Analytical target-agnostic piston sensing for segmented telescopes using sparse redundant baseline pairs

Piston correction is the key to achieving high resolution of segmented telescopes. Phasing with extended objects is still challenging. In this Letter, we propose an analytical target-agnostic phasing approach using redundant baseline pairs. It is derived that the mixed phase distribution caused by redundant sampling can be decoupled via phase modulation. Then the pistons can be resolved by performing phase cross-correlation to remove the object phase. We validate this theory through simulations and experiments. It does not require additional optical paths and is relatively robust against noise, thus providing a simple, fast, and low-system-complexity solution for piston monitoring of the segmented telescope over the period of imaging complex scenes.