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Program to calculate the Fourier Ring/Shell Correlation of two 2-D images / 3-D volumes.

The three-dimensional Fourier Shell Correlation (FSC) was introduced by Harauz and van Heel in 1986. It measures the normalised cross correlation coefficient between two 3D volumes over corresponding shells in Fourier space, i.e., as a function of spatial frequency:

The FSC is the straightforward three-dimensional generalisation of the earlier two-dimensional Fourier Ring Correlaton (FRC) function (Saxton and Baumeister [1982], Van Heel et al. [1982]).

The (modified) 3-sigma criterion indicates where the FSC systematically emerges above the expected random correlations of the background noise.

This criterion indicates at which spatial frequency we are systematically gaining information significantly above the random noise level. Where we to continue collecting information by adding more data of the same quality to the dataset we would certainly improve the dataset up to - and maybe even somewhat beyond - this point.

The 1/2-bit information threshold criteria express where we have already collected a sufficient amount of data in the final 3D reconstruction to allow a direct structural interpretation at that resolution level. The 1/2-bit curve is calibrated to approximately yield resolution values comparable to resolution values in use in X-ray crystallography (FOM).

We suggest using the 1/2-bit threshold curve as a general purpose indicator of interpretable resolution in FSC curves.


Undersampling remains one of the worst sins one can commit in this field. You should never claim any resolution level beyond 2/3rd of the Nyquist frequency.

The FSC is a measure to compare the simularity of two 3D data-sets. If it is used to estimate the resolution of a 3D reconstruction you have to make sure that the two 3D subsets do not contain artificial similarities.


Groups running IMAGIC or having signed a Shared Resources agreement will find FSC within their IMAGIC system. The commands are F-R-C or F-S-C.

If you do not use IMAGIC you can download your FREE FSC copy here.

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