  The mean-free path (MFP) accumulation function for the effective thermal
conductivity, introduced by Dames and Chen is a compact, universal and highly
useful summary of the effect of ballistic thermal transport on the effective
thermal conductivity measured by various experiments. The frequency domain
thermoreflectance (FDTR) experiment is especially well suited to its
determination. Extraction of the accumulation function from this experiment
uses the thermal penetration depth (TPD) of phonons at each frequency as a
cut-off for classifying phonons as ballistic or diffusive at that frequency. In
this paper, we show that using the TPD as a cut-off is arbitrary and prone to
serious error. We report on a new technique to deduce the MFP accumulation
function from the FDTR experiment by numerical solution of an enhanced Fourier
law.
