Abstract

A method is presented to determine simultaneously the temperature distribution and the intrinsic emissivities of a cavity surface when radiance distributions along the cavity wall for two wavelengths are given. The intrinsic emissivity and reflection characteristics are assumed not to depend on position on the cavity wall. The intrinsic emissivity and reflection characteristics giving the smallest difference between calculated temperature distributions for the two wavelengths are found. The values found and thus the temperature distributions are verified to be close to the true ones. The method is examined on a cylindrocone by a simulation and applied to radiance temperature distributions measured on a commercially available double cone.

© 2000 Optical Society of America

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References

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  1. J. L. Gardner, T. P. Jones, “Multi-wavelength radiation pyrometry where reflectance is measured to estimate emissivity,” J. Phys. E 13, 306–310 (1980).
    [Crossref]
  2. T. Iuchi, “Radiation thermometry making use of specular reflection,” Trans. Soc. Instrum. Controlled Eng. 16, 233–238 (1980).
  3. T. Makino, T. Kosaka, J. Arima, S. Aoyama, Y. Tsujimura, “A method for multi wavelength radiation pyrometry measuring emission and reflection simultaneously and remotely,” Trans. Soc. Instrum. Controlled Eng. 24, 331–336 (1988).
  4. N. Yamada, S. Fujimura, “Radiation thermometry for simultaneous measurement of temperature and emissivity,” in Temperature, Its Measurement and Control in Science and Industry, J. F. Schooley, ed. (American Institute of Physics, New York, 1992), Vol. 6, Part 2, pp. 843–847.
  5. W. A. Rense, “Polarization studies of light diffusely reflected from ground and etched surfaces,” J. Opt. Soc. Am. 57, 55–59 (1950).
    [Crossref]
  6. T. S. Trowbridge, K. P. Reitz, “Average irregularity representation of a rough surface for ray reflection,” J. Opt. Soc. Am. 65, 531–536 (1975).
    [Crossref]
  7. Y. Ohwada, “Calculation of the effective emissivity of a cavity having non-Lambertian isothermal surfaces,” J. Opt. Soc. Am. A 16, 1059–1065 (1999).
    [Crossref]
  8. F. Sakuma, L. Ma, Y. Ohwada, C. Li, J. Wu, “Measurement of radiance temperature distribution of a comparison blackbody,” in Proceedings of the 38th SICE Annual Conference, July 28–30, 1999, Iwate University, Iwate, Japan, Domestic Session Papers Vol. 1, pp. 133–134 (in Japanese).
  9. Y. Ohwada, “A method for calculating the temperature variation along a cavity wall,” Meas. Sci. Technol. 2, 907–911 (1991).
    [Crossref]
  10. R. E. Bedford, C. K. Ma, “Emissivities of diffuse cavities: isothermal and nonisothermal cones and cylinders,” J. Opt. Soc. Am. 64, 339–349 (1974).
    [Crossref]
  11. Y. Ohwada, “Influence of deviation from Lambertian reflectance on the effective emissivity of a cavity,” Metrologia 32, 713–716 (1996).
    [Crossref]
  12. E. M. Sparrow, R. D. Cess, Radiation Heat Transfer (Hemispere, Washington, D.C., 1978).
  13. M. Kobayashi, M. Ohtsuki, H. Sakate, F. Sakuma, A. Ono, “Normal spectral emissivity of metal material,” National Research Laboratory of Metrology, 1-1-4, Umezone, Tsukuba, Ibaraki, 305-8563, Japan (personal communication, 1998).

1999 (1)

1996 (1)

Y. Ohwada, “Influence of deviation from Lambertian reflectance on the effective emissivity of a cavity,” Metrologia 32, 713–716 (1996).
[Crossref]

1991 (1)

Y. Ohwada, “A method for calculating the temperature variation along a cavity wall,” Meas. Sci. Technol. 2, 907–911 (1991).
[Crossref]

1988 (1)

T. Makino, T. Kosaka, J. Arima, S. Aoyama, Y. Tsujimura, “A method for multi wavelength radiation pyrometry measuring emission and reflection simultaneously and remotely,” Trans. Soc. Instrum. Controlled Eng. 24, 331–336 (1988).

1980 (2)

J. L. Gardner, T. P. Jones, “Multi-wavelength radiation pyrometry where reflectance is measured to estimate emissivity,” J. Phys. E 13, 306–310 (1980).
[Crossref]

T. Iuchi, “Radiation thermometry making use of specular reflection,” Trans. Soc. Instrum. Controlled Eng. 16, 233–238 (1980).

1975 (1)

1974 (1)

1950 (1)

W. A. Rense, “Polarization studies of light diffusely reflected from ground and etched surfaces,” J. Opt. Soc. Am. 57, 55–59 (1950).
[Crossref]

Aoyama, S.

