Telescopes Alignment Using the Sharpness Function Method Based on Undersampled Images

In astronomy, the images are sometimes undersampled. In the previous research works, image reconstructions have to be employed to recover the lost information from a set of undersampled images to achieve a high-resolution image using dithering or drizzle methods, which increase the complexity of alignment processes and make the real-time correction impossible. In this paper, the telescope is aligned by changing the positions of the secondary mirror using sharpness function method combined with the stochastic parallel gradient descent algorithm based on both well-sampled and undersampled images without image reconstructions. To improve the accuracy and robustness of the alignment, a new metric called relative root mean square error is proposed. Both numerical simulations and experiments are implemented, and the alignment precisions are measured by wavefront residual errors using Shack-Hartmann wavefront sensors. The results show that the correction processes can converge stably and quickly whether the images are well-sampled or undersampled. In experiments, the average wavefront error is 0.0595 λ for undersampled images and 0.0548 λ for well-sampled images after the telescope alignment, indicating that the misalignments are well compensated for both well-sampled and undersampled images.