Cusp-artifacts in high order superresolution optical fluctuation imaging

Abstract

This document provides the appendix to "Cusp-artifacts in high order Super-resolution Optical Fluctuation Imaging". It contains more details for the derivations, simulation descriptions and comparison cases.

Cusp-artifacts in high order Superresolution Optical Fluctuation Imaging

“…Simulated filamentous morphology was populated with emitters from either P1, P2, P3, or P4. Signs of virtual brightnesses (red for positive, green for negative) of virtual emitters are mostly in keeping with predicted ones in (ii) for different orders, with exception of out-of-focus (P2) regions (details are given in Appendix 2 [28]) and case with imbalanced population of virtual brightnesses, where smaller portion is more attenuated (4 thorder cumulant of P3 contains 14.5% positive virtual emitters, and positive virtual brightnesses are attenuated by small amplitude of cumulant). Scale bars: 933 nm.…”

“…If, for simplicity, we set all the time lags equal to zero in the cumulant calculations, we find that the cumulants with orders higher than two will exhibit positive-negative oscillations as a function of k. The expressions for the first six cumulants (2 nd order to 7 th order) as functions of k are given as follows (the derivations are given in Appendix 1 [28]):…”

“…This can lead to unexpected cusp artifacts for cumulants of certain orders in the regions that are predicted to be free of these artifacts. Appendix 2 [28] shows that the higher the SOFI order, the higher the number of frames needed for SOFI processing to realize the theoretically predicted cuspartifact-free images. Moreover, since the high-order virtual brightnesses exhibit greater oscillations, they are more susceptible to heterogeneities in the photophysical properties of the emitters and hence more vulnerable to cusp artifacts.…”

“…5). The time trajectories simulated during Simulation-1 for P1 were stochastically truncated (using Poisson bleaching statistics) to simulate the bleaching events (see Appendix 3 [28] and Fig. 5i -iii).…”

“…The "bleached" state also affects the assumption of independence of the blinking trajectories of the different emitters, rendering the predictions less reliable. Next, we used a bleaching correction algorithm [14] with minor modifications (Appendix 3 [28]) on the simulated data by dividing the movie into individual blocks of frames, wherein each block had a signal decrease (from the beginning to the end of the block) of f bc = 1% of the overall signal decrease (from the beginning to the end of the whole movie; f bc is called the "bleaching correction factor"). The final cumulant reconstruction was computed as the average of the cumulants of all the time blocks of the same cumulant order.…”