  Optical absorption in rhombohedral BiFeO$_3$ starts at photon energies below
the photoemission band gap of $\approx$ 3 eV calculated from first principles.
A shoulder at the absorption onset has so far been attributed to low-lying
electronic transitions or to oxygen vacancies. In this work optical spectra are
calculated ab initio to determine the nature of the optical transitions near
the absorption onset of pristine BiFeO$_3$, the effect of electron-hole
interaction, and the spectroscopic signatures of typical defects, i.e. doping
(excess electrons or holes), intrinsic defects (oxygen and bismuth vacancies),
and low-energy structural defects (ferroelectric domain walls).
