All-purpose automatic image stacking for sparse aperture telescopes using dynamic metric stochastic parallel gradient descent algorithm

Image stacking is the first step of alignment of the sparse aperture telescopes. We propose an all-purpose automatic image stacking technique using dynamic metric stochastic parallel gradient descent algorithm (DM-SPGD). With the image stacking modeled as an optimization problem, the dynamic metric functions consisting of a distance metric and an energy metric are defined. According to the judgment of the spot state, the two metrics, both computed from the focal spot at each step, are switched dynamically to perform SPGD optimization. By use of the dynamic metric functions, DM-SPGD can exactly and quickly correct any-amplitude tip/tilt errors, regardless of the array arrangements, aperture numbers and coherence as verified by simulation. In addition, jitter and changes in piston brought about by the environment have no effect on the image stacking. Multiple closed-loop image stacking experiments are performed, demonstrating that the offsets of randomly distributed spots can be all controlled below 0.5 pixels within 300 iterations (within 30 s).