Cophasing calibration for a segmented telescope based on two-dimensional dispersed interferograms

Abstract

Astronomical telescopes with increasingly larger apertures are essential for increasing the diffraction limit and improving the efficiency of light collection, thereby enabling the observation of fainter and more distant objects with higher angular resolution. Consequently, ground-based telescopes typically employ smaller segmented mirrors as primary mirrors, particularly those in the 10-meter class or larger. In the case of segmented mirror telescopes, precise alignment between the apertures is indispensable to achieve optimum system resolution. To tackle the challenge of cophasing segmented mirrors, a calibration method is proposed where the sum of the ratio of the second peak to the third peak in a two-dimensional dispersed interferogram serves as the cophasing error function. Simulation analysis and experimental verification were carried out to validate this approach. The simulation results show an accuracy of 1 nm for the cophasing calibration error between two mirrors. The experimental results indicate that this method allows the cophasing error between two plane mirrors with an accuracy of approximately 10 nm and a dynamic range of several hundred microns. Furthermore, the proposed calibration method was successfully employed to achieve a cophasing error of 20 nm for a telescope consisting of four parabolic sub-mirrors with a diameter of 150 mm. The discrepancies in precision between the simulation and the experimental outcomes are examined and elucidated, along with the scope of the measurement range of the method. This method can be employed for the initial calibration of displacement sensors in both ground-based and space-based segmented telescopes, as well as for the direct facilitation of accurate cophasing between submirrors.