Model-based tip-tilt correction for segmented mirror of space telescope using extended beacon

A model-based tip-tilt correction method using extended beacons is proposed for aligning the segmented mirror of space telescopes. This method is based on the relationship between the low spatial frequency content of images and the coefficients of Chebyshev segmented tip-tilt (CSTT) modes. Tip-tilt correction is accomplished by introducing positive CSTT modal biases with known amplitudes and capturing 2N-1 focal images in each correction cycle, where N is the number of segments. The performance of the method is evaluated through both simulations and experiments. The results demonstrate that the tip-tilt errors can be effectively corrected within only a small number of iterations, achieving an accuracy of λ/30. Additionally, the impacts of various factors on the correction performance are analyzed, including spectral bandwidth, image noise, the presence of piston errors and figure errors, and the number of mirror segments. The proposed method does not require additional optical components and offers high accuracy along with low computational complexity, making it highly suitable for cophasing of earth-observation segmented space telescopes.