Abstract

The general problem of obtaining correct emittance values from broadband IR radiometric measurements on nongray samples is discussed. If the spectral emittance has structure in a band, the emittance, averaged over that band, will be temperature dependent, even if the spectral emittance is insensitive to the temperature change. We point out that a widely used expression, with correction for radiance from the surroundings reflected by the sample, is valid only if the spectral emittance is temperature and wavelength independent, i.e., gray. If the spectral emittance is nongray, the conventional emission factor, as determined by a broadband radiometer, is temperature dependent and the numerical value is significantly different from the averaged band emittance sought. Two algorithms are suggested to extract the correct band-averaged emittance from the temperature-dependent radiometric emission factor obtained with the conventional expression. The algorithms are demonstrated with a step model for the spectral emittance, and it is shown that the agreement with the correct average band emittance is significantly improved.

© 1996 Optical Society of America

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References

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  1. D. P. DeWitt, G. D. Nutter, eds., Theory and Practice of Radiation Thermometry (Wiley, New York, 1988), Part 4, p. 861.
  2. R. McCluney, Introduction to Radiometry and Photometry (Artech House, Boston, 1994).
  3. Ref. 1, Chap. 5, p. 341.
  4. J. F. Snell, “Radiometry and photometry,” in Handbook of Optics, W. Driscoll, S. Vaughan, eds. (McGraw-Hill, New York, 1978), Sec. 1.
  5. C. G. Ribbing, Ö Staaf, S. K. Andersson, “Selective suppression of thermal emission from radomes and materials therefore,” Opt. Eng. 34, 3314–3322 (1995).
    [CrossRef]
  6. B. E. Emilsson, A. R. Roos, “A method and uipment for measuring infrared emissivity,” in Second International Conference on Low Light and Thermal Imaging, IEE Conf. Publ. (Nottingham, UK, 1979), Vol. 173, pp. 5–6.
  7. C. Öhman, “Practical methods for improving thermal measurements,” in Thermal Infrared Sensing Applied to Energy Conservation in Building Envelopes (Thermosense IV), R. A. Grot, J. T. Wood, eds., Proc. SPIE313, 204–212 (1981).
  8. J. Vlcek, “A field method for determination of emissivity with imaging radiometers,” Photogramm. Eng. Remote Sensing 48, 609–614 (1982).
  9. L. Chen, B. T. Yang, “Design principle for simultaneous emissivity and temperature measurements,” Infrared Technology XI, R. A. Mollicone, I. J. Spiro, eds., Proc. SPIE572, 83–88 (1985).
  10. Y.-W. Zhang, C.-G. Zhang, V. Klemas, “Quantitative measurements of ambient radiation, emissivity, and truth temperature of a greybody: methods and experimental results,” Appl. Opt. 25, 3683–3689 (1986).
    [CrossRef] [PubMed]
  11. T. Togawa, “Non-contact skin emissivity: measurement from reflectance using step change in ambient radiation temperature,” Clin. Phys. Physiol. Meas. 10, 39–48 (1989).
    [CrossRef] [PubMed]
  12. H. Svendsen, H. E. Jensen, S. E. Jensen, V. O. Mogensen, “The effect of clear sky radiation on crop surface temperature determined by thermal thermometry,” Agric. For. Meteorol. 50, 239–243 (1990).
    [CrossRef]
  13. D. E. Schmieder, G. W. Walker, “Camouflage, supression, and screening systems,” in The Infrared and Electro-Optical Systems Handbook, D. H. Pollock, ed. (Infrared Information Analysis Center, Environmental Research Institute of Michigan, Ann Arbor, Mich.; The Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), Vol. 7, Sec. 2.3.2.
  14. T. Chibuye, C. G. Ribbing, E. Wäckelgård, “Reststrahlen band studies of polycrystalline beryllium oxide,” Appl. Opt. 33, 5975–5981 (1994).
    [CrossRef] [PubMed]
  15. Ö Staaf, C.-G. Ribbing, S. K. Andersson, “Broadband emission factors—temperature variation for nongray samples,” in Thermosense XVII: An International Conference on Thermal Sensing and Imaging Diagnostic Applications, D. D. Burleigh, J. Spicer, eds., Proc. SPIE2766, 334–345 (1996).

