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)