Image Science's

FSC

Program to calculate the Fourier Shell Correlation (FSC)
of two 3D volumes

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Fourier Shell Correlation
Program and Download

Fourier Shell Correlation

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.

PLEASE NOTE:

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.

Image Science / Imperial College FSC program

You can download a FREE copy here.

Author of the FSC wrapper:
Cecilia Bebeacua (CBEM / Imperial College) Funded by a grant of the European Union (3D-EM / FP6 NOE)

Groups running IMAGIC or having signed a Shared Resources agreement will also find a Fourier Shell Correlation command within their IMAGIC system. This command is F-S-C.