Abstract

The correct consideration of the index of refraction when using blackbody radiators as standard sources for optical radiation is derived and discussed. It is shown that simply using the index of refraction of air at laboratory conditions is not sufficient. A combination of the index of refraction of the media used inside the blackbody radiator and for the optical path between blackbody and detector has to be used instead. A worst case approximation for the introduced error when neglecting these effects is presented, showing that the error is below 0.1 % for wavelengths above 200 nm. Nevertheless, for the determination of the spectral radiance for the purpose of radiation temperature measurements the correct consideration of the refractive index is mandatory. The worst case estimation reveals that the introduced error in temperature at a blackbody temperature of 3000 °C can be as high as 400 mk at a wavelength of 650 nm and even higher at longer wavelengths.

© 2006 Optical Society of America

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References

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  1. B. Edlén, "The refractive index of air," Metrologia 2, 71-80 (1966).
    [CrossRef]
  2. K. P. Birch and M. J. Downs, "An updated Edlén equation for the refractive index of air," Metrologia 30, 155-162 (1993).
    [CrossRef]
  3. R. Muijlwijk, "Update of the Edlén formulae for the refractive index of air," Metrologia 25, 189 (1988).
    [CrossRef]
  4. K. P. Birch and M. J. Downs, "Correction to the updated Edlén equation for the refractive index of air," Metrologia 31, 315-316 (1994)
    [CrossRef]
  5. G Bönsch, and E Potulski, "Measurement of the refractive index of air and comparison with modified Edlén's formulae," Metrologia 35, 133-139 (1998).
    [CrossRef]
  6. T. Quinn, Temperature, 2nd ed., (Academic Press, London 1990).
  7. V. I. Sapritsky, B. B. Khlevnoy, V. B. Khromchenko, B. E. Lisiansky, S. N. Mekhontsev, U. A. Melenevsky, S. P. Morozova, A. V. Prokhorov, L. N. Samoilov, V. I. Shapoval, K. A. Sudarev and M. F. Zelener, "Precision blackbody sources for radiometric standards," Appl. Opt. 36, 5403-5408 (1997).
    [CrossRef] [PubMed]
  8. H. W. Yoon, C. E. Gibson, and J. L. Gardner, "Spectral radiance comparison of two blackbodies with temperatures determined using absolute detectors and ITS-90 techniques," in Temperature: Its Measurement and Control in Science and Industry, D C Ripple, ed., (AIP, New York, 2003) Vol. 7, pp. 601-606.
  9. K. Anhalt, J. Hartmann, D. Lowe, G. Machin, M. Sadli, and Y. Yamada, "Thermodynamic temperature determinations of Co-C, Pd-C, Pt-C and Ru-C eutectic fixed-points cells," Metrologia 43, S78-S83 (2006).
    [CrossRef]
  10. J. Hollandt, R. Friedrich, B. Gutschwager, D. Taubert, and J. Hartmann, "High-accuracy radiation thermometry at the National Metrology Institute of Germany, the PTB," High Temperatures - High Pressures 35/36, 379-415 (2005).
    [CrossRef]
  11. Y. Yamada, "Advances in high-temperature standards above 1000 °C," J. Metrol. Soc. India (India) 20, 183-191 (2005).

2006 (1)

K. Anhalt, J. Hartmann, D. Lowe, G. Machin, M. Sadli, and Y. Yamada, "Thermodynamic temperature determinations of Co-C, Pd-C, Pt-C and Ru-C eutectic fixed-points cells," Metrologia 43, S78-S83 (2006).
[CrossRef]

2005 (1)

Y. Yamada, "Advances in high-temperature standards above 1000 °C," J. Metrol. Soc. India (India) 20, 183-191 (2005).

1998 (1)

G Bönsch, and E Potulski, "Measurement of the refractive index of air and comparison with modified Edlén's formulae," Metrologia 35, 133-139 (1998).
[CrossRef]

1997 (1)

1994 (1)

K. P. Birch and M. J. Downs, "Correction to the updated Edlén equation for the refractive index of air," Metrologia 31, 315-316 (1994)
[CrossRef]

1993 (1)

K. P. Birch and M. J. Downs, "An updated Edlén equation for the refractive index of air," Metrologia 30, 155-162 (1993).
[CrossRef]

1988 (1)

R. Muijlwijk, "Update of the Edlén formulae for the refractive index of air," Metrologia 25, 189 (1988).
[CrossRef]

1966 (1)

B. Edlén, "The refractive index of air," Metrologia 2, 71-80 (1966).
[CrossRef]

Anhalt, K.

