A recurrent suggestion in the literature is that the spatial variability of cloud might best be studied through the power spectrum of the cloud field. In this paper this proposal is examined in the context of radiative transfer by broken cloud. Through the analysis of numerical models in one and two dimensions, three conclusions are drawn: (1) Fields with the same power spectrum may transmit different average fluxes, so the power spectrum alone does not determine the radiative transfer. (2) The power spectrum of both the models and real cloud fields (advanced very high resolution radiometer satellite images) oscillate so rapidly that quantitative analysis of the power spectrum is very sensitive to the manner in which the power spectrum is sampled. The most stable analysis of the power spectrum involves integration over all spatial frequencies. It will be shown how this procedure permits the calculation of infrared transfer in a one-dimensional cloud model. (3) A proposal for a satellite-mounted optical Fourier analyzer is examined, and it is shown that while such an instrument eliminates aliasing and computational restraints, the need to compress the data by logarithmic sampling of the power spectrum impairs the resolution of the correlation function of the cloud field. Furthermore, the degradation of the resolution increases with the correlation length. ¿American Geophysical Union 1987