Detection of co-phasing error in segmented mirror based on extended Young’s interferometry combined with Vision Transformer
doi: 10.37188/CO.EN-2025-0030
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摘要:
由于单块镜难以达到10 m级水平，拼接镜已成为现代天文研究中不可或缺的工具。然而，为了达到单块镜的成像能力，拼接子镜之间必须保持高度共相，piston误差作为影响分段镜成像质量的关键因素，亟需进行高效、精确的检测。针对目前圆孔衍射结合双波长算法易受偏心误差干扰，传统卷积神经网络（CNN）局部感受野难以捕捉大量程误差下全局特征的问题，本文提出了一种融合扩展杨氏干涉原理与Vision Transformer(ViT)的平移误差检测新方法。通过双孔对称布局抑制偏心误差的干扰，结合589nm和600nm的双波长消模糊算法将检测量程扩展至±7.95 μm，并基于ViT的自注意力机制建模干涉条纹的全局特征，相较于CNN依赖局部卷积核的局限性，ViT 显著提高了对干涉图中周期性变化的灵敏度。仿真结果表明，该方法在高斯噪声（SNR≥15 dB）、泊松噪声（
λ ≥9 photons/pixel）及子镜间隙误差（E gap≤ 0.2）干扰下能够在[−7.95 μm, 7.95 μm]范围内实现5 nm的检测精度，同时保持95%以上的准确率，相较于互相关算法检测速度有较大提升。本研究为拼接镜误差检测提供了一种高精度、高鲁棒性的创新技术路线，为高精度天文观测提供了理论支持。Abstract: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 (
0.0083 λ 0) 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.-
Key words:
- segmented mirror /
- Co-phasing /
- piston errors /
- ViT /
- Young’s interference principles
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Figure 2. Theoretical interferogram of a dual-aperture system with radius r and separation D.
Figure 7. Noisy sample images (a) AGWN with Signal-to-Noise Ratio (SNR) = 10 dB; (b) Salt-and-Pepper noise with density p=0.1; (c) Poisson noise with photon flux λ=9 photons/pixel
Figure 9. Distribution of test sample predictions under different levels of Salt-and-Pepper noise
Figure 10. Distribution of test sample predictions under different levels of Poisson noise
Figure 11. Theoretical interference pattern with different gap errors for piston=0 and λ
Figure 12. Distribution of prediction results of test samples with different gap error
Figure 13. Accuracy and loss curves after dataset expansion (a) Training process; (b) Validation process
Figure 14. Effect of horizontal vibration on interference pattern and distribution of predicted results for test samples
Figure 15. Effect of vertical vibration on interference pattern and distribution of predicted results for test samples
Table 1. Composition of the dataset containing gap error
Piston tip\tilt gap Train
datasetsValid
datasets[−7.95, 7.95] [−0.03λ, 0.03λ] [0.8r, 1.2r] 47715 15905 
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Table 2. Comparison with other algorithms
Literature Operating
wavelengthDetection
rangeDetection
accuracyAnti- Decentration
Errorgeneralization
capabilityresponse
timeB. Li，2019 580 nm, 650 nm 2.9 μm 32 nm weak weak 942s Guerra-Ramos
D, 2018λ0=700 nm,
0.930λ0±11λ0 ± 0.0087 λ0-- medium -- X.-F. Ma, 2020 500-600 nm
(λ0=600 nm)(0, 10λ) 0.02λ0 -- medium -- Y.-R. Wang, 2021 632 nm (−0.5λ, 0.5λ) 0.0065 λ-- medium -- A.-K. Yang, 2023 737 nm, 750 nm (−14λ, 14λ) 0.0083 λ0weak medium 75s ViT 589 nm, 600 nm (−13.25λ, 13.25λ) 0.0083 λ0strong strong 26.8s
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