Computational phase correction algorithms for multi-aperture systems

Aperture cophasing can increase the resolution of a multi-aperture array while reducing optical system size and accounting for phase errors from hardware misalignments and atmospheric turbulence. Remapping apertures using an anamorphic pupil relay can separate the spatial frequency spectrum of a previously continuous modulation transfer function to facilitate a posteriori piston corrections between apertures [J. Opt. Soc. Am. A34, A47 (2017)JOAOD60740-323210.1364/JOSAA.34.000A47]. This study expands this method from two apertures to six using maximum likelihood estimation to calculate piston phase errors and least squares for tip and tilt. Perturbed test targets were generated for specific turbulence and noise values, providing random realizations of pistons, tips, tilts, and atmospheric phase screens. Results show improved Strehl ratios for corrected images in the presence of noise and atmospheric turbulence.