The imaginary part of the dielectric function of zinc-blende and wurtzite I
nN has been calculated using a full-potential linearized augmented plane wa
ve method. We show that the exchange potential of Engel and Vosko gives an
insulating ground state for both structures. The real part of the dielectri
c function has been obtained from the Kramers-Kronig dispersion relations,
assuming a quasiparticle band-gap correction according to Bechstedt and Del
Sole. We have found that it is necessary to have a good account of the ban
d gap in order to derive the low-frequency optical properties. We present t
he longitudinal as wen as the transverse components in wurtzite InN, showin
g that the anisotropy is small.