Comparative metrics for far-field intensity and piston error in sparse optical synthetic aperture telescope system

In recent years, sparse-optical-synthetic-aperture telescope has emerged as an important developing trend for large-scale telescope, where the piston error among different sub-apertures plays an important role for achieving high resolution. Here, the effect of piston error on the far-field intensity of system was analyzed theoretically. Then the bi-sub-aperture system was taken as an example to establish the metrics for symmetry of far-field intensity, SPSF and relative peak intensity (RP). In addition, the variation of the metrics with piston errors for different system parameters was analyzed by simulation. Furthermore, we suggested an innovative way to solve piston errors out using the metrics synthetically and analyzed its corresponding utility for different system parameters. From the results, it could be seen that employing the metrics for SPSF and RP synthetically to solve piston errors out is theoretically correct, which could provide effective references for the development of co-phasing detecting techniques.