Co-phase quantization and adjustment of segmented mirrors based on dual-wavelength vortex interference.

It is imperative to achieve the co-phase state for large segmented mirrors of telescopes. This paper proposes a novel method for quantifying the co-phase errors of the segmented mirrors, as well as to detect any residual errors by analyzing the surface shape of segmented mirrors using conformal mapping after the correction of the co-phase errors, aiming to achieve a more precise co-phase state. This method applies a dual-wavelength phase-shifting interferometry based on optical vortex to measure the co-phase errors (i.e., tip, tilt, and piston), and measures the surface shape of segmented mirrors based on conformal mapping phase-shifting interferometry to identify which kind of co-phase errors still exist there, and then adjust the segmented mirrors to achieve a more precise co-phase state. The functional relationships between piston error or tip/tilt error and phase distribution in the image plane are derived, and the mathematical tool of conformal mapping is used for surface shape demodulation. The experiment results indicate that the resolution of the piston error measurements is 1.878 nm, and the resolution of the tip/tilt error measurements is 0.760″. Furthermore, the surface shape measurement after adjustment based on conformal mapping phase-shifting interferometry is 7.503 nm (RMS). [ABSTRACT FROM AUTHOR]