K. Anhalt, J. Hartmann, D. Lowe, G. Machin, M. Sadli, and Y. Yamada, "Thermodynamic temperature determinations of Co-C, Pd-C, Pt-C and Ru-C eutectic fixed-points cells," Metrologia 43, S78-S83 (2006).
[CrossRef]

Birch, K. P.

K. P. Birch and M. J. Downs, "Correction to the updated Edlén equation for the refractive index of air," Metrologia 31, 315-316 (1994)
[CrossRef]

K. P. Birch and M. J. Downs, "An updated Edlén equation for the refractive index of air," Metrologia 30, 155-162 (1993).
[CrossRef]

Bönsch, G

G Bönsch, and E Potulski, "Measurement of the refractive index of air and comparison with modified Edlén's formulae," Metrologia 35, 133-139 (1998).
[CrossRef]

Downs, M. J.

K. P. Birch and M. J. Downs, "Correction to the updated Edlén equation for the refractive index of air," Metrologia 31, 315-316 (1994)
[CrossRef]

K. P. Birch and M. J. Downs, "An updated Edlén equation for the refractive index of air," Metrologia 30, 155-162 (1993).
[CrossRef]

Edlén, B.

B. Edlén, "The refractive index of air," Metrologia 2, 71-80 (1966).
[CrossRef]

Hartmann, J.

K. Anhalt, J. Hartmann, D. Lowe, G. Machin, M. Sadli, and Y. Yamada, "Thermodynamic temperature determinations of Co-C, Pd-C, Pt-C and Ru-C eutectic fixed-points cells," Metrologia 43, S78-S83 (2006).
[CrossRef]

Khlevnoy, B. B.

Khromchenko, V. B.

Lisiansky, B. E.

Lowe, D.

K. Anhalt, J. Hartmann, D. Lowe, G. Machin, M. Sadli, and Y. Yamada, "Thermodynamic temperature determinations of Co-C, Pd-C, Pt-C and Ru-C eutectic fixed-points cells," Metrologia 43, S78-S83 (2006).
[CrossRef]

Machin, G.

K. Anhalt, J. Hartmann, D. Lowe, G. Machin, M. Sadli, and Y. Yamada, "Thermodynamic temperature determinations of Co-C, Pd-C, Pt-C and Ru-C eutectic fixed-points cells," Metrologia 43, S78-S83 (2006).
[CrossRef]

Mekhontsev, S. N.

Melenevsky, U. A.

Morozova, S. P.

Muijlwijk, R.

R. Muijlwijk, "Update of the Edlén formulae for the refractive index of air," Metrologia 25, 189 (1988).
[CrossRef]

Potulski, E

G Bönsch, and E Potulski, "Measurement of the refractive index of air and comparison with modified Edlén's formulae," Metrologia 35, 133-139 (1998).
[CrossRef]

Prokhorov, A. V.

Sadli, M.

K. Anhalt, J. Hartmann, D. Lowe, G. Machin, M. Sadli, and Y. Yamada, "Thermodynamic temperature determinations of Co-C, Pd-C, Pt-C and Ru-C eutectic fixed-points cells," Metrologia 43, S78-S83 (2006).
[CrossRef]

Samoilov, L. N.

Sapritsky, V. I.

Shapoval, V. I.

Sudarev, K. A.

Yamada, Y.

K. Anhalt, J. Hartmann, D. Lowe, G. Machin, M. Sadli, and Y. Yamada, "Thermodynamic temperature determinations of Co-C, Pd-C, Pt-C and Ru-C eutectic fixed-points cells," Metrologia 43, S78-S83 (2006).
[CrossRef]

Y. Yamada, "Advances in high-temperature standards above 1000 °C," J. Metrol. Soc. India (India) 20, 183-191 (2005).

Zelener, M. F.

