Some other examples of Fourier tranforms:
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The Fourier transform of two points is a grating. This is a common optical transform which can be performed with a laser and two pinholes.

Eight points in an array make a very small crystal lattice. Since the lattice is very small, the diffraction spots are very large.

Fifteen points in an array make a more realistic crystal lattice. The reciprocal lattice is clearer now.

A molecule.

Two molecules.

Eight molecules.

Fifteen molecules.

A duck with a missing shell of data:

The edges are sharp, but there is smearing around them from the missing intermediate resolution terms. The core of the duck is at the correct level, but the edges are weak.

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