# High-Resolution, Broad-Range Detection Setup for Polarimetric Optical Fiber Sensors
## 4 Discussion  
An analysis of the influence of the quantization errors on the accuracy of the measurement yielded some expected and some unexpected results. As expected, the calculated error decreases with the increasing resolution of the A/D converter. The decrease is not exactly proportional to the increase in the resolution. When moving from an 8-bit resolution to a 10-bit resolution, the error is reduced by less than four times, as one would expect, while moving from a 10-bit resolution to a 12-bit resolution can yield a reduction that is greater or smaller than four times. While the error decreases with an increasing number of points in the row, interesting behavior is observed for the 8-bit resolution and 512 and 1024 pixels (Figures 5 and 6, respectively), for which the peak-to-peak error decreases by only 24%, while a much greater _average_ error reduction is readily apparent. This may be an indication that a more in-depth investigation into the behavior of this error should be performed in the future. At present, however, we should note that predicted error is sufficiently small for the measurement resolutions obtained in this paper. It should also be noted here that in most available CMOS image sensors, the analog-to-digital conversion is internally performed with a resolution of 10-14 bits (cf. e.g., [43]), and the result is subsequently rounded down to 8-10 bits. Consequently, the eight-bit output exhibits little nonlinearity. The measurement range of the presented interferometer depends on the number of fringes in the field of view of the detector. However, since the identification of the central fringe in the fringe pattern is often difficult based only on its amplitude, the shape of the interference pattern is often used for that purpose. This requires that some fringes from both sides of the central fringe always be visible, restricting the movement of the central fringe by a margin on both sides of the detector. It can be safely assumed that this margin can be 5% of the total number of fringes, corresponding to twelve and seven fringes for the two cases discussed in the previous Section. Therefore the fringe pattern is allowed to move by 215 fringes or 125 fringes, which corresponds to the measurement range of 1352 rad and 786 rad. While setups using other detection methods, such as a polarization analysis [9; 10; 11; 12; 13], can attain such a range, they are only capable of doing so by tracking the change in the state of polarization, with any interruption of the tracking process invalidating the measurement. Setups employing low-coherence interferometry [34; 35; 36; 37; 38; 39] can also attain such a measurement range, but this typically comes at the cost of a reduced measurement resolution. The demonstrated resolution of the presented interferometer (0.002 rad) is comparable to the resolution of setups using polarization analysis or low-coherence interferometry. Further work is needed to provide a better, more accurate evaluation of this parameter. In particular, a setup for generating retardance with an improved resolution and accuracy must be devised. Temperature is a factor that limits the performance of the presented interferometer. It can be shown that temperature affects its performance mainly via the change of the birefringence of the material from which the Wollaston prism is made. In the experiments presented in this paper, a prism made from quartz was used. The birefringence \(\Delta n\) of quartz, measured at room temperature (25 \({}^{\circ}\)C) at a wavelength of 632.8 nm, is approximately 9.02\(\cdot\)10\({}^{-3}\), while its change with temperature \(\delta n\) is approximately 1.0\(\cdot\)10\({}^{-6}\) per \({}^{\circ}\)C (cf. e.g., Figure 4 in [45]).