**4. Conclusions**

By applying digital image post-processing, digital-grating moiré effect was successfully used to measure the focal length and curvature with percent errors lower than 0.5%. The measurement uncertainty and conditions were analyzed and discussed. The field intensity distribution was derived and visualized using simulations, leading to simplified measurements. The proposed method has the advantages of a simple set up, easy operation, high stability, high accuracy, and low cost, and it can be applied to various spherical simple lenses and mirrors.

**Author Contributions:** J.-H.C. and C.-Y.H. conceived and designed the experiments; W.-T.L. performed the experiments; J.-H.C., C.-Y.H., W.-T.L. and J.-Y.L. analyzed the data; K.-H.C. and C.-H.Y. contributed materials and analysis tools; J.-H.C. and W.-T.L. wrote the paper. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Ministry of Science and Technology of the Republic of China, gran<sup>t</sup> number MOST109-2221-E-035-073-MY2.

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

**Informed Consent Statement:** Not applicable.

**Acknowledgments:** We acknowledge Jung-Ping Liu and Danjia Shen of Feng Chia University for their assistance on the derivation of equations. We also acknowledge Melissa Andrews for editing this manuscript.

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