OSA's Digital Library

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)

View Full Text Article

Acrobat PDF (265 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



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.

W. MALKMUS, "Random Band Models with Lines of Pure Doppler Shape," J. Opt. Soc. Am. 58, 1214-1216 (1968)

Sort:  Author  |  Journal  |  Reset


  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.

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited