High-precision piston detection method for segments based on a single convolutional neural network

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.