  Stellar population models of absorption line indices are an important tool
for the analysis of stellar population spectra. They are most accurately
modelled through empirical calibrations of absorption line indices with the
stellar parameters effective temperature, metallicity, and surface gravity, the
so-called fitting functions. Here we present new empirical fitting functions
for the 25 optical Lick absorption line indices based on the new stellar
library MILES. The major improvements with respect to the Lick/IDS library are
the better sampling of stellar parameter space, a generally higher signal-
to-noise, and a careful flux calibration. In fact we find that errors on
individual index measurements in MILES are considerably smaller than in
Lick/IDS. Instead we find the rms of the residuals between the final fitting
functions and the data to be dominated by errors in the stellar parameters. We
provide fitting functions for both Lick/IDS and MILES spectral resolutions, and
compare our results with other fitting functions in the literature. A Fortran
90 code is available online in order to simplify the implementation in stellar
population models. We further calculate the offsets in index measurements
between the Lick/IDS system to a flux calibrated system. For this purpose we
use the three libraries MILES, ELODIE, and STELIB. We find that offsets are
negligible in some cases, most notably for the widely used indices Hbeta, Mgb,
Fe5270, and Fe5335. In a number of cases, however, the difference between flux
calibrated library and Lick/IDS is significant with the offsets depending on
index strengths. Interestingly, there is no general agreement between the three
libraries for a large number of indices, which hampers the derivation of a
universal offset between the Lick/IDS and flux calibrated systems.
