(a) Schematic of our excitation/detection scheme. Behind the dichroic beam splitter, the annular and polarizing beam splitters are used to detect three orientation-dependent components of fluorescence emission. (b) Sketch indicating the angles used in the text, the polar angle , the cutoff angle defined by the annular beam splitter, and the rim angle defined by the aperture angle of the microscope objective. [(c) and (d)] Sketch of the two limiting cases for the polar orientation, parallel or perpendicular to the optical axis of the microscope objective. (e) Contrast of the inclination as a function of the cutoff angle for a 1.2 NA water-immersion microscope objective. (f) Fluorescence intensities of a dipole emitter as a function of its polar angle detected in the low aperture region of the microscope objective (circles) and in the high aperture region (triangles), and the sum of both (squares).
Results of MC simulations of 3D orientation determination (see text for details). (a) Apparent polar angle vs input angle for two types of analysis: without (circles) and with (triangles) healing of invalid datasets. The percentage of invalid datasets is also plotted (squares). (b) Apparent azimuthal angle vs input angle with healing for different polar angles. The arrow indicates increasing polar angles (0°, 10°,…,90°), i.e., larger in-plane components of the emission dipole. A constant number of 500 photons per dataset was used throughout. [(c) and (d)] Influence of the number of photons per dataset on the reproducibility of the polar (c) and azimuthal (d) angles. The arrow indicates an exponential increase from 100 to 3200 photons per dataset. [(e) and (f)] Influence of background contribution on the reproducibility of the polar (e) and azimuthal (f) angles. The arrow indicates increasing background fraction from 0% to 100%.
Results of experiments with fluorescent latex beads. [(a) and (b)] Images representing color-coded polar (a) and azimuthal (b) angles. [(c) and (d)] Distributions of (c) polar and (d) azimuthal angles from datasets obtained from experimental (bars) and simulated (lines) photon streams from a bead centered in the laser focus. In the experiment, the integration time was with an average photon number of 150 photons per bin. The same number of detected photons per bin was achieved in the simulation using photons per dataset.
Results of experiments with single dye molecules (PMI) embedded in a poly(methylmetacrylate) film. [(a) and (b)] Color-coded images of (a) the polar and (b) the azimuthal angles. (c) Experimental and (d) accordingly simulated transient orientation of a single PMI molecule centered in the laser focus. The totally detected fluorescence intensity is also plotted showing single-step bleaching behavior for the PMI molecule. The integration time per bin was . [(e) and (f)] Distributions of (e) polar and (f) azimuthal angles from datasets obtained from the experimental (bars) and simulated (lines) transients [(c) and (d), respectively].
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