Rendering participating media requires significant computation, but the effect of volumetric scattering is often eventually smooth. This article proposes an innovative analysis of absorption and scattering of local light fields in the Fourier domain and derives the corresponding set of operators on the covariance matrix of the power spectrum of the light field. This analysis brings an efficient prediction tool for the behavior of light along a light path in participating media. We leverage this analysis to derive proper frequency prediction metrics in 3D by combining per-light path information in the volume. We demonstrate the use of these metrics to significantly improve the convergence of a variety of existing methods for the simulation of multiple scattering in participating media. First, we propose an efficient computation of second derivatives of the fluence, to be used in methods like irradiance caching. Second, we derive proper filters and adaptive sample densities for image-space adaptive sampling and reconstruction. Third, we propose an adaptive sampling for the integration of scattered illumination to the camera. Finally, we improve the convergence of progressive photon beams by predicting where the radius of light gathering can stop decreasing. Light paths in participating media can be very complex. Our key contribution is to show that analyzing local light fields in the Fourier domain reveals the consistency of illumination in such media and provides a set of simple and useful rules to be used to accelerate existing global illumination methods.