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Co-phase state detection for segmented mirrors by dual-wavelength optical vortex phase-shifting interferometry.

The application of large-aperture telescopes requires the support of co-phase measurement techniques for segmented mirrors. This paper proposes a novel method to detect the co-phase state of segmented mirrors by applying a dual-wavelength phase-shifting interferometer based on optical vortex. Theory and experiments indicate that the wrapped phase map edges obtained by phase-shifting interference of the vortex beam are distributed in the form of a Fermat spiral. The piston error of the segmented mirrors corresponds to the rotation of the standard Fermat spiral center. In contrast, the tip/tilt error corresponds to the alteration of the center position of the deformed Fermat spiral. The rotation angle and the center position of the spiral are obtained by curve fitting, and the co-phase errors can be inversely solved. The experiments achieved an accuracy of approximately 4.04 nm in the piston and 0.16″ in the tip/tilt. The method avoids using complex lens arrays and devices, has an extended measurement range, high accuracy, and allows the co-phase errors between all sub-mirrors to be obtained in real-time. This study provides a novel and general method for detecting co-phase errors in a segmented primary mirror.