Analyzing movement of fringes
...take the FFT of the image, and discard the DC (constant) components. 


That would result in removing the mean brightness from an image. Due to the fact that grayscale images have positive numbers between 0-255, what would be returned from that "high pass" filter (that only "cuts" the DC) would be the image with the same grayscale variance but now centered around 0 (instead of its original mean level).


  I want to analyze how much these fringes are moving around. Is there an easy way to do this?


You could obtain the absolute difference between two successive frames and then the sum of all values of that quantitty as a simple metric of how much movement was there.

If you would also like to be able to estimate how much displacement was there between two successive frames then the simplest thing would be to use cross correlation (on successive frames) and track the position of its maximum.