During my Ph.D. I made a java applet demonstrating an inverse problem. This article brings the applet back. When light passes throug e.g. air it gets blurred. That is why telescopes are built on top of mountains so that the weak light from the stars travels through less air. The extreme case is the Hubble telescope placed in orbit around the earhth without any atmosphere to distort, i.e., blur the image.
The problem is to deduce how the temperature changes (we will call this a temperature profile) at one place from measurements at another place. We restrict ourselves to a 1-D problem. Assume that we can apply a temperature profile (f(t)) to the end of a rod (at the position x = 0). We now define the forward problem that gives the temperature profile at any point by means of a Partial Differential Equation (PDE):