在超快時(shí)間尺度上，收集晶體材料的相干衍射圖案，通過(guò)相位恢復(fù)，可對(duì)其納米尺度的晶疇結(jié)構(gòu)進(jìn)行成像。外延晶體薄膜生長(zhǎng)過(guò)程中，由于外延失配，會(huì)自發(fā)形成疇結(jié)構(gòu)。由于薄膜中的晶疇和晶界的散射作用，其相應(yīng)的面內(nèi)電阻率會(huì)受到一定影響。在超快時(shí)間尺度上，通過(guò)布拉格相干X射線衍射，觀察晶疇和晶界的動(dòng)力學(xué)，對(duì)理解薄膜如電輸運(yùn)和應(yīng)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(fù)一直是一個(gè)具有計(jì)算挑戰(zhàn)的任務(wù)。特別地，對(duì)于超快時(shí)間尺度的成像，單次實(shí)驗(yàn)將會(huì)有海量的實(shí)驗(yàn)數(shù)據(jù)。

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

近期，來(lái)自美國(guó)布魯克海文國(guó)家實(shí)驗(yàn)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(yùn)特性，該團(tuán)隊(duì)使用自由電子激光器（XFEL），對(duì)該LSCO薄膜進(jìn)行了超快布拉格相干衍射成像研究。為解決XFEL實(shí)驗(yàn)中相干衍射數(shù)據(jù)的相位恢復(fù)問(wèn)題，該團(tuán)隊(duì)提出了一種新穎的基于復(fù)數(shù)卷積神經(jīng)網(wǎng)絡(luò)的相位恢復(fù)方法。這一方法改進(jìn)了實(shí)數(shù)卷積神經(jīng)網(wǎng)絡(luò)，將復(fù)數(shù)運(yùn)算融入卷積計(jì)算，從而考慮到了幅值和相位之間的關(guān)系。在仿真數(shù)據(jù)和真實(shí)實(shí)驗(yàn)數(shù)據(jù)上，相對(duì)于傳統(tǒng)的實(shí)數(shù)卷積神經(jīng)網(wǎng)絡(luò)，復(fù)數(shù)卷積神經(jīng)網(wǎng)絡(luò)均展現(xiàn)出更優(yōu)真實(shí)空間復(fù)雜結(jié)構(gòu)的重構(gòu)效果。

相比較于傳統(tǒng)實(shí)數(shù)卷積神經(jīng)網(wǎng)絡(luò)，復(fù)數(shù)卷積神經(jīng)網(wǎng)絡(luò)有以下兩點(diǎn)不同之處：1. 在神經(jīng)網(wǎng)絡(luò)結(jié)構(gòu)上，實(shí)數(shù)網(wǎng)絡(luò)輸入是測(cè)量空間的強(qiáng)度，其輸出網(wǎng)絡(luò)包含兩個(gè)分支分別輸出強(qiáng)度和相位。復(fù)數(shù)網(wǎng)絡(luò)的輸入和輸出都是單一分支，其輸入輸出都為復(fù)數(shù)。2. 實(shí)數(shù)網(wǎng)絡(luò)的強(qiáng)度分支和相位分支是獨(dú)立的互不影響的，因此忽視實(shí)部和虛部的聯(lián)系。而復(fù)數(shù)網(wǎng)絡(luò)其內(nèi)部計(jì)算則是嚴(yán)格按照復(fù)數(shù)運(yùn)算進(jìn)行，充分考慮了樣品的實(shí)部和虛部的聯(lián)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(yàn)證所提出的復(fù)數(shù)模型在相位恢復(fù)問(wèn)題上適用性和魯棒性?；诒O(jiān)督學(xué)習(xí)，根據(jù)XFEL實(shí)驗(yàn)條件，該團(tuán)隊(duì)首先將復(fù)數(shù)神經(jīng)網(wǎng)絡(luò)模型應(yīng)用于擬合數(shù)據(jù)。通過(guò)與傳統(tǒng)的實(shí)數(shù)神經(jīng)網(wǎng)絡(luò)模型進(jìn)行對(duì)比，發(fā)現(xiàn)所提出的復(fù)數(shù)神經(jīng)網(wǎng)絡(luò)模型能夠更好的重構(gòu)相應(yīng)的是空間樣品信息。由于實(shí)驗(yàn)數(shù)據(jù)通常都存在不同程度的噪聲，將該復(fù)數(shù)神經(jīng)網(wǎng)絡(luò)進(jìn)一步應(yīng)用于不同信噪比的擬合數(shù)據(jù)，發(fā)現(xiàn)其具有很好的魯棒性。最終，通過(guò)分類處理XFEL數(shù)據(jù)，應(yīng)用該復(fù)數(shù)神經(jīng)網(wǎng)絡(luò)模型到應(yīng)用XFEL所測(cè)量的超快布拉格相干衍射數(shù)據(jù)流上。在超快時(shí)間尺度，實(shí)驗(yàn)上觀察到了相應(yīng)的晶疇結(jié)構(gòu)及變化。

