Point spread functions for four fixed fluorophores with different spatial orientations. (**a–d**): Fixed rhodamine molecules were imaged as described in **Methods**. (**e–h**): MLEwT applied to fixed probes (**a–d**) with 578 nm peak emission wavelength. We found orientations in polar angles, of 0.28, 0.60, 0.89, and 1.18 radians, respectively, for (**e–h**), and in azimuthal angles of 0.68, 2.23, 3.61, and 5.03. (**i–l**): Measured signal values compared to expected values. We binned the expected signals, and associated pixels with a bin if the expected signal falls within it. For each bin, the mean experimental signal is plotted against the expected signal. Error bars indicate the theoretical s.e.m. with which data should scatter about the straight line through the origin with unit slope. (**m–p**): Histograms of pixel fluctuations around their expected values. For each pixel in the experimental images (**a–d**), the fluctuation is the measured signal value minus its expected value, scaled by its theoretical r.m.s. deviation. For sufficiently large expected pixel signals, theory predicts the standard normal distribution (solid line) for the fluctuations. (**q–t**): Comparing the theoretical PSF to its analytical approximation (Supplementary Data). At (0,0) the two functions coincide. For each fit in (**e–h**), we show the percentile deviation of the analytical approximation from the theoretical PSF as a contour plot. Contour lines are plotted for 0.01, 0.1 (both solid lines), and −0.1 (dashed lines).

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