  We propose a new data analysis method for obtaining transmission spectra of
exoplanet atmospheres and brightness variation across the stellar disk from
transit observations. The new method is capable of recovering exoplanet
atmosphere absorption spectra and stellar specific intensities without relying
on theoretical models of stars and planets. We fit both stellar specific
intensity and planetary radius simultaneously directly to transit light curves.
This allows stellar models to be removed from the data analysis. Furthermore,
we use a data-quality weighted filtering technique to achieve an optimal
trade-off between spectral resolution and reconstruction fidelity homogenising
the signal to noise ratio across the wavelength range. Such approach is more
efficient than conventional data binning onto a low resolution wavelength grid.
We demonstrate that our analysis is capable of re-producing results achieved by
using explicit quadratic limb darkening equation, and that the filtering
technique helps eliminating spurious spectral features in regions with strong
telluric absorption. The method is applied to the VLT FORS2 observations of the
exoplanets GJ 1214 b and WASP-49 b, and our results are in agreement with
previous studies. Comparisons between obtained stellar specific intensity and
numerical models indicates that the method is capable of accurately
reconstructing the specific intensity. The proposed method enables more robust
characterization of exoplanetary atmospheres by separating derivation of
planetary transmission and stellar specific intensity spectra (that is
model-independent) from chemical and physical interpretation.
