A volume hologram has two degenerate Bragg-phase-matching dimensions and provides the capability of volume holographic imaging. We demonstrate two volume holographic imaging architectures and investigate their imaging resolution, aberration, and sensitivity. The first architecture uses the hologram directly as an objective imaging element where strong aberration is observed and confirmed by simulation. The second architecture uses an imaging lens and a transmission geometry hologram to achieve linear two-dimensional optical sectioning and imaging of a four-dimensional (spatial plus spectral dimensions) object hyperspace. Multiplexed holograms can achieve simultaneously three-dimensional imaging of an object without a scanning mechanism. © 2004 Optical Society of America.