在超快時間尺度上，收集晶體材料的相干衍射圖案，通過相位恢復，可對其納米尺度的晶疇結構進行成像。外延晶體薄膜生長過程中，由于外延失配，會自發形成疇結構。由于薄膜中的晶疇和晶界的散射作用，其相應的面內電阻率會受到一定影響。在超快時間尺度上，通過布拉格相干X射線衍射，觀察晶疇和晶界的動力學，對理解薄膜如電輸運和應力等特性提供重要線索。在X射線相干衍射成像中，相位恢復一直是一個具有計算挑戰的任務。特別地，對于超快時間尺度的成像，單次實驗將會有海量的實驗數據。

Fig. 1 Domain structure expected due to misfit between a thin film and its substrate.

近期，來自美國布魯克海文國家實驗室的Xi Yu，Longlong Wu和Ian Robinson等，為研究外延La_2-xSr_xCuO₄（LSCO）薄膜中觀察到的異常的電輸運特性，該團隊使用自由電子激光器（XFEL），對該LSCO薄膜進行了超快布拉格相干衍射成像研究。為解決XFEL實驗中相干衍射數據的相位恢復問題，該團隊提出了一種新穎的基于復數卷積神經網絡的相位恢復方法。這一方法改進了實數卷積神經網絡，將復數運算融入卷積計算，從而考慮到了幅值和相位之間的關系。在仿真數據和真實實驗數據上，相對于傳統的實數卷積神經網絡，復數卷積神經網絡均展現出更優真實空間復雜結構的重構效果。

相比較于傳統實數卷積神經網絡，復數卷積神經網絡有以下兩點不同之處：1. 在神經網絡結構上，實數網絡輸入是測量空間的強度，其輸出網絡包含兩個分支分別輸出強度和相位。復數網絡的輸入和輸出都是單一分支，其輸入輸出都為復數。2. 實數網絡的強度分支和相位分支是獨立的互不影響的，因此忽視實部和虛部的聯系。而復數網絡其內部計算則是嚴格按照復數運算進行，充分考慮了樣品的實部和虛部的聯系。

Fig. 3 Representative results for the C-CNN and R-CNN for simulated test sets with different number of domains and domain structure.

為了驗證所提出的復數模型在相位恢復問題上適用性和魯棒性。基于監督學習，根據XFEL實驗條件，該團隊首先將復數神經網絡模型應用于擬合數據。通過與傳統的實數神經網絡模型進行對比，發現所提出的復數神經網絡模型能夠更好的重構相應的是空間樣品信息。由于實驗數據通常都存在不同程度的噪聲，將該復數神經網絡進一步應用于不同信噪比的擬合數據，發現其具有很好的魯棒性。最終，通過分類處理XFEL數據，應用該復數神經網絡模型到應用XFEL所測量的超快布拉格相干衍射數據流上。在超快時間尺度，實驗上觀察到了相應的晶疇結構及變化。

該工作提出了一種復數卷積神經網絡用于解決X射線相干衍射成像中的相位恢復問題。為今后，研究超快相干衍射實驗的相位恢復問題中提供了一種新思路。可廣泛應用于各類超快相干衍射實驗的成像問題上，如全息成像和以及其他外延薄膜應力分布研究等。相關論文近期發布于npj?Computational Materials?10:?24?(2024)。手機閱讀原文，請點擊本文底部左下角“閱讀原文”，進入后亦可下載全文PDF文件。

Editorial Summary

During thin film growth, domain wall structures spontaneously form due to epitaxial mismatch. Observingthe dynamics of domains and domain walls at ultrafast timescales can provide fundamental clues for understanding important characteristics that affect electron transport in electronic devices. Thought phase retrieval, single-shot coherent X-ray diffraction patterns allows the imaging of nanoscale domain and domain wall structures. However, phase retrieval, a long-standing computational challenge, involves reconstructing complex-valued image from measured coherent diffraction pattern, which is fundamental in many coherent imaging techniques such as holography, and ptychography.

Xi Yu et.al., from Brookhaven National Laboratory proposed a novel phase retrieval method based on complex-valued convolutional neural networks (C-CNN). This method improves upon traditional real-valued convolutional neural networks by incorporating complex operations into convolutional calculations, thereby considering the relationship between amplitude and phase. On simulated data and real experimental data, the complex-valued CNN demonstrated superior reconstruction performance for complex structures in real space compared to traditional real-valued CNNs.As the C-CNN model can deal with large amounts of coherent diffraction patterns simultaneously, it will benefit experiments where large amounts of data are generated from the same experiments, for example, XFEL experiments. The proposed C-CNN model will be critical to the coherent imaging technique, especially in the case that the conventional method fails. The demonstrated reconstruction method is general for all epitaxial thin-film systems and can be widely applied to coherent diffraction experiments using other sources, so long as they are stable over the exposure time. This?article was recently?published in?npj?Computational Materials?10:?24?(2024).?

原文Abstract及其翻譯

Ultrafast Bragg coherent diffraction imaging of epitaxial thin films using deep complex-valued neural networks (基于復數卷積神經網絡的外延薄膜超快布拉格相干衍射成像)

Abstract 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 La2-xSrxCuO4 (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.

摘要?外延薄膜生長過程中，隨著薄膜厚度增加，由于失配位錯，會自發形成疇壁結構。在超快時間尺度上，觀察疇和疇壁的動力學可為理解相應電子器件輸運等特性提供基本線索。最近，在解決相位恢復問題上，基于深度學習的方法展現出不錯的效果。其可將僅有強度信息的倒空間相干衍射圖像快速轉換為實空間樣品信息。盡管在相位恢復時，重構過程涉及到復數變量，但是目前基于深度學習的相位恢復方法主要使用基于實數值的模型來解決相位恢復問題，忽略了樣品振幅和相位之間的聯系。因此，為在重構過程中保留幅值和相位之間的聯系，我們采用復數神經網絡來解決相應的相位恢復問題。基于應用X射線自由電子激光器所測量的外延La_2-xSr_xCuO₄（LSCO）薄膜的超快布拉格相干衍射信號，對該神經網絡進行評估。所提出的基于復數運算的神經網絡，在相位恢復時，無論是對于監督學習，還是非監督學習，其表現均優于傳統神經網絡。同時使用該神經網絡，在超快時間尺度上，我們觀察到了LSCO薄膜中的疇結構。