**4. Conclusions**

We presented a method to implement the experimental error analysis of azimuth and the incident angle specifically for the RPAE in this work. The dielectric functions of bulk Au were determined from the measured *ψ* and ∆ at incident angles in a range of 55◦–80◦ , with an interval of 5◦ , to study the effect on the instrument. The results acquired at an incident angle close to the principal angle were observed to exhibit higher accuracy and better stability, according to the discrepancies between the two solutions, and the values of the MARE. The azimuthal error analysis was performed experimentally with the initial orientations of polarizing elements deviating from the zero azimuth. The fitting curves of the MARE versus azimuthal error suggest that δ*θ*<sup>P</sup> more seriously affects the accuracy of the RPAE. The demonstrated error analysis reveals the relationship between the acquired data and experimental conditions, which gives access to achieving accurate and reliable measurement by using the RPAE, and is easily generalized to other rotating element ellipsometers.

**Author Contributions:** Conceptualization, H.T. and Y.Z.; methodology, H.T.; validation, Y.S., Y.C., and H.Z.; formal analysis, H.T. and Y.S.; investigation, Y.C. and H.Z.; data curation, Y.Z., Y.L. and L.C.; writing—original draft preparation, H.T.; writing—review and editing, Y.Z., R.Z., S.W., J.L., Y.L. and L.C.; supervision, Y.Z. and L.C.; project administration, Y.Z. and L.C.; funding acquisition, Y.Z. and L.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China, grant number 61775042 11674062 and the Fudan University CIOMP Joint Fund, grant number FC2017-003.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** We would like to express our sincere appreciations to the anonymous referees for valuable suggestions and corrections.

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