What to do when you are falsely accused of scientific fraud?

AccusedOne of the most distressing experiences for a scientist are false allegations of scientific fraud. As a result of technological progress it is easy to screen publications and PhD theses for plagiarism, photo manipulation and statistical abnormalities. A disadvantage is that false accusations are distributed quickly all over the world and ‘haters’, ‘trolls’ and ‘stalkers’ can stay anonymous while damaging the career of a scientist. What to do if you are falsely accused?