Fourier shell correlation

In structural biology, the three-dimensional Fourier shell correlation (FSC) measures the normalised cross-correlation coefficient between two 3-dimensional volumes over corresponding shells in Fourier space (i.e., as a function of spatial frequency). The FSC is the three-dimensional extension of the two-dimensional Fourier ring correlation (FRC); also known as: spatial frequency correlation function.

where ${\displaystyle F_{1}}$ is the complex structure Factor for volume 1, ${\displaystyle F_{2}^{\ast }}$ is the complex conjugate of the structure Factor for volume 2, and ${\displaystyle r_{i}}$ is the individual voxel element at radius ${\displaystyle r}$. In this form, the FSC takes two three-dimensional data sets and converts them into a one-dimensional array.

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