Piston error correction of sparse aperture systems using the metaheuristic stochastic parallel gradient descent algorithm.

The next generation of optical telescopes will provide high-resolution imaging of celestial objects by using the aperture synthesis technique. To preserve the quality of the image, fast corrections of the pistons among subapertures have to be applied, namely, the co-phasing of the array. The image-based co-phasing method via an optimization procedure has been newly developed. Despite simplicity and strong commonality, when dealing with large piston errors, this correction method is also faced with a problem in which the metric function easily falls into the local convergence, especially in the case of broadband imaging with many subapertures. In this study, an improved stochastic parallel gradient descent (SPGD) algorithm based on heuristic search is proposed for co-phasing, termed the metaheuristic SPGD algorithm. The heuristic research scheme assists the original SPGD algorithm in getting rid of local extrema. By iterations of this algorithm, the synthetic system can be co-phased without any additional instruments and operations. The effectiveness of the proposed algorithm is verified by means of simulation. Given the efficiency and superiority, it is expected that the method proposed in this study may find wide applications in multi-aperture imaging.