Abstract

Two schemes for the simulation of IR images of ground terrain are presented. Both preserve the statistics and power spectra of the temperature variation over the scene according to the experimental findings. The first scheme generates the scene directly in the spatial domain, while the second generates it in the spatial-frequency domain. Each is advantageous according to the simulation task needed.

© 1983 Optical Society of America

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References

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  1. D. F. Barbe, ed., “Smart Sensors,” Proc. Soc. Photo-Opt. Instrum. Eng.178, all volume (1979).
  2. Y. Itakura, S. Tsutsumi, T. Takagi, Infrared Phys. 14, 10 (1974).
    [Crossref]
  3. A. J. Larocca, J. R. Maxwell, “Statistical Analysis of Terrain Data,” Report ERIM-132300-2-F (Environmental Research Institute of Michigan, Ann Arbor, 1978).
  4. J. R. Maxwell, “Statistical Analysis of Selected Terrain and Water Background Measurement Data,” Report ERIM-132300-1-F (Environmental Research Institute of Michigan, Ann Arbor, 1978).
  5. J. T. Ator, K. P. White, Proc. Soc. Photo-Opt. Instrum. Eng. 156, 157 (1978).
  6. A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill, New York, 1965).
  7. R. Salemme, D. Bowyer, R. Merritt, AGARD Conf. Proc. 292, 26/1 (1980), ADA-092-606.
  8. M. Abramowitz, I. A. Stegun, Eds., Handbook of Mathematical Functions (Dover, New York, 1972), Chap. 11.
  9. A. P. Sage, J. L. Melsa, Estimation Theory (McGraw-Hill, New York, 1971), Chap. 2.

1980 (1)

R. Salemme, D. Bowyer, R. Merritt, AGARD Conf. Proc. 292, 26/1 (1980), ADA-092-606.

1978 (1)

J. T. Ator, K. P. White, Proc. Soc. Photo-Opt. Instrum. Eng. 156, 157 (1978).

1974 (1)

Y. Itakura, S. Tsutsumi, T. Takagi, Infrared Phys. 14, 10 (1974).
[Crossref]

Ator, J. T.

J. T. Ator, K. P. White, Proc. Soc. Photo-Opt. Instrum. Eng. 156, 157 (1978).

Bowyer, D.

R. Salemme, D. Bowyer, R. Merritt, AGARD Conf. Proc. 292, 26/1 (1980), ADA-092-606.

Itakura, Y.

Y. Itakura, S. Tsutsumi, T. Takagi, Infrared Phys. 14, 10 (1974).
[Crossref]

Larocca, A. J.

A. J. Larocca, J. R. Maxwell, “Statistical Analysis of Terrain Data,” Report ERIM-132300-2-F (Environmental Research Institute of Michigan, Ann Arbor, 1978).

Maxwell, J. R.

A. J. Larocca, J. R. Maxwell, “Statistical Analysis of Terrain Data,” Report ERIM-132300-2-F (Environmental Research Institute of Michigan, Ann Arbor, 1978).

J. R. Maxwell, “Statistical Analysis of Selected Terrain and Water Background Measurement Data,” Report ERIM-132300-1-F (Environmental Research Institute of Michigan, Ann Arbor, 1978).

Melsa, J. L.

A. P. Sage, J. L. Melsa, Estimation Theory (McGraw-Hill, New York, 1971), Chap. 2.

Merritt, R.

R. Salemme, D. Bowyer, R. Merritt, AGARD Conf. Proc. 292, 26/1 (1980), ADA-092-606.

Papoulis, A.

A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill, New York, 1965).

Sage, A. P.

A. P. Sage, J. L. Melsa, Estimation Theory (McGraw-Hill, New York, 1971), Chap. 2.

Salemme, R.

R. Salemme, D. Bowyer, R. Merritt, AGARD Conf. Proc. 292, 26/1 (1980), ADA-092-606.

Takagi, T.

Y. Itakura, S. Tsutsumi, T. Takagi, Infrared Phys. 14, 10 (1974).
[Crossref]

Tsutsumi, S.

Y. Itakura, S. Tsutsumi, T. Takagi, Infrared Phys. 14, 10 (1974).
[Crossref]

White, K. P.

