Rescaling FSC curves

Similarity between two periodic functions is commonly assessed by comparing their Fourier coefficients within resolution shells. In particular, this approach is widely used in both crystallography and cryo-electron microscopy (cryoEM). The definition of these shells, that is the choice of resolution scale for their boundaries, can be guided by the specific goals of the analysis, by the expected features of the studied functions or simply by convention. In cryoEM, shell boundaries are traditionally defined uniformly in inverse resolution. This convention results in a vast imbalance in the number of Fourier coefficients per shell, which may bias statistical comparisons and can make function plots misleading. Constructing resolution shells with approximately equal numbers of Fourier coefficients can be achieved automatically by defining shell boundaries uniformly on the inverse cubic resolution scale. This transformation effectively zooms into the high-resolution region, which is typically the primary focus of analysis. For Fourier shell correlation (FSC) calculations between half-maps, the characteristic sigmoidal curves were observed to transform into profiles that permit piecewise linear interpolation, which may make FSC analysis more robust.