  Direct imaging of widely separated exoplanets from space will obtain their
reflected light spectra and measure their atmospheric properties, and small and
temperate planets will be the focus of the next generation telescopes. In this
work, we used our Bayesian retrieval algorithm ExoReL$^{\Re}$ to determine the
constraints on the atmospheric properties of sub-Neptune planets from
observations taken with a HabEx-like telescope. Small and temperate planets may
have a non-H$_2$-dominated atmosphere, and therefore, we introduced the
compositional analysis technique in our framework to explore the bulk
atmospheric chemistry composition without any prior knowledge about it. We have
developed a novel set of prior functions for the compositional analysis free
parameters. We compared the performances of the framework with the flat prior
and the novel prior and we reported a better performance when using the novel
priors set. We found that the retrieval algorithm can not only identify the
dominant gas of the atmosphere but also to constraint other less abundant gases
with high statistical confidence without any prior information on the
composition. The results presented here demonstrates that reflected light
spectroscopy can characterize small exoplanets with diverse atmospheric
composition. The Bayesian framework should be applied to design the instrument
and the observation plan of exoplanet direct imaging experiments in the future.
