Examples of continuous functions with uncertainty

chiphogg edited this page Jul 20, 2012 · 1 revision
  1. 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?
  2. 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?