  We present a compelling evidence for the opening of a bandgap in exfoliated
bottom-gated bilayer graphene by fitting the gate-voltage modulated infrared
reflectivity spectra in a large range of doping levels with a tight-binding
model and the Kubo formula. A close quantitative agreement between the
experimental and calculated spectra is achieved, allowing us to determine
self-consistently the full set of Slonczewski-Weiss-McClure tight-binding
parameters together with the gate-voltage dependent bandgap. The doping
dependence of the bandgap shows a good agreement with the existing calculations
that take the effects of self-screening into account. We also identify certain
mismatches between the tight-binding model and the data, which can be related
to electron-electron and electron-phonon interactions.