T. Makino, T. Kosaka, J. Arima, S. Aoyama, Y. Tsujimura, “A method for multi wavelength radiation pyrometry measuring emission and reflection simultaneously and remotely,” Trans. Soc. Instrum. Controlled Eng. 24, 331–336 (1988).

Arima, J.

T. Makino, T. Kosaka, J. Arima, S. Aoyama, Y. Tsujimura, “A method for multi wavelength radiation pyrometry measuring emission and reflection simultaneously and remotely,” Trans. Soc. Instrum. Controlled Eng. 24, 331–336 (1988).

Bedford, R. E.

Cess, R. D.

E. M. Sparrow, R. D. Cess, Radiation Heat Transfer (Hemispere, Washington, D.C., 1978).

Fujimura, S.

N. Yamada, S. Fujimura, “Radiation thermometry for simultaneous measurement of temperature and emissivity,” in Temperature, Its Measurement and Control in Science and Industry, J. F. Schooley, ed. (American Institute of Physics, New York, 1992), Vol. 6, Part 2, pp. 843–847.

Gardner, J. L.

J. L. Gardner, T. P. Jones, “Multi-wavelength radiation pyrometry where reflectance is measured to estimate emissivity,” J. Phys. E 13, 306–310 (1980).
[Crossref]

Iuchi, T.

T. Iuchi, “Radiation thermometry making use of specular reflection,” Trans. Soc. Instrum. Controlled Eng. 16, 233–238 (1980).

Jones, T. P.

J. L. Gardner, T. P. Jones, “Multi-wavelength radiation pyrometry where reflectance is measured to estimate emissivity,” J. Phys. E 13, 306–310 (1980).
[Crossref]

Kobayashi, M.

M. Kobayashi, M. Ohtsuki, H. Sakate, F. Sakuma, A. Ono, “Normal spectral emissivity of metal material,” National Research Laboratory of Metrology, 1-1-4, Umezone, Tsukuba, Ibaraki, 305-8563, Japan (personal communication, 1998).

Kosaka, T.

T. Makino, T. Kosaka, J. Arima, S. Aoyama, Y. Tsujimura, “A method for multi wavelength radiation pyrometry measuring emission and reflection simultaneously and remotely,” Trans. Soc. Instrum. Controlled Eng. 24, 331–336 (1988).

Li, C.

F. Sakuma, L. Ma, Y. Ohwada, C. Li, J. Wu, “Measurement of radiance temperature distribution of a comparison blackbody,” in Proceedings of the 38th SICE Annual Conference, July 28–30, 1999, Iwate University, Iwate, Japan, Domestic Session Papers Vol. 1, pp. 133–134 (in Japanese).

Ma, C. K.

Ma, L.

F. Sakuma, L. Ma, Y. Ohwada, C. Li, J. Wu, “Measurement of radiance temperature distribution of a comparison blackbody,” in Proceedings of the 38th SICE Annual Conference, July 28–30, 1999, Iwate University, Iwate, Japan, Domestic Session Papers Vol. 1, pp. 133–134 (in Japanese).

Makino, T.

T. Makino, T. Kosaka, J. Arima, S. Aoyama, Y. Tsujimura, “A method for multi wavelength radiation pyrometry measuring emission and reflection simultaneously and remotely,” Trans. Soc. Instrum. Controlled Eng. 24, 331–336 (1988).

Ohtsuki, M.

M. Kobayashi, M. Ohtsuki, H. Sakate, F. Sakuma, A. Ono, “Normal spectral emissivity of metal material,” National Research Laboratory of Metrology, 1-1-4, Umezone, Tsukuba, Ibaraki, 305-8563, Japan (personal communication, 1998).

Ohwada, Y.

Y. Ohwada, “Calculation of the effective emissivity of a cavity having non-Lambertian isothermal surfaces,” J. Opt. Soc. Am. A 16, 1059–1065 (1999).
[Crossref]

Y. Ohwada, “Influence of deviation from Lambertian reflectance on the effective emissivity of a cavity,” Metrologia 32, 713–716 (1996).
[Crossref]

Y. Ohwada, “A method for calculating the temperature variation along a cavity wall,” Meas. Sci. Technol. 2, 907–911 (1991).
[Crossref]

F. Sakuma, L. Ma, Y. Ohwada, C. Li, J. Wu, “Measurement of radiance temperature distribution of a comparison blackbody,” in Proceedings of the 38th SICE Annual Conference, July 28–30, 1999, Iwate University, Iwate, Japan, Domestic Session Papers Vol. 1, pp. 133–134 (in Japanese).

Ono, A.

M. Kobayashi, M. Ohtsuki, H. Sakate, F. Sakuma, A. Ono, “Normal spectral emissivity of metal material,” National Research Laboratory of Metrology, 1-1-4, Umezone, Tsukuba, Ibaraki, 305-8563, Japan (personal communication, 1998).

