In an optical fiber, concentricity is important for low loss and wide band. To measure the homogeneous light intensity over fiber cross section, one can use a microscope camera sensitive to the particular wavelength band. What is also important is a perfect light source coupling to the fiber. I would start with the light source coupled to a short fiber length with a connector, and test the connector output with the mentioned camera with a lens adjusted so that the light intensity across the fiber diameter can be seen on camera display on a full scale.
This "calibrated" light source then can be connected to other fiber sections, and camera used on the other end to compare any difference . Photo software allows to measure the differences.
- - - Updated - - -
FRom your .pdf I can see that you wrote about "Fiber cable plant" while the problem shown is about coaxial cables.
There cannot be any "sensor" to detect eccentricity I think. THe precision adjustment of the machine inserting the insulator over the central conductor is in my opinion the only important issue. Any distortion in a coaxial cable like eccentricity or shape inhomogeneity is detected later by testing the cable section, by TDR or by loss vers.frequency test.
Due to an improper coiling and temperature effects, good coax can also be damaged.