Fig 1.
The SOFI principle in a one dimensional example.
(a) 1D profile is taken from the input image sequence of two blinking emitters. (b) Corresponding 1D intensity time traces. (c) 2nd order cross-cumulants calculated from the intensity time traces for all time lags. In practice, mainly the zero-time lag (τ = 0) is used. Using cross-cumulants, the interleaving pixels are also calculated. Note that the 2nd order cross-cumulant is equivalent to cross-correlation. (d) The widefield image (the temporal average of intensity time traces). (e) The 2nd order cross-cumulants for τ = 0. (f) The resulting 2D SOFI images up to the 4th cumulant order after flattening and linearization.
Fig 2.
Screenshot of the main menu of the SOFI simulation tool.
The user can specify the fluorophore distribution, various parameters of the fluorophores, camera and optics. For more details, see S1 Appendix.
Fig 3.
SOFI algorithm, cross-cumulant calculation.
The nth order cross-cumulant κn of a pixel δ is calculated as a weighted sum over all partitions of a set G of n pixels. The position of pixel δ is given by the geometrical mean of the n pixels within G. By using different sets of n pixels, the nth order cross-cumulant of an arbitrary large pixel grid can be calculated. Formulas are shown for any n and sketches for n = 4.
Fig 4.
Widefield, SOFI and FALCON STORM images with the generated emitter distributions for different imaging conditions. Standard conditions represent a scenario in which the simulator displays comparable performance for FALCON and SOFI in terms of resolution enhancement. All following experimental scenarios deviate from the standard conditions as follows: Short off-state lifetime, the sample is composed of emitters with fast off-switching kinetics; Short acquisition time, the super-resolution images are generated from an image sequence of only 600 frames; low SNR, the number of photons emitted per switching event per emitter is low which results in low signal-to-noise ratios (8 dB). Emitters shown in the left column are enlarged for the visualization purposes. All parameters of the standard conditions can be found in the S1 Appendix and on our project website [16].
Fig 5.
High-labelling density simulations.
Widefield, SOFI and FALCON STORM images of the simulated structures labelled with a relatively high density of emitters (1000/μm2) Standard conditions represent a scenario well suited for STORM. in the case of Short acquisition time, the super-resolution images are generated from an image sequence of only 1000 frames. Short acquisition time and higher on-time ratio represent a situation with very high density of activated emitters per frame which makes it challenging for STORM algorithms. Emitters shown in the left column are enlarged for the visualization purposes. All parameters of the standard conditions can be found in the S1 Appendix and on our project website [16].
Fig 6.
Balanced SOFI (bSOFI) images of different orders for the test case with only 600 input frames.
With increasing order of the SOFI analysis, resolution improvement also increases, but higher orders generally require more input frames in order to avoid apparent artifacts.
Fig 7.
Experimental data compared to simulations.
(a)-(d) 2nd order bSOFI images computed from experimental data. (e)-(h) 2nd order bSOFI images computed from simulated data. Table below the figure shows the parameters estimated from experimental data and used for the simulations. S/B and Ipeak denote respectively the signal-to-background ratio and the intensity peak of the average images. Density for simulation was set to 600 fluorescent proteins per micrometer.