Analysis of relationship between far-field images and piston error of synthetic-aperture telescopes for the broadband target wave

The technology of detecting and correcting piston error is one of the key technologies for synthetic-aperture telescopes to achieve high resolution. In this paper, the relationship between the far-field images of synthetic-aperture system and the piston error was deduced, and the effect of the piston error was described from these equations. Afterwards, the point spread function (PSF) of dual-aperture systems of Fizeau-type under various phase errors was theoretically analyzed in detail, which, led to a description of the relationship between far-field images and piston error. Based on some calculations and simulations, patterns of PSFs' distribution under different piston errors were analyzed for the cases of monochromatic and broadband target wave. And, regulars between intensities and corresponding coordinate of the peaks of PSF and piston error were analyzed, which would provide theoretical supports for our next step research of new methods of detecting piston error.