  Optical constants of non-stoichiometric amorphous magnesium-iron silicates
are determined. It is demonstrated that these can well reproduce the observed
mid-infrared emission spectra of evolved stars. Stoichiometric and
non-stoichiometric amorphous magnesium-iron silicate films are fabricated by
pulsed laser deposition. Transmittance and ellipsometry measurements are
performed in the wavelength range between 2 and 200 $\mu$m and 1.7 and 33
$\mu$m, respectively. Optical constants are derived from transmittance and
ellipsometric $\Psi$ and $\Delta$ spectra by means of oscillator models. The
optical constants are applied in radiative transfer models for examining
reproducibility of the observed spectral features of circumstellar dust shells
around supergiants. The spectra of four selected supergiants are dominated by
amorphous silicate dust emission in the wavelength range of 9 and 25 $\mu$m. To
obtain a good fit to the observed spectra, we take into account amorphous
corundum and metallic iron particles as additional dust components to account
for dust emission at $\lambda<8 \mu$m and in between the two silicate features.
For each of the objects, a set of model parameters (dust mass, condensation
temperature) is derived by an automated optimization procedure which well
reproduces the observation. Consequently, our model spectra using the new
optical data find that the silicate bands at $\approx 10$ and $\approx 18 \mu$m
depend on the magnesium and iron ratio in the silicate system, and that a good
fit requires a significant iron content of the amorphous silicate dust
component to reproduce the observed peak positions and shape of the silicate
bands.
