Abstract

Accurate knowledge of surface emissivity is essential for applications in remote sensing (remote temperature measurement), radiative transport, and modeling of environmental energy balances. Direct measurements of surface emissivity are difficult when there is considerable background radiation at the same wavelength as the emitted radiation. This occurs, for example, when objects at temperatures near room temperature are measured in a terrestrial environment by use of the infrared 8–14-μm band. This problem is usually treated by assumption of a perfectly diffuse surface or of diffuse background radiation. However, real surfaces and actual background radiation are not diffuse; therefore there will be a systematic measurement error. It is demonstrated that, in some cases, the deviations from a diffuse behavior lead to large errors in the measured emissivity. Past measurements made with simplifying assumptions should therefore be reevaluated and corrected. Recommendations are presented for improving experimental procedures in emissivity measurement.

© 2003 Optical Society of America

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References

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  2. W. C. Snyder, Z. Wan, Y. Zhang, Y. Z. Feng, “Thermal infrared (3–14 μm) bidirectional reflectance measurements of sands and soils,” Remote Sens. Environ. 60, 101–109 (1997).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2000 (1)

1999 (1)

1998 (1)

1997 (2)

W. C. Snyder, Z. Wan, Y. Zhang, Y. Z. Feng, “Thermal infrared (3–14 μm) bidirectional reflectance measurements of sands and soils,” Remote Sens. Environ. 60, 101–109 (1997).
[CrossRef]

D. Especel, S. Matteï, “Total emissivity measurements without use of an absolute reference,” Infrared Phys. Technol. 37, 777–784 (1997).
[CrossRef]

1994 (1)

K. S. Humes, W. P. Kustas, M. S. Moran, W. D. Nichols, M. A. Weltz, “Variability of emissivity and surface temperature over a sparsely vegetated surface,” Water Res. Res. 30, 1299–1310 (1994).
[CrossRef]

1992 (1)

W. G. Rees, S. P. James, “Angular variation of the infrared emissivity of ice and water surfaces,” Int. J. Remote Sens. 13, 2873–2886 (1992).
[CrossRef]

1990 (1)

1988 (2)

X. Berger, “A simple model for computing the spectral radiance of clear skies,” Sol. Energy 40, 321–343 (1988).
[CrossRef]

J. W. Salisbury, N. M. Milton, “Thermal infrared (2.5 to 13.5 μm) directional hemispherical reflectance of leaves,” Photogram. Eng. 54, 1301–1304 (1988).

1987 (1)

A. K. Das, M. Iqbal, “A simplified technique to compute spectral atmospheric radiation,” Sol. Energy 39, 143–155 (1987).
[CrossRef]

1966 (1)

M. Fuchs, C. B. Tanner, “Infrared thermometry of vegetation,” Agron. J. 58, 597–601 (1966).
[CrossRef]

1965 (1)

K. J. K. Buettner, C. D. Kern, “The determination of infrared emissivities of terrestrial surfaces,” J. Geophys. Res. 70, 1329–1337 (1965).
[CrossRef]

Berger, X.

X. Berger, “A simple model for computing the spectral radiance of clear skies,” Sol. Energy 40, 321–343 (1988).
[CrossRef]

Buettner, K. J. K.

K. J. K. Buettner, C. D. Kern, “The determination of infrared emissivities of terrestrial surfaces,” J. Geophys. Res. 70, 1329–1337 (1965).
[CrossRef]

Cuenca, J.

Das, A. K.

A. K. Das, M. Iqbal, “A simplified technique to compute spectral atmospheric radiation,” Sol. Energy 39, 143–155 (1987).
[CrossRef]

Devir, A. D.

Donlon, C. G.

Especel, D.

D. Especel, S. Matteï, “Total emissivity measurements without use of an absolute reference,” Infrared Phys. Technol. 37, 777–784 (1997).
[CrossRef]

Feng, Y. Z.

W. C. Snyder, Z. Wan, Y. Zhang, Y. Z. Feng, “Thermal infrared (3–14 μm) bidirectional reflectance measurements of sands and soils,” Remote Sens. Environ. 60, 101–109 (1997).
[CrossRef]

Fuchs, M.

M. Fuchs, C. B. Tanner, “Infrared thermometry of vegetation,” Agron. J. 58, 597–601 (1966).
[CrossRef]

Howell, J. R.

R. Siegel, J. R. Howell, Thermal Radiation Heat Transfer (Taylor Francis, New York, 2002).

Humes, K. S.

K. S. Humes, W. P. Kustas, M. S. Moran, W. D. Nichols, M. A. Weltz, “Variability of emissivity and surface temperature over a sparsely vegetated surface,” Water Res. Res. 30, 1299–1310 (1994).
[CrossRef]

Iqbal, M.

