|Plenoptic particle image velocimetry (PIV) was used to perform instantaneous three-dimensional (3D) velocity measurements in the near-wake of a wall-mounted hemispherical roughness element at a Reynolds number (based on roughness height) of 4.57 X 10^3 and boundary layer to roughness height-ratio of 4.67. The experiment was performed in a refractive index matched flow facility to mitigate laser reflections from the hemispherical surface. Data gathered from this experiment represents one of the first applications of plenoptic PIV. The time-average flow is characterized by a separated shear layer off of the hemisphere, a symmetric recirculation region, and an arch-shaped vortex. In the instantaneous 3D velocity fields, a separated boundary layer and recirculation region with asymmetric characteristics are present. Additionally, arch vortices are found that are both attached and detached to the hemispherical surface, similar to previously studied recirculation arch (RA) vortices. The proper orthogonal decomposition (POD) was applied to both the 3D velocity and 3D vorticity fields. Velocity modes produced features associated with the overall flow whereas vorticity modes produced features associated with the wake. The most energetic POD modes confirm the fluctuations in the boundary layer and recirculation region, as well as suggest the existence of shed arch-shaped vortices.