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. Back to the index.