## Animal Magic

Here is our old friend; the Fourier Duck, and his Fourier transform:

And here is a new friend; the Fourier Cat and *his* Fourier transform:

Now we will mix them up. Let us combine the the magnitudes from the
Duck transform with the phases from the Cat transform. (You can see
the brightness from the duck and the colours from the cat). If we then
transform the mixture, we get the following:

We can do the same thing the other way round. Using the magnitudes
from the Cat transform and the phases from the Duck transform, we
get:

In each case, the image which contributed the phases is still visible,
whereas the image which contributed the magnitudes has gone!

### Crystallographic Interpretation:

In X-ray diffraction experiments, we collect only the diffraction
magnitudes, and not the phases. Unfortunately the phases contain the
bulk of the structural information. That is why crystallography is
difficult.

More Fourier transforms.
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