Abstract

A methodology for the estimation of ladar cross sections from high-resolution image data of geometrically complex targets is presented. Coherent CO2 laser radar was used to generate high-resolution amplitude imagery of a UC-8 Buffalo test aircraft at a range of 1.3 km at nine different aspect angles. The average target ladar cross section was synthesized from these data and calculated to be σT = 15.4 dBsm, which is similar to the expected microwave radar cross sections. The aspect angle dependence of the cross section shows pronounced peaks at nose on and broadside, which are also in agreement with radar results. Strong variations in both the mean amplitude and the statistical distributions of amplitude with the aspect angle have also been observed. The relative mix of diffuse and specular returns causes significant deviations from a simple Lambertian or Swerling II target, especially at broadside where large normal surfaces are present.

© 1992 Optical Society of America

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References

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  1. A. E. Siegman, “The antenna properties of optical heterodyne receivers,” Proc. IEEE 54, 1350–1356 (1966).
    [CrossRef]
  2. C. DiMarzio, K. Seeber, “Radar and ladar range equations,” Memor. EM85-0251 (Raytheon Company, Sudbury, Mass., 17May1985).
  3. D. K. Barton, Radar Systems Analysis (Prentice-Hall, Englewood Cliffs, N.J., 1964), Chap. 3.
  4. J. V. DiFranco, W. L. Rubin, Radar Detection (Artech House, Dedham, Mass., 1980), p. 380.
  5. J. W. Crispin, K. M. Siegel, Methods of Radar Cross Section Analysis (Academic, San Diego, Calif., 1968), Chap. 4.
  6. RCA Electro-Optics Handbook (Radio Corporation of America, Burlington, Mass., 1968), p. 12–5.
  7. W. L. Wolfe, G. J. Zissis, eds., The Infrared Handbook (Office of Naval Research, Department of the Navy, Washington, D.C., 1978), pp. 23–8, 23–9.
  8. M. I. Skolnik, Introduction to Radar Systems (McGraw-Hill, New York, 1980), pp. 47–52.
  9. J. C. Dainty, Laser Speckle and Related Phenomena, Vol. 9 of Topics in Applied Physics, (Springer-Verlag, New York, 1984), p.25.
  10. J. D. Wilson, “Probability of detecting aircraft targets,” IEEE Trans. Aerosp. Electron. Syst. AES-8, 757–761 (1972).
    [CrossRef]
  11. P. H. R. Scholefield, “Statistical aspects of ideal radar targets,” Proc. IEEE 55, 587–589 (1967).
    [CrossRef]

1972 (1)

J. D. Wilson, “Probability of detecting aircraft targets,” IEEE Trans. Aerosp. Electron. Syst. AES-8, 757–761 (1972).
[CrossRef]

1967 (1)

P. H. R. Scholefield, “Statistical aspects of ideal radar targets,” Proc. IEEE 55, 587–589 (1967).
[CrossRef]

1966 (1)

A. E. Siegman, “The antenna properties of optical heterodyne receivers,” Proc. IEEE 54, 1350–1356 (1966).
[CrossRef]

Barton, D. K.

D. K. Barton, Radar Systems Analysis (Prentice-Hall, Englewood Cliffs, N.J., 1964), Chap. 3.

Crispin, J. W.

J. W. Crispin, K. M. Siegel, Methods of Radar Cross Section Analysis (Academic, San Diego, Calif., 1968), Chap. 4.

Dainty, J. C.

J. C. Dainty, Laser Speckle and Related Phenomena, Vol. 9 of Topics in Applied Physics, (Springer-Verlag, New York, 1984), p.25.

DiFranco, J. V.

J. V. DiFranco, W. L. Rubin, Radar Detection (Artech House, Dedham, Mass., 1980), p. 380.

DiMarzio, C.

C. DiMarzio, K. Seeber, “Radar and ladar range equations,” Memor. EM85-0251 (Raytheon Company, Sudbury, Mass., 17May1985).

Rubin, W. L.

J. V. DiFranco, W. L. Rubin, Radar Detection (Artech House, Dedham, Mass., 1980), p. 380.

Scholefield, P. H. R.

P. H. R. Scholefield, “Statistical aspects of ideal radar targets,” Proc. IEEE 55, 587–589 (1967).
[CrossRef]

Seeber, K.

C. DiMarzio, K. Seeber, “Radar and ladar range equations,” Memor. EM85-0251 (Raytheon Company, Sudbury, Mass., 17May1985).

Siegel, K. M.

J. W. Crispin, K. M. Siegel, Methods of Radar Cross Section Analysis (Academic, San Diego, Calif., 1968), Chap. 4.

Siegman, A. E.

A. E. Siegman, “The antenna properties of optical heterodyne receivers,” Proc. IEEE 54, 1350–1356 (1966).
[CrossRef]

Skolnik, M. I.