1995 (1)

C. G. Ribbing, Ö Staaf, S. K. Andersson, “Selective suppression of thermal emission from radomes and materials therefore,” Opt. Eng. 34, 3314–3322 (1995).
[CrossRef]

1994 (1)

1990 (1)

H. Svendsen, H. E. Jensen, S. E. Jensen, V. O. Mogensen, “The effect of clear sky radiation on crop surface temperature determined by thermal thermometry,” Agric. For. Meteorol. 50, 239–243 (1990).
[CrossRef]

1989 (1)

T. Togawa, “Non-contact skin emissivity: measurement from reflectance using step change in ambient radiation temperature,” Clin. Phys. Physiol. Meas. 10, 39–48 (1989).
[CrossRef] [PubMed]

1986 (1)

1982 (1)

J. Vlcek, “A field method for determination of emissivity with imaging radiometers,” Photogramm. Eng. Remote Sensing 48, 609–614 (1982).

Andersson, S. K.

C. G. Ribbing, Ö Staaf, S. K. Andersson, “Selective suppression of thermal emission from radomes and materials therefore,” Opt. Eng. 34, 3314–3322 (1995).
[CrossRef]

Ö Staaf, C.-G. Ribbing, S. K. Andersson, “Broadband emission factors—temperature variation for nongray samples,” in Thermosense XVII: An International Conference on Thermal Sensing and Imaging Diagnostic Applications, D. D. Burleigh, J. Spicer, eds., Proc. SPIE2766, 334–345 (1996).

Chen, L.

L. Chen, B. T. Yang, “Design principle for simultaneous emissivity and temperature measurements,” Infrared Technology XI, R. A. Mollicone, I. J. Spiro, eds., Proc. SPIE572, 83–88 (1985).

Chibuye, T.

Emilsson, B. E.

B. E. Emilsson, A. R. Roos, “A method and uipment for measuring infrared emissivity,” in Second International Conference on Low Light and Thermal Imaging, IEE Conf. Publ. (Nottingham, UK, 1979), Vol. 173, pp. 5–6.

Jensen, H. E.

H. Svendsen, H. E. Jensen, S. E. Jensen, V. O. Mogensen, “The effect of clear sky radiation on crop surface temperature determined by thermal thermometry,” Agric. For. Meteorol. 50, 239–243 (1990).
[CrossRef]

Jensen, S. E.

H. Svendsen, H. E. Jensen, S. E. Jensen, V. O. Mogensen, “The effect of clear sky radiation on crop surface temperature determined by thermal thermometry,” Agric. For. Meteorol. 50, 239–243 (1990).
[CrossRef]

Klemas, V.

McCluney, R.

R. McCluney, Introduction to Radiometry and Photometry (Artech House, Boston, 1994).

Mogensen, V. O.

H. Svendsen, H. E. Jensen, S. E. Jensen, V. O. Mogensen, “The effect of clear sky radiation on crop surface temperature determined by thermal thermometry,” Agric. For. Meteorol. 50, 239–243 (1990).
[CrossRef]

Öhman, C.

C. Öhman, “Practical methods for improving thermal measurements,” in Thermal Infrared Sensing Applied to Energy Conservation in Building Envelopes (Thermosense IV), R. A. Grot, J. T. Wood, eds., Proc. SPIE313, 204–212 (1981).

Ribbing, C. G.

C. G. Ribbing, Ö Staaf, S. K. Andersson, “Selective suppression of thermal emission from radomes and materials therefore,” Opt. Eng. 34, 3314–3322 (1995).
[CrossRef]

T. Chibuye, C. G. Ribbing, E. Wäckelgård, “Reststrahlen band studies of polycrystalline beryllium oxide,” Appl. Opt. 33, 5975–5981 (1994).
[CrossRef] [PubMed]

Ribbing, C.-G.

Ö Staaf, C.-G. Ribbing, S. K. Andersson, “Broadband emission factors—temperature variation for nongray samples,” in Thermosense XVII: An International Conference on Thermal Sensing and Imaging Diagnostic Applications, D. D. Burleigh, J. Spicer, eds., Proc. SPIE2766, 334–345 (1996).

Roos, A. R.

B. E. Emilsson, A. R. Roos, “A method and uipment for measuring infrared emissivity,” in Second International Conference on Low Light and Thermal Imaging, IEE Conf. Publ. (Nottingham, UK, 1979), Vol. 173, pp. 5–6.

Schmieder, D. E.

D. E. Schmieder, G. W. Walker, “Camouflage, supression, and screening systems,” in The Infrared and Electro-Optical Systems Handbook, D. H. Pollock, ed. (Infrared Information Analysis Center, Environmental Research Institute of Michigan, Ann Arbor, Mich.; The Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), Vol. 7, Sec. 2.3.2.

Snell, J. F.

J. F. Snell, “Radiometry and photometry,” in Handbook of Optics, W. Driscoll, S. Vaughan, eds. (McGraw-Hill, New York, 1978), Sec. 1.

