Fast, efficient piston correction of deployable space telescopes using machine learning

Alignment of segmented telescopes is essential in creating an effective monolithic primary mirror. A fast, two-step piston sensing technique has been developed to enable diffraction-limited imaging. Achieving such performance requires a Strehl ratio exceeding 0.8, which corresponds to a wavefront RMS error below 32 nm at λ = 450 nm. A machine learning model has been implemented for a four-petal telescope to retrieve piston errors directly from PSF images and enable mirror correction. When tested on synthetic misalignments drawn from a uniform distribution within ±300 nm (or ±2λ/3), the model improved the mean Strehl ratio from a degraded state to 0.95 after one iteration, and to 0.99 after a second iteration. An SNR greater than 40 was found sufficient to achieve phasing corresponding to a Strehl ratio of at least 0.97.