A phase mask design that we term a "bisected pupil" (BSP) provides several advantages for single-molecule optical imaging. When using the BSP with a dual-polarization optical Fourier processing system, both the position and dipole orientation of individual fluorescent molecules may be measured from a single camera image. In the context of single-molecule super-resolution microscopy, this technique permits one to diagnose, and subsequently to remove imaging artifacts resulting from orientation-induced localization errors. If the molecules labeling a structure are rotationally mobile, thus mitigating dipole orientation errors, this technique enables super-resolution imaging in three dimensions. We present simulations and experimental verification.