Staaf, Ö

C. G. Ribbing, Ö Staaf, S. K. Andersson, “Selective suppression of thermal emission from radomes and materials therefore,” Opt. Eng. 34, 3314–3322 (1995).
[CrossRef]

Ö Staaf, C.-G. Ribbing, S. K. Andersson, “Broadband emission factors—temperature variation for nongray samples,” in Thermosense XVII: An International Conference on Thermal Sensing and Imaging Diagnostic Applications, D. D. Burleigh, J. Spicer, eds., Proc. SPIE2766, 334–345 (1996).

Svendsen, H.

H. Svendsen, H. E. Jensen, S. E. Jensen, V. O. Mogensen, “The effect of clear sky radiation on crop surface temperature determined by thermal thermometry,” Agric. For. Meteorol. 50, 239–243 (1990).
[CrossRef]

Togawa, T.

T. Togawa, “Non-contact skin emissivity: measurement from reflectance using step change in ambient radiation temperature,” Clin. Phys. Physiol. Meas. 10, 39–48 (1989).
[CrossRef] [PubMed]

Vlcek, J.

J. Vlcek, “A field method for determination of emissivity with imaging radiometers,” Photogramm. Eng. Remote Sensing 48, 609–614 (1982).

Wäckelgård, E.

Walker, G. W.

D. E. Schmieder, G. W. Walker, “Camouflage, supression, and screening systems,” in The Infrared and Electro-Optical Systems Handbook, D. H. Pollock, ed. (Infrared Information Analysis Center, Environmental Research Institute of Michigan, Ann Arbor, Mich.; The Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), Vol. 7, Sec. 2.3.2.

Yang, B. T.

L. Chen, B. T. Yang, “Design principle for simultaneous emissivity and temperature measurements,” Infrared Technology XI, R. A. Mollicone, I. J. Spiro, eds., Proc. SPIE572, 83–88 (1985).

Zhang, C.-G.

Zhang, Y.-W.

Agric. For. Meteorol. (1)

H. Svendsen, H. E. Jensen, S. E. Jensen, V. O. Mogensen, “The effect of clear sky radiation on crop surface temperature determined by thermal thermometry,” Agric. For. Meteorol. 50, 239–243 (1990).
[CrossRef]

Appl. Opt. (2)

Clin. Phys. Physiol. Meas. (1)

T. Togawa, “Non-contact skin emissivity: measurement from reflectance using step change in ambient radiation temperature,” Clin. Phys. Physiol. Meas. 10, 39–48 (1989).
[CrossRef] [PubMed]

Opt. Eng. (1)

C. G. Ribbing, Ö Staaf, S. K. Andersson, “Selective suppression of thermal emission from radomes and materials therefore,” Opt. Eng. 34, 3314–3322 (1995).
[CrossRef]

Photogramm. Eng. Remote Sensing (1)

J. Vlcek, “A field method for determination of emissivity with imaging radiometers,” Photogramm. Eng. Remote Sensing 48, 609–614 (1982).

Other (9)

L. Chen, B. T. Yang, “Design principle for simultaneous emissivity and temperature measurements,” Infrared Technology XI, R. A. Mollicone, I. J. Spiro, eds., Proc. SPIE572, 83–88 (1985).

B. E. Emilsson, A. R. Roos, “A method and uipment for measuring infrared emissivity,” in Second International Conference on Low Light and Thermal Imaging, IEE Conf. Publ. (Nottingham, UK, 1979), Vol. 173, pp. 5–6.

C. Öhman, “Practical methods for improving thermal measurements,” in Thermal Infrared Sensing Applied to Energy Conservation in Building Envelopes (Thermosense IV), R. A. Grot, J. T. Wood, eds., Proc. SPIE313, 204–212 (1981).

D. P. DeWitt, G. D. Nutter, eds., Theory and Practice of Radiation Thermometry (Wiley, New York, 1988), Part 4, p. 861.

R. McCluney, Introduction to Radiometry and Photometry (Artech House, Boston, 1994).

Ref. 1, Chap. 5, p. 341.

J. F. Snell, “Radiometry and photometry,” in Handbook of Optics, W. Driscoll, S. Vaughan, eds. (McGraw-Hill, New York, 1978), Sec. 1.

D. E. Schmieder, G. W. Walker, “Camouflage, supression, and screening systems,” in The Infrared and Electro-Optical Systems Handbook, D. H. Pollock, ed. (Infrared Information Analysis Center, Environmental Research Institute of Michigan, Ann Arbor, Mich.; The Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), Vol. 7, Sec. 2.3.2.

