  The technique of transmission spectroscopy -- the variation of the planetary
radius with wavelength due to opacity sources in the planet's terminator region
-- has been to date one of the most successful in the characterization of
exoplanet atmospheres, providing key insights into the composition and
structure of these distant worlds. A common assumption made when using this
technique, however, is that the variations are the same in the entire
terminator region. In reality, the morning and evening terminators might have
distinct temperature, pressure and thus compositional profiles due to the
inherent 3-D nature of the planet which would, in turn, give rise to different
spectra on each side of it. Constraining those might be fundamental for our
understanding of not only the weather patterns in these distant worlds, but
also of planetary formation signatures which might only be possible to extract
once these features are well understood. Motivated by this physical picture, in
this work we perform a detailed study on the observational prospects of
detecting this effect. We present an open-source semi-analytical framework with
which this information can be extracted directly from transit lightcurves, and
perform a detailed study on the prospects of detecting the effect with current
missions such as TESS and upcoming ones such as JWST. Our results show that
these missions show great promise for the detection of this effect.
Transmission spectroscopy studies with JWST, in particular, could provide
spectra of each of the limbs allowing us to convey 3-D information previously
accessible only via phase-curves.
