Fig. 1. Experimental demonstration of superresolution interferometric measurements for \begin{document}$ N(=2, 3, 4;6, 8, 12) $\end{document}. (a) Schematic of the experimental setup; (b) Measured superresolved interference between conjugate OAM modes \begin{document}${{L}{G}}_{\pm N}^{p}$\end{document}( SC：single-mode fiber collimator, HW: half-wave plate, QW: quarter-wave plate, QP: Q-plate, UC: upconversion crystal, DC: downconversion crystal, PBS: polarizing beam splitter, DM: dichroic mirror, FL: Fourier lens, SLM: spatial light modulator, CMOS: camera)

Fig. 2. Key technological improvement in the ongoing study, a SOC convertor based on true zero-order astigmatic transformation enabled by liquid-crystal geometric phase（ BD: Polarizing beam displacing prism, QW: Quarter-wave plate, GP: Geometric phase elements）