We present a plenoptic microscopy configuration for 3D snapshot imaging, which is dual telecentric and can directly record true projection images corresponding with different viewing angles. It also allows blocking high-angle stray rays without sacrificing the light collection efficiency. This configuration named as snapshot projection optical tomography (SPOT) arranges an objective lens and a microlens array (MLA) in a 4-f telecentric configuration and places an aperture stop at the back focal plane of a relay lens. We develop a forward imaging model for SPOT, which can also be applied to existing light field microscopy techniques using an MLA as tube lens. Using the developed system, we demonstrate snapshot 3D imaging of various fluorescent beads and a biological cell, which confirms the capability of SPOT for imaging specimens with an extended fluorophore distribution as well as isolated fluorochromes. The transverse and vertical resolutions are measured to be 0.8 $μ$m and 1.6 $μ$m, respectively.