How to measure the distance between two circle-like-lines over 360 degree
As @A_A said, it's a relatively straightforward problem once you've got good images. 

Assuming you do have that:


Use the Hough transform to find the two main circles in the image
From the center of the inner circle, for each alpha, get a segment (by rotating your image and extracting a triangle) which should contain both your blue and black line
within that triangle, use appropriate signal processing (a simple "average per triangle column" or something, followed by a low pass filter, followed by a threshold, for example) to detect the exact position of the blue and black line