What you see is what you get... except when the thing you are
looking at is either very small or very far away (all a matter
of perspective). Take, for instance, the light from a street
lamp projected through a hole the size of a fork tine in a
screen. If you place another screen just behind the hole what
you will see is an image of the hole. But as you move the second
screen further and further away, the image of the hole starts to
blur. Move the second screen far enough away, and — if your eyes
are sensitive enough — you will see light and dark rings appear.
These rings are the diffraction pattern of the hole in the first
screen, known to mathematicians as the Fourier transform of the
hole, or at least the amplitude thereof. Not many people can
look at a diffraction pattern and recognize what the original
object is. Watson, Crick and Franklin famously "decoded" xray
diffraction patterns to reveal the true structure of DNA. Thanks
to the Fast Fourier Transform — and fast microprocessors —
Fourier transforms