  We investigate rotational diffusion of fluorescent molecules in angular
potential wells, the excitation and subsequent emissions from these diffusing
molecules, and the imaging of these emissions with high-NA aplanatic optical
microscopes. Although dipole emissions only transmit six low-frequency angular
components, we show that angular structured illumination can alias higher
frequency angular components into the passband of the imaging system. We show
that the number of measurable angular components is limited by the
relationships between three time scales: the rotational diffusion time, the
fluorescence decay time, and the acquisition time. We demonstrate our model by
simulating a numerical phantom in the limits of fast angular diffusion, slow
angular diffusion, and weak potentials.
