To improve the measurement and evaluation of form error of an elliptic section, an evaluation method based on least squares fitting is investigated to analyze the form and profile errors of an ellipse using coordinate...To improve the measurement and evaluation of form error of an elliptic section, an evaluation method based on least squares fitting is investigated to analyze the form and profile errors of an ellipse using coordinate data. Two error indicators for defining ellipticity are discussed, namely the form error and the profile error, and the difference between both is considered as the main parameter for evaluating machining quality of surface and profile. Because the form error and the profile error rely on different evaluation benchmarks, the major axis and the foci rather than the centre of an ellipse are used as the evaluation benchmarks and can accurately evaluate a tolerance range with the separated form error and profile error of workpiece. Additionally, an evaluation program based on the LS model is developed to extract the form error and the profile error of the elliptic section, which is well suited for separating the two errors by a standard program. Finally, the evaluation method about the form and profile errors of the ellipse is applied to the measurement of skirt line of the piston, and results indicate the effectiveness of the evaluation. This approach provides the new evaluation indicators for the measurement of form and profile errors of ellipse, which is found to have better accuracy and can thus be used to solve the difficult of the measurement and evaluation of the piston in industrial production.展开更多
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...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 ad-dress the limitations that the conventional circular-aperture diffraction with two-wavelength algorithm is sus-ceptible 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 pro-poses a method that integrates extended Young’s interference principles with a Vision Transformer(ViT)to detect piston error.By suppressing decentration error interference through two symmetrically arranged aper-tures and extending the measurement range to±7.95μm 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 inter-ferogram periodicity.The simulation results demonstrate that the proposed method achieves a measurement accuracy of 5 nm(0.0083λ0)across the range of±7.95μm,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 er-ror(Egap≤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.展开更多
基金Supported by National Natural Science Foundation of China(Grant No.51575438)
文摘To improve the measurement and evaluation of form error of an elliptic section, an evaluation method based on least squares fitting is investigated to analyze the form and profile errors of an ellipse using coordinate data. Two error indicators for defining ellipticity are discussed, namely the form error and the profile error, and the difference between both is considered as the main parameter for evaluating machining quality of surface and profile. Because the form error and the profile error rely on different evaluation benchmarks, the major axis and the foci rather than the centre of an ellipse are used as the evaluation benchmarks and can accurately evaluate a tolerance range with the separated form error and profile error of workpiece. Additionally, an evaluation program based on the LS model is developed to extract the form error and the profile error of the elliptic section, which is well suited for separating the two errors by a standard program. Finally, the evaluation method about the form and profile errors of the ellipse is applied to the measurement of skirt line of the piston, and results indicate the effectiveness of the evaluation. This approach provides the new evaluation indicators for the measurement of form and profile errors of ellipse, which is found to have better accuracy and can thus be used to solve the difficult of the measurement and evaluation of the piston in industrial production.
文摘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 ad-dress the limitations that the conventional circular-aperture diffraction with two-wavelength algorithm is sus-ceptible 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 pro-poses a method that integrates extended Young’s interference principles with a Vision Transformer(ViT)to detect piston error.By suppressing decentration error interference through two symmetrically arranged aper-tures and extending the measurement range to±7.95μm 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 inter-ferogram periodicity.The simulation results demonstrate that the proposed method achieves a measurement accuracy of 5 nm(0.0083λ0)across the range of±7.95μm,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 er-ror(Egap≤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.
