In the applications of wave-front detection using second-harmonic generation, the spatial phase distribution needs to calculate accurately before and after frequency doubling in real-time. This letter presents a learning-based method called extreme learning machine to fit the corresponding relationship of phase between the fundamental frequency wave and the second-harmonic. The Zernike coefficients of the fundamental frequency wave wave-front and the second-harmonic wave-front are used as input data for Extreme Learning Machine model training and testing. The effects of the intensity-dependent phase shift and walk-off are also considered. The reliability of the trained Extreme Learning Machine model was accessed based on simulation results. The proposed method has shown distinct competitive advantages in real-time calculation efficiency. The well-trained Extreme Learning Machine model only needs 0.026 seconds to accurately predict the phase distribution of the fundamental frequency wave. The runtime is three orders of magnitude smaller than the traditional numerical calculation method.

中文翻译：

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极限学习机对二次谐波波前分布的预测

在使用二次谐波产生的波前检测应用中，需要实时准确计算倍频前后的空间相位分布。这封信提出了一种称为极限学习机的基于学习的方法来拟合基频波和二次谐波之间的相位对应关系。基频波波前和二次谐波波前的泽尼克系数用作极限学习机模型训练和测试的输入数据。还考虑了依赖于强度的相移和走离的影响。基于模拟结果访问经过训练的极限学习机模型的可靠性。所提出的方法在实时计算效率方面表现出明显的竞争优势。训练有素的极限学习机模型只需要 0.026 秒即可准确预测基频波的相位分布。运行时间比传统的数值计算方法小三个数量级。