Self-calibrating phase measurement based on diffraction theory and numerical simulation experiments

Abstract

To achieve a full-aperture, diffraction-limited image, a telescope’s segmented primary mirror must be properly phased. Furthermore, it is crucial to detect the piston errors between individual segments with high accuracy. Based on the diffraction imaging theory, the symmetrically shaped aperture with an arbitrarily positioned entrance pupil would focus at the optical axis with a symmetrical diffraction pattern. By selecting a single mirror as a reference mirror and regarding the diffraction image’s center as the calibration point, a function can be derived that expresses the relationship between the piston error and the distance from the center of the inference image to the calibration point is linearity within one-half wavelength. These theoretical results are shown to be consistent with the results of a numerical simulation. Using this method, not only the piston error, but also the tip–tilt error can be detected. This method is simple and effective; it yields high-accuracy measurements and requires less computation time.