Optimising Blackbody Cavity Shape for Spatially Uniform Integrated Emissivity

  • P. SaundersEmail author
Part of the following topical collections:
  1. TEMPMEKO 2016: Selected Papers of the 13th International Symposium on Temperature, Humidity, Moisture and Thermal Measurements in Industry and Science


The emissivity of a blackbody cavity, as seen by a radiation thermometer viewing the cavity, depends on both the field of view of the thermometer and the distribution of local effective emissivity values within the field of view. For cylindro-conical cavities, the local effective emissivity generally attains a maximum value at the apex of the cone and drops along the conical section. Thus, radiation thermometers with different fields of view see different blackbody emissivity values. This impacts, particularly, on the calibration of wide-angle low-temperature radiation thermometers and thermal imaging systems where each pixel responds to a different radiance. The spatial uniformity of the effective emissivity profile depends principally on the cone angle, with a weaker dependence on the length-to-diameter ratio of the cavity, the intrinsic emissivity of the cavity surfaces, and the temperature gradient along the cavity. In this paper, a nonlinear least-squares method is used to determine the optimal cone angle as a function of the cavity parameters. It is concluded that full cone angles close to 160\({^{\circ }}\) provide the flattest effective emissivity profile across the conical section of the cavity for typical cavity parameters. A method is also described for calculating the value of integrated emissivity, which includes the umbral and penumbral regions seen by an imaging radiation thermometer.


Blackbody cavity Blackbody emissivity Integrated emissivity Penumbra Umbra 


  1. 1.
    R.E. Bedford, C.K. Ma, J. Opt. Soc. Am. 65, 565 (1975)ADSCrossRefGoogle Scholar
  2. 2.
    S. Chen, Z. Chu, H. Chen, Metrologia 16, 69 (1979)Google Scholar
  3. 3.
    A. Ono, in Temperature: Its Measurement and Control in Science and Industry, vol. 5, ed. by J.F. Schooley (AIP, New York, 1982), pp. 513–516Google Scholar
  4. 4.
    V.I. Sapritsky, A.V. Prokhorov, Metrologia 29, 9 (1992)ADSCrossRefGoogle Scholar
  5. 5.
    V.I. Sapritsky, A.V. Prokhorov, Appl. Opt. 34, 5645 (1995)ADSCrossRefGoogle Scholar
  6. 6.
    A.V. Prokhorov, Metrologia 35, 465 (1998)ADSCrossRefGoogle Scholar
  7. 7.
    A.V. Prokhorov, L.M. Hanssen, Metrologia 41, 421 (2004)ADSCrossRefGoogle Scholar
  8. 8.
    J. De Lucas, Int. J. Thermophys. 36, 267 (2015)ADSCrossRefGoogle Scholar
  9. 9.
    R.E. Bedford, C.K. Ma, J. Opt. Soc. Am. 64, 339 (1974)ADSCrossRefGoogle Scholar
  10. 10.
    R.E. Bedford, C.K. Ma, J. Opt. Soc. Am. 66, 724 (1976)ADSCrossRefGoogle Scholar
  11. 11.
    Y. Ohwada, in Temperature: Its Measurement and Control in Science and Industry, vol. 5, ed. by J.F. Schooley (AIP, New York, 1982), pp. 517–519Google Scholar
  12. 12.
    R.E. Bedford, C.K. Ma, Z. Chu, Y. Sun, S. Chen, Appl. Opt. 24, 2971 (1985)ADSCrossRefGoogle Scholar
  13. 13.
    Y. Ohwada, Jpn. J. Appl. Phys. 23, L167 (1984)ADSCrossRefGoogle Scholar
  14. 14.
    Z. Chu, R.E. Bedford, W. Xu, X. Liu, Appl. Opt. 28, 1826 (1989)ADSCrossRefGoogle Scholar
  15. 15.
    W.H. Press, B.R. Flannery, S.A. Teukolsky, W.T. Vettering, Numerical Recipes (Cambridge University Press, Cambridge, 1986)zbMATHGoogle Scholar
  16. 16.
    J. De Lucas, Metrologia 51, 402 (2014)ADSCrossRefGoogle Scholar
  17. 17.
    C.K. Ma, R.E. Bedford, Rev. Sci. Instrum. 63, 3213 (1992)ADSCrossRefGoogle Scholar
  18. 18.
    P. Saunders, Callaghan Innovation Report 18 (2016)Google Scholar
  19. 19.
    J. De Lucas, Private communication (2016)Google Scholar
  20. 20.

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Measurement Standards Laboratory of New ZealandLower HuttNew Zealand

Personalised recommendations