne detection of random Gaussian signals in the optical and infrared: optimization of pulse duration,” Opt. Commun. 27, 257–261 (1978).
[CrossRef]

Opt. Eng. (1)

C. L. Matson, E. P. Magee, and D. E. Holland, “Reflective tomography using a short-pulselength laser: system analysis for artificial satellite imaging,” Opt. Eng. 34, 2811–2820 (1995).
[CrossRef]

Other (13)

C. L. Matson, “Short pulselength heterodyne laser radar reflective tomography: projection generation and signal-to-noise ratios,” in Radar/Ladar Processing and Applications, W. J. Miceli, ed., Proc. SPIE 2562, 184–194 (1995).
[CrossRef]

C. L. Matson and J. Boger, “Laboratory validation of heterodyne laser radar signal-to-noise expressions for intensity projection generation and image reconstruction,” in Radar/Ladar Processing and Applications, W. J. Miceli, ed., Proc. SPIE 2562, 195–202 (1995).
[CrossRef]

C. L. Matson, “Tomographic satellite image reconstruction using ladar E-field or intensity projections: computer simulation results,” in Advanced Imaging Technologies and Commercial Applications, N. Clark and J. D. Gonglewski, eds., Proc. SPIE 2566, 166–176 (1995).
[CrossRef]

F. K. Knight, D. I. Klick, D. P. Ryan-Howard, J. R. Theriault, Jr., B. K. Tussey, and A. M. Beckman, “Two-dimensional tomographs using range measurements,” in Laser Radar III, R. J. Becherer, ed., Proc. SPIE 999, 269–280 (1988).

R. M. Marino, R. N. Capes, W. E. Keicher, S. R. Kulkarni, J. K. Parker, L. W. Swezey, J. R. Senning, M. F. Reiley, and E. B. Craig, “Tomographic image reconstruction from laser radar reflective projections,” in Laser Radar III, R. J. Becherer, ed., Proc. SPIE 999, 248–268 (1988).

R. M. Gagliardi and S. Karp, Optical Communications, (Wiley, New York, 1976).

A. Yariv, Introduction to Optical Electronics, 2nd ed. (Holt, Rinehart and Winston, New York, 1976).

A. L. Kachelmyer, “Range-Doppler imaging: waveforms and receiver design,” in Laser Radar III, R. J. Becherer, ed., Proc. SPIE 999, 138–161 (1988).

C. L. Matson, D. Holland, S. Czyzak, D. Pierrottet, and D. Ruffatto, “Heterodyne laser radar for space object imaging: results from recent field experiments,” in Optics in Atmospheric Propagation and Adaptive Systems, A. Kohnle, ed., Proc. SPIE 2580, 288–295 (1995).
[CrossRef]

M. E. Bair, D. Carmer, D. Zuk, and G. Suits, “Determination of satellite observables: Volume IV, optical properties of satellite materials,” NTIS report AD-782 093 (National Technical Information Service, University of Maryland, College Park, Md., 1974).

D. Letalick and I. Renhorn, “Phase front and signal-to-noise measurements in a coherent CO2 laser radar system,” 5th Conference on Coherent Laser Radar: Technology and Applications, J. W. Bilbro and C. Werner, eds., Proc. SPIE 1181, 190–195 (1989).
[CrossRef]

W. W. Hines and D. C. Montgomery, Probability and Statistics in Engineering and Management Science (Wiley, New York, 1980).

H. Z. Cummins and H. L. Swinney, “Light beating spectroscopy,” Vol. 8 of Progress in Optics Series (North-Holland, Amsterdam, 1967).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Laboratory experimental setup.

Fig. 2
Fig. 2

Conceptual schematic of the HI-CLASS ladar system. The heterodyne detection system is not shown.

Fig. 3
Fig. 3

Single projection SNR’s as a function of the signal photon rate for the laboratory setup described in the text, with a 50-Hz heterodyne frequency. The solid curve denotes theoretical predictions and the asterisks are laboratory data points.

Fig. 4
Fig. 4

Single projection SNR’s as a function of the signal photon rate for the laboratory setup described in the text, with a 25-Hz heterodyne frequency. The solid curve denotes theoretical predictions and the asterisks are laboratory data points.

