Domain wall structures form spontaneously due to epitaxial misfit during thin film growth. Imaging the dynamics of domains and domain walls at ultrafast timescales can provide fundamental clues to features that impact electrical transport in electronic devices. Recently, deep learning based methods showed promising phase retrieval (PR) performance, allowing intensity-only measurements to be transformed into snapshot real space images. While the Fourier imaging model involves complex-valued quantities, most existing deep learning based methods solve the PR problem with real-valued based models, where the connection between amplitude and phase is ignored. To this end, we involve complex numbers operation in the neural network to preserve the amplitude and phase connection. Therefore, we employ the complex-valued neural network for solving the PR problem and evaluate it on Bragg coherent diffraction data streams collected from an epitaxial La_2-xSr_xCuO₄ (LSCO) thin film using an X-ray Free Electron Laser (XFEL). Our proposed complex-valued neural network based approach outperforms the traditional real-valued neural network methods in both supervised and unsupervised learning manner. Phase domains are also observed from the LSCO thin film at an ultrafast timescale using the complex-valued neural network.

由于薄膜生长过程中外延失配，畴壁结构自发形成。在超快时间尺度上对磁畴和磁畴壁的动态进行成像可以为影响电子设备中电传输的特征提供基本线索。最近，基于深度学习的方法显示出有前途的相位检索（PR）性能，允许将仅强度测量转换为快照真实空间图像。虽然傅立叶成像模型涉及复值量，但大多数现有的基于深度学习的方法都是通过基于实值的模型来解决 PR​​ 问题，其中忽略了幅度和相位之间的联系。为此，我们在神经网络中涉及复数运算以保留幅度和相位连接。因此，我们采用复值神经网络来解决 PR​​ 问题，并使用 X 射线自由电子激光器从外延 La _2-x Sr _x CuO ₄ (LSCO) 薄膜收集的布拉格相干衍射数据流对其进行评估（ XFEL）。我们提出的基于复值神经网络的方法在监督和无监督学习方式上都优于传统的实值神经网络方法。还使用复值神经网络以超快的时间尺度从 LSCO 薄膜观察到相域。