目的 基于BP神经网络使用法拉第杯扫描离子束流实现离子束抛光去除函数的在位快速计算。方法 对于空间分布不同的离子束流，通过法拉第杯扫描方法获得电流密度分布信息，通过刻蚀实验计算去除函数分布信息，使用BP神经网络对电流密度和去除函数分布之间的关系进行拟合，建立基于BP神经网络计算去除函数的模型。使用该模型可以实现对去除函数的在位快速计算，并应用于光学元件的离子束抛光实验中。结果 利用上述方法建立的BP神经网络模型计算的去除函数体积去除率和实验方法获得的去除函数体积去除率的误差为5.09%，使用计算的去除函数进行了离子束抛光实验，抛光样件为直径320 mm的融石英，抛光后光学元件表面PV值为0.197λ(波长λ=632.8 nm)，RMS值为0.009λ，收敛率达到4.19，实现了光学元件表面的超精密抛光。结论 使用建立的BP神经网络模型可以实现离子束抛光去除函数的在位快速计算，该模型对融石英及其他材料的光学元件均适用，计算的去除函数精度满足光学元件离子束超精密加工需求，并提高了离子束抛光的效率。

The work aims to realize the in-situ fast calculation of the removal function for ion beam polishing by Faraday cup scanning based on BP neural network. For ion beams with different spatial distributions, the information of the current density distribution was determined by Faraday cup scanning, and the information of the removal function was determined by etching experiment. A BP neural network was used to fit the relationship between current density distribution and removal function distribution. The BP neural network created was a three-layer back propagation neural network, containing one hidden layer. The input signal of the BP neural network was the full width at half height of the ion beam current density and the output signal was the full width at half height of the removal function. After 408 iterations, the mean square error of the BP neural network was 2.451×10?10. Based on this, the model to calculate the distribution information of the removal function based on BP neural network was established. With this model, the in-situ fast calculation of the removal function could be realized and used for ion beam polishing. For a set of ion source determined parameters, the peak current density obtained by Faraday cup scanning was 0.722 mA/cm2 with a full width at half height of 13.923 mm. The removal function obtained by the groove etch experiment had a peak removal rate of 1.153 nm/s, a full width at half height of 12.899 mm, and a volumetric removal rate of 0.012 898 mm3/s. According to the current density distribution, the removal function calculated by the established BP neural network model had a peak removal rate of 1.192 nm/s, with a full width at half height of 13.006 mm and a volumetric removal rate of 0.013 556 mm3/s, respectively. The error between the volume removal rate of the removal function calculated by the BP neural network and the experimental method was 5.09%, which met the requirements of optical ultra-precision polishing. Ion beam polishing experiment was carried out by the calculated removal function on a 320 mm diameter fused silica element. After ion beam polishing, the PV value of the surface of the optical element decreased to 0.197λ (wavelength λ=632.8 nm), and the RMS value decreased to 0.009λ, which realized the ultra-precision polishing of optical element surfaces. The convergence rate in the polishing process reached 4.19. The experimental results showed that the BP neural network established could bring about the in-situ fast calculation of the removal function for ion beam polishing. The accuracy of the removal function calculated from this model met the demand for ultra-precision processing of optical components. The model is applicable to the calculation of removal functions for fused silica and other material optics. The time to determine the removal function using this model is reduced from 2 hours to 2 minutes, which improves the efficiency of ion beam polishing.