Reitz, K. P.

Rense, W. A.

W. A. Rense, “Polarization studies of light diffusely reflected from ground and etched surfaces,” J. Opt. Soc. Am. 57, 55–59 (1950).
[Crossref]

Sakate, H.

M. Kobayashi, M. Ohtsuki, H. Sakate, F. Sakuma, A. Ono, “Normal spectral emissivity of metal material,” National Research Laboratory of Metrology, 1-1-4, Umezone, Tsukuba, Ibaraki, 305-8563, Japan (personal communication, 1998).

Sakuma, F.

M. Kobayashi, M. Ohtsuki, H. Sakate, F. Sakuma, A. Ono, “Normal spectral emissivity of metal material,” National Research Laboratory of Metrology, 1-1-4, Umezone, Tsukuba, Ibaraki, 305-8563, Japan (personal communication, 1998).

F. Sakuma, L. Ma, Y. Ohwada, C. Li, J. Wu, “Measurement of radiance temperature distribution of a comparison blackbody,” in Proceedings of the 38th SICE Annual Conference, July 28–30, 1999, Iwate University, Iwate, Japan, Domestic Session Papers Vol. 1, pp. 133–134 (in Japanese).

Sparrow, E. M.

E. M. Sparrow, R. D. Cess, Radiation Heat Transfer (Hemispere, Washington, D.C., 1978).

Trowbridge, T. S.

Tsujimura, Y.

T. Makino, T. Kosaka, J. Arima, S. Aoyama, Y. Tsujimura, “A method for multi wavelength radiation pyrometry measuring emission and reflection simultaneously and remotely,” Trans. Soc. Instrum. Controlled Eng. 24, 331–336 (1988).

Wu, J.

F. Sakuma, L. Ma, Y. Ohwada, C. Li, J. Wu, “Measurement of radiance temperature distribution of a comparison blackbody,” in Proceedings of the 38th SICE Annual Conference, July 28–30, 1999, Iwate University, Iwate, Japan, Domestic Session Papers Vol. 1, pp. 133–134 (in Japanese).

Yamada, N.

N. Yamada, S. Fujimura, “Radiation thermometry for simultaneous measurement of temperature and emissivity,” in Temperature, Its Measurement and Control in Science and Industry, J. F. Schooley, ed. (American Institute of Physics, New York, 1992), Vol. 6, Part 2, pp. 843–847.

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (1)

J. Phys. E (1)

J. L. Gardner, T. P. Jones, “Multi-wavelength radiation pyrometry where reflectance is measured to estimate emissivity,” J. Phys. E 13, 306–310 (1980).
[Crossref]

Meas. Sci. Technol. (1)

Y. Ohwada, “A method for calculating the temperature variation along a cavity wall,” Meas. Sci. Technol. 2, 907–911 (1991).
[Crossref]

Metrologia (1)

Y. Ohwada, “Influence of deviation from Lambertian reflectance on the effective emissivity of a cavity,” Metrologia 32, 713–716 (1996).
[Crossref]

Trans. Soc. Instrum. Controlled Eng. (2)

T. Iuchi, “Radiation thermometry making use of specular reflection,” Trans. Soc. Instrum. Controlled Eng. 16, 233–238 (1980).

T. Makino, T. Kosaka, J. Arima, S. Aoyama, Y. Tsujimura, “A method for multi wavelength radiation pyrometry measuring emission and reflection simultaneously and remotely,” Trans. Soc. Instrum. Controlled Eng. 24, 331–336 (1988).

Other (4)

N. Yamada, S. Fujimura, “Radiation thermometry for simultaneous measurement of temperature and emissivity,” in Temperature, Its Measurement and Control in Science and Industry, J. F. Schooley, ed. (American Institute of Physics, New York, 1992), Vol. 6, Part 2, pp. 843–847.

F. Sakuma, L. Ma, Y. Ohwada, C. Li, J. Wu, “Measurement of radiance temperature distribution of a comparison blackbody,” in Proceedings of the 38th SICE Annual Conference, July 28–30, 1999, Iwate University, Iwate, Japan, Domestic Session Papers Vol. 1, pp. 133–134 (in Japanese).

E. M. Sparrow, R. D. Cess, Radiation Heat Transfer (Hemispere, Washington, D.C., 1978).

M. Kobayashi, M. Ohtsuki, H. Sakate, F. Sakuma, A. Ono, “Normal spectral emissivity of metal material,” National Research Laboratory of Metrology, 1-1-4, Umezone, Tsukuba, Ibaraki, 305-8563, Japan (personal communication, 1998).

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Figures (6)

Fig. 1
Fig. 1

Geometry of cavity dyO is the direction of the observation.

Fig. 2
Fig. 2

Temperature distributions a, b, and c along the cavity wall: (a) for the bottom and (b) for the side wall.

