Axial image registration. (A) Final lateral (x and y) and missing axial (z) position of each plane in the two fluorescent channels (gray and black frames). (B) To determine the correct axial (z) position for each imaging plane the information entropy is computed over the entire axial range of the imaged cell using a stack acquired for each cell using a Piezo stage with nanometer step size. Maxima in the entropy function of each plane mark the point where the center of the image is in focus in each plane. (C) As the DNA signal is recorded in both channels, pairwise matching of the nine entropy functions from both channel stacks yields a set of 153 relative distances. For robustness of the method, outliers are removed. The axial offset is the distance the gray entropy curve needs to be shifted (arrow) to optimally overlap with the black entropy curve. Black and gray represent the two fluorescent channels. (D) Data in each channel were fit to individual linear functions yielding the final relative position of each image plane in its stack. Because of the resolution of nine z-planes, transformations are not applied to avoid image artifacts but instead applied to all extracted coordinates during subsequent analysis steps. (E) Fully aligned stack of all nine planes recorded by the camera. Each cell is sampled with 10-nm step size once, resulting in n = 153 distance measures for registration. The error is dominated by the step width of the Piezo to ±5 nm indicated either as line width in C or as error bar in D.