J. T. Ator, K. P. White, Proc. Soc. Photo-Opt. Instrum. Eng. 156, 157 (1978).

AGARD Conf. Proc. (1)

R. Salemme, D. Bowyer, R. Merritt, AGARD Conf. Proc. 292, 26/1 (1980), ADA-092-606.

Infrared Phys. (1)

Y. Itakura, S. Tsutsumi, T. Takagi, Infrared Phys. 14, 10 (1974).
[Crossref]

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

J. T. Ator, K. P. White, Proc. Soc. Photo-Opt. Instrum. Eng. 156, 157 (1978).

Other (6)

A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill, New York, 1965).

A. J. Larocca, J. R. Maxwell, “Statistical Analysis of Terrain Data,” Report ERIM-132300-2-F (Environmental Research Institute of Michigan, Ann Arbor, 1978).

J. R. Maxwell, “Statistical Analysis of Selected Terrain and Water Background Measurement Data,” Report ERIM-132300-1-F (Environmental Research Institute of Michigan, Ann Arbor, 1978).

M. Abramowitz, I. A. Stegun, Eds., Handbook of Mathematical Functions (Dover, New York, 1972), Chap. 11.

A. P. Sage, J. L. Melsa, Estimation Theory (McGraw-Hill, New York, 1971), Chap. 2.

D. F. Barbe, ed., “Smart Sensors,” Proc. Soc. Photo-Opt. Instrum. Eng.178, all volume (1979).

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Figures (7)

Fig. 1
Fig. 1

Spatial arrangement of the scene pixels for the case of space-domain simulation.

Fig. 2
Fig. 2

(a) An example of a scene generated in space domain: N = 128, nominal σ = 3, correlation length 7. (b) As in Fig. 2(a), the same random number string was used: N = 128, nominal σ = 3, correlation length 50. Note the lower dynamic range (due to higher correlation length) and the difference in high spatial-frequency components.

Fig. 3
Fig. 3

(a) 2-D correlation function of Fig. 2(a); r = 0 at the center of the picture. (b) The 2-D correlation function of Fig. 2(b).

Fig. 4
Fig. 4

(a) Temperature distribution of Fig. 2(a) measured σ = 2.3; (b) the temperature distribution of Fig. 2(b) measured σ = 1.7.

Fig. 5
Fig. 5

(a) An example of a scene generated in spatial-frequency domain: N = 64, nominal σ = 3, correlation length is 3. (b) As in Fig. 5(a), with the same random number string: N = 64, nominal σ = 3, correlation length is 27. Notice the differences compared with Fig. 5(a); they are the same kind as the differences between Figs. 2(a) and (b).

Fig. 6
Fig. 6

(a) Correlation function of Fig. 5(a); (b) the correlation function of Fig. 5(b).

Fig. 7
Fig. 7

(a) Temperature distribution of Fig. 5(a) measured σ = 2.6; (b) the temperature distribution of Fig. 5(b) measured σ = 1.87.

Equations (11)

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P ( T ) = 1 2 π σ exp { ( T T ) 2 2 σ 2 } ,
W ( u , υ ) = 2 π α σ 2 [ α 2 + ( 2 π u ) 2 + ( 2 π υ ) 2 ] 3 / 2 ,
P ( β ) = 1 [ det ( V ) ] 1 / 2 ( 2 π ) N / 2 exp { 1 2 β T V 1 β } ,
P ( T 4 | T 2 , T 3 ) = 1 2 π σ β exp [ C ( T 4 ) 2 σ 2 β 2 ] ,
β = 1 + Z 2 2 Z 2 1 + Z 2 , C ( T 4 ) = ( T 4 Z 1 + Z 2 T Z 1 + Z 2 T 3 ) 2 ,
T 4 = Z 1 + Z 2 T 2 + Z 1 + Z 2 T 3
F ( u , υ ) = ( T ( r ) u , υ = 0 0 , otherwise in the present case T = 0 , F ( u , υ ) F * ( u , υ ) = ( W ( u , υ ) , u = u , υ = υ 0 , otherwise
W ( u , υ ) = 2 π α σ 2 [ α 2 + ( 2 π u ) 2 + ( 2 π υ ) 2 ] 3 / 2 .
V = σ 2 | 1 Z Z 2 Z 1 Z Z 2 Z 1 |
V 1 = σ 4 det ( V ) | 1 Z 2 Z ( Z 2 1 ) Z 2 Z 2 Z ( Z 2 1 ) 1 Z 2 2 Z ( Z 2 1 ) Z 2 Z 2 Z ( Z 2 1 ) 1 Z 2 |
P ( T 4 | T 2 , T 3 ) = P ( T 2 , T 4 , T 3 ) P ( T 2 , T 3 ) .

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