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.

Digital phase correction of a partially coherent sparse aperture system.

A digital piston phase correction method is presented for partially coherent synthesis with active or passive illumination. An anamorphic pupil relay causes a linear shift of a two subaperture array between the entrance and exit pupils. This shift separates the subapertures' cross- and auto-correlations while retaining their common spatial frequency information. Digital analysis of these common frequencies finds the separation distance and piston phase error of the cross-correlations and enables lossless correction of phase error. Corrected images are diffraction limited. Partial coherence affects the contrast of each spatial frequency, causing optical path difference tolerances to relax as system bandwidth decreases.