**Fourier Transform** calculates the 3D Fourier transform of
a set of volume data.

There are several ways to call
**Fourier Transform**, a tool in the **Volume Data** category
(including from the
**Volume Viewer**
**Tools** menu).

Calling the tool calculates the 3D Fourier transform
of the current set of data
in **Volume Viewer**.
When step > 1, the calculation
will use the displayed subsample rather than the full data set.
The transform is opened as a new volume data set and is made the current set,
while the original data set is hidden.
The new data set can be
saved to a file with
**Volume Viewer**.

Only the magnitudes of the complex Fourier components are included in
the new data set; the phases are discarded.
Further, the constant component is set to zero, because it is usually
large compared to all other components and including it would make the
**Volume Viewer**
histogram difficult to use. The box containing the Fourier transform
(with axes in units of reciprocal space) is centered on the original data
and scaled to have the same total volume.

Some properties of the original data are evident from the Fourier transform. High-frequency components are near the edges of the box, low-freqency components near the center. Volume data is typically oversampled (voxel size two to three times smaller than the actual data resolution) and this causes the Fourier transform to have nonzero values only in the middle half or third of its bounding box. The missing wedge in electron microscope tomograms can also be seen. Spikes radiating along the principal axes in the Fourier transform are caused by nonperiodicity of the original data.

UCSF Computer Graphics Laboratory / February 2008