This thesis is part of larger survey conducted using the OSIRIS IFU on the W. M. Keck Telescope to directly image exoplanets. I begin this publication with an overview of direct detection and characterization of exoplanets, the current key scientific questions plaguing the field such as the formation of these objects and how they are distinct from low-mass brown dwarfs, and my contributions using OSIRIS. OSIRIS is an ideal instrument for this type of imaging; an integral field spectrograph (IFU) allows us to distinguish scattered starlight and speckle artifacts from the planet itself. OSIRIS observations of directly imaged planets have greatly improved our understanding of their atmospheres, hinted at formation pathways, and, with sufficient SNR, can reveal individual molecular lines.
The three substellar companions were observed, spectrally extracted, and atmospherically characterized with OSIRIS in K-band (~2.2 um) -- kappa And b, VHS 1256 b, and HD 284149 b. The R~4,000 spectra were analyzed via a forward modeling framework with custom PHOENIX atmosphere models and Husser et al. 2013 models. This framework allowed for the derivation of effective temperatures, surface gravities, metallicities, and carbon and oxygen abundances. In particular, the C/O ratio was derived for each source as a possible formation tracer diagnostic.
Finally, this thesis analyzed the C/O ratio formation tracer. Directly imaged planets remain a mystery for the two main formation pathways--core accretion/pebble accretion. It was believed an elevated C/O ratio would point towards formation via core accretion, and a stellar C/O ratio would insinuate formation through gravitational instability. The C/O ratios of the planets in this thesis, as well as the C/O ratios from other works show that all directly imaged planets have stellar C/O. A small fraction of transit/eclipse planets also have derived C/O ratios, thus they were compared to the directly imaged planet C/O ratios against various system parameters. A trend was revealed between companion mass and the C/O ratio, which showed that there may be two distinct populations of exoplanets with possible different formation mechanisms. This thesis expresses a need for new formation diagnostics, a more in depth study into why the directly imaged planet population have the same C/O ratios, and more analyses that span across the different exoplanet populations.