  Gravitational microlensing is a powerful tool to probe the inner structure of
strongly lensed quasars and to constrain parameters of the stellar mass
function of lens galaxies. This is done by analysing microlensing light curves
between the multiple images of strongly lensed quasars, under the influence of
three main variable components: 1- the continuum flux of the source, 2-
microlensing by stars in the lens galaxy and 3- reverberation of the continuum
by the Broad Line Region (BLR). The latter, ignored by state-of-the-art
microlensing techniques, can introduce high-frequency variations which we show
carry information on the BLR size. We present a new method which includes all
these components simultaneously and fits the power spectrum of the data in the
Fourier space, rather than the observed light curve itself. In this new
framework, we analyse COSMOGRAIL light curves of the two-image system
QJ0158-4325 known to display high-frequency variations. Using exclusively the
low frequency part of the power spectrum our constraint on the accretion disk
radius agrees with the thin disk model estimate and previous work that fit the
microlensing light curves in real space. However, if we also take into account
the high-frequency variations, the data favour significantly smaller disk sizes
than previous microlensing measurements. In this case, our results are in
agreement with the thin disk model prediction only if we assume very low mean
masses for the microlens population, i.e. <M> = 0.01 $M_\odot$. Eventually,
including the differentially microlensed continuum reverberation by the BLR
successfully explains the high frequencies without requiring such low mass
microlenses. This allows us to measure, for the first time, the size of the BLR
using single-band photometric monitoring, $R_{BLR}$ = $1.6^{+1.5}_{-0.8}\times
10^{17}$cm, in agreement with estimates using the BLR size-luminosity relation.
