Abstract

We propose a simple pyrometric algorithm to retrieve the temperature from a radiating body during heating or cooling with no prior knowledge of the spectral emissivity. We ratio the measured fluxes at two different temperatures in two narrow bands. The error budget of this method is calculated. We consider its application for the rover-based exploration of the Martian ground, which is subjected to daily and seasonal temperature variations. The method is optimized to increase accuracy in the retrieval of temperature variation, which is the most interesting parameter for ground heat-flux studies.

© 2006 Optical Society of America

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References

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  1. G. B. Hunter, C. D. Allemand, and T. W. Eagar, Opt. Eng. (Bellingham) 24, 108l (1985).
  2. K. A. Bertness, J. Vac. Sci. Technol. B 18, 1426 (2000).
    [CrossRef]
  3. D. Ya. Svet, in Temperature: Its Measurement and Control in Science and Industry, Vol. 7, D.C.Ripple, ed., AIP Conference Proceedings 684 (American Institute of Physics, 2003) Vol. 7, p. 681.
  4. O. Eyal, V. Scharf, and A. Katzir, Appl. Opt. 37, 5945 (1998).
    [CrossRef]
  5. K. Watson, Remote Sens. Earth Resour. 42, 117 (1992).
    [CrossRef]

2000 (1)

K. A. Bertness, J. Vac. Sci. Technol. B 18, 1426 (2000).
[CrossRef]

1998 (1)

1992 (1)

K. Watson, Remote Sens. Earth Resour. 42, 117 (1992).
[CrossRef]

1985 (1)

G. B. Hunter, C. D. Allemand, and T. W. Eagar, Opt. Eng. (Bellingham) 24, 108l (1985).

Allemand, C. D.

G. B. Hunter, C. D. Allemand, and T. W. Eagar, Opt. Eng. (Bellingham) 24, 108l (1985).

Bertness, K. A.

K. A. Bertness, J. Vac. Sci. Technol. B 18, 1426 (2000).
[CrossRef]

Eagar, T. W.

G. B. Hunter, C. D. Allemand, and T. W. Eagar, Opt. Eng. (Bellingham) 24, 108l (1985).

Eyal, O.

Hunter, G. B.

G. B. Hunter, C. D. Allemand, and T. W. Eagar, Opt. Eng. (Bellingham) 24, 108l (1985).

Katzir, A.

Scharf, V.

Svet, D. Ya.

D. Ya. Svet, in Temperature: Its Measurement and Control in Science and Industry, Vol. 7, D.C.Ripple, ed., AIP Conference Proceedings 684 (American Institute of Physics, 2003) Vol. 7, p. 681.

Watson, K.

K. Watson, Remote Sens. Earth Resour. 42, 117 (1992).
[CrossRef]

Appl. Opt. (1)

J. Vac. Sci. Technol. B (1)

K. A. Bertness, J. Vac. Sci. Technol. B 18, 1426 (2000).
[CrossRef]

Opt. Eng. (Bellingham) (1)

G. B. Hunter, C. D. Allemand, and T. W. Eagar, Opt. Eng. (Bellingham) 24, 108l (1985).

Remote Sens. Earth Resour. (1)

K. Watson, Remote Sens. Earth Resour. 42, 117 (1992).
[CrossRef]

Other (1)

D. Ya. Svet, in Temperature: Its Measurement and Control in Science and Industry, Vol. 7, D.C.Ripple, ed., AIP Conference Proceedings 684 (American Institute of Physics, 2003) Vol. 7, p. 681.

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Tables (1)

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Table 1 Error e in the Retrieval of T 1 , T 2 , and Δ T with Bands [ 9.5 , 10.5 ] μ m , [ 19 , 21 ] μ m and Varying Ratio Accuracy

Equations (20)

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B ( λ , T ) = 2 h c 2 λ 5 [ exp ( h c λ k T ) 1 ] [ W ( m 2 Sr ) ] ,
S ( λ , T ) = η ( λ ) F ( Ω ) B ( λ , T ) d λ ,
R 1 S ( λ 1 , T 1 ) S ( λ 1 , T 2 ) = X 1 W 1 ,
R 2 S ( λ 2 , T 1 ) S ( λ 2 , T 2 ) = X λ 1 λ 2 1 W λ 1 λ 2 1 ,
X = ( W 1 ) R 1 + 1 ,
R 2 W λ 1 λ 2 [ ( W 1 ) R 1 + 1 ] λ 1 λ 2 + 1 R 2 = 0 .
T 1 = h c [ λ 1 k log 2 R 1 R 2 R 1 2 ( R 2 R 1 2 ) ] ,
T 2 = h c [ λ 1 k log R 2 2 R 2 R 1 + R 1 2 ( R 2 R 1 2 ) ] .
d R R = d S ( λ , T 1 ) S ( λ , T 1 ) d S ( λ , T 2 ) S ( λ , T 2 ) = Y λ , T 1 d T T 1 Y λ , T 2 d T T 2 ,
( T 2 T 1 ) d R R T 2 Y min d T .
R S ( λ a , λ b , T 1 ) S ( λ a , λ b , T 2 ) = λ a λ b η ( λ ) ϵ ( λ ) B ( λ , T 1 ) d λ λ a λ b η ( λ ) ϵ ( λ ) B ( λ , T 2 ) d λ .
η ϵ ¯ ( λ a , λ b , T ) = λ a λ b η ( λ ) ϵ ( λ ) B ( λ , T ) d λ λ a λ b B ( λ , T ) d λ ,
S ( λ a , λ b , T 1 ) S ( λ a , λ b , T 2 ) = η ϵ ¯ ( λ a , λ b , T 1 ) η ϵ ¯ ( λ a , λ b , T 2 ) λ a λ b B ( λ , T 1 ) d λ λ a λ b B ( λ , T 2 ) d λ = ( 1 + d ( η ϵ ¯ 1 ) d T Δ T ) λ a λ b B ( λ , T 1 ) d λ λ a λ b B ( λ , T 2 ) d λ + O ( Δ T ) 2 .
d B ( λ , T ) d T B ( λ , T ) h c λ k T 2 ,
d ( η ϵ ¯ ) d T max η ϵ ( λ ) η ϵ ¯ h c k T 2 λ a λ b B ( λ , T ) λ d λ λ a λ b B ( λ , T ) d λ max η ϵ ( λ ) η ¯ ϵ h c λ a k T 2 ,
e ( η ϵ ¯ , T , Δ T ) = d ( η ϵ ¯ ) d T Δ T max η ϵ ( λ ) η ϵ ¯ 0.014 λ a T 2 Δ T .
max η ϵ ( λ ) η ϵ ¯ d T T .
R S ( λ a , λ b , T 1 ) S ( λ a , λ b , T 2 ) = λ a λ b B ( λ , T 1 ) d λ λ 1 , a λ 1 , b B ( λ , T 2 ) d λ .
S ( λ a , λ b , T 1 ) S ( λ a , λ b , T 2 ) = λ a λ b ( B ( λ , T 2 ) + d B ( λ , T 2 ) d T Δ T ) d λ λ a λ b B ( λ , T 2 ) d λ
1 + 0.014 λ b T 2 2 Δ T S ( λ a , λ b , T 1 ) S ( λ a , λ b , T 2 ) 1 + 0.014 λ a T 2 2 Δ T .

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