  A space telescope capable of high-contrast imaging has been recognized as the
avenue toward finding terrestrial planets around nearby Sun-like stars and
characterizing their potential habitability. It is thus essential to quantify
the capability of reflected light spectroscopy obtained through direct imaging
for terrestrial exoplanets, and existing work focused on planetary analogs of
modern Earth. Here we go beyond Earth analogs and use a Bayesian retrieval
algorithm, ExoReL$^\Re$, to determine what we could learn about terrestrial
exoplanets from their reflected light spectra. Recognizing the potential
diversity of terrestrial exoplanets, our focus is to distinguish atmospheric
scenarios without any a priori knowledge of the dominant gas. We find that,
while a moderate-resolution spectrum in the optical band ($0.4-1.0\ \mu$m) may
sufficiently characterize a modern Earth analog, it would likely result in
incorrect interpretation for planets similar to Archean Earth or having
CO$_2$-dominated atmospheres. Including observations in the near-infrared bands
($1.0-1.8\ \mu$m) can prevent this error, determine the main component (N$_2$,
O$_2$, or CO$_2$), and quantify trace gases (H$_2$O, O$_3$, and CH$_4$) of the
atmosphere. These results are useful to define the science requirements and
design the wavelength bandwidth and observation plans of exoplanet direct
imaging missions in the future.
