File:Stormsuperresolution.webm
Summary
| Description |
English: Super-resolution (Storm): even if you can't resolve them, if you can make the fluorophores in the object you want to image to turn on a few at a time, you can localize them as the centroid of your point spread function and thus beat the diffraction limit. |
| Date | |
| Source | https://twitter.com/j_bertolotti/status/1239490363968163840 |
| Author | Jacopo Bertolotti |
| Permission (Reusing this file) |
https://twitter.com/j_bertolotti/status/1030470604418428929 |
Mathematica 12.0 code
data = Abs[ExampleData[{"TestImage", "Clock"}, "GrayLevels"] - 1];
data2 = data[[64 ;; 191, 128 ;; 255]];
pos = Position[data2, _?(# > 0.4 &)];
sample = RandomSample[pos];
h = Round[10*((data2[[#[[1]], #[[2]] ]] & /@ sample) - 0.4)/Max[data2 - 0.4]];
size = Dimensions[data2][[1]];
kernel = RotateRight[PadRight[GaussianMatrix[{15, 5}], {size, size}], {-15, -15}];
cd = RotateRight[InverseFourier[Fourier[data2]*Conjugate[Fourier[kernel]]], {10, 10}];
p0 = Table[
GraphicsRow[{
ArrayPlot[cd, PlotLabel -> "Diffraction limited image", LabelStyle -> {Black, Bold}],
ArrayPlot[RotateRight[kernel, {-sample[[n, 1]] + 128, sample[[n, 2]]} ], DataReversed -> True, PlotLabel -> "Image of blinking fluorophores", LabelStyle -> {Black, Bold}],
Graphics[{Black, PointSize[0.01], Table[{Opacity[h[[j]]/10], Point[{sample[[j, 2]], -sample[[j, 1]] + 128} ]}, {j, 1, n}]},
PlotRange -> {{0, 128}, {0, 128}}, Frame -> True, FrameTicks -> None, PlotLabel -> "Reconstructed image", LabelStyle -> {Black, Bold}]}, ImageSize -> 1000]
, {n, 1, 5000, 10}];
ListAnimate[p0]
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
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This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. |
| The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
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This file, which was originally posted to
https://twitter.com/j_bertolotti/status/1239490363968163840, was reviewed on 6 July 2020 by reviewer GRuban, who confirmed that it was available there under the stated license on that date. |