FisherInformation and seFRET

THIS REPOSITORY IS GETTING UPDATED TO SHARE ALSO CODE USED TO GENERATE https://www.biorxiv.org/content/10.1101/774919v1 The code related to this pre-print, but currently prepared for peer-riview is in the zipped archive seFRET_FLIM_FisherInformation.zip Together with it, we are redistributing also code downloaded from: https://figshare.com/articles/Cram_r-Rao_lower_bond_CRLB_on_lifetime_estimates/8332733 linked to the following publication: D. Bouchet, V. Krachmalnicoff, and I. Izeddin, "Cramér-Rao analysis of lifetime estimations in time-resolved fluorescence microscopy," Opt. Express 27, 21239-21252 (2019)

Numerical evaluation of Fisher Information Matrix

FPT files are related to our publication (MATLAB, codes working since Matlab 2013, last tested with Matlab 2018a) https://doi.org/10.1371/journal.pone.0077392 "Maximizing the Biochemical Resolving Power of Fluorescence Microscopy" Alessandro Esposito , Marina Popleteeva, Ashok R. Venkitaraman 2013 PLOS ONE

the main file is fpt_optimize_time_gates.m which handles the execution of code and the visualization of the results fpt_fvalue.m computes the Fisher Information (I) and the figure of merit (F) for the evaluation of a lifetime value on a borad ranges of lifetimes fpt_tg_bu.m partitions the photon arrival statistics onto an histogram of higher resolutions to identify the optimal partition (bottom-up method). Each bin is plit into two symmetric bins until there is a significant gain of Fisher information. fpt_tg_fcost.m cost function used to optimize the edges of histrograms of even bins

fpt_optimize_time_gates.m computes F and I for a range of fluorescence lifetimes using:

1. Use fpt_tg_bu.m to identify an optimal partition (optim_par and FO). The bins are of uneven width but they are all multiples of the smallest bin width
2. Use the in-built function fminsearch and the bespoke fpt_tg_fcost.m to optimize the boundaries of optim_par, to obtain a refine_par with Fisher information FF.
3. Evaluate the Fisher information (FE) for an a histrogam with bins of even size (even_par). The number of bins is the same identified with step #1
4. Evaluate the Fisher information (FR) for a dense reference histrogram of equal bins (dense_par, e.g. n=256) as for TCSPC

fpt_optimize_time_gates.m then visualize the F-value curves and the partitions resulting from these optimization processes