Motivated by the potential of nondiffraction limited, real-time computational image sharpening with neural networks in astronomical telescopes, we studied wavefront sensing with convolutional neural networks based on a pair of in-focus and out-of-focus point spread functions. By simulation, we generated a large dataset for training and validation of neural networks and trained several networks to estimate Zernike polynomial approximations for the incoming wavefront. We included the effect of noise, guide star magnitude, blurring by wide-band imaging, and bit depth. We conclude that the “ResNet” works well for our purpose, with a wavefront RMS error of 130 nm for r0 = 0.3 m, guide star magnitudes 4 to 8, and inference time of 8 ms. It can also be applied for closed-loop operation in an adaptive optics system. We also studied the possible use of a Kalman filter or a recurrent neural network and found that they were not beneficial to the performance of our wavefront sensor.

中文翻译：

---

使用神经网络的基于图像的天文学波前感测

受天文望远镜中使用神经网络进行无衍射限制的实时计算图像锐化的潜力的启发，我们研究了基于一对聚焦和离焦点扩散函数的卷积神经网络的波前感测。通过仿真，我们生成了一个用于训练和验证神经网络的大型数据集，并训练了多个网络以估计传入波前的Zernike多项式逼近。我们包括了噪声的影响，引导星的大小，宽带成像造成的模糊以及位深度。我们得出的结论是，“ ResNet”可以很好地满足我们的目的，对于r0 = 0.3 m，波前RMS误差为130 nm，引导星等4到8，推断时间为8 ms。它也可以用于自适应光学系统中的闭环操作。