Ö Staaf, C.-G. Ribbing, S. K. Andersson, “Broadband emission factors—temperature variation for nongray samples,” in Thermosense XVII: An International Conference on Thermal Sensing and Imaging Diagnostic Applications, D. D. Burleigh, J. Spicer, eds., Proc. SPIE2766, 334–345 (1996).

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Figures (4)

Fig. 1
Fig. 1

Two-model emittance spectra and Planck curves for two temperatures, demonstrating the temperature dependence of band emittance. A change in temperature redistributes the weights of the Planck function, which changes the average ε ¯ even though ε(λ) is assumed to be temperature independent. Also indicated is the detector sensitivity range, a = 7.7 and b = 13.0 μm. The gray model, 1, is a constant, ε1 = 0.5, and the step function model, 2, drops from ε2 = 0.9 to ε2 = 0.1 at the wavelength, c = 10 μm.

Fig. 2
Fig. 2

Band emittance and radiometric emission values for the 7.7–13-μm wavelength band as a function of sample temperature calculated with the model emittance spectra in Fig. 1. For the gray spectral emittance, model 1, the conventional expression [Eq. (8)] agrees with the definition [Eq. (2)], as seen by the dotted line. Both curves are temperature independent. The nongray model, 2, with a spectral step results in a significant difference between the correct band average according to Eq. (2) (solid curve) and the conventional expressions [Eq. (8)] (dashed curve), which both vary with sample temperature. The 〈ε〉-values were calculated for the ambient temperature, Ta = 20 °C.

Fig. 3
Fig. 3

Comparison of emittance values calculated from the emittance model, 2, in Fig. 1 and the linearized approximations described in Section 2.A. The solid curve is the exact model according to Eq. (2). The dashed curve with diamonds is the result of the linear approximations according to Eqs. (14) and (16). The dotted curve is the result from Eq. (10) with the 〈ε(Ta )〉 value from the linear algorithm described in the text. Finally, the dashed curve is the result of using Eq. (21).

Fig. 4
Fig. 4

Comparison of band emittance values from the iterations according to Eqs. (22) and (23) with the correct band emittance from Eq. (2).

Equations (23)

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L e ( a , b , T ) = a b ε ( λ ) L bb ( λ , T ) d λ ,
ε ¯ ( T ) = a b ε ( λ ) L bb ( λ , T ) d λ a b L bb ( λ , T ) d λ ,
L r ( T a ) = a b [ 1 ε ( λ ) ] L bb ( λ , T a ) d λ .
L A ( T , T a ) = ε ¯ ( T ) a b L bb ( λ , T ) d λ + [ 1 ε ¯ ( T a ) ] a b L bb ( λ , T a ) d λ .
L B ( T ) = a b L bb ( λ , T ) d λ ,
L C ( T a ) = a b L bb ( λ , T a ) d λ .
L A ( T , T a ) = ε ¯ ( T ) L B ( T ) + [ 1 ε ¯ ( T a ) ] L C ( T a ) .
ε = L A L C L B L C .
ε ( T a ) = d L A / d T d L B / d T
ε ¯ ( T ) = L A ( T , T a ) [ 1 ε ¯ ( T a ) ] L C ( T a ) L B ( T ) ,
ε ( T ) = ε ( T a ) + k 1 ( T T a ) ,
ε ¯ ( T ) = ε ¯ ( T a ) + c 1 ( T T a ) .
ε ( T ) = ε ¯ ( T a ) + c 1 ( T T a ) L B ( T ) L B ( T ) L C .
ε ( T a ) = ε ¯ ( T a ) + c 1 τ 0.499 .
ε ¯ ( T ) = ε ( T a ) + c 1 ( T T 1 ) .
c 1 = k 1 L B ( T ) L B ( T ) L C T 1 T a T T a ,
L B ( T ) = L C + β ( T T a ) + γ ( T T a ) 2 .
ε ( T ) = ε ¯ ( T a ) + c 1 ( T T a ) + c 1 L C / β [ 1 + γ β ( T T a ) ] .
ε ( T ) = ε ¯ ( T a ) + c 1 L C / β + c 1 ( 1 L C γ β 2 ) ( T T a ) .
c 1 = k 1 / ( 1 L C γ β 2 ) 1.475 k 1 ,
ε ¯ ( T a ) = ε ( T a ) k 1 L C β ( β 2 L C γ ) ε ( T a ) 88.34 k 1 .
ε ¯ ( T ) = ε ( T ) [ ε ¯ ( T ) ε ¯ ( T a ) ] L C ( T a ) L B ( T ) L C ( T a ) ,
ε ( T ) corr = ε ( T ) k 1 ( T T a ) L C L B ( T ) L C .

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