- In X-ray scattering experiments, samples deflect X-rays in different
directions with varying intensity. The intensity is a continuous
function of the direction, which tells us how the atoms are arranged
inside the sample.
- We take noisy measurements of this function at a finite number of
directions. What does that tell us about the whole function, and how
certain can we be?
- Pull on a steel plate, and it stretches: i.e., it undergoes strain. The
strain is a little different from place to place: strain is a
continuous function of position on the plate.
- We measure the strain everywhere except a gap in the middle (the
measurements alter the sample, but we need an unaltered region for
other measurements). How well can we know the strain in the gap,
based on the strain everywhere around it?