Fig. 3
Fig. 3

(a) Average difference ΔT¯ between temperature calculated for two wavelengths versus ε90, where ε65 and ε90 are intrinsic emissivities for λ=650 nm and λ=900 nm and (b) ε90 versus ε65, where ε90 gives the minimum value of ΔT¯ at a given ε65 value.

Fig. 4
Fig. 4

(a) Minimum average difference ΔT¯mi versus ε65 and (b) difference of temperature T¯(y) averaged over two wavelengths from the true temperature t(y) versus y. The true function of g(γ) is g(γ)=exp(-αγ2) with α=0.5; the true values of ε65 and ε90 are 0.90 and 0.85, respectively, δM<10-4, and l/r1=5.

Fig. 5
Fig. 5

Numerical results for δM<10-3. The other conditions for the calculation are the same as those for Fig. 4.

Fig. 6
Fig. 6

Numerical results for the experiment. (a) ΔT¯mi versus ε65 with radiance temperature measured on a commercially available cavity. The curves shown by the crosses and the solid line represent the case where ε(λ65, ϕ)=ε65 for ϕ80° and ε(λ65, ϕ) changes from ε65 to ε1 when ϕ changes from 80° to 90° with α=0.4. (b) |t(x)-T¯(y)|/t(y) versus y, where T¯(y) is rewritten calculated by assuming β=0.80 as t(y). The other conditions are the same as those for Fig. 4.

Tables (5)

Tables Icon

Table 1 Coefficients α and β of the Facet Distribution Function, ε65 and ε90 Giving the Smallest (ΔT¯mi)mi Value, and Calculated Temperature Accuracy with δM < 10-4

Tables Icon

Table 2 Same as Table 1 but for δM < 10-3, Where 0 < y < l

Tables Icon

Table 3 Change of (ΔT¯mi)mi/10-5, ε65, and ε90 with N for α = 0.4 and β = 0.8

Tables Icon

Table 4 Average Tλ(yi)¯ and Difference ΔTλ of Measured Radiance Temperatures Tλ(yi, xi) and Tλ(yi, -xi) and Average T(yi)¯ and Difference ΔT(yi) a

Tables Icon

Table 5 Uncertainty (°C) in the Radiance Temperature Measurements

Equations (30)

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Ek(λ, φi)=Mk(λ, φi)/b(λ, Tk(λ, yi))
fork0,i=1, 2,  , I,
b(λ, Tk(λ, yi))=m(λ, φi)/Ek-l(λ, φi)
fork1, i=1, 2,  , I,
Mk,j(λ, Ψi)=Mk,j-1(λ, Ψi)+ΔΦif(Ψi: Φi)×{[Mk,j-1(λ, Φi)-Mk,j-2(λ, Φi)]FdyiΔΦi,fork0, j2,i=1, 2,  , I,
Mk,0(λ, Ψi)=0fork0,
Mk,1(λ, Ψi)=ε(λ, Ψi)b(λ, Tk(λ, yi))fork0,
f(Φ : Ψ)=ρ(λ, Φ)g(γΦΨ)/G(sr-1),
ρ(λ, Φ)=1-ε(λ, Φ),
G=Ψg(γΦΨ)ΔωyΨ(sr),
m(λ, φi)=m(λ, φn)forxixn,zizn,
T(λa, y)=T(λb, y).
t(y)
=t0(1+2×10-3y/l1)for0yl1t(l1)+2.5×10-3t0{[l1-(l+l1)/2]2-[y-(l+l1)/2]2}/r12forlyl1,
g(γ)=exp(-αγ2)forα0β4/(β2 cos2 γ+sin2 γ)2forβ1 .
δM=|m(λ, φ)-Mk(λ, φ)|/m(λ, φ).
T¯(y)=[T(λ65, y)+T(λ90, y)]/2,
ΔT(y)=|T(λ65, y)-T(λ90, y)|/T¯(y).
ΔT¯=i=1NΔT(yi)/N,
t(y)
=t0(1-10-3y/l1)for0yl1t(l1)-0.25×10-3t0(y-l1)/r1forlyl1,
t(y)
 =t0(1-2×10-3y/l1)for0yl1t(l1)-5×10-3t0(y-l1)/r1forlyl1.
yi=4.33(i-1)l1/r1withi=1, 2,  , 7forthebottoml1+19.97(i-8)+0.05.withi=8, 9,  , 15forthesidewall
Tλ(yi)¯=[Tλ(xi, yi)+Tλ(xi, -yi)]/2,
ΔTλ(yi)=Tλ(xi, yi)-Tλ(xi, -yi).
ε(λ, ϕ)=ελforϕτ ,
ε(λ, ϕ)=aϕ+bforϕτ ,
a=(ε1-ελ)/(90°-τ),
b=(90°ελ-τε1)/(90°-τ).

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