Appl. Opt. (1)

J. Metrol. Soc. India (India) (1)

Y. Yamada, "Advances in high-temperature standards above 1000 °C," J. Metrol. Soc. India (India) 20, 183-191 (2005).

Metrologia (6)

K. Anhalt, J. Hartmann, D. Lowe, G. Machin, M. Sadli, and Y. Yamada, "Thermodynamic temperature determinations of Co-C, Pd-C, Pt-C and Ru-C eutectic fixed-points cells," Metrologia 43, S78-S83 (2006).
[CrossRef]

B. Edlén, "The refractive index of air," Metrologia 2, 71-80 (1966).
[CrossRef]

K. P. Birch and M. J. Downs, "An updated Edlén equation for the refractive index of air," Metrologia 30, 155-162 (1993).
[CrossRef]

R. Muijlwijk, "Update of the Edlén formulae for the refractive index of air," Metrologia 25, 189 (1988).
[CrossRef]

K. P. Birch and M. J. Downs, "Correction to the updated Edlén equation for the refractive index of air," Metrologia 31, 315-316 (1994)
[CrossRef]

G Bönsch, and E Potulski, "Measurement of the refractive index of air and comparison with modified Edlén's formulae," Metrologia 35, 133-139 (1998).
[CrossRef]

Other (3)

T. Quinn, Temperature, 2nd ed., (Academic Press, London 1990).

J. Hollandt, R. Friedrich, B. Gutschwager, D. Taubert, and J. Hartmann, "High-accuracy radiation thermometry at the National Metrology Institute of Germany, the PTB," High Temperatures - High Pressures 35/36, 379-415 (2005).
[CrossRef]

H. W. Yoon, C. E. Gibson, and J. L. Gardner, "Spectral radiance comparison of two blackbodies with temperatures determined using absolute detectors and ITS-90 techniques," in Temperature: Its Measurement and Control in Science and Industry, D C Ripple, ed., (AIP, New York, 2003) Vol. 7, pp. 601-606.

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Figures (2)

Fig. 1.
Fig. 1.

Refractive index of air a 1013 hPa, 0.03 % CO2 content and 50 % relative humidity.

Fig. 2.
Fig. 2.

Relative difference (solid line) between the spectral radiance of a blackbody radiator with the correct consideration of the medium with refractive index of unity inside and of ambient air outside [according Eq. (9)] with respect to the spectral radiance only considering the refractive index of the ambient air [according Eq. (5)]. Also shown is the resulting error (dashed line) in determining the radiance temperature of a blackbody at 3000 °C (a) overview, b) detail at short wavelengths; the arrow in the graphics indicates that the right ordinate is valid for the dashed line while the left ordinate is valid for the solid line).

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

L s , ν = 2 h n 2 c 2 ν 3 exp ( kT ) 1 .
c n = c n = νλ ,
ν = c
L s , ν = d L s = d L s = L s , ν , i . e L s , λ = L s , ν with
= c n λ 2 .
L s , λ = 2 h n 2 c 3 c 2 n 3 λ 3 exp ( hc k T ) 1 = 2 hc n λ 3 ( c n λ 2 ) exp ( hc k T ) 1 = 2 h c 2 n 2 λ 5 exp ( hc k T ) 1 .
L s , λ 0 = 2 h c 2 n 2 λ o 5 n 5 exp ( hc k n λ 0 n T ) 1 = 2 h n 3 c 2 λ 0 5 exp ( hc k λ 0 T ) 1 .
L s , λ = 2 h n 3 c 2 n amb 5 λ o 5 exp ( hc k n amb λT ) 1 = 2 h c 2 n amb 2 n amb 3 n 3 λ 5 exp ( hc k n amb λT ) 1 .
R = ( n amb n n amb + n ) 2 .
L s , λ = [ 1 ( n amb n n amb + n ) 2 ] n 3 n amb 3 2 h c 2 n amb 2 λ 5 exp ( hc k n amb λT ) 1 = a ( n amb , n ) 2 h c 2 n amb 2 λ 5 exp ( hc k n amb λT ) 1

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