I mean, would we be able to know in detail the composition of the atmosphere, or would we just be able to tell, for example, whether or not there's some oxygen in it?
According to the TPF site:
Does this represent about the limit of presently plausible technology or could we get more detailed information on things like the amount of oxygen in an exoplanet's atmosphere?JPL wrote:The oxygen and ozone absorption features in the visible and thermal infrared respectively could indicate the presence of photosynthetic biological activity on Earth anytime during the past 50% of the age of the solar system. In the Earth's atmosphere, the 9.6 µm ozone band is a poor quantitative indicator of the oxygen amount, but an excellent qualitative indicator for the existence of even traces of oxygen. The ozone 9.6 µm band is a very nonlinear indicator of oxygen for two reasons. First, for the present atmosphere, low resolution spectra of this band show little change with the ozone abundance because it is strongly saturated. Second, the apparent depth of this band remains nearly constant as oxygen increases from 0.01 times the present atmosphere level of oxygen (PAL) to 1 PAL.