Abstract

The temporal behavior of the contrast in a thermal image is related to the temporal change of the radiance statistics over such an image. It is shown that, due to the statistical distribution of the thermal properties over an object, the statistics of the radiance vary with time during temporal changes in the heat balance. In specific cases the contrast of a thermal image can obtain a transient maxima larger than the steady-state values.

© 1985 Optical Society of America

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References

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  1. Y. Itakura, S. Tsutsumi, T. Takagi, “Statistical Properties of the Background Noise for the Atmospheric Windows in the Intermediate Infrared Region,” Infrared Phys. 14, 10 (1974).
    [CrossRef]
  2. A. J. Larocca, J. R. Maxwell, “Statistical Analysis of Terrain Data,” Report ERIM-132300-2-F (Environmental Research Institute of Michigan, Ann Arbor, 1978).
  3. J. R. Maxwell, “Statistical Analysis of Selected Terrain and Water Background Measurement Data,” Report ERIM-132300-I-F (Environmental Research Institute of Michigan, Ann Arbor, 1978).
  4. N. Ben-Yosef, B. Rahat, A. Feigin, “Simulation of IR Images of Natural Backgrounds,” Appl. Opt. 22, 190 (1983).
    [CrossRef] [PubMed]
  5. K. Watson, “Geological Applications of Thermal Infrared Images,” Proc. IEEE 63, 128 (1975).
    [CrossRef]
  6. A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill Kogahusha, Tokyo, 1965, Chap. 7.

1983

1975

K. Watson, “Geological Applications of Thermal Infrared Images,” Proc. IEEE 63, 128 (1975).
[CrossRef]

1974

Y. Itakura, S. Tsutsumi, T. Takagi, “Statistical Properties of the Background Noise for the Atmospheric Windows in the Intermediate Infrared Region,” Infrared Phys. 14, 10 (1974).
[CrossRef]

Ben-Yosef, N.

Feigin, A.

Itakura, Y.

Y. Itakura, S. Tsutsumi, T. Takagi, “Statistical Properties of the Background Noise for the Atmospheric Windows in the Intermediate Infrared Region,” 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-I-F (Environmental Research Institute of Michigan, Ann Arbor, 1978).

Papoulis, A.

A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill Kogahusha, Tokyo, 1965, Chap. 7.

Rahat, B.

Takagi, T.

Y. Itakura, S. Tsutsumi, T. Takagi, “Statistical Properties of the Background Noise for the Atmospheric Windows in the Intermediate Infrared Region,” Infrared Phys. 14, 10 (1974).
[CrossRef]

Tsutsumi, S.

Y. Itakura, S. Tsutsumi, T. Takagi, “Statistical Properties of the Background Noise for the Atmospheric Windows in the Intermediate Infrared Region,” Infrared Phys. 14, 10 (1974).
[CrossRef]

Watson, K.

K. Watson, “Geological Applications of Thermal Infrared Images,” Proc. IEEE 63, 128 (1975).
[CrossRef]

Appl. Opt.

Infrared Phys.

Y. Itakura, S. Tsutsumi, T. Takagi, “Statistical Properties of the Background Noise for the Atmospheric Windows in the Intermediate Infrared Region,” Infrared Phys. 14, 10 (1974).
[CrossRef]

Proc. IEEE

K. Watson, “Geological Applications of Thermal Infrared Images,” Proc. IEEE 63, 128 (1975).
[CrossRef]

Other

A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill Kogahusha, Tokyo, 1965, Chap. 7.

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-I-F (Environmental Research Institute of Michigan, Ann Arbor, 1978).

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Figures (2)

Fig. 1
Fig. 1

Behavior of the radiance standard deviation during heating and cooling. In both cases |F2/F1| = 0.2.

Fig. 2
Fig. 2

Average radiance and radiance standard deviation during a cooling transient; open circles, average radiance, solid circles, radiance standard deviation. For the solid lines see text.

Equations (15)

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d T d t + x z T = y z F ( t ) ,
σ R 2 = ( R x | x 0 , y 0 , z 0 , ɛ 0 ) 2 σ x 2 + ( R y | x 0 , y 0 , z 0 , ɛ 0 ) 2 σ y 2 + ( R z | x 0 , y 0 , z 0 , ɛ 0 ) 2 σ z 2 + ( R ɛ | x 0 , y 0 , z 0 , ɛ 0 ) 2 σ ɛ 2 ,
σ R 2 R 2 ( x 0 , y 0 , z 0 , ɛ 0 ) = σ x 2 x 0 2 + σ y 2 y 0 2 + σ ɛ 2 ɛ 0 2 .
σ R 2 R 0 2 = σ x 2 x 0 2 + σ y 2 y 0 2 + σ ɛ 2 ɛ 0 2 6 × 10 4 .
F ( t ) = F 0 t 0 F 1 t > 0 ;
T ( t ) = y x [ F 1 + F 2 exp ( x z t ) ]
R ( t ) = ɛ y x [ F 1 + F 2 exp ( x z t ) ] .
R ( t ) R ( t ) | x 0 , y 0 , z 0 , ɛ 0 .
σ R 2 = ( ɛ 0 y 0 x 0 F 1 ) 2 { ( σ ɛ ɛ 0 ) 2 [ 1 + F 2 F 1 exp ( τ ) ] 2 + ( σ x x 0 ) 2 × [ 1 + F 2 F 1 ( 1 + τ ) exp ( τ ) ] 2 + ( σ y y 0 ) 2 [ 1 + F 2 F 1 exp ( τ ) ] 2 + ( σ z z 0 ) 2 [ τ F 2 F 1 exp ( τ ) ] 2 } ,
( 1 ) ( σ ɛ ɛ 0 ) 2 + ( σ y y 0 ) 2 = 1 , ( σ x x 0 ) 2 = 1 , ( σ z z 0 ) 2 = 0 ,
( 2 ) ( σ ɛ ɛ 0 ) 2 + ( σ y y 0 ) 2 = 1 , ( σ x x 0 ) 2 = 1 , ( σ z z 0 ) 2 = 5 ,
( 3 ) ( σ ɛ ɛ 0 ) 2 + ( σ y y 0 ) 2 = 1 , ( σ x x 0 ) 2 = 1 , ( σ z z 0 ) 2 = 10 ,
( 4 ) ( σ ɛ ɛ 0 ) 2 + ( σ y y 0 ) 2 = 1 , ( σ x x 0 ) 2 = 1 , ( σ z z 0 ) 2 = 15 .
g ( t ) = log h ( t ) h min h max h min
( σ ɛ ɛ 0 ) 2 + ( σ y y 0 ) 2 = 1 , ( σ x x 0 ) 2 = 1 , and ( σ z z 0 ) 2 = 2 .

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