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Applied Optics

Applied Optics


  • Vol. 13, Iss. 9 — Sep. 1, 1974
  • pp: 2142–2152

Radiometric Properties of Isothermal, Diffuse Wall Cavity Sources

Raymond J. Chandos and Robert E. Chandos  »View Author Affiliations

Applied Optics, Vol. 13, Issue 9, pp. 2142-2152 (1974)

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Total radiant power emission from various diffuse wall cavity sources is calculated without approximation. In addition, a useful radiometric quantity, O-d, the fraction of blackbody power received by a distant viewer, is precisely defined and calculated. Extensive tabulation of numerical results and tutorial background are included. A new method, faster and more accurate than traditional quadrature methods, for the numerical solution of integral equations is described in an appendix. Results are applied to the practical problems of cavity design and analysis.

© 1974 Optical Society of America

Original Manuscript: January 1, 1971
Revised Manuscript: May 6, 1974
Published: September 1, 1974

Raymond J. Chandos and Robert E. Chandos, "Radiometric Properties of Isothermal, Diffuse Wall Cavity Sources," Appl. Opt. 13, 2142-2152 (1974)

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  1. M. W. Zemansky, Heat and Thermodynamics (McGraw-Hill, New York, 1951).
  2. … on a magnitude scale of about one wavelength.
  3. See Ref. 4 for a more rigorous proof of Eq. (8).
  4. M. Planck, The Theory of Heat Radiation (Dover, New York, 1959).
  5. F. E. Nicodemus, Appl. Opt. 4, 768 (1965). [CrossRef]
  6. Radiation entering the cavity from outside is neglected.
  7. M. L. Fecteau, Appl. Opt. 7, 1359 (1968). [CrossRef]
  8. A. Gouffe, Rev. Opt. 24 (1–3) (1945).
  9. See Ref. 10 for an alternate method based on angle factor algebra.
  10. E. M. Sparrow, V. K. Jonsson, J. Opt. Soc. Am. 53, 816 (1963). [CrossRef]
  11. All numerical values reported in the present work were computed independently. Although an iterative procedure was used as in Ref. 10, improved accuracy was obtained by (1) progressively increasing the number of subdivisions of the interval [0, L] until acceptable convergence occurred; (2) replacing the numerical quadrature of Ref. 10 with a more accurate integration technique especially suited to the weakly singular integrands under consideration (see Appendix); (3) using the exact analytical expression of Kelly (see Ref. 15) for ∊a(ξ = 0).
  12. The numerical quadrature used in Refs. 13 and 14 leads to some inaccuracy near x = 0. See Appendix.
  13. E. M. Sparrow, L. U. Albers, E. R. G. Eckert, J. Heat Transfer Trans. ASME Ser. C 84, 73 (1962). [CrossRef]
  14. E. M. Sparrow, R. P. Heinisch, Appl. Opt. 9, 2569 (1970). [CrossRef] [PubMed]
  15. F. J. Kelly, Appl. Opt. 5, 925 (1966). [CrossRef] [PubMed]
  16. For the cylindrical cavity, Sparrow and Heinisch have shown that receiver size has no significant effect on ∊o-d for d > 10R. See Ref. 14.
  17. This expression can be obtained by actually carrying out the two integrations or, more elegantly, by the methods of angle factor algebra as outlined in Ref. 13.
  18. It should be noted that ∊O-O = PO/AOWB, where AO = area of the cavity opening.
  19. See Ref. 20, Chap. 6.
  20. E. M. Sparrow, R. D. Cess, Radiation Heat Transfer (Brooks/Cole, Belmont, Calif., 1966).
  21. F. O. Bartell, W. L. Wolfe, Minutes of the Meeting of the IRIS Specialty Group on I.R. Standards 28 (Aug.1972).
  22. K. E. Atkinson, SIAM J. Numerical Anal. 4, 337 (1967). [CrossRef]

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