A. K. Das, M. Iqbal, “A simplified technique to compute spectral atmospheric radiation,” Sol. Energy 39, 143–155 (1987).
[CrossRef]

James, S. P.

W. G. Rees, S. P. James, “Angular variation of the infrared emissivity of ice and water surfaces,” Int. J. Remote Sens. 13, 2873–2886 (1992).
[CrossRef]

Kern, C. D.

K. J. K. Buettner, C. D. Kern, “The determination of infrared emissivities of terrestrial surfaces,” J. Geophys. Res. 70, 1329–1337 (1965).
[CrossRef]

Kustas, W. P.

K. S. Humes, W. P. Kustas, M. S. Moran, W. D. Nichols, M. A. Weltz, “Variability of emissivity and surface temperature over a sparsely vegetated surface,” Water Res. Res. 30, 1299–1310 (1994).
[CrossRef]

Li, X.

Matteï, S.

D. Especel, S. Matteï, “Total emissivity measurements without use of an absolute reference,” Infrared Phys. Technol. 37, 777–784 (1997).
[CrossRef]

Milton, N. M.

J. W. Salisbury, N. M. Milton, “Thermal infrared (2.5 to 13.5 μm) directional hemispherical reflectance of leaves,” Photogram. Eng. 54, 1301–1304 (1988).

Moran, M. S.

K. S. Humes, W. P. Kustas, M. S. Moran, W. D. Nichols, M. A. Weltz, “Variability of emissivity and surface temperature over a sparsely vegetated surface,” Water Res. Res. 30, 1299–1310 (1994).
[CrossRef]

Nichols, W. D.

K. S. Humes, W. P. Kustas, M. S. Moran, W. D. Nichols, M. A. Weltz, “Variability of emissivity and surface temperature over a sparsely vegetated surface,” Water Res. Res. 30, 1299–1310 (1994).
[CrossRef]

Nightingale, T. J.

Oppenheim, U. P.

Rees, W. G.

W. G. Rees, S. P. James, “Angular variation of the infrared emissivity of ice and water surfaces,” Int. J. Remote Sens. 13, 2873–2886 (1992).
[CrossRef]

Salisbury, J. W.

J. W. Salisbury, N. M. Milton, “Thermal infrared (2.5 to 13.5 μm) directional hemispherical reflectance of leaves,” Photogram. Eng. 54, 1301–1304 (1988).

Sheffer, D.

Siegel, R.

R. Siegel, J. R. Howell, Thermal Radiation Heat Transfer (Taylor Francis, New York, 2002).

Snyder, W. C.

W. C. Snyder, Z. Wan, X. Li, “Thermodynamic constraints on reflectance reciprocity and Kirchhoff’s law,” Appl. Opt. 37, 3464–3470 (1998).
[CrossRef]

W. C. Snyder, Z. Wan, Y. Zhang, Y. Z. Feng, “Thermal infrared (3–14 μm) bidirectional reflectance measurements of sands and soils,” Remote Sens. Environ. 60, 101–109 (1997).
[CrossRef]

Sobrino, J. A.

Tanner, C. B.

M. Fuchs, C. B. Tanner, “Infrared thermometry of vegetation,” Agron. J. 58, 597–601 (1966).
[CrossRef]

Wan, Z.

W. C. Snyder, Z. Wan, X. Li, “Thermodynamic constraints on reflectance reciprocity and Kirchhoff’s law,” Appl. Opt. 37, 3464–3470 (1998).
[CrossRef]

W. C. Snyder, Z. Wan, Y. Zhang, Y. Z. Feng, “Thermal infrared (3–14 μm) bidirectional reflectance measurements of sands and soils,” Remote Sens. Environ. 60, 101–109 (1997).
[CrossRef]

Weltz, M. A.

K. S. Humes, W. P. Kustas, M. S. Moran, W. D. Nichols, M. A. Weltz, “Variability of emissivity and surface temperature over a sparsely vegetated surface,” Water Res. Res. 30, 1299–1310 (1994).
[CrossRef]

Zhang, Y.

W. C. Snyder, Z. Wan, Y. Zhang, Y. Z. Feng, “Thermal infrared (3–14 μm) bidirectional reflectance measurements of sands and soils,” Remote Sens. Environ. 60, 101–109 (1997).
[CrossRef]

Agron. J. (1)

M. Fuchs, C. B. Tanner, “Infrared thermometry of vegetation,” Agron. J. 58, 597–601 (1966).
[CrossRef]

Appl. Opt. (4)

Infrared Phys. Technol. (1)

D. Especel, S. Matteï, “Total emissivity measurements without use of an absolute reference,” Infrared Phys. Technol. 37, 777–784 (1997).
[CrossRef]

Int. J. Remote Sens. (1)

W. G. Rees, S. P. James, “Angular variation of the infrared emissivity of ice and water surfaces,” Int. J. Remote Sens. 13, 2873–2886 (1992).
[CrossRef]

J. Geophys. Res. (1)

K. J. K. Buettner, C. D. Kern, “The determination of infrared emissivities of terrestrial surfaces,” J. Geophys. Res. 70, 1329–1337 (1965).
[CrossRef]

Photogram. Eng. (1)

J. W. Salisbury, N. M. Milton, “Thermal infrared (2.5 to 13.5 μm) directional hemispherical reflectance of leaves,” Photogram. Eng. 54, 1301–1304 (1988).

