The transmission of a randomly spaced array of Lorentz lines whose intensities are exponentially distributed may be simply corrected for doppler effects. Evaluation of the correction exponent requires an integration over the Voigt line profile, which may be done once and for all. The integration is described and results presented in a table. From these results, the mean curve of growth of a single Voigt line in such an array may easily be calculated. Curtis’ approximation, applied to such a band, gives equivalent widths several tens of percent too large in many situations.
John C. Gille and Robert G. Ellingson, "Correction of Random Exponential Band Transmissions for Doppler Effects," Appl. Opt. 7, 471-474 (1968)