Detection of co-phasing error in segmented mirror based on extended Young’s interferometry combined with Vision Transformer

Due to the inability of manufacturing a single monolithic mirror at the 10-meter scales, segmented mirrors have become indispensable tools in modern astronomical research. However, to match the imaging performance of the monolithic counterpart, the sub-mirrors must maintain precise co-phasing. Piston error critically degrades segmented mirror imaging quality, necessitating efficient and precise detection. To address the limitations that the conventional circular-aperture diffraction with two-wavelength algorithm is susceptible to decentration errors, and the traditional convolutional neural networks (CNNs) struggle to capture global features under large-range piston errors due to their restricted local receptive fields, this paper proposes a method that integrate enhanced Young’s interference principles with a Vision Transformer (ViT) to detect piston error. By suppressing decentration error interference through two symmetrically arranged apertures and extending the measurement range to ± 7.95 μm via a two-wavelength (589 nm/600 nm) algorithm, this approach exploits ViT’s self-attention mechanism to model global characteristics of interference fringes. Unlike CNNs constrained by local convolutional kernels, the ViT significantly improves sensitivity to interferogram periodicity. The simulation results demonstrate that the proposed method achieves a measurement accuracy of 5 nm (0.0083λ₀) across the range of ± 7.95 μm, while maintaining an accuracy exceeding 95% in the presence of Gaussian noise (SNR ≥ 15 dB), Poisson noise (λ ≥ 9 photons/pixel), and sub-mirror gap error (E_gap ≤ 0.2) interference. Moreover, the detection speed shows significant improvement compared to the cross-correlation algorithm. This study establishes an accurate, robust framework for segmented mirror error detection, advancing high-precision astronomical observation.