Results of the same rotational random walk simulations used for Figure 2 using the photons collected in each channel with no corrections – no threshold selection was used, the intensity distribution was not broadened, and no noise was added (see Materials and methods). The contributions of each of these experimentally determined conditions on <p> and Var(p) are more explicitly illustrated in Figure 2—figure supplement 4. The five rotational diffusion regimes (identified in (A) and (C)) are characterized as follows. (Regime I – very fast rotation) During the excited state of the fluorophore, the transition dipole orientation is virtually completely randomized. All measurements of p from collecting hundreds of photons are therefore close to 0 for each molecule, and hence, the polarization histograms are narrowly centered around 0 for both excitation modes. (Regime II – fast rotation) The fluorescent particle rotates significantly during its fluorescence lifetime, but the dipole orientation when excited influences the direction (polarization) of the observed emission. Thus, emission is preferentially observed toward the direction of linearly polarized excitation. However, the transition dipole is completely randomized between excitation events. Therefore, polarizations measured using circularly polarized excitation remain closely centered around 0. (Regime III – moderate rotation) The fluorescent particle does not rotate significantly during its fluorescence lifetime, and thus, linear excitation leads to strongly biased emission, with <p>lin ≈ 0.4. However, the transition dipole is essentially completely randomized between excitation events, and therefore, measured polarizations using circular excitation are closely centered around 0. (Regime IV – slow rotation) The transition dipole rotates between excitation events, but does not get completely randomized. Thus, individual polarization measurements are broadly distributed, with a width determined by the relationship between τ (is this the correct greek letter "tau"?) and Dr. (Regime V – very slow rotation) The transition dipole does not rotate significantly between excitation events. This time regime corresponds to particles that are essentially ‘stuck’, and returns all polarizations for a particle randomly oriented in three-dimensions. The threshold significantly affects <p> and Var(p) under conditions where the molecules are essentially immobile (regime V). Under circularly polarized excitation, dipoles having a large axial component are largely invisible when there is a 100 photon threshold due to the low excitation probability by the beam propagating in the z-direction. This causes a central dip in the histogram for Dr = 0.1 rad2/s with circular excitation (observed in Figure 2D, black, but not here in (D), due to the absence of a threshold), which increases Var(p)cir (compare (C) with Figure 2C). With linearly x-polarized excitation under low Dr conditions, molecules with negative polarizations are largely undetectable when there is a 100 photon threshold due to inefficient excitation (compare (B), black, with Figure 2B). The consequences of this threshold are an increase in <p> and a decrease in Var(p) (compare (A) with Figure 2A).