Equations (29)

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

ikt=2qNtakN˙loAp2βdβckξdξ1/2cosω12t-ϕL×Apt-2xca1kxdx-sinω12t-ϕL×Apt-2xca2kxdx+qN˙lo,
Ea1kxa1kξ=Ea2kxa2kξ=ckx2δx-ξ,
pˆkt=LPt*i˜kt-qN˙lo2-N˙lo  hd2ξdξ,
SNRtEpˆktvarpˆkt1/2,
Epˆkt=2q2NtakN˙loÃp2t-2xcc˜kxdx,
varpˆkt=4q4NtakN˙lo2 Ãp2t-2β1cc˜kβ1dβ12+8q4NtakN˙lo2  LP2t-α1×Ãp2α1-2β1cc˜kβ1dα1dβ1+N˙lo2 ×LPt-α1LPt-α2hdα1-β1×hdα1-β2hdα2-β1hdα2-β2×dα1dα2dβ1dβ2+N˙lo LPt-α1×LPt-α2hd2α1-β1hd2α2-β1×dα1dα2dβ1,
ÃpxApx Ap2βdβ1/2,c˜kxckx ckβdβ,
ENccdtj=δtN˙lo.
pccdtj=δt2LPtj * Nccdtjδt-N˙lo2-N˙lo hd2ξdξ=δt2LPtj *Nccdtjδt-N˙lo2-N˙lo/δt=LPtj *Nccdtj-δtN˙lo2-δtN˙lo,
Epccdtj=ELPtj*Nccdtj-δtN˙lo2-δtN˙lo=LPtj* ENccd2tj-δtN˙lo2-δtN˙lo.
ENccd2tj=ENccdtj2+ENccdtj=δtN˙lo2+δtN˙lo,
Epccdtj=LPtj*δtN˙lo2+δtN˙lo-δtN˙lo2-δtN˙lo=δtN˙lo2+δtN˙lo-δtN˙lo2-δtN˙lo=0.
varpccdtj=ELPtj*Nccdtj-δtN˙lo2-δtN˙lo2=lmLPtj-lLPtj-mENccdtL-δtN˙lo2-δtN˙loNccdtm-δtN˙lo2-δtN˙lo,
varpccdtj=mLP2tj-mENccdtm-δtN˙lo2-δtN˙lo2=mLP2tj-mENccd4tm-4Nccd3tmδtN˙lo+6Nccd2tmδtN˙lo2-2Nccd2tmδtN˙lo-4NccdtmδtN˙lo3+4NccdtmδtN˙lo2+δtN˙lo4-2δtN˙lo3+δtN˙lo2.
ENccdtm=δtN˙lo,
ENccd2tm=δtN˙lo2+δtN˙lo,
ENccd3tm=δtN˙lo3+3δtN˙lo2+δtN˙lo
ENccd4tm=δtN˙lo4+6δtN˙lo3+7δtN˙lo2+δtN˙lo.
varpccdtj=2δtN˙lo2+δtN˙lomLP2tm.
mLP2tm=2icutoff+1idim,
mLP2tm=2δtBWlp+1idim2δtBWlp.
varpccdtj=2δtN˙lo2+δtN˙lo 2δtBWlp=4δt3N˙lo2BWlp+2δt2N˙loBWlp.
varpˆlotj=4N˙lo2BWlpBWdet+2N˙loBWlpBWdet2.
varpˆkt=4NtakN˙lo2Ãp2t-2β1cc˜kβ1dβ12+8NtakN˙lo2 LP2t-α1×Ãp2α1-2β1cc˜kβ1dα1dβ1+4N˙lo2×BWlpBWdet+2N˙loBWlpBWdet2.
Epˆkt=2NtakN˙loÃp2t-2xcc˜kxdx.
Epˆkt=2NtakN˙lo× K22ut-2xc-ut-T-2xc K1δx0T K22dβ K1δβdβdx=2NtakTN˙lout-ut-T=2N˙takN˙lofor 0tT0otherwise,
varpˆkt=4N˙tak2N˙lo2+8˙NtakN˙lo2LP2t-αdα+4N˙lo2BWlpBWdet+2N˙loBWlpBWdet2, for 0tT,
varpˆkt=4N˙tak2 N˙lo2+16˙NtakN˙lo2BWlp+4N˙lo2BWlpBWdet+2N˙loBWlpBWdet2, for 0tT.
SNREpˆktvarpˆkt1/2=2N˙takN˙lo4N˙tak2N˙lo2+16N˙takN˙lo2BWlp+4N˙lo2BWlpBWdet+2N˙loBWlpBWdet21/2=N˙takN˙tak2+4˙NtakBWlp+BWlpBWdet+BWlpBWdet22N˙lo1/2, for 0tT.

Metrics