Deep tomography for the three-dimensional atmospheric turbulence wavefront aberration

Context. Multiconjugate adaptive optics (MCAO) can overcome atmospheric anisoplanatism to achieve high-resolution imaging with a large field of view (FOV). Atmospheric tomography is the key technology for MCAO. The commonly used modal tomography approach reconstructs the three-dimensional atmospheric turbulence wavefront aberration based on the wavefront sensor (WFS) detection information from multiple guide star (GS) directions. However, the atmospheric tomography problem is severely ill-posed. The incomplete GS coverage in the FOV coupled with the WFS detection error significantly affects the reconstruction accuracy of the three-dimensional atmospheric turbulence wavefront aberration, leading to a nonuniform aberration detection precision over the whole FOV.<br /> Aims. We propose an efficient approach for achieving accurate atmospheric tomography to overcome the limitations of the traditional modal tomography approach.<br /> Methods. We employed a deep-learning-based approach to the tomographic reconstruction of the three-dimensional atmospheric turbulence wavefront aberration. We propose an atmospheric tomography residual network (AT-ResNet) that is specifically designed for this task, which can directly generate wavefronts of multiple turbulence layers based on the Shack-Hartmann (SH) WFS detection images from multiple GS directions. The AT-ResNet was trained under different turbulence intensity conditions to improve its generalization ability. We verified the performance of the proposed approach under different conditions and compared it with the traditional modal tomography approach.<br /> Results. The well-trained AT-ResNet demonstrates a superior performance compared to the traditional modal tomography approach under different atmospheric turbulence intensities, various turbulence layer distributions, higher-order turbulence aberrations, detection noise, and reduced GSs conditions. The proposed approach effectively addresses the limitations of the modal tomography approach, leading to a notable improvement in the accuracy of atmospheric tomography. It achieves a highly uniform and high-precision wavefront reconstruction over the whole FOV. This study holds great significance for the development and application of the MCAO technology.