  We prove that it is impossible to distinguish two spatially overlapping
fluorescent molecules from a single rotating molecule, even if one modulates
the polarization of pumping light or the detection dipole-spread function
(DSF). If the target is known to be a dipole pair, existing imaging methods
perform poorly for measuring their angular separation. We propose
simultaneously modulating the excitation polarization and DSF, which
demonstrates robust discrimination between dipole pairs versus single
molecules. Our method improves the precision of measuring centroid orientation
by 50% and angular separation by 4- to 6-fold over existing techniques.
