Angular phase-shifting interferometry for surface shapes measurement using vortex beam

We proposed a novel optical surface shapes measurement method based on conformal mapping-angular phase -shifting interferometry (APSI). This method rotates a Q-plate in the reference light path to introduce a 90-degree phase shift. The mathematical tool of conformal mapping is used for surface shape demodulation. After removing the helical phase in the compound phase, high-precision surface shape measurement results are obtained, and the measurement surface shape deviations are 3.33 nm (PV) and 0.26 nm (RMS). This work paves the way for surface shape measurement and compound phase demodulation using vortex beams.