Joint optimization design of optical sparse aperture layout and image restoration under atmospheric turbulence

The Optical Sparse Aperture (OSA) imaging system captures multi-frequency information of objects through a specifically arranged array of sub-apertures, achieving coherent imaging on the focal plane to enhance spatial resolution while reducing system weight and cost. However, the sparse distribution of sub-apertures significantly degrades the mid-frequency response of the Modulation Transfer Function (MTF), leading to severe image blurring. This degradation is further exacerbated by atmospheric turbulence in astronomical observations. To address these challenges, two critical technologies are essential for OSA systems: optimizing the aperture layout to compensate for mid-frequency MTF and developing advanced image restoration algorithms to recover degraded images. This study investigates a 9-aperture OSA system for deep-space galaxy imaging, analyzing how turbulence-induced wavefront distortions impair mid-frequency MTF response. We propose a deep learning-based joint optimization method that simultaneously designs the OSA sub-aperture layout and trains an image restoration network. During optimization, random turbulence perturbations are introduced, and the restoration quality serves as the loss function to jointly update the coordinates of the sub-aperture and network parameters. The resulting system demonstrates turbulence-robust performance. Simulations show that at a 13.5% fill factor, our method outperforms the classical Golay-9 structure, delivering sharper images with enhanced edge clarity. Quantitative evaluations reveal improvements from 22.37 dB to 23.71 dB in PSNR and from 0.9071 to 0.9152 in SSIM on test datasets.