The segmented primary mirror telescope under the co-phasing condition can meet the observation requirements of high resolution. However, co-phase errors are always present, which seriously affects the imaging quality. The precise phase modulation requires that the root mean square error of wavefront is less than 𝜆 ⁄ 40. Therefore, the high-precision detection of tip-tilt error between the segments is one of the key technologies to realize the co-phase imaging. In this paper, we propose a simple and efficient tip-tilt error detection method based on single Convolution Neural Network (CNN). Without any preprocessing, the light intensity distribution images on the focal plane are used as the data set for training CNN. And a high-performance CNN model is built to learn the mapping between the tip-tilt errors and light intensity distribution images. After training, CNN can accurately capture the tip-tilt errors by inputting a single image of the light intensity distribution. The simulation model of a three-segment telescope system is established to test the accuracy and robustness of the method. Test results show that the method can achieve high-precision detection of tip-tilt error in a large detection range. This method can achieve a detection range of [-3𝜆,3𝜆] with an accuracy of 7.820×10-3𝜆RMS. The method is robust to the piston error and CCD noise: the tolerance of CCD noise is 5 dB and the tolerance of piston error is [-0.48 𝜆,0.48 𝜆]. This method is simple and does not require complex hardware. It can be widely applied in segmented and deployable primary mirror telescopes.
To achieve a diffraction-limited imaging, the piston errors between the segments of the segmented primary mirror telescope should be reduced to λ/40 RMS. The piston detection method using convolutional neural network (CNN) is an advanced technology with high precision and simplicity. However, such methods based on the deep learning strategy usually have generalization problems, that is, the network prediction precision will inevitably decrease if there is a certain difference between the test image and training set used in the network. This will directly affect the scope of application of the method. In this letter, we propose a CNN-based high-precision piston detection method and analyze its robustness. The point spread function (PSF) images acquired under the wide-spectrum light source are used to construct the dataset to overcome 2π ambiguity. In addition, a set of neural networks system including the classification CNN and the regression CNN with good generalization ability is designed to extract the piston value directly from the PSF image. Under the ideal condition, the piston detection precision can reach about 8.4 X 10-4 λοRMS in the capture range of the interference length of the operating light. Finally, we focus on testing the effect degree of the main disturbance factors in the actual system on the accuracy of the method, such as surface error, residual tip-tilt error, and CCD noise, so as to evaluate the robustness of the method. This method is robust and does not require complex hardware. It can be widely applied in segmented and deployable primary mirror telescopes. We believe that the study in this letter will contribute to the applications of the CNN-based technique for piston sensing.
High-precision detection of piston error is one of the key technologies for high-resolution large-aperture segmented telescopes. Most piston detection methods based on neural networks are difficult to achieve high accuracy. In this Letter, we propose a high-precision piston error detection method based on convolutional neural networks (CNN). A system with six sub-mirrors is used, and one of the sub-mirrors is set as the reference mirror. The network can simultaneously extract the piston information of the remaining five sub-mirrors to be tested from the point spread function (PSF). In the training phase, five sub-mirrors are set with 10,000 groups of random piston values with a range slightly less than one wavelength, and PSF images can be acquired accordingly. Then, 10,000 PSF images with corresponding piston errors are used to train the network. After training, we only need to input a PSF image into the pre-trained network, and the piston can be obtained directly. It is verified by simulation that the average piston’s measurement error of five submirrors is just 0.0089λ RMS (λ=632nm). In addition, this end-to-end method based on deep learning extremely reduces the complexity of the optical system, and just need to set a mask with a sparse multi-subaperture configuration in the conjugate plane of the segmented mirror. This method is accurate and fast, and can be widely used to detect the piston in phasing telescope arrays or segmented mirrors.
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