M. I. Skolnik, Introduction to Radar Systems (McGraw-Hill, New York, 1980), pp. 47–52.

Wilson, J. D.

J. D. Wilson, “Probability of detecting aircraft targets,” IEEE Trans. Aerosp. Electron. Syst. AES-8, 757–761 (1972).
[CrossRef]

IEEE Trans. Aerosp. Electron. Syst. (1)

J. D. Wilson, “Probability of detecting aircraft targets,” IEEE Trans. Aerosp. Electron. Syst. AES-8, 757–761 (1972).
[CrossRef]

Proc. IEEE (2)

P. H. R. Scholefield, “Statistical aspects of ideal radar targets,” Proc. IEEE 55, 587–589 (1967).
[CrossRef]

A. E. Siegman, “The antenna properties of optical heterodyne receivers,” Proc. IEEE 54, 1350–1356 (1966).
[CrossRef]

Other (8)

C. DiMarzio, K. Seeber, “Radar and ladar range equations,” Memor. EM85-0251 (Raytheon Company, Sudbury, Mass., 17May1985).

D. K. Barton, Radar Systems Analysis (Prentice-Hall, Englewood Cliffs, N.J., 1964), Chap. 3.

J. V. DiFranco, W. L. Rubin, Radar Detection (Artech House, Dedham, Mass., 1980), p. 380.

J. W. Crispin, K. M. Siegel, Methods of Radar Cross Section Analysis (Academic, San Diego, Calif., 1968), Chap. 4.

RCA Electro-Optics Handbook (Radio Corporation of America, Burlington, Mass., 1968), p. 12–5.

W. L. Wolfe, G. J. Zissis, eds., The Infrared Handbook (Office of Naval Research, Department of the Navy, Washington, D.C., 1978), pp. 23–8, 23–9.

M. I. Skolnik, Introduction to Radar Systems (McGraw-Hill, New York, 1980), pp. 47–52.

J. C. Dainty, Laser Speckle and Related Phenomena, Vol. 9 of Topics in Applied Physics, (Springer-Verlag, New York, 1984), p.25.

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Figures (10)

Fig. 1
Fig. 1

UC-8 test aircraft.

Fig. 2
Fig. 2

SNR versus the range of coherent CO2 ladar.

Fig. 3
Fig. 3

Coherent CO2 ladar.

Fig. 4
Fig. 4

Ladar image of the UC-8 Buffalo test aircraft: FM range image (lower right); a range sliced FM image (upper right); an amplitude image (lower left); an amplitude histogram (upper left). Scaled color bars are shown above each image. The bottom color bar corresponds to the amplitude image. The boxed region shows the pixels that are included in the histogram.

Fig. 5
Fig. 5

Ladar image the UC-8 Buffalo test aircraft: FM range image (lower right); a range sliced FM image (upper right); an amplitude image (lower left); an amplitude histogram (upper left). Scaled color bars are shown above each image. The bottom color bar corresponds to the amplitude image.

Fig. 6
Fig. 6

Detection probabilities versus the SNR for different target statistics.

Fig. 7
Fig. 7

Amplitude histogram of the sandpaper reflectivity standard.

Fig. 8
Fig. 8

LCS polar plot of test aircraft.

Fig. 9
Fig. 9

Amplitude histogram of all target files (36).

Fig. 10
Fig. 10

Swerling I and II log-amplitude distributions.

Tables (2)

Tables Icon

Table I Cross Section of Individual Target Files

Tables Icon

Table II Mean Cross Section per Aspect Angle

Equations (13)

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SNR = η E p h v ρ ( π ) λ 2 π w T 2 [ 1 - exp ( - 4 r T 2 / w T 2 ) ] η a ,
w T 2 = 1 4 [ ( 0.8 D ) 2 + ( 1.96 λ R D ) 2 ] ,
SNR = η E p h v D 4 π 2 λ 2 R 4 σ π η a ,
σ T = 4 π 2 ρ ( π ) r T 2 = 4 π ρ ( π ) A T
SNR = η E p h v ρ ( π ) D 2 π R 2 η a .
A exp ( i ϕ ) = j = 1 N A j exp ( i ϕ j ) = σ T exp ( i ϕ ) .
σ = k A E 2 / λ 2 ,
σ k = j = 1 N A j k 2 = j = 1 N σ j k ,
σ ¯ T = 1 N k = 1 N σ k ,
σ k = 4 π j = 1 n ρ j k ( π ) A j k = 4 π A p j = 1 n ρ j k ( π ) ,
ρ j k ( π ) = SNR j k K ,
σ k = 4 π A p K j = 1 n SNR j k .
P D = P D ( σ ¯ T ) .

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