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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 58, Iss. 9 — Sep. 1, 1968
  • pp: 1214–1216

Random Band Models with Lines of Pure Doppler Shape

W. MALKMUS  »View Author Affiliations


JOSA, Vol. 58, Issue 9, pp. 1214-1216 (1968)
http://dx.doi.org/10.1364/JOSA.58.001214


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Abstract

The behavior of random band models composed of lines of pure Doppler shape for several irradiance distribution functions is investigated. The particular irradiance distribution functions chosen are: (1) constant irradiance, (2) exponential distribution, (3) truncated S-1 distribution, and (4) the exponential-tailed S-1 distribution. The curves of growth for the first two models are found to have the asymptotic (log) ½behavior characteristic of an isolated Doppler line while the latter two models show a (log)½ dependence.

Citation
W. MALKMUS, "Random Band Models with Lines of Pure Doppler Shape," J. Opt. Soc. Am. 58, 1214-1216 (1968)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-58-9-1214


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References

  1. W. Malkmus, J. Opt. Soc. Am. 57, 323 (1967).
  2. A. Unsöld, Astrophys. J. 69, 214 (1929).
  3. O. Struve and C. T. Elvey, Astrophys. J. 79, 409 (1934).
  4. S. S. Penner, Quantitative Molecular Spectroscopy and Gas Emissivities (Addison-Wesley Publishing Company, Inc., Reading, Mass., 1959), p. 39. 1214
  5. This result could have been obtained directly from the general expression [R. M. Goody, Atmospheric Radiation. I. Theoretical Basis, (Oxford University Press, London, 1964), p. 133] for a random band model consisting of lines of arbitrary normalized contour f(ω) having an exponential irradiance distribution [Eq. (18)] W¯/d=(1/d) ∫-∞S0f(ω)u[1+S0f(ω)u]-1dω.
  6. This result is also derivable directly from a general expression given by C. D. Rodgers (private communication) for a random band model consisting of lines of arbitary normalized contour f(ω) having an exponential-tailed S-1 irradiance distribution [Eq. (34), R large] W¯/d=(1/d lnR) ∫-∞ ln[1+SMƒ(ω)u]dω.

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