該工作提出了一種復(fù)數(shù)卷積神經(jīng)網(wǎng)絡(luò)用于解決X射線相干衍射成像中的相位恢復(fù)問(wèn)題。為今后，研究超快相干衍射實(shí)驗(yàn)的相位恢復(fù)問(wèn)題中提供了一種新思路?？蓮V泛應(yīng)用于各類超快相干衍射實(shí)驗(yàn)的成像問(wèn)題上，如全息成像和以及其他外延薄膜應(yīng)力分布研究等。相關(guān)論文近期發(fā)布于npj?Computational Materials?10:?24?(2024)。手機(jī)閱讀原文，請(qǐng)點(diǎn)擊本文底部左下角“閱讀原文”，進(jìn)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(fù)數(shù)卷積神經(jīng)網(wǎng)絡(luò)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(zhǎng)過(guò)程中，隨著薄膜厚度增加，由于失配位錯(cuò)，會(huì)自發(fā)形成疇壁結(jié)構(gòu)。在超快時(shí)間尺度上，觀察疇和疇壁的動(dòng)力學(xué)可為理解相應(yīng)電子器件輸運(yùn)等特性提供基本線索。最近，在解決相位恢復(fù)問(wèn)題上，基于深度學(xué)習(xí)的方法展現(xiàn)出不錯(cuò)的效果。其可將僅有強(qiáng)度信息的倒空間相干衍射圖像快速轉(zhuǎn)換為實(shí)空間樣品信息。盡管在相位恢復(fù)時(shí)，重構(gòu)過(guò)程涉及到復(fù)數(shù)變量，但是目前基于深度學(xué)習(xí)的相位恢復(fù)方法主要使用基于實(shí)數(shù)值的模型來(lái)解決相位恢復(fù)問(wèn)題，忽略了樣品振幅和相位之間的聯(lián)系。因此，為在重構(gòu)過(guò)程中保留幅值和相位之間的聯(lián)系，我們采用復(fù)數(shù)神經(jīng)網(wǎng)絡(luò)來(lái)解決相應(yīng)的相位恢復(fù)問(wèn)題?；趹?yīng)用X射線自由電子激光器所測(cè)量的外延La_2-xSr_xCuO₄（LSCO）薄膜的超快布拉格相干衍射信號(hào)，對(duì)該神經(jīng)網(wǎng)絡(luò)進(jìn)行評(píng)估。所提出的基于復(fù)數(shù)運(yùn)算的神經(jīng)網(wǎng)絡(luò)，在相位恢復(fù)時(shí)，無(wú)論是對(duì)于監(jiān)督學(xué)習(xí)，還是非監(jiān)督學(xué)習(xí)，其表現(xiàn)均優(yōu)于傳統(tǒng)神經(jīng)網(wǎng)絡(luò)。同時(shí)使用該神經(jīng)網(wǎng)絡(luò)，在超快時(shí)間尺度上，我們觀察到了LSCO薄膜中的疇結(jié)構(gòu)。