The precise secondary mirror alignment is a key factor to ensure the imaging quality of a segmented telescope with a high resolution demand. In this paper, a two-step alignment method using an improved stochastic parallel gradient descent (SPGD) algorithm called Nadam SPGD algorithm is proposed. Simulation results show that our method can distinguish aberrations caused by phase errors of the primary mirror and position errors of the secondary mirror precisely, and align the secondary mirror quickly and accurately. The improved SPGD algorithm can enhance the correction efficiency by more than two times compared with the traditional SPGD algorithm.

To acquire images with higher accuracy of wide-field telescopes, deformable mirrors with more than 100 actuators are used, making the telescope alignment more complex and time-consuming. Furthermore, the position of the obscuration caused by the secondary mirror in the experiment system is changed with the difference of fields of view, making the response matrix of the deformable mirror different in various fields of view. To solve this problem, transfer functions corresponding to different fields of view are calculated according to the wavefront edge check and boundary conditions. In this paper, a model-based method combined with the stochastic parallel gradient descent (SPGD) algorithm is used. The experiment results show that our method can correct the aberrations with a high accuracy in both on-axis and off-axis fields, indicating that the effective actuators are well chosen corresponding to different fields of view.

To satisfy the demands of high image quality and resolutions, telescope alignment is indispensable. In this paper, a wavefront sensorless method based on a modified stochastic parallel gradient descent algorithm (SPGD) called the adaptive moment estimation SPGD (Adam SPGD) algorithm is proposed. Simulations are carried out using a four-mirror telescope, whose aperture is 6 m and fields of view are Φ2°. Three misalignments are shown as examples. Positions of the secondary mirror and third mirror are employed to compensate aberrations. The results show that merit functions and energy distributions of corrected images match with the designed ones. The mean RMS of residual wavefront errors is smaller than λ/14 (λ = 0.5 μm), indicating that the misalignments are well compensated. The results verify the effectiveness of our method.