**4. Discussion**

The proposed instrument for contactless thickness measurement is based on a modified low-coherence interferometer. It is realized in an all-fiber configuration, in order to take advantage of the high modulation speed of piezo stretcher, mandatory for measuring on a real bubble, vibrating at a frequency of a few hertz. In order to overcome the polarization problems induced by the optical fiber, standard techniques for thickness measurement are based on autocorrelation: the beating interference is given between the reflections of the two surfaces of the film. This technique exhibits good results in laboratory conditions, but it is not adequate to application in a real plant, because it requires strong focusing on the film, in order to ge<sup>t</sup> enough back-reflection. In this way, the depth of focus is too limited to include bubble vibrations. Our proposal is based on a standard low-coherence interferometer, enriched by two faraday rotators, able to compensate for the fiber birefringence, even if time-variant. To our knowledge, this configuration is original. The designed depth of focus is about 4 mm, coherent with the scanning range. From a measurement campaign on a real plant, the range proved to be adequate to compensate for bubbles' vibrations, considering the measurement frequency of 180 Hz.

With reference to performance, the instrument has a resolution lower than 1 μm, limited by the coherence length of the source (about 12 μm) improved by the parabolic regression on the peaks. The standard deviation, at a measurement rate of 180 Hz, in laboratory condition is about 0.1 μm, while on real bubble, it is between 1 μm and 2 μm, depending on the vibration conditions (function of the film thickness). Minimum measurable thickness is about 20 μm. As expected from theory, we cannot see any measurement error due to incident angle variation, with an angle tolerance of about ±1.6 degrees to still obtain some reflected signal: the error is a cosine function of the angle and it is negligible for this misalignment (lower than <sup>10</sup>−3). The main problem of misalignment is signal fading: on real bubble, the sensor should be carefully aligned to be perpendicular to the film surface, by looking at the signal amplitude. Experiments have shown rapid distance variations due to bubble vibrations, but small angular misalignment. On tens of measurement on real plants, we have noticed no signal fading due to misalignment.

In conclusion, the proposed instrument is a possible substitute for capacitive sensors, as these performances are adequate for the specific measuring application of plastic films.

**Author Contributions:** Conceptualization, M.N. and A.P.; methodology, M.N. and A.P.; software, A.P.; writing—original draft preparation, M.N.; writing—review and editing, A.P. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding. **Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.
