Emissions from polarized excitations and the numerical aperture. (A) Emission pattern from a fluorophore dipole located in water at z = 0 nm distance from a glass substrate. The fluorophore is shown as a small circle. The pattern is derived from the equations in Hellen and Axelrod (1987). The intensity into any polar angle is depicted as the radial distance from the dipole to the end of the shaded pattern; the gray horizontal stripe pattern and the uniform gray pattern indicates the emission from a dipole parallel and perpendicular to the surface, respectively. See Results for explanation. (B) Effect of objective NA on the collection efficiency for perpendicular and parallel dipole orientation. The relative amount of light captured from dipoles oriented parallel versus perpendicular to the substrate depends strongly on the objective NA and on distance z. These dependencies are shown in graphs of Q_┴/Q_‖ versus z for several different popular NAs. Objective-based TIR illumination requires an NA of at least 1.45; it is those objectives that show Q_┴/Q_‖ close to unity, with some undulations as a function of z. The 1.49 NA shows the smallest deviation from unity over the whole range of z distances and allows the conclusion that P+2S is a fairly good measure of total concentration. The 1.65 NA must use refractive index 1.78 (rather than 1.52) coverslip and oil, so the distortion of the emission pattern (as a result of near-field capture) is the strongest for that objective.