How Does a Michelson Interferometer Measure the Thickness of a Piece of Plastic?

[whatisreality]

I'm reading about an experiment done with a Michelson interferometer. The aim is to measure the thickness of a piece of plastic. They use white light, so the central fringe in the interference pattern, corresponding to equal path lengths in the two beams can be used as a reference. Why does that work? I'd really appreciate an explanation (as simple as possible) as to why they do this.

The central fringe corresponds to both beams having traveled equal distances... The displacement of one fringe has to be tracked when the plastic is placed. That's about as much as I understand. Why is the central fringe a reference? If it's the only one that doesn't move, why is that?

Thanks for any help!

 

[Domullus]

White light (WL) has a very short coherence length - so with WL interferometer you basically can get only one high contrast fringe (black/white). Other fringes will be in lower contrast, blurred and with rainbow-like features.
As you get only one high contrast fringe it is trivial to use it as a reference.
Most simple setup would be like this: adjust interferometer without the plastic sample in such a way that the highest contrast fringe is visible in the center. Then add sample and change interferometers arms length until you will see highest contrast fringe in the center again. The distance in arms length - is double times the optical distance of your sample.