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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 66, Iss. 7 — Jul. 1, 1976
  • pp: 724–730

Emissivities of diffuse cavities. III. Isothermal and nonisothermal double cones

R. E. Bedford and C. K. Ma  »View Author Affiliations

JOSA, Vol. 66, Issue 7, pp. 724-730 (1976)

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Local hemispherical effective emissivities and integrated cavity emissivities are computed for isothermal and nonisothermal diffuse double cones (a conical section joined to a conical frustum) with and without lids, and are compared with corresponding values for cylindrocones. The local emissivities increase and become more uniform with increasing taper of the frustum. They are also considerably higher when there is a lid. For cavities with the same conical section, length, and aperture, a lidded double cone is blacker than a lidded cylindrocone when the front half of the frustum is invisible, but less black otherwise. For double cones of the same length, diameter, and aperture, the best choice of cone and frustum angles depends upon the particular viewing conditions. The integrated cavity emissivities vary only slightly with the angles of cone and frustum when the frustum is relatively long, and the normal emissivity (for a small on-axis detector a large distance away) is higher than the hemispherical emissivity (for a detector that fills the cavity aperture). When the frustum is relatively short, all of these vary substantially with angle, and the hemispherical emissivity can be higher than the normal emissivity. There is a marked variation of both local and integrated emissivities with wavelength in nonisothermal double cones; e.g., for the particular cases illustrated, the normal spectral emissivities change by from 4% to 6% and the hemispherical spectral emissivities by from 17% to 20% between 0.3 and 1 µm for a 1% temperature variation at 1300 K. The amount of the change in these spectral emissivities also depends upon the geometry of the cavity.

© 1976 Optical Society of America

R. E. Bedford and C. K. Ma, "Emissivities of diffuse cavities. III. Isothermal and nonisothermal double cones," J. Opt. Soc. Am. 66, 724-730 (1976)

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  1. R. E. Bedford and C. K. Ma, "Emissivities of diffuse cavities: Isothermal and nonisothermal cones and cylinders," J. Opt. Soc. Am. 64, 339–349 (1974). We have found the following errata in this paper: (i) In Eq. (7) the factor ½ [εa(zf+1) + εa(zf)] should appear inside the summation. (ii) In the equation near the bottom of p. 341, xm should be replaced by xn. (iii) In Eq. (9) the variables xi and xi+1 should be interchanged. (iv) Delete (0.65 µm) from the caption to Fig. 10.
  2. R. E. Bedford and C. K. Ma, "Emissivities of diffuse cavities. II: Isothermal and nonisothermal cylindro-cones," J. Opt. Soc. Am. 65, 565–572 (1975). We have found the following errata in this paper: (i) In Eq. (5) an addition sign (+) should appear immediately before the quantity [1 - ε(z,λ,Tz)]. (ii) The final term in the numerator of ƒi [following Eq. (5)] should contain cos2θ instead of cos3θ. (iii) The denominator of Eq. (7) should contain a factor 2.
  3. See, e.g., J. S. Toor, R. Viskanta, and E. R. F. Winter, "Radiant heat transfer between simply arranged surfaces with direct dependent properties," J. Spacecr. Rockets 7, 382–384 (1970). In a series of papers these authors have compared values of local irradiances predicted by diffuse, specular, and more complex models that take account of the directional characteristics of the surfaces. For closed systems the overall heat transfer was found not very sensitive to the choice of model. The largest differences in predictions occurred for open systems having highly reflecting surfaces and large temperature differences. These are just the opposite of the conditions of interest here. For experimental measurements Viskanta et al. used polished and roughened gold-plated surfaces arranged in open configurations and even then the results frequently agreed as well with the diffuse as with the other models. We conclude therefore that the diffuse model is likely to suffice for calculating effective emissivities of blackbody simulators.
  4. M. Eppley and A. R. Karoli, "Absolute radiometry based upon a change in electrical resistance," J. Opt. Soc. Am. 47, 748–755 (1957).
  5. J. M. Kendall and C. M. Berdahl, "Twoblackbody radiometers of high accuracy," Appl. Opt. 9, 1082–1091 (1970).
  6. R. P. Heinisch and R. N. Schmidt, "Development and application of an instrument for the measurement of directional emittance of blackbody cavities," Appl. Opt. 9, 1920–1925 (1970).
  7. R. J. Chandos and R. E. Chandos, "Radiometric properties of isothermal, diffuse wall cavity sources," Appl. Opt. 13, 2142–2152 (1974). Note that there are two typographical errors within the large square brackets in their Eq. (24).
  8. F. O. Bartell and W. L. Wolfe, "Cavity Radiation Theory," Infrared Phys. 16, 13–24 (1976).

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