Remote Sens. Environ. (1)

W. C. Snyder, Z. Wan, Y. Zhang, Y. Z. Feng, “Thermal infrared (3–14 μm) bidirectional reflectance measurements of sands and soils,” Remote Sens. Environ. 60, 101–109 (1997).
[CrossRef]

Sol. Energy (2)

X. Berger, “A simple model for computing the spectral radiance of clear skies,” Sol. Energy 40, 321–343 (1988).
[CrossRef]

A. K. Das, M. Iqbal, “A simplified technique to compute spectral atmospheric radiation,” Sol. Energy 39, 143–155 (1987).
[CrossRef]

Water Res. Res. (1)

K. S. Humes, W. P. Kustas, M. S. Moran, W. D. Nichols, M. A. Weltz, “Variability of emissivity and surface temperature over a sparsely vegetated surface,” Water Res. Res. 30, 1299–1310 (1994).
[CrossRef]

Other (1)

R. Siegel, J. R. Howell, Thermal Radiation Heat Transfer (Taylor Francis, New York, 2002).

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Figures (5)

Fig. 1
Fig. 1

Geometry of the sample, detector, and background incident radiation.

Fig. 2
Fig. 2

(a) Nonuniform background radiation intensity corresponding to a split view of the ground and the sky. (b) The error in emissivity measurement increases with specular reflectivity component ρ s for a split hemisphere background. Two different atmospheric humidity conditions are shown. The gray area is where the error is less than 0.01.

Fig. 3
Fig. 3

The error in emissivity measurement under an anisotropic clear sky depends on the detector angle and on the specular reflectivity component. The gray area is the range where the error is less than 0.01.

Fig. 4
Fig. 4

The error in emissivity measurement for a sample with directional emissivity and nondiffuse background depends on the detector angle. The gray area is the range where the error is less than 0.01.

Fig. 5
Fig. 5

Directional emissivity of water as measured in Refs. 9 and 10 compared with values reconstructed from Ref. 9 under the assumption of anisotropic sky intensity.

Equations (21)

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iD=εibTS+1-εqBπ.
iλDλ, ΩD=ελdλ, ΩDiλbλ, TS+ ρλddλ, ΩD, ΩBiλBλ, ΩBcos θBdΩB.
iDΩD=εdΩDibTS+ ρddΩD, ΩBiBΩBcos θBdΩB.
iD=εibTS+1-επ iBΩBcos θBdΩB =εibTS+1-εqBπ.
εm=iD-qB/πibTS-qB/π.
 ρddΩD, ΩBiBΩBcos θBdΩB=iB ρddΩD, ΩBcos θBdΩB=iBρhdΩD=iB1-εdΩD.
ρddΩD, ΩB=ρdiff+ρspecδΩD-ΩBR.
εdΩD=1-ρdhΩD=1- ρddΩB, ΩDcos θBdΩB=1-πρdiff-ρspec.
ρdiff=1π1-ε-ρspec ρddΩD, ΩB=1-επ+ρspecδΩD-ΩBR-1π.
iBΩB=i¯B+iND0ϕBπi¯B-iNDπ<ϕB2π.
iD=εibTS+1-εi¯B±ρspeciND.
εm=ε±ρspeciNDibTS-i¯B.
Δε=±ρspeciNDibTS-i¯B.
iBΩB=εBΩBibTS=1-1-εBNcos θBibTS.
ε¯B=1π εBΩBcos θBdΩB=1+2εBN.
iD,reflΩD=1-ε-ρspecε¯BibTS-ρspecεBΩDibTS.
Δε=ρspec1-³/₂cos θD.
εdΩD=εN1-θD/½πp.
ρddΩD, ΩB=ρdiff+1-πρdiff-εN1-θD/½πpδΩD-ΩBR=ρdiff+ρspecΩDδΩD-ΩBR.
εmΩD=1-πρdiff-³/₂1-πρdiff-εdΩDcos θD=1-πρdiff-³/₂ρspecΩDcos θD,Δε=1-³/₂cos θDρspecΩD.
εdΩD=1-πρdiff-23 cos θD1-πρdiff-εmΩD.

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